tag:blogger.com,1999:blog-36684018670872182352024-03-05T13:59:37.688-08:00Materias 7mo Semestreguelmi_rickhttp://www.blogger.com/profile/00075155021794486805noreply@blogger.comBlogger19125tag:blogger.com,1999:blog-3668401867087218235.post-68726463247553517302012-11-20T13:00:00.000-08:002012-11-20T13:00:56.719-08:00Entrada Final<span style="font-family: Arial, Helvetica, sans-serif;">Liga en donde esta la entrada:</span><br />
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<a href="http://www.facebook.com/l.php?u=http%3A%2F%2Fautoycontrolave.blogspot.mx%2F2012%2F11%2Fproyecto-automatizacion-y-control.html&h=fAQGV91O2" rel="nofollow" style="background-color: white; color: #3b5998; cursor: pointer; font-size: 13px; line-height: 17px;" target="_blank"><span style="font-family: Arial, Helvetica, sans-serif;">http://autoycontrolave.blogspot.mx/2012/11/proyecto-automatizacion-y-control.html</span></a>guelmi_rickhttp://www.blogger.com/profile/00075155021794486805noreply@blogger.com0tag:blogger.com,1999:blog-3668401867087218235.post-44437849721643611422012-11-15T15:01:00.000-08:002012-11-15T15:01:00.232-08:00Entrada # 6<div style="text-align: left;">
<b style="background-color: white; color: #20124d; font-size: x-large; line-height: 33px; text-align: center;"><span style="font-family: Arial, Helvetica, sans-serif;">Laboratorio de Automatización y Control de Sistemas Dinámicos</span></b></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Para esta semana me toco realizar el siguiente problema:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCMuJj2oDj-1c2IXZ9Mrrzx2srbUh7Rg8fUqzqTqmrR2HIfXPT2MCsyA6kKj1NP5rUYQ50mAmvo3fJltG3-ykB7BPzX3Y7AC3zA0h2K1szLbwrSgVNLLrrZQZJQ4UOihQuVQYl4BE3Rf0/s1600/Lab6.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="337" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCMuJj2oDj-1c2IXZ9Mrrzx2srbUh7Rg8fUqzqTqmrR2HIfXPT2MCsyA6kKj1NP5rUYQ50mAmvo3fJltG3-ykB7BPzX3Y7AC3zA0h2K1szLbwrSgVNLLrrZQZJQ4UOihQuVQYl4BE3Rf0/s400/Lab6.jpg" width="400" /></span></a></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Viendo este problema tenemos que consiguir la señal de control óptima esta comúnmente se determina con:</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQLMD83avw3WgGFZ6AZsu3ETKdXgRH0HFe7q4nRujN71Ip0bBe-WaxwZzvmKwoKgVXR-3CBtTNHxTNyhoTgNcg75rseAsQdC117jbVXdzL2pwS3k-MEoJvj0yZrj9zJ_IImy9hpOyQDxc/s1600/Im1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhQLMD83avw3WgGFZ6AZsu3ETKdXgRH0HFe7q4nRujN71Ip0bBe-WaxwZzvmKwoKgVXR-3CBtTNHxTNyhoTgNcg75rseAsQdC117jbVXdzL2pwS3k-MEoJvj0yZrj9zJ_IImy9hpOyQDxc/s1600/Im1.png" /></span></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Ya con esto el siguiente paso sera el analizar la ecuación J.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Teniendo:</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDaseN2m14IyS_aKsayMxV21m1BfJ1KG5fWmaAOvDWQ5p_7VJ2KorBcvhsodgS_aqVdcPKYH2bhSYPntWUHSK2EeMJG1vYMpfry5M04P_37-esoxiGxPJr9TQfedrGl6cOkty25v-vd7U/s1600/Im2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhDaseN2m14IyS_aKsayMxV21m1BfJ1KG5fWmaAOvDWQ5p_7VJ2KorBcvhsodgS_aqVdcPKYH2bhSYPntWUHSK2EeMJG1vYMpfry5M04P_37-esoxiGxPJr9TQfedrGl6cOkty25v-vd7U/s1600/Im2.png" /></span></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Sustituimos el valor de U:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-D3aapJ85FrNV4_j4BcEicVwAHBZzy2QecRA9nCVfxFh8vqMu7tZqqNSdOUMkvy4AEpuffrlpcPnTUHo0EKOJdzMGC6g_Brhmh27G_K4L77EPhyphenhyphenYDg2oCrtshC8wcTt6ApfpbNCSAY8c/s1600/Im2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-D3aapJ85FrNV4_j4BcEicVwAHBZzy2QecRA9nCVfxFh8vqMu7tZqqNSdOUMkvy4AEpuffrlpcPnTUHo0EKOJdzMGC6g_Brhmh27G_K4L77EPhyphenhyphenYDg2oCrtshC8wcTt6ApfpbNCSAY8c/s1600/Im2.png" /></span></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Teniendo lo siguiente:</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCb3tHZi51tQIZ4kmgh287aBHTPr6aBRbdDSYG_zIx6R3u7MCEW4sjLRK-g13SvgALtmv4TfN_i-WJFLo0kt_3tZm3zaMTJBmLFCyZA80ij5RrntCrpGfjanUEcy8U5zDsFRMa6MDP6h4/s1600/Im4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhCb3tHZi51tQIZ4kmgh287aBHTPr6aBRbdDSYG_zIx6R3u7MCEW4sjLRK-g13SvgALtmv4TfN_i-WJFLo0kt_3tZm3zaMTJBmLFCyZA80ij5RrntCrpGfjanUEcy8U5zDsFRMa6MDP6h4/s1600/Im4.png" /></span></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0xY7ZOqL61n1i_xkQxROIK579llMswbVu0Qszc5YMPN1Ue2zqKPe1pHxKVlFs_0wI2sclhb5PHgDLUnUTXNcE92xpXmgXztpxXQBnO_sdgTMYWAr4MMYuEQ8utp91hHY2xxg2-9YjVfI/s1600/Im5.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0xY7ZOqL61n1i_xkQxROIK579llMswbVu0Qszc5YMPN1Ue2zqKPe1pHxKVlFs_0wI2sclhb5PHgDLUnUTXNcE92xpXmgXztpxXQBnO_sdgTMYWAr4MMYuEQ8utp91hHY2xxg2-9YjVfI/s1600/Im5.png" /></span></a></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Para cumplir con lo anterior hacemos el valor de Q por I, por lo tanto la factorización queda:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBAI4XBBdMazsCIS5NyYWyB7da82kZdvL92zMQXf6wFQHePlOT1iHcAVrspznZpE-zjpYuB1zIHX8qytO8rBCzWTRktQeMKbo3CypXF8fmtYvYv8qLR4IFjderoGATPdap5G9W_vZtXTY/s1600/Im6.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjBAI4XBBdMazsCIS5NyYWyB7da82kZdvL92zMQXf6wFQHePlOT1iHcAVrspznZpE-zjpYuB1zIHX8qytO8rBCzWTRktQeMKbo3CypXF8fmtYvYv8qLR4IFjderoGATPdap5G9W_vZtXTY/s1600/Im6.png" /></span></a></div>
<span style="font-family: Arial, Helvetica, sans-serif;">Teniendo la ecuación:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzL6H3jsYgWoSICbk0DJnBxznvwj1IgsIdEiJHOzmny7PBfG-SlAsEkFq11Dh9LwmW-HJzxxwTAbaEsRLVTgDFW_ps5E4d7Znyskl8AI1wZGTjN9fhpR4HJHz830njSugf6exBpNGD410/s1600/Im7.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="27" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjzL6H3jsYgWoSICbk0DJnBxznvwj1IgsIdEiJHOzmny7PBfG-SlAsEkFq11Dh9LwmW-HJzxxwTAbaEsRLVTgDFW_ps5E4d7Znyskl8AI1wZGTjN9fhpR4HJHz830njSugf6exBpNGD410/s400/Im7.png" width="400" /></span></a></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Sustituimos R por I, nos queda:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7aPnjG5eLlVTRCQ3iu0q5d8wOKBrJmKYq3x-cGh6aIZSx6GFkldSVRl7NOuk7LCrl0IFlBx1KE1dlQTN9qmzpHUL-71QAi3NwzzrfJZEDTRdfRvy3-eZYkmV-VDrfa1Wxe-OecRU-4qk/s1600/Im8.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="17" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7aPnjG5eLlVTRCQ3iu0q5d8wOKBrJmKYq3x-cGh6aIZSx6GFkldSVRl7NOuk7LCrl0IFlBx1KE1dlQTN9qmzpHUL-71QAi3NwzzrfJZEDTRdfRvy3-eZYkmV-VDrfa1Wxe-OecRU-4qk/s320/Im8.png" width="320" /></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">De la siguiente ecuación, el valor de R⁻¹ se elimina, quedando:</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgq4y4LfGkcatmDI0XYWyEKkcPZciOSwcIo8Le-0B2RQw75T_2mFr7YNr-MagN7SWfbQifUe6fE1rd3Mytfr2We9hlOSPncexRS_wZGWotZLYKlfrzGcfABtXO0FPhattqM1d3NxLtq7w/s1600/Im9.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="19" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhgq4y4LfGkcatmDI0XYWyEKkcPZciOSwcIo8Le-0B2RQw75T_2mFr7YNr-MagN7SWfbQifUe6fE1rd3Mytfr2We9hlOSPncexRS_wZGWotZLYKlfrzGcfABtXO0FPhattqM1d3NxLtq7w/s200/Im9.png" width="200" /></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Teniendo la ecuación de matrices de Riccati:</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgx-83LCZ3Nt9F6ZQcizXClctZpqQlcKFnOtyKrqdsAW_Qv9ZKuPLEZ4JyQPZJwaxLdvevLUe6Hl-pC-DMh-c7rqwdmN8-2gwpitwVYtEydqLKtj9zONY0QoOAurBVeo1VFbZMv7UxFH6E/s1600/Im10.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="32" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgx-83LCZ3Nt9F6ZQcizXClctZpqQlcKFnOtyKrqdsAW_Qv9ZKuPLEZ4JyQPZJwaxLdvevLUe6Hl-pC-DMh-c7rqwdmN8-2gwpitwVYtEydqLKtj9zONY0QoOAurBVeo1VFbZMv7UxFH6E/s320/Im10.png" width="320" /></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Teniendo que la transpuesta de B: </span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh633x4QzXa4NXbdG7DAwBlMEloaJLns35iXe5kHRAOGwu33C-2iHtiA2UWUDiYntGk__BSwQDK8Y_7VBMfz5ZbkkEyKRvk0BqlvCW5dToV23jCHw0jcqttbWcUeDFdBVqKF05YMLMsi14/s1600/Im11.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh633x4QzXa4NXbdG7DAwBlMEloaJLns35iXe5kHRAOGwu33C-2iHtiA2UWUDiYntGk__BSwQDK8Y_7VBMfz5ZbkkEyKRvk0BqlvCW5dToV23jCHw0jcqttbWcUeDFdBVqKF05YMLMsi14/s1600/Im11.png" /></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Y P:</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzKj0zet7Cn0Bija_09P2-bwBao_GzHaTEbfCeB4M3yZUHDeVGqYOfapa0rQGZnIIsVhomM60Fmvir4ZRTAxDw3rrsYSYEZqG2pnvyOMWzWN4DfFofzDkR2D1ABl6Vu4eu90R8X4ZOWoY/s1600/Im13.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhzKj0zet7Cn0Bija_09P2-bwBao_GzHaTEbfCeB4M3yZUHDeVGqYOfapa0rQGZnIIsVhomM60Fmvir4ZRTAxDw3rrsYSYEZqG2pnvyOMWzWN4DfFofzDkR2D1ABl6Vu4eu90R8X4ZOWoY/s1600/Im13.png" /></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Tenemos:</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXnP1L2Y-sVNkh-eH971evNjB7OuZArLDnfj7mzKq11-oKMLCyiTLb7xU0vXca8nrWlXSLi0Z1C7D8IkgKUN6qVxrbqVe6FlSf5Rr_rlHdXQnwyCMbPK_OxvhIN6y_LMRY4XTsvrGU8VM/s1600/Im12.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXnP1L2Y-sVNkh-eH971evNjB7OuZArLDnfj7mzKq11-oKMLCyiTLb7xU0vXca8nrWlXSLi0Z1C7D8IkgKUN6qVxrbqVe6FlSf5Rr_rlHdXQnwyCMbPK_OxvhIN6y_LMRY4XTsvrGU8VM/s1600/Im12.png" /></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Por lo tanto ya que los valores de K son 1 se sustituyen en lo que vale U, lo que nos deja por ultimo:</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiF0D_zatrQP1SZnQKML6zdzwC_S5zFjk4-cjis69jgFICuTjL8kCwSQkTPdx2coHSc1yzfuPHzuSbuhxJTpMcveWqVr2GnQMSlADexoJsL7BcrsIhFK9KbEmtVYB7cdpTwqsEvENtLkk0/s1600/Im14.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiF0D_zatrQP1SZnQKML6zdzwC_S5zFjk4-cjis69jgFICuTjL8kCwSQkTPdx2coHSc1yzfuPHzuSbuhxJTpMcveWqVr2GnQMSlADexoJsL7BcrsIhFK9KbEmtVYB7cdpTwqsEvENtLkk0/s1600/Im14.png" /></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Referencias:</span></div>
<br />
<span style="background-color: white; color: blue; font-family: Arial, Helvetica, sans-serif; font-size: 15px; line-height: 20px;"><b>Modern Control Engineering Fourth Edition</b></span><br style="background-color: white; color: #333333; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 15px; line-height: 20px;" /><span style="background-color: white; color: blue; font-family: Arial, Helvetica, sans-serif; font-size: 15px; line-height: 20px;"><b>Katsuhiko Ogata</b></span>guelmi_rickhttp://www.blogger.com/profile/00075155021794486805noreply@blogger.com1tag:blogger.com,1999:blog-3668401867087218235.post-66763777464384480552012-11-13T12:51:00.000-08:002012-11-13T13:02:29.926-08:00Reporte Propiedades Estructurales<span style="font-family: Arial, Helvetica, sans-serif;">Esta actividad la hice solo ya que mi compañero me dejo solo.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Pdf del Reporte en LaTex.</span><br />
<span style="color: #0000ee;"><u>https://www.dropbox.com/s/7kt9y94e86kh0p7/entrada.pdf</u></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Código del Pdf</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<script src="https://gist.github.com/4068289.js"> </script>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Código de las imágenes.</span><br />
<script src="https://gist.github.com/4068297.js"> </script>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>guelmi_rickhttp://www.blogger.com/profile/00075155021794486805noreply@blogger.com1tag:blogger.com,1999:blog-3668401867087218235.post-74775513421959909262012-11-06T14:56:00.003-08:002012-11-06T15:00:37.609-08:00Puntos Extra<span style="background-color: white; color: #333333; font-family: Arial, Helvetica, sans-serif; line-height: 14px; white-space: pre-wrap;">Resumen del Artículo</span><br />
<div class="fbChatMessage fsm direction_ltr" data-jsid="message" style="background-color: white; color: #333333; direction: ltr; line-height: 14px; margin-bottom: 3px; white-space: pre-wrap; word-wrap: break-word;">
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<b><div style="text-align: center;">
<b><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif; font-size: large;">Coverage Control for Mobile Sensing Networks</span></b></div>
<div style="text-align: center;">
<b><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;">(Control de cobertura para las redes de detección móviles)</span></b></div>
</b><div class="fbChatMessage fsm direction_ltr" data-jsid="message" style="background-color: white; direction: ltr; margin-bottom: 3px; word-wrap: break-word;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #333333;"></span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">Este artículo nos habla acerca de algoritmos para el control y la coordinación de los vehículos autónomos (aquellos que tienen la capacidad de manejarse por su propia cuenta).<br /><br />Estos vehículos son utilizados como sensores móviles (estos se sintonizan dependiendo la búsqueda), para poder realizar detecciones mediante estos.<br /><br />Cabe aclarar que los algoritmos no son los encargados de la detección (esto lo hacen los sensores); estos se encargan de definir la forma correcta con la que la cobertura sea lo mas óptima y de definir las políticas mediante la cual se realizara la detección.</span></div>
<div class="fbChatMessage fsm direction_ltr" data-jsid="message" style="background-color: white; direction: ltr; margin-bottom: 3px; word-wrap: break-word;">
<span style="font-family: Arial, Helvetica, sans-serif;">Todos los algoritmos presentados en el articulo son basados en el problema del Descenso mas Pronunciado (Gradiente), este nos dice que se encarga de buscar un mínimo que este asociado a la resolución de secuencial de varios problemas.</span></div>
<div class="fbChatMessage fsm direction_ltr" data-jsid="message" style="background-color: white; direction: ltr; margin-bottom: 3px; word-wrap: break-word;">
<span style="font-family: Arial, Helvetica, sans-serif;">La estructura común de estos algoritmos es el siguiente:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #333333;"></span></span><br />
<div class="fbChatMessage fsm direction_ltr" data-jsid="message" style="direction: ltr; line-height: 14px; margin-bottom: 3px; white-space: pre-wrap; word-wrap: break-word;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #333333;"><br /></span></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #333333;">
<div class="fbChatMessage fsm direction_ltr" data-jsid="message" style="direction: ltr; line-height: 14px; margin-bottom: 3px; white-space: pre-wrap; word-wrap: break-word;">
<div style="text-align: center;">
<img alt="metodo_del_gradiente" src="http://www.investigaciondeoperaciones.net/img/metodo_del_gradiente.jpg" /></div>
</div>
<div class="fbChatMessage fsm direction_ltr" data-jsid="message" style="direction: ltr; line-height: 14px; margin-bottom: 3px; white-space: pre-wrap; word-wrap: break-word;">
<br /></div>
</span></span><b><span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Tipos de Control </span></b><br /><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #333333;">
</span>Hace uso de los sistemas distribuidos para hacer uso de los sensores con los que cuenta cada automóvil.<span style="color: #333333;">
</span></span></div>
<div class="fbChatMessage fsm direction_ltr" data-jsid="message" style="background-color: white; direction: ltr; margin-bottom: 3px; word-wrap: break-word;">
<span style="color: #333333; line-height: 14px; white-space: pre-wrap;"><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></span></div>
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif; font-size: x-large;"><b>Referencias:</b></span><div class="fbChatMessage fsm direction_ltr" data-jsid="message" style="background-color: white; direction: ltr; margin-bottom: 3px; word-wrap: break-word;">
<a href="http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1284411"><span style="font-family: Arial, Helvetica, sans-serif;">http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=1284411</span></a></div>
<div class="fbChatMessage fsm direction_ltr" data-jsid="message" style="background-color: white; direction: ltr; margin-bottom: 3px; word-wrap: break-word;">
<a href="http://www.investigaciondeoperaciones.net/metodo_del_gradiente.html"><span style="font-family: Arial, Helvetica, sans-serif;">http://www.investigaciondeoperaciones.net/metodo_del_gradiente.html</span></a></div>
<br />guelmi_rickhttp://www.blogger.com/profile/00075155021794486805noreply@blogger.com1tag:blogger.com,1999:blog-3668401867087218235.post-90802518798193062032012-11-01T15:57:00.000-07:002012-11-01T16:10:28.722-07:00Entrada # 5<div style="text-align: center;">
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif; font-size: x-large;"><b>Laboratorio de Automatización y Control de Sistemas Dinámicos</b></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Para esta semana consistió en elegir un problema y resolverlo, el elegido es el siguiente:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdPUJavFYC7FUN6rI1nI0EbWua1FhVB8LYbIr8fVpDj448cXNe7wyQIdtbCFOSjSjx6GjrtMVDYF60clXK9g7UP5GxCSedi5i6prkNI0kqyTqX4d93i2ZA8_6-l77272_vUTRw4c3zQjo/s1600/Auto1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="73" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgdPUJavFYC7FUN6rI1nI0EbWua1FhVB8LYbIr8fVpDj448cXNe7wyQIdtbCFOSjSjx6GjrtMVDYF60clXK9g7UP5GxCSedi5i6prkNI0kqyTqX4d93i2ZA8_6-l77272_vUTRw4c3zQjo/s320/Auto1.png" width="320" /></span></a></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Considere el sistema en lazo cerrado con la siguiente función de transferencia en lazo abierto:
<b>Dibuje los diagramas polares directo e inverso de G(s)H(s) con K = 1 y K = 10.</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Aplique el criterio de estabilidad de Nyquist a las gráficas y determine la estabilidad del sistema con estos valores de K.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Primeramente que son los siguientes conceptos:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: #660000; font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>Diagrama Polar</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Representación de la función de transferencia senoidal, G( jω) , en coordenadas polares, para</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">variaciones de ω entre 0 e ∞</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Son conocidos también como Diagrama de Nyquist.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjWMkE4EM_fcIOGIAzS-hjRBTLbkBnblly8Yava7qo1DOwxQjKFMMSs2T-nnHuXThW6uo36ijLui7kZJYTMO26_smITOAtBj9ad0-2r57L6_W1LbCuVR7-C-pOEgH-1C-ojyXhHGOm_C0/s1600/Auto2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="171" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjWMkE4EM_fcIOGIAzS-hjRBTLbkBnblly8Yava7qo1DOwxQjKFMMSs2T-nnHuXThW6uo36ijLui7kZJYTMO26_smITOAtBj9ad0-2r57L6_W1LbCuVR7-C-pOEgH-1C-ojyXhHGOm_C0/s320/Auto2.png" width="320" /></span></a></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: #660000; font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>Criterio de Nyquist</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Medio encargado en estudiar la estabilidad en el dominio de la frecuencia.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Relaciona la respuesta en frecuencia de lazo abierto con el número de polos y ceros de la ecuación </span><span style="font-family: Arial, Helvetica, sans-serif;">característica ubicados en el SPD.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: #660000; font-family: Arial, Helvetica, sans-serif;"><b>Referente al problema hay que considerar unos puntos:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Para obtener el resultado de Nyquist, existe una función en Octave, mediante el paquete signal, que se llama <b>nyquist</b>().</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Aquí incluyo el código en Octave:</span><br />
<script src="https://gist.github.com/3997271.js"> </script>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Imagenes del resultado:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>con K = 1</b></span><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-v8ovlyx1ISP_LcyhAUMvoxtw4O1w2mwt2Eq1Zd0iB0hqFxpLknmrV2wpVBlYFzLuklzYfG2ZwUkSUQBkjyr6xCMW8YoDy83MEAu2sR3bRd1tBSuR_JvMj-XR8IXHgj9IPYfe0dQr46U/s1600/im1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="480" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-v8ovlyx1ISP_LcyhAUMvoxtw4O1w2mwt2Eq1Zd0iB0hqFxpLknmrV2wpVBlYFzLuklzYfG2ZwUkSUQBkjyr6xCMW8YoDy83MEAu2sR3bRd1tBSuR_JvMj-XR8IXHgj9IPYfe0dQr46U/s640/im1.png" width="640" /></a></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>con K = 10</b></span><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6K9T2CNEjkSfmtjHL-CwdHWLpXWn4k7qI8pfgiNuObOCDcn1b6h8SEuJGhWBAr1c8IPDri2kF29JJnF1WktuyCH7hnfh80nsBtVgKNGIVSUlKnfZkxb8Ngc1kELqs6dVQPocY1fkDbAw/s1600/im2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="473" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh6K9T2CNEjkSfmtjHL-CwdHWLpXWn4k7qI8pfgiNuObOCDcn1b6h8SEuJGhWBAr1c8IPDri2kF29JJnF1WktuyCH7hnfh80nsBtVgKNGIVSUlKnfZkxb8Ngc1kELqs6dVQPocY1fkDbAw/s640/im2.png" width="640" /></a></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Observando las gráficas vemos que las dos están de 0 a -infinito por lo tanto las dos gráficas son estables.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>Referencias:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<a href="http://www.disa.bi.ehu.es/spanish/profesores-etsi-bilbo/~jtpirgoe/Tema_7_Diagrama_Nyquist%20.pdf"><span style="font-family: Arial, Helvetica, sans-serif;">http://www.disa.bi.ehu.es/spanish/profesores-etsi-bilbo/~jtpirgoe/Tema_7_Diagrama_Nyquist%20.pdf</span></a><br />
<br />guelmi_rickhttp://www.blogger.com/profile/00075155021794486805noreply@blogger.com1tag:blogger.com,1999:blog-3668401867087218235.post-48605954896971304192012-10-30T13:20:00.000-07:002012-10-30T13:28:48.535-07:00Entrada # 3<div style="text-align: center;">
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif; font-size: x-large;"><b>Programa # 1 Estabilidad</b></span></div>
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">Para esta ocasión tenemos que demostrar la estabilidad de nuestras funciones de transferencia, antes de comenzar les muestro nuestra función:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgf50RqsX-EJsLEQUhJtFhyTK6Q-kmMhVK3HkdEgDeaLyyl311fRm0W4C-ea8i-Ogiv7_fITvS-JQ2MMBWDo_P9JQTgqcG5WUkeJF0ZK6mBE8_xBgCiVm1WFrIEP5NexAlrBx2BM9Ocze8/s1600/TF.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="94" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgf50RqsX-EJsLEQUhJtFhyTK6Q-kmMhVK3HkdEgDeaLyyl311fRm0W4C-ea8i-Ogiv7_fITvS-JQ2MMBWDo_P9JQTgqcG5WUkeJF0ZK6mBE8_xBgCiVm1WFrIEP5NexAlrBx2BM9Ocze8/s320/TF.gif" width="320" /></a></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<br />
<div style="text-align: left;">
<span style="font-family: Arial, Helvetica, sans-serif;">A continuación tenemos el comportamiento de los<span style="background-color: white; text-align: center;"><span style="color: #222222;"><span style="line-height: 18px;"> polos y ceros en forma gráfica de la función de transferencia:</span></span></span></span></div>
<div style="text-align: left;">
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="background-color: white; text-align: center;"><span style="color: #222222;"><span style="line-height: 18px;"><br /></span></span></span></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_8wQ32XV3TwfgACUQVrQrifieskDngVtwrG-lPSt9X3qn3ne81lW_xT9RP_n1sT61mkNj46CcWqJLzkmJo-hrkkhdfmtJwFifEkdttMZxIanLoUw5P4Zrg3N3OHJ-Rh_JFy4m8NdqgAA/s1600/locus.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="492" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi_8wQ32XV3TwfgACUQVrQrifieskDngVtwrG-lPSt9X3qn3ne81lW_xT9RP_n1sT61mkNj46CcWqJLzkmJo-hrkkhdfmtJwFifEkdttMZxIanLoUw5P4Zrg3N3OHJ-Rh_JFy4m8NdqgAA/s640/locus.png" width="640" /></a></div>
<div style="text-align: left;">
<br /></div>
<div style="text-align: left;">
<span style="background-color: white; text-align: center;"><span style="color: #222222; font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 18px;">Como vemos en la imagen vemos en la imagen, la función tiende a ser estable hasta un cierto punto en el cuál su comportamiento se vuelve inestable.</span></span></span></div>
<div style="text-align: left;">
<span style="background-color: white; text-align: center;"><span style="color: #222222; font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 18px;"><br /></span></span></span></div>
<div style="text-align: left;">
<span style="color: #222222; font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 18px;">Después</span></span><span style="background-color: white; text-align: center;"><span style="color: #222222; font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 18px;"> tenemos el código utilizado como vemos en los comentarios, los valores de la Resistencia y el Calor son Constantes, estos son inicializados a 1 para que no apliquen un gran cambio en el resultado:</span></span></span></div>
<div style="text-align: left;">
<div style="text-align: left;">
<span style="background-color: white; text-align: center;"><span style="color: #222222; font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 18px;"><br /></span></span></span></div>
</div>
<div style="text-align: left;">
<span style="background-color: white; text-align: center;"><span style="color: #222222; font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 18px;"></span></span></span></div>
<div style="text-align: left;">
<br /></div>
<script src="https://gist.github.com/3982018.js"> </script>
<div style="text-align: left;">
<div style="text-align: left;">
<span style="background-color: white; text-align: center;"><span style="color: #222222; font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 18px;">El resultado del código lo mostramos a continuación, el resultado no muestra el comportamiento con distintas Intensidades de entrada y con sus respectiva gráfica cuando se le aplica un ruido (este ruido fue realizado mediante la función seno y un tiempo de 0 y 20 con .001 entre cada uno):</span></span></span></div>
</div>
<div style="text-align: left;">
<span style="background-color: white; text-align: center;"><span style="color: #222222; font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 18px;"><br /></span></span></span></div>
<div style="text-align: left;">
<span style="background-color: white; text-align: center;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #660000; font-size: large; line-height: 18px;"><b>Con 2</b></span></span></span></div>
<div style="text-align: left;">
<span style="background-color: white; text-align: center;"><span style="color: #222222; font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 18px;"><br /></span></span></span></div>
<div style="text-align: left;">
<span style="background-color: white; text-align: center;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #274e13; line-height: 18px;"><b> Entradas</b></span></span></span></div>
<div style="text-align: left;">
<span style="background-color: white; text-align: center;"><span style="color: #222222; font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 18px;"><br /></span></span></span></div>
<div style="text-align: left;">
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhk4OQ7BxGWC2A6HcfzEv7Hkh-kjNve7y5Mu893XdFcUyGdj1Bi3jsRhpl2lWR4t0643NnKy1dmdPy15ON-isW_JL_pQeVWtqEgmTSrtJebb_WlWaS4yLyIfCqg3xKCh_WQy-dr8x5_QMM/s1600/AutoconI2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="492" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhk4OQ7BxGWC2A6HcfzEv7Hkh-kjNve7y5Mu893XdFcUyGdj1Bi3jsRhpl2lWR4t0643NnKy1dmdPy15ON-isW_JL_pQeVWtqEgmTSrtJebb_WlWaS4yLyIfCqg3xKCh_WQy-dr8x5_QMM/s640/AutoconI2.png" width="640" /></a></div>
<br />
<b style="background-color: white; font-family: Arial, Helvetica, sans-serif; line-height: 18px; text-align: center;"><span style="color: #274e13;"> Con Ruido</span></b><br />
<b style="background-color: white; font-family: Arial, Helvetica, sans-serif; line-height: 18px; text-align: center;"><br /></b>
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<span style="background-color: white; text-align: center;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #660000; font-size: large; line-height: 18px;"><b>Con 12</b></span></span></span></div>
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<span style="background-color: white; color: #274e13; font-family: Arial, Helvetica, sans-serif; line-height: 18px; text-align: center;"><b> Entradas</b></span><br />
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<span style="background-color: white; color: #274e13; font-family: Arial, Helvetica, sans-serif; line-height: 18px; text-align: center;"><b> Con Ruido</b></span><br />
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<span style="background-color: white; text-align: center;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #660000; font-size: large; line-height: 18px;"><b>Con 32</b></span></span></span></div>
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<span style="background-color: white; color: #274e13; font-family: Arial, Helvetica, sans-serif; line-height: 18px; text-align: center;"><b> Entradas</b></span><br />
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<b style="color: #274e13; font-family: Arial, Helvetica, sans-serif; line-height: 18px; text-align: center;"> Con Ruido</b><br />
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<span style="background-color: white; text-align: center;"><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #660000; font-size: large; line-height: 18px;"><b>Con 100</b></span></span></span></div>
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<span style="background-color: white; color: #274e13; font-family: Arial, Helvetica, sans-serif; line-height: 18px; text-align: center;"><b> Con Ruido</b></span><br />
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<span style="background-color: white; color: #222222; font-family: Arial, Helvetica, sans-serif; line-height: 18px; text-align: center;">Como vemos en todas las imágenes anteriores, las gráficas nunca se detienen en un punto en especifico, por lo tanto se mantiene la propuesta de que nuestra función tiende a ser inestable.</span></div>guelmi_rickhttp://www.blogger.com/profile/00075155021794486805noreply@blogger.com1tag:blogger.com,1999:blog-3668401867087218235.post-65211874175376833772012-10-25T07:27:00.000-07:002012-10-25T07:31:17.738-07:00Entrada # 8<span style="color: #073763; font-family: Arial, Helvetica, sans-serif; font-size: x-large;"><b>Stream Ciphers</b></span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 19.200000762939453px;">The stream ciphers are algorithms that can to perform encryption incrementally converting plaintext into ciphertext bitwise.</span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 19.200000762939453px;"><br /></span></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 19.200000762939453px;">To accomplish this we construct a keystream generator (bit sequence undefined size which can be used to encrypt the data stream by combining the keystream to the data stream using the XOR function).</span></span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 19.200000762939453px;">If the key stream is secure, encrypted data flow will be too.</span></span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 19.200000762939453px;">For this week commissioned us choose a stream cipher and explain, for this occasion I chose:</span></span><b style="font-family: Arial, Helvetica, sans-serif;">ISAAC</b><span style="font-family: Arial, Helvetica, sans-serif;">.</span><br />
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<span style="color: #660000; font-family: Arial, Helvetica, sans-serif; font-size: x-large;"><b>Stream Cipher ISAAC</b></span></div>
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<span style="color: #274e13; font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>History</b></span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">The letters are an acronym of ISAAC Indirection, Shift, Accumulate, Add, and Count, this was created in 1996 by Robert John Jenkins Jr.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">This is not only a stream cipher safe but also a pseudorandom number generator.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">This encryption shares many similarities with the RC4.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">ISAAC is used by Unix Shred as a tool to overwrite data securely.</span><br />
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<span style="color: #274e13; font-family: Arial, Helvetica, sans-serif; font-size: large;"><span style="background-color: white;"><span style="line-height: 19.200000762939453px;"><b>Description oh the Cipher</b></span></span></span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 19.200000762939453px;">It consists of an array of 256 of 4-bit integers (known as 'mm') as input, writing the results in another vector of 256 integers (known as 'm'), which are read one at a time until it is empty, and is then recomputed.</span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 19.200000762939453px;"><br /></span></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 19.200000762939453px;">The calculation is to alter the vector mm [i] with (i ⊕ 128) to each vector element, two elements are found by vector mm indirectly, an accumulator and a counter, for all values of i from 0 to 255 .</span></span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="line-height: 19.200000762939453px;">As you only need 19 operations of 32 bits for each output word of 32 bits, is extremely fast 32-bit computers.</span></span><br />
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<span style="color: #274e13; font-family: Arial, Helvetica, sans-serif; font-size: large;"><span style="line-height: 19.200000762939453px;"><b>Atacks y/o Vulnerabilitys</b></span></span><br />
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<span style="background-color: white; font-family: Arial, Helvetica, sans-serif; line-height: 19.200000762939453px;">In 2001, Marina Pudovkina in said an attack can recover the input data about a complexity less than the time required to search through the square root of all possible initial states.</span><br />
<span class="" style="background-color: white; font-family: Arial, Helvetica, sans-serif; line-height: 19.200000762939453px;"><br /></span>
<span class="" style="background-color: white; font-family: Arial, Helvetica, sans-serif; line-height: 19.200000762939453px;">To achieve such an attack would mean that this attack needs <img alt="4.67 \times 10^{1240}" class="tex" src="http://upload.wikimedia.org/math/6/5/f/65f94b7ac53c30381e4adfc72bb3174b.png" style="border: none; margin: 0px; vertical-align: middle;" /> time instead </span><img alt="10^{2466}" class="tex" src="http://upload.wikimedia.org/math/f/e/c/fec77442ba5baf3f2cc67a74f170603a.png" style="background-color: white; border: none; font-family: Arial, Helvetica, sans-serif; line-height: 19.200000762939453px; margin: 0px; vertical-align: middle;" /><span style="background-color: white; font-family: Arial, Helvetica, sans-serif; line-height: 19.200000762939453px;">.</span><span style="background-color: white; font-family: Arial, Helvetica, sans-serif; line-height: 19.200000762939453px;">This result has no practical impact on the security of ISAAC .</span><br />
<span class="" style="background-color: white; font-family: Arial, Helvetica, sans-serif; line-height: 19.200000762939453px;"><br /></span>
<span class="" style="background-color: white; font-family: Arial, Helvetica, sans-serif; line-height: 19.200000762939453px;">Among the most important is that in 2006, Jean-Philippe Aumasson discovered several series of weak states in the encryption, as this is based on RC4 has a weakness like this (this exit leads to a very similar to the ISAAC first round, and allows the derivation of the internal state, so that they could detect the input data).</span><br />
<span class="" style="background-color: white; font-family: Arial, Helvetica, sans-serif; line-height: 19.200000762939453px;"><br /></span>
<span class="" style="background-color: white; font-family: Arial, Helvetica, sans-serif; line-height: 19.200000762939453px;">Although it is unclear whether this weakness an attacker can ensure the output only if the generator is in one of these states or weak.</span><br />
<span class="" style="background-color: white; font-family: Arial, Helvetica, sans-serif; line-height: 19.200000762939453px;"><br /></span>
<span class="" style="background-color: white; font-family: Arial, Helvetica, sans-serif; line-height: 19.200000762939453px;">There is an attack on this cipher ISAAC in 2006 in </span><a href="http://www.informatik.uni-trier.de/~ley/db/conf/asiacrypt/asiacrypt2006.html" style="font-family: Arial, Helvetica, sans-serif;">Asiacrypt'06</a><span style="background-color: white; font-family: Arial, Helvetica, sans-serif; line-height: 19.200000762939453px;"> by Paul and Bart Preneel Souradyuti, this attack demonstrate that it is of great importance, since it is based on an algorithm wrong.</span><br />
<span class="" style="background-color: white; font-family: Arial, Helvetica, sans-serif; line-height: 19.200000762939453px;"><br /></span>
<span class="" style="background-color: white; font-family: Arial, Helvetica, sans-serif; line-height: 19.200000762939453px;">Finally, a modified algorithm is proposed to fix the weaknesses discovered in the states, this change arises in an improved version called ISAAC +.</span><br />
<span class="" style="background-color: white; font-family: Arial, Helvetica, sans-serif; line-height: 19.200000762939453px;"><br /></span>
<span class="" style="background-color: white; font-family: Arial, Helvetica, sans-serif; line-height: 19.200000762939453px;">So far not been a successful attack, but that does not ensure that in the future there is the possibility of an attack.</span><br />
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<span style="color: #274e13; font-family: Arial, Helvetica, sans-serif; font-size: large;"><span style="background-color: white;"><span style="line-height: 19.200000762939453px;"><b>Start the Cipher</b></span></span></span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">For explanation it will be used encryption 8 data entry is required because the key which is required in the same length as the output, so that the size of the key will be the same size or 8.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Before encryption must consider a few things that you use this:</span><br />
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<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">Size: The size of the key and, on this occasion is 8.</span><br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">mm: Fix input</span><br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">m: Output Agreement</span><br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">It makes use of a process that is widely used, this is known as mix ():</span><br />
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<span style="color: #073763;"><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span><span style="font-family: Arial, Helvetica, sans-serif;">This use elements of the key y save in variable (a ... h)</span></span><br />
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<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">Graphic Form:</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglqop0rPxKqo6s9CzdRxbkf6YjI-FR2Jy9HYCOC11dnxix8_0tIM9F2-TZRUM4CrvrEB3rRnY2GUW02MyUSp-SSN_mFpn7ealiX6IZp5qXhkWavM6P0WgOhsbbxvf0S2q0hTZ7C2RUclw/s1600/mix().2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglqop0rPxKqo6s9CzdRxbkf6YjI-FR2Jy9HYCOC11dnxix8_0tIM9F2-TZRUM4CrvrEB3rRnY2GUW02MyUSp-SSN_mFpn7ealiX6IZp5qXhkWavM6P0WgOhsbbxvf0S2q0hTZ7C2RUclw/s640/mix().2.png" width="332" /></span></a></div>
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<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">Another important function is the function rngstep (), this is the most important of this encryption key generator.</span></div>
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<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">This does the following:</span></div>
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<ul>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #073763;">Stores the current memory into a register</span></span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #073763;">Set the new value of the accumulator</span></span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #073763;">Set the next memory bit to the addition of 2-9 bits xo current memory and the accumulator with the above result.</span></span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #073763;">Finally, the results of the matrix is increased and began adding bits x 10 -17 and right scroll 8 bits.</span></span></li>
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<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">This code form and in visual form:</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizXf_l-TPDudQQdjzsicUdNL2NdMF1EvXSRWfqFwWx6qo6mFRYPw0S1Pn3PxU5K0xm4ayZsSRubM9Gs9sK4p3GVirFR2uhprRZGvYwq8B2YLVLKuUmS77_dlL3si_ZMrl8v941qQGV0Og/s1600/rngstep1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="124" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEizXf_l-TPDudQQdjzsicUdNL2NdMF1EvXSRWfqFwWx6qo6mFRYPw0S1Pn3PxU5K0xm4ayZsSRubM9Gs9sK4p3GVirFR2uhprRZGvYwq8B2YLVLKuUmS77_dlL3si_ZMrl8v941qQGV0Og/s320/rngstep1.png" width="320" /></span></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjio2xLvBKfOdF5mRigiEL8ZDF-kMwgo7mEU25M5YJTeK1sN_CtHgT9feJTvXXGGdAwY9YaywnGqE5NKNFp7wuVXH2EkkC5qRDCaGnXM2sC0jCeIqV37bEEd7d5zlweDBlqXvwkLymMgmU/s1600/rngstep2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="452" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjio2xLvBKfOdF5mRigiEL8ZDF-kMwgo7mEU25M5YJTeK1sN_CtHgT9feJTvXXGGdAwY9YaywnGqE5NKNFp7wuVXH2EkkC5qRDCaGnXM2sC0jCeIqV37bEEd7d5zlweDBlqXvwkLymMgmU/s640/rngstep2.png" width="640" /></span></a></div>
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<span style="color: #274e13; font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>Beginning with Steps</b></span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><b>Firsth.- </b>Load the eight elements of the key variables, run the mix () to randomize them, the results are loaded into the eight elements of the array. This process is repeated until the key has expired.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgm5pmM9ID09tex_mxPQjYhTOWYsGmfi9zp4vU0mxQqH-jgsb8srknlEeCbORWX71YIGwIfV7I_vmoQKxoz1lVvNoDEYi5dstC6d5yXcX1v54PHxECOQM2YI5TLTw7DnYdsA7RLCYxOHBk/s1600/ini1.1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="131" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgm5pmM9ID09tex_mxPQjYhTOWYsGmfi9zp4vU0mxQqH-jgsb8srknlEeCbORWX71YIGwIfV7I_vmoQKxoz1lVvNoDEYi5dstC6d5yXcX1v54PHxECOQM2YI5TLTw7DnYdsA7RLCYxOHBk/s400/ini1.1.png" width="400" /></span></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaIymAK5YtCskg5YIIQ81lpmAKm9ESeQ-4V_upm50eEUyNzOiWPwgnXIaI5A7FFHS-fj6YJ17TIb1-JrL9mhY6ocU96AJmZXuWCU_Qm-vIJXh9E4Zs2GJvks7oYzS0LjluDP_si6aIjAw/s1600/ini1.2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="370" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhaIymAK5YtCskg5YIIQ81lpmAKm9ESeQ-4V_upm50eEUyNzOiWPwgnXIaI5A7FFHS-fj6YJ17TIb1-JrL9mhY6ocU96AJmZXuWCU_Qm-vIJXh9E4Zs2GJvks7oYzS0LjluDP_si6aIjAw/s400/ini1.2.png" width="400" /></span></a></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Second.- </b>The same process is made to mix more thoroughly, but now load the items in the array instead of the key elements in integers.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwK9aa7HXcWmxxE97JU-nPHxLl25twB6LR5dQrgSBjRYJSXsM0QiYYc8kmJNJuaNMfZjApz4Y6cYg-Yif2zUl08UCPRVKIdK91_PipwnerzWvwmpftiQCGKWMIBHKnzLb69QGm8mCl-jk/s1600/ini2.1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="259" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgwK9aa7HXcWmxxE97JU-nPHxLl25twB6LR5dQrgSBjRYJSXsM0QiYYc8kmJNJuaNMfZjApz4Y6cYg-Yif2zUl08UCPRVKIdK91_PipwnerzWvwmpftiQCGKWMIBHKnzLb69QGm8mCl-jk/s320/ini2.1.png" width="320" /></span></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZUJaWkJRznC_y4EpChyEAGDdZWA38YOLDIh7z4CudmtK0fpx-NDoCjDyhsWovxBWPmUq9twEA_dKFsxdQtlV6pstHzxvJ8J8zH4wVPiX0aSrBT1Gvogp656GXsEWF5nOtfDFyNNcwGTY/s1600/ini2.2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZUJaWkJRznC_y4EpChyEAGDdZWA38YOLDIh7z4CudmtK0fpx-NDoCjDyhsWovxBWPmUq9twEA_dKFsxdQtlV6pstHzxvJ8J8zH4wVPiX0aSrBT1Gvogp656GXsEWF5nOtfDFyNNcwGTY/s400/ini2.2.png" width="400" /></span></a></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">All this was to hold the keys and mixing arrangement as possible.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">Would then process the main part, this has two steps:</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><b>Firsth.-</b> It adds a counter called B, then calls the function rngstep () four times with different bitshifts of A for which the mix is best.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKr6_PDsFmTwd67fhfE9P4HQ79ciazB3wNpwjbzoOHXBJ7zI7-0koDLihgWbWe1Owl0IWQHtEu1xrxMAGz9Wd1ydodTzfG0tEFyY6tvsaBH1D62wKZebbdzCNI-ltq6S2jFKOYBBdesgo/s1600/main1.1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="117" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKr6_PDsFmTwd67fhfE9P4HQ79ciazB3wNpwjbzoOHXBJ7zI7-0koDLihgWbWe1Owl0IWQHtEu1xrxMAGz9Wd1ydodTzfG0tEFyY6tvsaBH1D62wKZebbdzCNI-ltq6S2jFKOYBBdesgo/s400/main1.1.png" width="400" /></span></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj99Z6qj_nxhEsYBU-Mg1mOZ-xmcI_IYrBmp-DZmxYTAYvZuEa0LtXoobrMVJ1He_yBzyhchGIvUm3FMUozmx11UtG1EhuQa_NltadNu4oAPpKif9JcuOLof7yb9ggKgCRC6GdiZj1katU/s1600/main1.2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj99Z6qj_nxhEsYBU-Mg1mOZ-xmcI_IYrBmp-DZmxYTAYvZuEa0LtXoobrMVJ1He_yBzyhchGIvUm3FMUozmx11UtG1EhuQa_NltadNu4oAPpKif9JcuOLof7yb9ggKgCRC6GdiZj1katU/s640/main1.2.png" width="505" /></span></a></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Second.-</b> Make a second M2 for but, going from the first element to be repaired, calling rngstep () four times in each iteration.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">This step is designed to Ensure That m2 at each array is at least one index for rngstep ().</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3JzhW1kvA_7A5MSysWG3UgrvFAJINaYHFWpkyVjXH2WPNkgxdAFPguebVM9brqifYfn38VplFTOv4EaGAMdWYzVX37U86kQoBPHO_DIxuvovNw5D3qYucJHH_LvzkQLCTCVjDW_eLY5c/s1600/main2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg3JzhW1kvA_7A5MSysWG3UgrvFAJINaYHFWpkyVjXH2WPNkgxdAFPguebVM9brqifYfn38VplFTOv4EaGAMdWYzVX37U86kQoBPHO_DIxuvovNw5D3qYucJHH_LvzkQLCTCVjDW_eLY5c/s400/main2.png" width="391" /></span></a></div>
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<span style="color: #274e13; font-family: Arial, Helvetica, sans-serif; font-size: large;"><span style="background-color: white;"><span style="line-height: 19.200000762939453px;"><b>References</b></span></span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="background-color: white;"><span style="line-height: 19.200000762939453px;"><br /></span></span></span>
<a href="http://es.wikipedia.org/wiki/Cifrador_de_flujo"><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>http://es.wikipedia.org/wiki/Cifrador_de_flujo</b></span></a><br />
<a href="http://burtleburtle.net/bob/rand/isaacafa.html"><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>Aquí puedes encontrar el código de este cifrado en distintos lenguajes.</b></span></a><br />
<a href="http://en.wikipedia.org/wiki/ISAAC_(cipher)"><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>http://en.wikipedia.org/wiki/ISAAC_(cipher)</b></span></a><br />
<a href="http://www.cs.rit.edu/~ark/spring2012/482/team/u3/presentation1.pdf"><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>http://www.cs.rit.edu/~ark/spring2012/482/team/u3/presentation1.pdf</b></span></a><br />
<a href="http://www.burtleburtle.net/bob/rand/isaac.html"><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>http://www.burtleburtle.net/bob/rand/isaac.html</b></span></a><br />
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><a href="http://docs.python.org/reference/expressions.html#binary-bitwise-operations"><b>http://docs.python.org/reference/expressions.html#binary-bitwise-operations</b></a></span><br />
<a href="http://eprint.iacr.org/2006/438"><b><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;">http://eprint.iacr.org/2006/438</span></b></a>guelmi_rickhttp://www.blogger.com/profile/00075155021794486805noreply@blogger.com1tag:blogger.com,1999:blog-3668401867087218235.post-5060636872913317842012-10-18T08:57:00.003-07:002012-10-18T08:57:29.299-07:00Entrada # 4<br />
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<span style="color: #20124d;"><b><span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Laboratorio de Automatización y Control de Sistemas Dinámicos</span></b></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Para esta semana consistió en elegir un problema y resolverlo.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Primeramente el Problema Elegido:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Determine el rango de valores de K para la estabilidad de un sistema de control con realimentación unitaria cuya función de transferencia en lazo abierto es</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipn6xdGh1-lcuwf3d6UdZuJ07an0z_HWVc54IQ7LzVrlURsaQ9YY0YozO4mEu1fiv_rGNXZVzo_63vSI0z-j0wD3dORsqTzuk71GcGTcL8J8E8_-Lv9wK9zy3MDEIRsccyzNWF50a2x74/s1600/uno.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEipn6xdGh1-lcuwf3d6UdZuJ07an0z_HWVc54IQ7LzVrlURsaQ9YY0YozO4mEu1fiv_rGNXZVzo_63vSI0z-j0wD3dORsqTzuk71GcGTcL8J8E8_-Lv9wK9zy3MDEIRsccyzNWF50a2x74/s1600/uno.gif" /></span></a></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">En base al libro de Ogata nos dice que para los problemas de estabilidad hay que multiplicar el denominador y nominador con tal de que no exista multiplicación alguna en ellos, quedaría:</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXJTINqgnRYwlHyazTkAhsrqKWysrJsZTBZ9Q4wVA4X4nQAusV7Ce9BqFceLnONxhoG7szXfAnIzIHNhu928rxN65aY2GGMygNiwPNaIc4XJ6MINHt69-YZ5ryGqwxwl2tM9PqBBwlUvg/s1600/dos.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhXJTINqgnRYwlHyazTkAhsrqKWysrJsZTBZ9Q4wVA4X4nQAusV7Ce9BqFceLnONxhoG7szXfAnIzIHNhu928rxN65aY2GGMygNiwPNaIc4XJ6MINHt69-YZ5ryGqwxwl2tM9PqBBwlUvg/s1600/dos.gif" /></span></a></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Pero como tenemos un valor en el numerador tenemos que pasarlo al denominador, nos quedaría:</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqSMiES-W_AXAkgBG4VhGUHksM2ODxydBTGleDIVFNSzV53x3qvTBCvKI_hffKKwiTCGVXknqwpvwqHcGKhbF3MXHt95iTYKmflOG_1ZQjte898tAoac1FxnXZuAbOgdDzINexCa2Ow3s/s1600/cuatro.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhqSMiES-W_AXAkgBG4VhGUHksM2ODxydBTGleDIVFNSzV53x3qvTBCvKI_hffKKwiTCGVXknqwpvwqHcGKhbF3MXHt95iTYKmflOG_1ZQjte898tAoac1FxnXZuAbOgdDzINexCa2Ow3s/s1600/cuatro.gif" /></span></a></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Tenemos que:</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXaK4W_928Ixdo9r5HCgiEZjrS-e0oRrYIGZFQmv1syGVUnyon2Y_xpgRpMk85r8Hd2KI57SyOAMUuhtMxjI9qs34HQawzQWRaCwGkszfbPcebj4BLYLuJ7Cyi3zKZ59azSfPE7NmhZ68/s1600/Auto4.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="46" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgXaK4W_928Ixdo9r5HCgiEZjrS-e0oRrYIGZFQmv1syGVUnyon2Y_xpgRpMk85r8Hd2KI57SyOAMUuhtMxjI9qs34HQawzQWRaCwGkszfbPcebj4BLYLuJ7Cyi3zKZ59azSfPE7NmhZ68/s400/Auto4.png" width="400" /></span></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Y</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0bkm-cBqgkTJJpqxeqj4ungaEwyF5x_NpMLqT2eAg2dGJfI2TNc-v2DeWjjXdsA60SHKSTBvjtZn7QkjRJIW8KFdULY8VIn8CUY7mH4MpXLrOU7xO7uaoBzLhx6AmD22ZlyG0wbrixxY/s1600/Auto2.1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="320" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg0bkm-cBqgkTJJpqxeqj4ungaEwyF5x_NpMLqT2eAg2dGJfI2TNc-v2DeWjjXdsA60SHKSTBvjtZn7QkjRJIW8KFdULY8VIn8CUY7mH4MpXLrOU7xO7uaoBzLhx6AmD22ZlyG0wbrixxY/s320/Auto2.1.png" width="249" /></span></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">En base a las ecuaciones anteriores nos quedaría lo siguiente:</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhl45uv1I_STMIG3E6Y6uwbv4Q17TNMfioYmX9k9q_4OP_ux4rGsNWGM2NQ05Trn-kuAJtjRQh28pEfcH5HOecUIsC8O1EXsW9O5fs6SpSmPTX1Fp2t2e7MtEL0uLX9sROF8jWaMmoFm9A/s1600/tres.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhl45uv1I_STMIG3E6Y6uwbv4Q17TNMfioYmX9k9q_4OP_ux4rGsNWGM2NQ05Trn-kuAJtjRQh28pEfcH5HOecUIsC8O1EXsW9O5fs6SpSmPTX1Fp2t2e7MtEL0uLX9sROF8jWaMmoFm9A/s1600/tres.gif" /></span></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">En base a la imagen anterior nos quedaría que:</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhI-5nhrq4JTNqvCv3hvkcgOuYEbCCwxBG1GP_5Myb_Ib-HcfDDfkX34SozhT7knvjFx0ZQsK_s6gPvM6YgLdZkdLj0J3x7qNYw1ks-5wkewbUDgqwULP0eAUtAKTI3-b-qfTXVKPylpm0/s1600/Auto5.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="368" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhI-5nhrq4JTNqvCv3hvkcgOuYEbCCwxBG1GP_5Myb_Ib-HcfDDfkX34SozhT7knvjFx0ZQsK_s6gPvM6YgLdZkdLj0J3x7qNYw1ks-5wkewbUDgqwULP0eAUtAKTI3-b-qfTXVKPylpm0/s640/Auto5.jpg" width="640" /></span></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Para determinar el rango de K habrá que tomar los términos de s que contengan a K e igualarlos a 0 cada uno, y esos dos valores serian el rango de K.</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikYpwRf-TDJ96SqqCPt5lgp0nSEYTLEOzEcO6LCnZcph54nL1hAWyoCfDp-y3LKF6Lj4gy1vASgBAzSsdAZl-EgqMuoDxAAoCEqYUd-4lYiEz3PKKRMHbLC8lgfIhN0SWmadpscO-hJTk/s1600/seis.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikYpwRf-TDJ96SqqCPt5lgp0nSEYTLEOzEcO6LCnZcph54nL1hAWyoCfDp-y3LKF6Lj4gy1vASgBAzSsdAZl-EgqMuoDxAAoCEqYUd-4lYiEz3PKKRMHbLC8lgfIhN0SWmadpscO-hJTk/s1600/seis.gif" /></span></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiklTLxnrdbyiL9md9bWVjJOSozXTY12STOfRsagk6pTukMubkBt-A2E3LzNZKSxAGe6lqXkgOO5I1uk1Ks2j9jAI7lbNNBiuZuF5JIcoor5mw-p2zNebgFHHXEPQ-EgypExZdEtFWw05o/s1600/siete.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiklTLxnrdbyiL9md9bWVjJOSozXTY12STOfRsagk6pTukMubkBt-A2E3LzNZKSxAGe6lqXkgOO5I1uk1Ks2j9jAI7lbNNBiuZuF5JIcoor5mw-p2zNebgFHHXEPQ-EgypExZdEtFWw05o/s1600/siete.gif" /></span></a></div>
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<span style="text-align: left;"><span style="font-family: Arial, Helvetica, sans-serif;">Por lo tanto el rango de K debería de ser:</span></span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKzoohMmPpQ_mFkxivgmz96F1PDCPKaM0hetvJbe_v8nOttV4OpAA4du-P52YTR93LP6wvZ1V21owmvkh-yO_Ng5iaY_jGA8t2DfFlo7cbDo3ikWeTLQEouqunbOkUUD_t_UoIcNXH4pA/s1600/ocho.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiKzoohMmPpQ_mFkxivgmz96F1PDCPKaM0hetvJbe_v8nOttV4OpAA4du-P52YTR93LP6wvZ1V21owmvkh-yO_Ng5iaY_jGA8t2DfFlo7cbDo3ikWeTLQEouqunbOkUUD_t_UoIcNXH4pA/s1600/ocho.gif" /></span></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">y</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-U46BBquWCV6lZnotIKB0UKBE1MshzimrVjYyBC-1WuJefD3tGNjzIY1tiQ9Ii8EdDPBhm2GRnTuMwYAPEicE5_IRmMJjsYULGEhem27ycYLcArmsBkLzBRU9aCRWnytLBoHVNx_Y1Hk/s1600/nueve.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-U46BBquWCV6lZnotIKB0UKBE1MshzimrVjYyBC-1WuJefD3tGNjzIY1tiQ9Ii8EdDPBhm2GRnTuMwYAPEicE5_IRmMJjsYULGEhem27ycYLcArmsBkLzBRU9aCRWnytLBoHVNx_Y1Hk/s1600/nueve.gif" /></span></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"> O dicho de otra manera:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8myVrGvVAzLEerMkBLtFHVl2LD4RCZGbWQiVN9w7CJMQXQ4Iwq31xgLBWQqsZMsyvXqOGlwtfeJLb5X2VIxeNqYA5lY0rQAHHXTeSq9A1mKh1q1iA7R1ruuqB5hYLfgiv_GTCPq9QVSc/s1600/diez.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg8myVrGvVAzLEerMkBLtFHVl2LD4RCZGbWQiVN9w7CJMQXQ4Iwq31xgLBWQqsZMsyvXqOGlwtfeJLb5X2VIxeNqYA5lY0rQAHHXTeSq9A1mKh1q1iA7R1ruuqB5hYLfgiv_GTCPq9QVSc/s1600/diez.gif" /></span></a></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>Referencias:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: blue; font-family: Arial, Helvetica, sans-serif;"><b>Modern Control Engineering Fourth Edition</b></span><br />
<span style="color: blue; font-family: Arial, Helvetica, sans-serif;"><b>Katsuhiko Ogata</b></span>guelmi_rickhttp://www.blogger.com/profile/00075155021794486805noreply@blogger.com1tag:blogger.com,1999:blog-3668401867087218235.post-31064863233876919312012-10-18T04:58:00.001-07:002012-10-18T05:18:11.443-07:00Entrada # 7<span style="color: #7f6000; font-family: Arial, Helvetica, sans-serif;">Reporte # 2</span><br />
<span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>Blocks Ciphers</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">First shall begin with a little explanation about what this is.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Consists of a symmetric key cipher (in which the same key is used to encrypt and decrypt messages) that operates on groups of bits of fixed length, called blocks, applying a transformation invariant.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">When performing encryption, this takes a block of plain text as input and produces a ciphertext of the same size as the original text.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">For this week is to choose one of the existing encrypted and explain.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br />
</span><br />
<div style="text-align: center;">
<span style="color: blue; font-family: Arial, Helvetica, sans-serif; font-size: x-large;"><b>Akelarre Cipher</b></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /><span style="color: red; font-size: large;"><b>Who and When Proposing</b></span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br />
Was design for <span style="background-color: white; line-height: 19.200000762939453px;">G. Álvarez Marañón, D. Guía Martínez, F. Montoya Vitini, A. Peinado Domínguez in 1996.</span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br />
<span style="color: red; font-size: large;"><b>Mejoras que tenía de los ya existentes</b></span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br />
Akelarre combines the best of this cipher's:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br />
<span style="color: #20124d;"><b> IDEA.-</b> </span></span><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;">Handles multiple arithmetic.</span><br />
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b> RC5.-</b> Rotation of Keys.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">This encryption aims to be a strong encryption system most efficient.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">
<span style="color: red; font-size: large;"><b>How it Works</b></span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br />First we have a define the next points:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br />
</span><br />
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>Variable numbers of rounds</b></span><br />
<ul>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #20124d;"> The autors claim the 4 rounds is more safe.</span></span></li>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #20124d;"> </span></span><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;">Although the reality is unsafe for any number of rounds!</span></li>
</ul>
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>Block length is 128 bits</b></span><br />
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>Key length can be any multiple of 64 bits</b></span><br />
<ul>
<li><span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #20124d;"> The common lenght of the key is the 128 bits.</span></span></li>
</ul>
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>Lots of blocks subkey: 13R + 8</b></span><br />
<ul>
<li><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;">Every of the subkeys its a word of 32 bits.</span></li>
</ul>
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>Mod also employs 232 and XOR</b></span><br />
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>Adding rotation (AR) structure</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: #274e13; font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>Proceso del Cifrado</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>For the encryption:</b></span><br />
<br />
<ul>
<li><span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">Inputs data, this we have transformating for your use</span></li>
<li><span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">Round 0,1,2, ..., R-1</span></li>
<li><span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">Cifred data</span></li>
</ul>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Explain of more extensing form:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivSlpcBvhSx6RTDWZ57Bvt5y0TSpgJyTLNOftNo45QZvwYSvawhpEKbhuOLzrFiYlOM0De-45s6Xq_8ibd2QXUNHfXQNCAHAt4P8TsLeiAbM1eO5yw0UZH8jTuvtbETpzxmyAv_VFVmYI/s1600/Uno.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="492" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivSlpcBvhSx6RTDWZ57Bvt5y0TSpgJyTLNOftNo45QZvwYSvawhpEKbhuOLzrFiYlOM0De-45s6Xq_8ibd2QXUNHfXQNCAHAt4P8TsLeiAbM1eO5yw0UZH8jTuvtbETpzxmyAv_VFVmYI/s640/Uno.png" width="640" /></span></a></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
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<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>Taking: </b></span><br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><br /></span>
<br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">(A0, A1, A2, A3), this would be the input to round r.</span><br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">(B0, B1, B2, B3), the output would rotation keys.</span><br />
<br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>Then Apply the struct of Akelarre</b></span><br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><span style="text-align: center;">(B0, B1, B2, B3) = (A0, A1, A2, A3) <<<<</span><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQ_TZfrdhiCZRhDrOAgU_oj9ePRiZMUyeN7QoEoerDPUqpj5_aP5iInRjZ7CJCx6yY4t3T5lN3VFm0307SX-wUYHtNDgKGH6HlvbCeJaFFiTrC-pXBYGpgVLLot35YKh2L_XkY2LD-oeM/s1600/dos.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em; text-align: center;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQ_TZfrdhiCZRhDrOAgU_oj9ePRiZMUyeN7QoEoerDPUqpj5_aP5iInRjZ7CJCx6yY4t3T5lN3VFm0307SX-wUYHtNDgKGH6HlvbCeJaFFiTrC-pXBYGpgVLLot35YKh2L_XkY2LD-oeM/s1600/dos.gif" /></a></span><br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">Where "<<<" is left rotation and <img alt="(X)_i_\ldots_j" src="http://rinconmatematico.com/latexrender/pictures/af7b0e463b0381d5737bdf936a119a87.gif" />, this means bits i thru j (inclusive) of X</span><br />
<br />
<ul>
<li><span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">Recall, the bits enumerating the left to right, started in 0</span></li>
</ul>
<br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>Explain of visual form:</b></span><br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><br /></span>
<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXlFmlg6FXK0_nbJUjUkTjddGmvZp9IDyIdOI98Zef7RHAn7xN_5ZdeAAjuWV8Wom_FqAfu33SXfOdeoWNbesiwZ80KJj8GwRZ2VHo4tNQbhwz6bqZ9TpkCTqYxRDdIyv1m-JVnpKtbkY/s1600/tres.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><img border="0" height="640" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjXlFmlg6FXK0_nbJUjUkTjddGmvZp9IDyIdOI98Zef7RHAn7xN_5ZdeAAjuWV8Wom_FqAfu33SXfOdeoWNbesiwZ80KJj8GwRZ2VHo4tNQbhwz6bqZ9TpkCTqYxRDdIyv1m-JVnpKtbkY/s640/tres.png" width="555" /></span></a></div>
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>Where:</b></span><br />
<ul>
<li><span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">W = X</span></li>
<li><span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">W1 make first</span></li>
<li><span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">Rotate 31 bits, with 1 bit fixed</span></li>
</ul>
<b style="color: #073763; font-family: Arial, Helvetica, sans-serif;">Taking</b><span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>:</b></span><br />
<br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">(T0 ,T1), output would AR structure</span><br />
<br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">(T0 ,T1) = AR(B0 ⊕ B2, B1 ⊕ B3), indicating the input values and which has the form AR obtain these.</span><br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>Later: </b></span><br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">(D0, D1, D2, D3), output would round r.</span><br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>Then:</b></span><br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">(D0, D1, D2, D3) = (B0⊕T1, B1⊕T0, B2⊕T1, B3⊕T0)</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>One Time to Finished This:</b></span><br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">The Block (D0, D1, D2, D3) whold:</span><br />
<ul>
<li><span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">The entrance of the next round.</span></li>
<li><span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">If the last one, whold the output of all the process.</span></li>
</ul>
<span style="font-family: Arial, Helvetica, sans-serif;">For the decryption process would use the same process only data that would introduce a little different.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYeWvRsiE27HUQ0l75yE0w4MWrBZUMA0PYRqgluUu2tHOYiIs8Zlytn9q-3SSSKHu6t-xbThd53waVE8c16Zasej3yZanqVR9uzDx5c7_hLnWXbpfysUCY3KO3RithUuNO7QnU2oEkX7E/s1600/cuatro.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="362" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjYeWvRsiE27HUQ0l75yE0w4MWrBZUMA0PYRqgluUu2tHOYiIs8Zlytn9q-3SSSKHu6t-xbThd53waVE8c16Zasej3yZanqVR9uzDx5c7_hLnWXbpfysUCY3KO3RithUuNO7QnU2oEkX7E/s400/cuatro.png" width="400" /></a></div>
<br />
<br />
<span style="color: red; font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>Math Type which is based</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br />As based on IDEA uses XOR (⊕) combined with rotation values, and modular arithmetic.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">
<br /><b><span style="color: red; font-size: large;">
Example</span></b></span><br />
<br />
<span style="font-family: Arial, Helvetica, sans-serif;">The following is a problem which show difficulties if used have certain values in this.</span><br />
<br />
<div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">-------------------------------------------------------------------------------------------------------------------</span></div>
<div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<br />
<span style="font-family: Arial, Helvetica, sans-serif;">Only to start:</span><br />
<br />
<ul>
<li><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;">z is K in the explication.</span></li>
</ul>
<br />
<span style="font-family: Arial, Helvetica, sans-serif;">Given X = (0x53,0x8d,0x86,0x80), Y = (0x74,0x21,0x9c,0xca):</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /><span style="color: #073763;"><b>Create an equation, substituting in the values for x and y:</b></span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #073763;"><b><br /></b></span></span>
<br />
<div style="text-align: center;">
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">(0x53-z5) ^ 0x86 ^ z7 = (0x74 + z1) ^ 0x9c ^ z3</span></div>
<div style="text-align: center;">
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>
Starting with the low-order bit (denoted zi[0]), determine which of the following bit combinations solve the above equation:</b></span><br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><br /></span>
<br />
<div style="text-align: center;">
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">(z5[i],z1[i],z3[i]^z7[i]) = ((0,0,0),(0,0,1),...,(1,1,0),(1,1,1))</span></div>
<div style="text-align: center;">
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>
Provided sufficient plaintext-ciphertext pairs, it should theoretically be possible to uniquely determine the values of the unknown subkeys using this technique.</b></span><br />
<div>
<div>
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span></div>
<div>
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>In order to solve for the unknown plaintext, we need to solve the below equation:</b></span></div>
<div>
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8YAJhfm9mH4qby6Hz-a-osaOuSYpbNj44YjsTnYCzsl8j75mO1CgfRqhjLW2uEapmoUO0P5n0Z_MA-2Q1BIbdX-NWNFEb-61jCfR43tiYhiagwx2WJVDoIthdvuxRncs3EyYEBBi9AL0/s1600/cinco.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><img border="0" height="34" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8YAJhfm9mH4qby6Hz-a-osaOuSYpbNj44YjsTnYCzsl8j75mO1CgfRqhjLW2uEapmoUO0P5n0Z_MA-2Q1BIbdX-NWNFEb-61jCfR43tiYhiagwx2WJVDoIthdvuxRncs3EyYEBBi9AL0/s320/cinco.png" width="320" /></span></a></div>
<div>
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div>
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>We know the entire right-hand side of the equation and z1 on the left-hand side.</b></span></div>
<div>
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span></div>
<div>
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>Given sufficient redundancy, it is possible to determine the values of x1 and x3. The papers we read did not go into detail about how to perform this recovery.</b></span></div>
</div>
<div>
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span></div>
<div>
<div>
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>Determining z1...z8:</b></span><br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span></div>
<div>
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">Tried multiple approaches that either resulted in hundreds of potential subkey values, or did not find a single subkey value</span><br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div>
<b><span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"> </span><span style="color: #0c343d; font-family: Arial, Helvetica, sans-serif;"> Bit-by-bit as described</span></b></div>
<div>
<span style="color: #0c343d; font-family: Arial, Helvetica, sans-serif;"> Resulted in hundreds of matches</span></div>
<div>
<span style="color: #0c343d; font-family: Arial, Helvetica, sans-serif;"><b> Bit-by-bit, taking carry bits into consideration</b></span></div>
<div>
<span style="color: #0c343d; font-family: Arial, Helvetica, sans-serif;"> Resulted in zero matches</span></div>
<div>
<span style="color: #0c343d; font-family: Arial, Helvetica, sans-serif;"><b> Byte-by-byte bruteforce attack</b></span></div>
<div>
<span style="color: #0c343d; font-family: Arial, Helvetica, sans-serif;"> Worked if the input size was a single byte, but did not work otherwise</span><br />
<br />
<span style="font-family: Arial, Helvetica, sans-serif;">-------------------------------------------------------------------------------------------------------------------</span></div>
</div>
<br />
<span style="font-family: Arial, Helvetica, sans-serif;">Let</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>A = (A0, A1, A2, A3), be input to round r</b></span><br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>U = (U0, U1, U2, U3), be result of rotation</b></span><br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>T = (T0, T1), be output of AR structure</b></span><br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>B = (B0, B1, B2, B3), be output of round r</b></span><br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>Denote A = (a0 ,a1,…,a127)</b></span><br />
<ul>
<li><span style="color: #073763; font-family: Arial, Helvetica, sans-serif;">And similarly for U,T,B</span></li>
</ul>
<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="color: #073763;">Let l be size of keyed rotation</span></b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="color: #073763;"><br /></span></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="color: #073763;">Then U = (A <<< l) and (B0, B1, B2, B3) = (U0⊕T1, U1⊕T0, U2⊕T1, U3⊕T0)</span></b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="color: #073763;"><br /></span></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="color: #073763;">It follows that B0⊕B2 = U0⊕U2 and B1⊕B3 = U1⊕U3</span></b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="color: #073763;"><br /></span></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="color: #073763;">AR structure has vanished!</span></b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="color: #073763;"><br /></span></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="color: #073763;">The crucial observation for attack</span></b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: red; font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>Atacks Y/O Vulnerabilities</b></span><br />
<br />
<span style="font-family: Arial, Helvetica, sans-serif;">Akelarre shows that your design is complicated encryption.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">An attack is conceptually simple, but the details are not so simple.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">There is an attack in the year 1997, using Ciphertext-only attack.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">It therefore proves to be very vulnerable to attacks.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br />
<span style="color: red; font-size: large;"><b>References:</b></span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br />
<a href="http://www.schneier.com/paper-akelarre.pdf">http://www.schneier.com/paper-akelarre.pdf</a></span><br />
<a href="http://es.wikipedia.org/wiki/Akelarre_(cifrado)"><span style="font-family: Arial, Helvetica, sans-serif;">http://es.wikipedia.org/wiki/Akelarre_(cifrado)</span></a><br />
<a href="http://www.sacconference.org/proc/SAC_96_002.pdf"><span style="font-family: Arial, Helvetica, sans-serif;">http://www.sacconference.org/proc/SAC_96_002.pdf</span></a><br />
<a href="http://es.wikipedia.org/wiki/Cifrado_por_bloques"><span style="font-family: Arial, Helvetica, sans-serif;">http://es.wikipedia.org/wiki/Cifrado_por_bloques</span></a><br />
<a href="http://en.wikipedia.org/wiki/Akelarre_(cipher)"><span style="font-family: Arial, Helvetica, sans-serif;">http://en.wikipedia.org/wiki/Akelarre_(cipher)</span></a><br />
<a href="http://cs.sjsu.edu/~stamp/crypto/PowerPoint_PDF/12_Akelarre.pdf"><span style="font-family: Arial, Helvetica, sans-serif;">http://cs.sjsu.edu/~stamp/crypto/PowerPoint_PDF/12_Akelarre.pdf</span></a>guelmi_rickhttp://www.blogger.com/profile/00075155021794486805noreply@blogger.com1tag:blogger.com,1999:blog-3668401867087218235.post-56871507213646682002012-10-09T12:39:00.001-07:002012-10-09T12:39:06.834-07:00Entrada 2<br />
<div style="background-color: white; color: #333333; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 15px; line-height: 20px; text-align: center;">
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif; font-size: medium;"><b><br /></b></span></div>
<div style="background-color: white; color: #333333; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 20px; text-align: center;">
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b><span style="font-size: x-large;">Automatización y Control de Sistemas</span></b></span><b style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><span style="font-size: x-large;"> Dinámicos</span></b></div>
<div style="background-color: white; color: #333333; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; font-size: 15px; line-height: 20px; text-align: center;">
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif; font-size: medium;"><b><br /></b></span></div>
<br />
<span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>Diagrama de Bloques</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Para esta entrada consiste en mostrar el diagrama de bloques de la función de transferencia de nuestro proyecto.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Antes de hacer esto, completare la función de transferencia que había hecho en el reporte pasado.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Viendo los valores de entrada y salida (<a href="http://materiasdepedrito.blogspot.mx/2012/09/reporte-1.html">http://materiasdepedrito.blogspot.mx/2012/09/reporte-1.html</a>) tenemos que:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">El valor de entrada sería seria la Potencia de la corriente eléctrica, la ecuación de esta es:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<div class="separator" style="clear: both; text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><img alt="P = \frac{dq}{dt} I R" src="http://rinconmatematico.com/latexrender/pictures/7e4b35eb91569f69f02724ff62bde6d4.gif" /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>P = Potencia de la corriente eléctrica.</b></span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>I = Intensidad de la corriente.</b></span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>R = Resistencia del material del que esta hecho la punta del cautín.</b></span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>dq/dt = Derivada del calor respecto al tiempo.</b></span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="font-family: Arial, Helvetica, sans-serif;">El valor de salida seria el Calor producido por el cautín, la ecuación de esta seria:</span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglczmpb_AaQnbckjVkia7SCSwUl0VtzEL6BxCB-E06HMW3RHPhbqNmRnw2Gm4HaRh6YcNxUGh12AXw_ZIXbXPFCkz9Wgds4-mo_SaZXPnBsmV19oqSgbIKWWpfREQthrbYqbhFbe1viVI/s1600/dos.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglczmpb_AaQnbckjVkia7SCSwUl0VtzEL6BxCB-E06HMW3RHPhbqNmRnw2Gm4HaRh6YcNxUGh12AXw_ZIXbXPFCkz9Wgds4-mo_SaZXPnBsmV19oqSgbIKWWpfREQthrbYqbhFbe1viVI/s1600/dos.gif" /></span></a></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>Q = Calor</b></span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>m = Masa del Cautín</b></span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>c = Calor especifico del cautín</b></span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>Delta T = Diferencia de Temperaturas (Entrada y de Salida)</b></span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div class="separator" style="clear: both; text-align: left;">
<span style="font-family: Arial, Helvetica, sans-serif;">Teniendo esto la función de transferencia seria:</span></div>
<div class="separator" style="clear: both; text-align: left;">
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGiWMRnHEqo6pHK9QEkkhiOyX9_LRg61t1IrD4WAR_-f0_6Pmr48qUzFdj1T-noCO4vccY-wpLhSvm4qER6lKI6wPLsn8N_CIVO5AcsyGMKTRrai0tfWiGDH_MlnxgHXPiTS-hYyiHoXU/s1600/tres.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGiWMRnHEqo6pHK9QEkkhiOyX9_LRg61t1IrD4WAR_-f0_6Pmr48qUzFdj1T-noCO4vccY-wpLhSvm4qER6lKI6wPLsn8N_CIVO5AcsyGMKTRrai0tfWiGDH_MlnxgHXPiTS-hYyiHoXU/s1600/tres.gif" /></span></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDyNf7HK6INOqrK6PTqaO6LRYyvk0WZPFfjbVFdKDNnm7aj1qAytLqMZLQY4rOgdGrAcPWVOmlmlK_OoCggNRaXw5VVuZe7lh4OVtGoiBxSoPKeA-qgQxMenY-iqVEOcQnq3oRG6F0UYk/s1600/tres-1.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiDyNf7HK6INOqrK6PTqaO6LRYyvk0WZPFfjbVFdKDNnm7aj1qAytLqMZLQY4rOgdGrAcPWVOmlmlK_OoCggNRaXw5VVuZe7lh4OVtGoiBxSoPKeA-qgQxMenY-iqVEOcQnq3oRG6F0UYk/s1600/tres-1.gif" /></span></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Aplicando la transformada de Laplace a cada una de las funciones:</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><b>Función de Entrada</b></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><img alt="X(s) = L\left\{{\frac{dq}{dt} I R}\right\}" src="http://rinconmatematico.com/latexrender/pictures/4dfb90b20e4c511b0ccd748280b3465b.gif" /></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><img alt="X(s) = sQ(s) I R " src="http://rinconmatematico.com/latexrender/pictures/cef13de6f87f9b2c6123939402d17362.gif" /></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><b>Función de Salida</b></span></div>
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<img alt="Y(s) = L\left\{{c m \Delta T}\right\}" src="http://rinconmatematico.com/latexrender/pictures/5ce594dcef94fd1d25bfe6f14a64ca3b.gif" /></div>
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<img alt="Y(s) = \frac{c m \Delta T}{s}" src="http://rinconmatematico.com/latexrender/pictures/467a5e949bec00ece91fd7203e637208.gif" /></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Aplicando la estas funciones a la de transferencia tenemos nuestra función de transferencia</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><img alt="G(s) = \frac{\frac{c m \Delta T}{s}}{sQ(s) I R }" height="60" src="http://rinconmatematico.com/latexrender/pictures/73cd4d5ca46ac9224124029fffb01d10.gif" width="200" /></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><img alt="G(s) = \frac{\frac{c m (T_f - T_o)}{s}}{sQ(s) I R }" height="59" src="http://rinconmatematico.com/latexrender/pictures/3e390e9ceff3feb775f8291c0cf69673.gif" width="200" /></span></div>
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<b><span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Ya a continuación muestro el diagrama de bloques:</span></b></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgk5U4L-OoFdglyOv4_R1M1K6eztNmSmvO8h1th_i6rOHjtas_ldqqWAPeHFCsQG2ovtNFwZfgZiNl4i3H1KsKrEVtOfCeisv6iIZUmFemhFBdn5QFqXIM_-AjIKlNMhzZFzYIh750LYcU/s1600/Untitled+drawing.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="281" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgk5U4L-OoFdglyOv4_R1M1K6eztNmSmvO8h1th_i6rOHjtas_ldqqWAPeHFCsQG2ovtNFwZfgZiNl4i3H1KsKrEVtOfCeisv6iIZUmFemhFBdn5QFqXIM_-AjIKlNMhzZFzYIh750LYcU/s640/Untitled+drawing.jpg" width="640" /></a></div>
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guelmi_rickhttp://www.blogger.com/profile/00075155021794486805noreply@blogger.com1tag:blogger.com,1999:blog-3668401867087218235.post-78794671927251325042012-09-20T15:11:00.001-07:002012-10-09T10:08:09.110-07:00Entrada # 3<div style="text-align: center;">
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>Laboratorio de Automatización y Control de Sistemas Dinámicos</b></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Para esta semana, al igual que la anterior, consistió en elegir un problema y resolverlo.</span><br />
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El problema nos dice:</span><br />
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</span><br />
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<span style="color: #4c1130; font-family: Arial, Helvetica, sans-serif;"><b>"Considere el que sistema que se muestra a continuación. </b><b>Calcular la expresión del error en estado estacionario cuando están presentes tanto la señal de entrada de referencia R(s) como la entrada de perturbación D(s)."</b></span></div>
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</span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMrDzpNP7WKxQdO-pnZCN3vYNRj7BdPYqmFJjlt0nib0ndQvd_3z6Wumwt1aOxk32vayRJv_x152a2Svou8R8GXGwNd2U-rOv8LSFsMHJURGGloxdOk7Ge7dQi1X4rJ1rKTXpXWafZ0iE/s1600/IMG278+(copia).jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="243" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgMrDzpNP7WKxQdO-pnZCN3vYNRj7BdPYqmFJjlt0nib0ndQvd_3z6Wumwt1aOxk32vayRJv_x152a2Svou8R8GXGwNd2U-rOv8LSFsMHJURGGloxdOk7Ge7dQi1X4rJ1rKTXpXWafZ0iE/s640/IMG278+(copia).jpg" width="640" /></span></a></div>
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Primeramente definir unos conceptos:</span><br />
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<span style="color: #073763;"><b>Entrada de Referencia.-</b> Impulsos que se le dan al sistema para observar las salidas que tendrían el sistema.</span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #073763;"><br /></span>
<span style="color: #073763;"><b>Entrada de Perturbación.-</b> Señales que tienden a afectar al sistema, afectan la salida del sistema; como esta señal es una entrada, por lo tanto esa es externa y se genera fuera del sistema.</span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: #073763;"><br /></span>
<span style="color: #073763;"><b>Expresión de Error.- </b>Es un valor que nos indica el rango que nos daria el sistema.</span></span><br />
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De nuestro problema tenemos los siguientes: </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: magenta; font-family: Arial, Helvetica, sans-serif; font-size: x-small;"><b>Entrada de Referencia R(s), Entrada de Perturbación D(s) y la Expresión de Error es E(s); C(s) seria la salida que produzca el sistema.</b></span><br />
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El problema nos pide encontrar la<b> Expresión de Error</b> <span style="text-align: center;">en estado estacionario (No hay algo externo, aparte de lo mencionado, que pueda afectar la salida) cuando están presentes tanto la señal de entrada de referencia como la entrada de perturbación.</span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="text-align: center;"><br /></span>
<span style="text-align: center;"><b>La Expresión de Error se calcula como la suma de salidas (La Esperada + la Producida en estado estacionario), en base a las variables y las definiciones tenemos:</b></span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="text-align: center;"><br /></span>
<span style="color: #20124d; font-size: x-small; text-align: center;"><b>La Esperada seria cuando solamente este presente la variable de referencia en el sistema (para este no incluiremos la de perturbación)</b></span></span><br />
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif; font-size: x-small;"><b><span style="text-align: center;"><br /></span>
<span style="text-align: center;">La Producida seria las salidas usando solamente la entrada de perturbación (ya que la referencia se vuelve constante y la de perturbación daría un resultado distinto).</span></b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="text-align: center;"><br /></span>
<span style="text-align: center;">Por lo tanto la ecuación de Error seria:</span></span><br />
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<span style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em; text-align: center;"><img alt="E(s) = ErrorReferenciaEstacio + ErrorProducidaEstacio" height="36" src="http://rinconmatematico.com/latexrender/pictures/8b73254c64308f2b83e61ba9f5f0d44d.gif" width="640" /></span><span style="font-family: Arial, Helvetica, sans-serif;"></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="text-align: center;"><br /></span>
<span style="text-align: center;">Y ya que como es estacionario tiene que ver con el tiempo nos queda que:</span></span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="text-align: center;"><img alt="E(s) = E_e_e (t) = E_e_e_R (t) + E_e_e_D (t)" src="http://rinconmatematico.com/latexrender/pictures/41412f8a2ab8ddecf410778707196be8.gif" /></span></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="text-align: center;"><br /></span>
<span style="text-align: center;"><span style="font-size: large;">El siguiente paso seria solucionar cada uno de los errores, aquí comenzaremos por el de <b>referencia</b></span>.</span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="text-align: center;"><br /></span>
<span style="text-align: center;">Antes de encontrar cuando el de referencia sea estacionario primero habrá que determinarlo cuando no este así.</span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="text-align: center;"><br /></span>
<span style="text-align: center;">Este error se calcula como el valor de la referencia menos la salida producida por el efecto de este:</span></span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="text-align: center;"><img alt="E_R(s) = R(s) - C_R(s)" src="http://rinconmatematico.com/latexrender/pictures/fbe027b0390deabcb28bd8b90ea76cb8.gif" /></span></span></div>
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Teniendo que la salida de sistema es:</span><br />
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Tenemos que <img alt="\frac{C_R(s)}{R(s)} = \frac{G_1(s) G_2(s)}{1 + G_1(s) G_2(s)}" src="http://rinconmatematico.com/latexrender/pictures/f8757ad5864ce021a8fb95a5a2be08a9.gif" /></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br />Sustituyendo el error de la referencia en la ecuación.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><img alt="E_R(s) = R(s) - C_R(s) = R(s)[1 -\frac{C_R(s)}{R(s)}]" src="http://rinconmatematico.com/latexrender/pictures/346454195288edd8bcbb418fe3c6b9be.gif" /></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><img alt="E_R(s) = R(s)[1 - \frac{G_1(s) G_2(s)}{1 + G_1(s) G_2(s)}]" src="http://rinconmatematico.com/latexrender/pictures/660135e2fbd4fe1ca7b5303c55709026.gif" /></span></div>
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<img alt=" E_R (s) = {[\frac{1}{1 + G_1(s) G_2(s)}R(s)]}" src="http://rinconmatematico.com/latexrender/pictures/04635220d07f251516e321914c137f4a.gif" /></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Ya aplicandolo de forma estacionaria la de referencia</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><img alt=" E_e_e_R (t) = \displaystyle\lim_{t \to\infty}E_R(t) = \displaystyle\lim_{s \to\ 0} s E_R(s)" src="http://rinconmatematico.com/latexrender/pictures/011f972427c132fdb9ba93b8ea5e68a1.gif" /></span></div>
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<img alt=" E_e_e_R (t) = \displaystyle\lim_{s \to\ 0} {s [\frac{1}{1 + G_1(s) G_2(s)}R(s)]}" src="http://rinconmatematico.com/latexrender/pictures/4fc3086bdd22622139eeb8491a3824cb.gif" /></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Ahora aplicando a las <b>Perturbaciones</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
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<span style="font-family: Arial, Helvetica, sans-serif;"><img alt=" E_D(s) = 0 - C_D(s) = - C_D(s) = - \frac{C_D(s)}{D(s)} D(s)" src="http://rinconmatematico.com/latexrender/pictures/d76a2fcec94f141580ee5788f86f0210.gif" /></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Teniendo que:<img alt="\frac{C_D(s)}{D(s)} = \frac{G_2(s)}{1 + G_1(s) G_2(s)}" src="http://rinconmatematico.com/latexrender/pictures/ec280980d4bea2a09c04f8ebdb098de9.gif" /></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<br />
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><img alt=" E_D(s) = - \frac{G_2(s)}{1 + G_1(s) G_2(s)} D(s)" src="http://rinconmatematico.com/latexrender/pictures/91f044742605621b977c6efa235de5d8.gif" /></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Sacando la forma estacionaria de las perturbaciones</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
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<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><img alt=" E_e_e_D (t) = \displaystyle\lim_{t \to\infty} E_D(t) = \displaystyle\lim_{s \to0} s E_D(s)" src="http://rinconmatematico.com/latexrender/pictures/397dfe7c991c5b3466e638f3456c5f9c.gif" /></span></div>
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><img alt=" E_e_e_D (t) = \displaystyle\lim_{s \to0} [-\frac{G_2(s)}{1 + G_1(s) G_2(s)} D(s)] s" src="http://rinconmatematico.com/latexrender/pictures/23a3f1cf37f100235ce21a4c58709dcb.gif" /></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif; font-size: large;">Sustituyendo las estacionarias:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<br />
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><img alt=" E_e_e (t) = E_e_e_R (t) + E_e_e_D (t)" src="http://rinconmatematico.com/latexrender/pictures/07ecdcab83b168a21f201bc3cf36ebd0.gif" /></span></div>
<img alt=" E_e_e (t) = \displaystyle\lim_{s \to\ 0} {s [\frac{1}{1 + G_1(s) G_2(s)}R(s)]} + \displaystyle\lim_{s \to0} [-\frac{G_2(s)}{1 + G_1(s) G_2(s)} D(s)] s" src="http://rinconmatematico.com/latexrender/pictures/22ad5db88992527dc90edda7ff7d31b6.gif" /><br />
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<span style="color: #660000; font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>Referencias</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><a href="http://www.slideshare.net/ptah_enki/definiciones-de-control-326816">http://www.slideshare.net/ptah_enki/definiciones-de-control-326816</a></span><br />
<a href="http://isa.uniovi.es/docencia/raeuitig/tema1.pdf"><span style="font-family: Arial, Helvetica, sans-serif;">http://isa.uniovi.es/docencia/raeuitig/tema1.pdf</span></a>guelmi_rickhttp://www.blogger.com/profile/00075155021794486805noreply@blogger.com2tag:blogger.com,1999:blog-3668401867087218235.post-16013875803355238632012-09-20T04:47:00.002-07:002012-09-20T08:44:58.952-07:00Entrada # 6<div style="text-align: center;">
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif; font-size: large;"><b style="background-color: white;">Implementing the RSA algorithm in an HTTP (Authenticating Users)</b></span></div>
<div style="text-align: center;">
</div>
<span style="font-family: Arial, Helvetica, sans-serif;"></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">For this week we have to implement the RSA algorithm into a web server.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Be has a user to validate your user name, for it makes use of the RSA algorithm, the server and the client need certain values (the server already has the information about your name and values of 'e' and 'n 'while the client would have' d 'and' n ').</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">The process would be the client requests a value of 'x' to the server, this does just that along with the link to download a script to determine the values of 'and' and 'r'.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br />
The client downloads this file and determines the values mentioned above, then the client will provide the server user your name (as must be added, only find the name that is to avoid errors Language Script) together with the value of 'r '.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br />
The server receives this data and using the user name extracts the values of 'e' and 'n' (for storing information this data can use files or databases) and together with the value of 'x' that provides the client.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br />
Obtains two different 'y' (one with a specific function for us - this function is the same as in the script that I download the client - and by the formula r ^ e mod n) and compare these values, if these are the same you sends a message to the user indicating that authentication was successful.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: red; font-family: Arial, Helvetica, sans-serif;"><b>Code in PHP </b></span><br />
<script src="https://gist.github.com/3756071.js"> </script>
<span style="color: red; font-family: Arial, Helvetica, sans-serif;"><b>Script of Python
<script src="https://gist.github.com/3754278.js"> </script>
</b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="color: red;"><b>Code of SQL</b></span><script src="https://gist.github.com/3755172.js"> </script>
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<span style="color: red; font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTm-Jar-GPKJoRk8AzwA7lAnLYr17eIU-0PKT19N2H9M1X3obt67anCNd8ammJIsDm-_jFkUo44_PxCxGzqsmBUwdAaHcUtukq_hueissmud_E757gdIqEIFGjyUzrVr02A7KUaK2HCwQ/s1600/cuatro.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="303" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhTm-Jar-GPKJoRk8AzwA7lAnLYr17eIU-0PKT19N2H9M1X3obt67anCNd8ammJIsDm-_jFkUo44_PxCxGzqsmBUwdAaHcUtukq_hueissmud_E757gdIqEIFGjyUzrVr02A7KUaK2HCwQ/s400/cuatro.png" width="400" /></a></div>
<span style="color: red; font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="color: red; font-family: Arial, Helvetica, sans-serif;"><b>Vídeo mostrando la ejecución</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;">En Proceso</span>guelmi_rickhttp://www.blogger.com/profile/00075155021794486805noreply@blogger.com1tag:blogger.com,1999:blog-3668401867087218235.post-10712226691429983902012-09-13T06:27:00.001-07:002012-09-13T09:45:04.744-07:00Entrada # 5<div style="text-align: center;">
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>Implementación de la Autentificación RSA</b></span></div>
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">En este código se hicieron todos los cálculos para encontrar los valores de n, d y e y los guarda en un archivo junto con los nombres de usuario.
</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<script src="https://gist.github.com/3714654.js"> </script><span style="font-family: Arial, Helvetica, sans-serif;">
Como logran ver los valores de d y de p y q fueron asignados por mí (Obviamente respetando las reglas).</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikR4AiH8Er6fv8ETPuc9As2X_FK7O-1swhgIRqOzNS7dTTHzdkt0uUP7zZko7mOfnh9I0z8K1WmRyocRjg2hdPioJz_vIjPUgy823UPlB5D2OHLmY4dn2DGpgKWbKg2pC3SfE3K3-6xKs/s1600/dos1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="200" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEikR4AiH8Er6fv8ETPuc9As2X_FK7O-1swhgIRqOzNS7dTTHzdkt0uUP7zZko7mOfnh9I0z8K1WmRyocRjg2hdPioJz_vIjPUgy823UPlB5D2OHLmY4dn2DGpgKWbKg2pC3SfE3K3-6xKs/s200/dos1.png" width="197" /></span></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZKZBRtFOtobjHGRfSSfH3oGq2FuE0qqtmdaU5bZwUckzQLrn8AauWCfviMk8n4P5nsE1IYuKafLDn0PV7l-4fgjx2E1EIvS7VeQMvh0Ki0FXMj5gURxe7c_DVGW1OqdLaPIUfrl31coE/s1600/Captura+de+pantalla+de+2012-09-13+09:52:55.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiZKZBRtFOtobjHGRfSSfH3oGq2FuE0qqtmdaU5bZwUckzQLrn8AauWCfviMk8n4P5nsE1IYuKafLDn0PV7l-4fgjx2E1EIvS7VeQMvh0Ki0FXMj5gURxe7c_DVGW1OqdLaPIUfrl31coE/s1600/Captura+de+pantalla+de+2012-09-13+09:52:55.png" /></a></div>
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<b><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif; font-size: x-small;">El orden del texto es: Usuario, valor de e, valor de d y valor de n</span></b></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Imágenes donde se determino el valor de d:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDCLhTu_FTnw64Fhvgk6WSDbLoytiXPYW1oX5RC-jywn9rs88N7ZQGVczMmEqksm7fpvknD-8NRndnAyvdoK4milRmEW-PLyIuXO6je4vzOHjAZLGtAdjmDXqFcsg8oa2XknKG128xn5o/s1600/IMG309.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="371" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDCLhTu_FTnw64Fhvgk6WSDbLoytiXPYW1oX5RC-jywn9rs88N7ZQGVczMmEqksm7fpvknD-8NRndnAyvdoK4milRmEW-PLyIuXO6je4vzOHjAZLGtAdjmDXqFcsg8oa2XknKG128xn5o/s400/IMG309.jpg" width="400" /></a></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcOECnpC-Rz1kbfsuUIQpJSN4VZtJIv8J7YDevsyMmIPRzyuszlP5e0mvUXDgv2caVRmPIYECp4VQ7mpBePL7iATTsfrnPX-OZDxd6dYYy4thfMs418_NpWPaixIPCmLnPLus6fo1-SEc/s1600/IMG310.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgcOECnpC-Rz1kbfsuUIQpJSN4VZtJIv8J7YDevsyMmIPRzyuszlP5e0mvUXDgv2caVRmPIYECp4VQ7mpBePL7iATTsfrnPX-OZDxd6dYYy4thfMs418_NpWPaixIPCmLnPLus6fo1-SEc/s400/IMG310.jpg" width="361" /></a></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Después se muestra los códigos donde se hizo uso de los sockets
</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>Cliente</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><b><br /></b></span>
<script src="https://gist.github.com/3715567.js"> </script><span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>
Servidor
</b></span><script src="https://gist.github.com/3715599.js"> </script>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif; font-size: large;"><b><br /></b></span><br />
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif; font-size: large;"><b><br /></b></span>
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>Referencias:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<a href="http://mundogeek.net/archivos/2008/04/12/sockets-en-python/"><span style="font-family: Arial, Helvetica, sans-serif;">http://mundogeek.net/archivos/2008/04/12/sockets-en-python/</span></a><br />
<a href="http://es.wikipedia.org/wiki/N%C3%BAmero_primo"><span style="font-family: Arial, Helvetica, sans-serif;">http://es.wikipedia.org/wiki/N%C3%BAmero_primo</span></a><br />
<a href="http://es.wikipedia.org/wiki/N%C3%BAmeros_primos_entre_s%C3%AD"><span style="font-family: Arial, Helvetica, sans-serif;">http://es.wikipedia.org/wiki/N%C3%BAmeros_primos_entre_s%C3%AD</span></a><br />
<a href="http://www.slideshare.net/jpadillaa/criptografia-asimetrica-rsa"><span style="font-family: Arial, Helvetica, sans-serif;">http://www.slideshare.net/jpadillaa/criptografia-asimetrica-rsa</span></a>guelmi_rickhttp://www.blogger.com/profile/00075155021794486805noreply@blogger.com1tag:blogger.com,1999:blog-3668401867087218235.post-34887413298256300242012-09-11T00:27:00.004-07:002012-09-11T12:26:05.584-07:00Reporte # 1<div style="text-align: center;">
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>Automatización y Control de Sistemas Dinámicos</b></span></div>
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">Para esta ocasión hay que realizar la Función de Tranferencia de la idea del proyecto que tenemos contemplado para esta materia.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Primeramente en que consiste nuestro proyecto:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<br />
<div style="text-align: center;">
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>"Sera para el control del cautín, en especifico controlar la cantidad de temperatura que ha producido el cautín, para así regular la temperatura y evitar que ocurran incrementos que puedan dañar algún componente."</b></span></div>
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">Entendido lo anterior, lo siguiente seria la función de transferencia:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b style="color: #073763;">Función de Transferencia: Función que nos permite relacionar la salida de un proceso, proyecto con la entrada de este.</b></span></div>
<br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">La entradas y salidas serian acciones que produciría este proceso, comúnmente tienden a ser funciones o ecuaciones. </span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Para nuestro problema la entradas seria el cantidad de voltaje que entra al cautín para que este funcione, la temperatura, la masa de este y el material de la punta del cautín; la salida sería el calor y la temperatura del cautín.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">De los valores anteriores solo del calor y de la intensidad de voltaje necesitaremos sus formulas.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: #274e13; font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>Calor</b></span><br />
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><img alt="Calor (Q) = cm\Delta T" height="41" src="http://rinconmatematico.com/latexrender/pictures/e37f430490e93999fd1587d7e26dd360.gif" width="320" /></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>Q = Calor producido</b></span><br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>c = Calor especifico del material la punta</b></span><br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>m = masa del cautín.</b></span><br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b><img alt="\Delta T" src="http://rinconmatematico.com/latexrender/pictures/3ecdbbc9a64a9bfc57883ae306bf51cd.gif" /> = Diferencia de Temperatura (Temperatura Final del cautín - Temperatura inicial del cautín)</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: #274e13; font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>Voltaje</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<br />
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><img alt=" I = \frac{V}{R} " height="148" src="http://upload.wikimedia.org/math/f/9/a/f9ae53a99f2b2b6a74146fb04fb3ff73.png" width="200" /></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>I = Intensidad</b></span><br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>V = Voltaje conectado al cautín</b></span><br />
<span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>R = Resistencia (Seria la resistencia del material del cautín)</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">De la ecuación:</span><br />
<div style="text-align: center;">
<img alt="G(s) \Rightarrow{L\left\{{G(t)}\right\} = {\frac{L\left\{{Y(t) = Salida}\right\}}{L\left\{{X(t) = Entrada}\right\}}}" height="72" src="http://rinconmatematico.com/latexrender/pictures/fa697dbb06fae8f430a7f01c69217b40.gif" width="640" /></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br />
</span><br />
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><img alt="G(s) = \frac{Y(s) = Salida}{X(s) = Entrada}
" height="63" src="http://rinconmatematico.com/latexrender/pictures/58e6a710db2c91224b968e5a59375144.gif" width="320" /></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span><span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>Ahora aplicando esto a mi problema:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Tenemos que:</span><br />
<u><strike><br /></strike></u>
<br />
<div class="separator" style="clear: both; text-align: center;">
<strike style="margin-left: 1em; margin-right: 1em;"><img alt="G(t) = \frac{Y(t)}{X(t)}" height="67" src="http://rinconmatematico.com/latexrender/pictures/c0cf900670bbdc8f08e025e4978ac361.gif" style="text-align: center;" width="200" /></strike></div>
<span style="font-family: Arial, Helvetica, sans-serif;">Y también que:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<img alt="Y = \frac{V}{R}" src="http://rinconmatematico.com/latexrender/pictures/16d8fa0cacfeccd3b9cacebac4f0b09b.gif" /><br />
<img alt="X = cm\Delta T" src="http://rinconmatematico.com/latexrender/pictures/a729ad0415d3c6909bacb57dfc4a8995.gif" /><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Ahora sustituimos los valores de Y y X en G(t), teniendo: </span><br />
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"></span></div>
<div style="text-align: center;">
<img alt="
G(t) = \frac{\frac{V(t)}{R}}{cm\Delta T(t)}" height="100" src="http://rinconmatematico.com/latexrender/pictures/742d0701e24d32dc29687ccadac7d2f5.gif" width="320" /></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Después ap</span><span style="font-family: Arial, Helvetica, sans-serif;">licamos la regla de medios por medios y extremos por extremos y aplicando la transformada de Laplace en G(t).</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<br />
<div style="text-align: center;">
<img alt="G(t) = \frac{V(t)}{cm\Delta T(t) R}
" height="76" src="http://rinconmatematico.com/latexrender/pictures/df8fd8e4aeab4747457f82d39adcc6ef.gif" width="320" /></div>
<div style="text-align: center;">
<img alt="L\left\{G(t)}\right\} = L\left\{{\frac{V(t)}{cm\Delta T(t) R}}\right\}" height="54" src="http://rinconmatematico.com/latexrender/pictures/c062c8e065c69509f1e3982a11e0b064.gif" width="320" /></div>
<br />
<span style="font-family: Arial, Helvetica, sans-serif;">Nos queda, la función de transferencia:</span><br />
<br />
<div style="text-align: center;">
<img alt="G(s) = L\left\{{\frac{V(t)}{cm\Delta T (t) R}}\right\}" height="64" src="http://rinconmatematico.com/latexrender/pictures/55359e946c253f1e6d9daa689175ce4c.gif" width="320" /></div>
<div style="text-align: center;">
<img alt="G(s) = {\frac{V(s)}{cm\Delta T(s) R}}" height="74" src="http://rinconmatematico.com/latexrender/pictures/8315fec83cf57de7256b37c1bc865827.gif" width="320" /></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br />
<span style="color: #20124d; font-size: large;"><b>Referencias</b></span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br />
<a href="http://www.fing.edu.uy/iq/cursos/dcp/teorico/7_FUNCION_DE_TRANSFERENCIA_PRIMER_ORDEN.pdf"><span style="color: #073763;"><b>http://www.fing.edu.uy/iq/cursos/dcp/teorico/7_FUNCION_DE_TRANSFERENCIA_PRIMER_ORDEN.pdf</b></span></a></span><br />
<a href="http://es.wikipedia.org/wiki/Electricidad"><span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>http://es.wikipedia.org/wiki/Electricidad</b></span></a><br />
<a href="http://es.wikipedia.org/wiki/Corriente_el%C3%A9ctrica"><span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>http://es.wikipedia.org/wiki/Corriente_el%C3%A9ctrica</b></span></a><br />
<a href="http://hyperphysics.phy-astr.gsu.edu/hbasees/tables/sphtt.html#c1"><b><span style="color: #073763;"><span style="font-family: Arial, Helvetica, sans-serif;">Tabla de Calores </span><span style="font-family: Arial, Helvetica, sans-serif;">Específicos</span></span></b></a><br />
<a href="http://imagenes.unicrom.com/tabla_resistividad.gif"><span style="color: #073763; font-family: Arial, Helvetica, sans-serif;"><b>Tabla de Resistencias</b></span></a>guelmi_rickhttp://www.blogger.com/profile/00075155021794486805noreply@blogger.com1tag:blogger.com,1999:blog-3668401867087218235.post-60120167034972259962012-09-06T07:58:00.001-07:002012-09-06T10:49:58.831-07:00Entrada # 2<br />
<div style="background-color: white; color: #333333; font-family: Arial, Tahoma, Helvetica, FreeSans, sans-serif; line-height: 20px; text-align: center;">
<span style="font-size: large;"><b><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;">Laboratorio de Automatización y Control de Sistemas </span></b><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>Dinámicos</b></span></span></div>
<div>
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif; font-size: medium;"><b><br /></b></span></div>
<div>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Para esta semana consistió en elegir un problema y resolverlo:</b></span></div>
<div>
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span></div>
<div>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Resolver la siguiente ecuación diferencial:</b></span></div>
<div>
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimObJTO5oYshGr6rN4VnBeQ2SasKLnZcjflaFAJHYvh55UT44nHX5TQFXhb_j6eejrlrdljhsXplvHzudw02cIig_FYpyYf8Ams0REqlEkPGU18zspjnfmGjHo5Xg6bbAht7I71H2HxvI/s1600/1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="color: black; font-family: Arial, Helvetica, sans-serif;"><b><img border="0" height="52" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEimObJTO5oYshGr6rN4VnBeQ2SasKLnZcjflaFAJHYvh55UT44nHX5TQFXhb_j6eejrlrdljhsXplvHzudw02cIig_FYpyYf8Ams0REqlEkPGU18zspjnfmGjHo5Xg6bbAht7I71H2HxvI/s400/1.png" width="400" /></b></span></a></div>
<div>
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span></div>
<div>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Con las siguientes características:</b></span></div>
<div>
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHKKpVhO714KL2vI6aKD9LyHeBOodY84Y0pezGPhEiC6lxBzinDd-H530NpVxw50mmqzCL8TWzblQ_PXdv4-JdzrUAeQBs_urnl-OeGu2b6WauZGP4s3cXOuMoVRhZhDtsEnx01-0uBDk/s1600/2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="color: black; font-family: Arial, Helvetica, sans-serif;"><b><img border="0" height="46" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHKKpVhO714KL2vI6aKD9LyHeBOodY84Y0pezGPhEiC6lxBzinDd-H530NpVxw50mmqzCL8TWzblQ_PXdv4-JdzrUAeQBs_urnl-OeGu2b6WauZGP4s3cXOuMoVRhZhDtsEnx01-0uBDk/s320/2.png" width="320" /></b></span></a></div>
<div>
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span></div>
<div>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Primeramente explicar algunas expresiones que vienen en el problema:</b></span></div>
<div>
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span></div>
<div>
<div class="separator" style="clear: both; text-align: justify;">
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b><span style="font-size: large;"> ẍ</span> = Segunda Derivada</b></span></div>
<div class="separator" style="clear: both; text-align: justify;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKlVuth2mzejY-KBCsi2-X2WmZlCeK-Zt60BXdoewhkXspeGqsJF12KiQvIHn85DLknyqOA2wKnGnTU2QbPnE5s1p8frf9Zajj0vcOrYvkjHkQxKRQ8BfnaO1mFfk1f-ErQD0wY4kOD-Y/s1600/Pantallazo+del+2012-09-06+12:39:52.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhKlVuth2mzejY-KBCsi2-X2WmZlCeK-Zt60BXdoewhkXspeGqsJF12KiQvIHn85DLknyqOA2wKnGnTU2QbPnE5s1p8frf9Zajj0vcOrYvkjHkQxKRQ8BfnaO1mFfk1f-ErQD0wY4kOD-Y/s1600/Pantallazo+del+2012-09-06+12:39:52.png" /></a>= <b style="color: #20124d; font-family: Arial, Helvetica, sans-serif;">Primera Derivada</b></div>
<div class="separator" style="clear: both; text-align: justify;">
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b><span style="font-size: large;"> Wn </span>= Frecuencia Natural (Para mi problema sera tratado como constante)</b></span></div>
<div class="separator" style="clear: both; text-align: justify;">
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b><span style="font-size: large;"> <img alt=" \zeta" src="http://rinconmatematico.com/latexrender/pictures/6878583a6277711f19eb4c29bc65d5bc.gif" /> </span>= <span style="background-color: white; line-height: 19.200000762939453px;">Factor de amortiguamiento</span></b></span></div>
<div class="separator" style="clear: both; text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Por lo tanto la ecuación podría expresarse como:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<br />
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><b><img alt="X'' + 2 \zeta WnX' + W²nX = 0
" src="http://rinconmatematico.com/latexrender/pictures/605ad046e507af332590a203e0934dca.gif" /></b></b></span></div>
<br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Para resolverlo seria mediante las Transformadas de Laplace.</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<br />
<div class="separator" style="clear: both; text-align: center;">
<b style="margin-left: 1em; margin-right: 1em;"><img alt="L\left\{{X''}\right\} + 2 \zeta Wn L\left\{{X'}\right\} + W²n L\left\{{X}\right\}
" src="http://rinconmatematico.com/latexrender/pictures/e0763dc6bc46dca664e4c862e60f6586.gif" /></b></div>
<span style="font-family: Arial, Helvetica, sans-serif;"></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Teniendo que:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>L{X''} = s²x(s) - sx(0) - x'(0)</b></span><br />
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>L{X'} = sx(s) - s¹⁻¹x(0) = sx(s) - 1*x(0) = sx(s) - x(0)</b></span><br />
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>L{X} = s¹⁻¹ x(s) = s⁰x(s) = 1*x(s) = x(s)</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Nos da como resultado:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<br />
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><b><img alt="s²x(s) - sx(0) - x'(0) + 2 \zeta Wn[sx(s) - x(0)] + Wn²[x(s)]
" src="http://rinconmatematico.com/latexrender/pictures/fccaae18f4040fbf421da08d37e3996b.gif" /></b></b></span></div>
<br />
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><img alt="s²x(s) - sx(0) - x'(0) + 2 \zeta Wn[sx(s)] - 2 \zeta Wnx(0) + Wn²[x(s)]
" src="http://rinconmatematico.com/latexrender/pictures/09203b180e7983302f8aa43cd1299dac.gif" /></b></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="background-color: white; line-height: 19.200000762939453px;"><br /></span>
<span style="background-color: white; line-height: 19.200000762939453px;">Sustituyendo los valores de x' y de x'' en la ecuación anterior:</span></b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><span style="background-color: white; line-height: 19.200000762939453px;"><br /></span>
</b></span><br />
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><img alt="s²x(s) - sa - b + 2 \zeta Wnsx(s) - 2 \zeta Wna + Wn²[x(s)] " src="http://rinconmatematico.com/latexrender/pictures/3c90369c41915ba12786260809d4d341.gif" /></b></span></div>
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><img alt="s²[x(s)] - as - b + 2 \zeta Wn s[x(s)] - 2 \zeta Wna + Wn²[x(s)]" src="http://rinconmatematico.com/latexrender/pictures/3ff72ee031a372d392c35382361e5988.gif" /></b></span></div>
<div>
<div style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;">
</div>
<div class="separator" style="clear: both; text-align: center;">
<b style="margin-left: 1em; margin-right: 1em;"><img alt="x(s)[s²x + 2 \zeta Ws + Wn²] = as + b + 2 \zeta Wna " border="0" src="http://rinconmatematico.com/latexrender/pictures/5ee1aa7a487039298d043b6b50784a1b.gif" /></b></div>
<div class="separator" style="clear: both; text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"></span><b style="margin-left: 1em; margin-right: 1em;"><img alt="x(s) = \frac{as + b + 2 \zeta Wn a}{s² + 2 \zeta Wns + Wn²}" border="0" src="http://rinconmatematico.com/latexrender/pictures/165fde473d6c6a839ae0cb980d4ffaee.gif" /></b></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Hay que factorizar el denominador la forma sencilla para mi es mediante la formula para resolver ecuaciones de 2do grado.</b></span></div>
<div>
<span style="background-color: white; font-family: Arial, Helvetica, sans-serif; line-height: 19.200000762939453px;"><b><br /></b></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Esta formula es:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<br />
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><b><img alt="x = \frac{-b \pm \sqrt {b^2-4ac}}{2a}" height="80" src="http://upload.wikimedia.org/math/3/c/a/3ca857f705daba6b9e6e6d3ccad7990f.png" width="320" /></b></b></span></div>
<br />
<div>
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>De ahí tenemos que:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b><img alt="x = s" src="http://rinconmatematico.com/latexrender/pictures/317251eeeb5f7783c27f2867dd912029.gif" /></b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><img alt="a = 1" src="http://rinconmatematico.com/latexrender/pictures/fd352b68bf83391284e044021cab0339.gif" /></b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><img alt="b = 2 \zeta Wn
" src="http://rinconmatematico.com/latexrender/pictures/16c0c91f5baa567be1e7787b2fbab9ca.gif" /></b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><img alt="c = Wn²" src="http://rinconmatematico.com/latexrender/pictures/d80481806baa119f10847bd23460431c.gif" /></b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Sustituyendo en la ecuación tenemos:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<br />
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><b><img alt="s = \frac{-2 \delta Wn \pm \sqrt[2]{(2 \zeta Wn)² - 4(1) (Wn²)} }{2(1)}" src="http://rinconmatematico.com/latexrender/pictures/eca0a01cce187efcd3959338c5866487.gif" /></b></b></span></div>
<br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Resolviéndolo:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b><img alt=" s = \frac{-2 \zeta Wn \pm \sqrt[2]{(2 \zeta Wn)²-4(1)(Wn²)}}{2(1)}" src="http://rinconmatematico.com/latexrender/pictures/69eefecb6bcde794b3d99e6cd2d4e0c8.gif" /></b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><img alt=" s = \frac{-2 \zeta Wn \pm \sqrt[2]{4 \zeta² Wn²-4Wn²}}{2}" src="http://rinconmatematico.com/latexrender/pictures/c46e2c30499bf4c1503c712993e1819f.gif" /></b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><img alt=" s = \frac{-2 \zeta Wn \pm \sqrt[2]{4 (\zeta² Wn²-Wn²)}}{2}" src="http://rinconmatematico.com/latexrender/pictures/f3da3f4bdd9801aac07b3c7cb9cccc78.gif" /></b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><img alt=" s = \frac{-2 \zeta Wn \pm \sqrt[2]{4}\sqrt[2]{\zeta² Wn²-Wn²}}{2}" src="http://rinconmatematico.com/latexrender/pictures/cf4265049468ed25f8a360cf3af7d84d.gif" /></b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><img alt=" s = \frac{-2 \zeta Wn \pm (2)\sqrt[2]{\zeta² Wn²-Wn²}}{2}" src="http://rinconmatematico.com/latexrender/pictures/8a369d15ff751539ecde75963de4a378.gif" /></b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><img alt=" s = -\zeta Wn \pm \sqrt[2]{\zeta² Wn²-Wn²}" src="http://rinconmatematico.com/latexrender/pictures/fd37f7e6b3ab3f3e32e923acf0ca8feb.gif" /></b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Como ya no se puede simplificar más la factorización es igual a:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span><br />
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><b><img alt=" (s + \zeta Wn - \sqrt[2]{\zeta² Wn²-Wn²})(s + \zeta Wn + \sqrt[2]{\zeta² Wn²-Wn²})" src="http://rinconmatematico.com/latexrender/pictures/efd13f81825c7aea06a62032b1f35158.gif" /></b></b></span></div>
<br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Sustituyendo esto en la ecuación original:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<br />
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><b><img alt=" x(s) = \frac{as + b + 2 \zeta Wna}{(s + \zeta Wn - \sqrt[2]{\zeta² Wn²-Wn²})(s + \zeta Wn + \sqrt[2]{\zeta² Wn²-Wn²})}" src="http://rinconmatematico.com/latexrender/pictures/a6ce082d5b76c2a520785b284345aac9.gif" /></b></b></span></div>
<br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Para que las operaciones se nos resulten mas fácil y los estos son constantes los sustituimos por variables:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b><img alt=" x = \zeta Wn - \sqrt[2]{\zeta² Wn²-Wn²})" src="http://rinconmatematico.com/latexrender/pictures/a73d25fb39e7d12c567af27f64c664e7.gif" /></b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><img alt=" y = \zeta Wn + \sqrt[2]{\zeta² Wn²-Wn²})" src="http://rinconmatematico.com/latexrender/pictures/460f8f17f46cefa9bac4dc91a70bc6ba.gif" /></b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><img alt=" z = b + 2 \zeta Wna" src="http://rinconmatematico.com/latexrender/pictures/9b4c3d0c7415fe900c2265505c328b2d.gif" /></b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Por lo tanto nos queda:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<br />
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><b><img alt=" x(s) = \frac{as + z}{(s + x)(s + y)}" height="66" src="http://rinconmatematico.com/latexrender/pictures/f8f83f3a1ad52a9a4deb33f1a1bf8857.gif" width="320" /></b></b></span></div>
<br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Aplicando fracciones parciales:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<br />
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><b><img alt=" x(s) = \frac{A}{(s + x)}\frac{B}{(s + y)}" height="70" src="http://rinconmatematico.com/latexrender/pictures/42d5c2b66c909541c8f52319fe60a76e.gif" width="320" /></b></b></span></div>
<br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Tenemos que:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<br />
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><b><img alt=" A = \displaystyle\lim_{s \to{-}x}{\frac{as+Z}{s+y}} = \frac{a(-x)+Z}{-x+y} = \frac{Z-ax}{y-x}" src="http://rinconmatematico.com/latexrender/pictures/76758c7e75b209cbc20b3bb9c01b5b56.gif" /></b></b></span></div>
<br />
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><img alt=" B = \displaystyle\lim_{s \to{-}y}{\frac{as+z}{s+x}} = \frac{a(-y)+z}{-y+x} = \frac{z-ay}{x-y}" src="http://rinconmatematico.com/latexrender/pictures/0c7a4a6fcf3ce8c088c337913c30cda1.gif" /></b></span></div>
<div>
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Sustituyendo los valores de A y B en la ecuación original tenemos:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<br />
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><b><img alt=" x(s) = (\frac{z - ax}{y-x})(\frac{1}{s+x})+(\frac{z - ay}{x-y})(\frac{1}{s+y})" src="http://rinconmatematico.com/latexrender/pictures/85e593199d4374e4b170db6035fc2894.gif" /></b></b></span></div>
<br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>A continuación aplicamos la transformada inversa de laplace a la ecuación, ya que las variables x, y y z son constantes solo sera hará con los términos de s:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<br />
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><b><img alt=" x(t) = (\frac{z - ax}{x-y})L^-1 \left\{{(\frac{1}{s+x})}\right\}x^n+(\frac{z - ay}{x-y})L^-1 \left\{(\frac{1}{s+y})\right\}" src="http://rinconmatematico.com/latexrender/pictures/e4752e92b675376e99b134a01ed200b7.gif" /></b></b></span></div>
<br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Resultado:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<br />
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><b><img alt=" x(t) = (\frac{z - ax}{y-x})e^-xt+(\frac{z - ay}{x-y})e^-yt" src="http://rinconmatematico.com/latexrender/pictures/d1ef5137d363dccb3d5ff385e201f147.gif" /></b></b></span></div>
<br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Sustituyendo los valores de x, y y z en la ecuación:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<br />
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b><b><img alt=" x(t) = (\frac{ b + 2 \zeta Wna - a( \zeta Wn - \sqrt[2]{\zeta² Wn²-Wn²})}{(\zeta Wn + \sqrt[2]{\zeta² Wn²-Wn²})-( \zeta Wn - \sqrt[2]{\zeta² Wn²-Wn²})})e^-( \zeta Wn - \sqrt[2]{\zeta² Wn²-Wn²})t+(\frac{ b + 2 \zeta Wna - a(\zeta Wn + \sqrt[2]{\zeta² Wn²-Wn²})}{( \zeta Wn - \sqrt[2]{\zeta² Wn²-Wn²})-y})e^-(\zeta Wn + \sqrt[2]{\zeta² Wn²-Wn²})t
" height="80" src="http://rinconmatematico.com/latexrender/pictures/974ecbe55b595bd3482d3110c7f13e54.gif" width="640" /></b></b></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Referencias:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<a href="http://es.wikipedia.org/wiki/Ecuaci%C3%B3n_de_segundo_grado"><span style="font-family: Arial, Helvetica, sans-serif;"><b>http://es.wikipedia.org/wiki/Ecuaci%C3%B3n_de_segundo_grado</b></span></a><br />
<a href="http://matematicas.udea.edu.co/~jescobar/docs/cap6.pdf"><span style="font-family: Arial, Helvetica, sans-serif;"><b>http://matematicas.udea.edu.co/~jescobar/docs/cap6.pdf</b></span></a></div>
</div>
guelmi_rickhttp://www.blogger.com/profile/00075155021794486805noreply@blogger.com1tag:blogger.com,1999:blog-3668401867087218235.post-41624372628695984562012-09-05T17:06:00.001-07:002012-09-05T19:58:24.116-07:00Entrada # 4<div class="separator" style="clear: both; text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>For this week consisted of make an example with the Diffie-Hellman protocol.</b></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">The Diffie-Hellman protocol can be explained by the following problem:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: #660000; font-family: Arial, Helvetica, sans-serif;"><b>We have two people (Alice and Bob) who are in the same communication with Eve, to the problem Alice and Bob want to communicate among themselves.</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br />To do this it have the following procedure</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Define values: 'p' and 'g' (this makes him Alice or Bob), as these values have to pass the Alice to Bob (or vice versa), as Eve learns them.</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>The following Alice and Bob define the values of 'x' and 'y' respectively, these are not the pass to the other Eve therefore not know the value of these.</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Making note:</b></span><br />
<div style="text-align: center;">
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>Alice have the values of 'x', 'p' y de 'g'</b></span></div>
<div style="text-align: center;">
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>Bob have the values</b></span><b style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"> of 'y', 'p' y de 'g'</b></div>
<div style="text-align: center;">
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>Eve have 'p' y 'g'</b></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>As these values are not sufficient to make the communication must provide other data but must be one with which Eve can not easily discover the values of 'x' and 'y'let alone give those values.</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>So Alice uses the following equation to obtain 'X' and Bob to obtain 'Y':</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<br />
<div style="text-align: center;">
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>Alice(X) ó Bob (Y) = (g^(x ó y)) mod p</b></span></div>
<br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Once they both have those values, be the pass to each other is: 'Alice passes Bob X' and 'Bob passes Y to Alice', these values Eve finds out them and takes them.</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Making note again:</b></span><br />
<div style="text-align: center;">
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>Alice have the values of 'x', 'p', 'g', 'X', 'Y'</b></span></div>
<div style="text-align: center;">
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>Bob have the values of 'y', 'p', 'g', 'X', 'Y'</b></span></div>
<div style="text-align: center;">
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>Eve have 'p', 'g', 'X', 'Y'</b></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Please note that not all values there are none in which only Alice and Bob know therefore be drawn more to a value that can be used as a shared key for them and communicate through that.</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>This value will call K, this can be found by the following equations:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<b><span style="font-family: Arial, Helvetica, sans-serif;"></span>
</b>
<br />
<div style="text-align: center;">
<b><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>K = (X^y) mod p</b></span></b></div>
<b>
</b>
<div style="text-align: center;">
<b><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>K = (Y^x) mod p</b></span></b><br />
<b><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>K = ((g^x)^y) mod p -> If know the values of 'x' and 'y'</b></span></b><br />
<b><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>K = ((g^y)^x) mod p -> If know the values of 'x' and 'y'</b></span></b></div>
<b><br />
</b><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Eve can not find K because do not have 'x' and 'y'.</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span>
<br />
<div style="text-align: center;">
<div style="text-align: start;">
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Making note for the last time, we determined that:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b><br /></b></span></div>
<div style="text-align: start;">
<b><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"></span></b></div>
<div style="text-align: center;">
<b><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>Alice have the values of 'x', 'p', 'g', 'X', 'Y', 'K'</b></span></b></div>
</div>
<b>
</b>
<br />
<div style="text-align: center;">
<b><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>Bob have the values of 'y', 'p', 'g', 'X', 'Y', 'K'</b></span></b></div>
<b>
</b>
<br />
<div style="text-align: center;">
<b><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b>Eve have 'p', 'g', 'X', 'Y'</b></span></b></div>
<b>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b>
<b><span style="font-family: Arial, Helvetica, sans-serif;">The way for Eve can find the values of 'x' and 'y', would be testing random numbers using the formula of X and Y; find these comparing them having Eve, obtain the values originally wished.</span></b><br />
<b><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b>
<b><span style="font-family: Arial, Helvetica, sans-serif;">Now with that could determine K.</span></b><br />
<b><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b>
<b><span style="font-family: Arial, Helvetica, sans-serif;">As an aside, you have to make clear a few things when making use of this protocol:</span></b><br />
<b>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b> p -> Must be a </b> <a href="http://es.wikipedia.org/wiki/N%C3%BAmero_primo">número entero primo</a></span></b><br />
<b>
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b> g-> Must a number integer to less than p</b></span><br />
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b> x-> Number chosen by Alice, be less than p</b></span><br />
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b> y-> Number chosen by Bob, be less than p</b></span><br />
<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;"><b> mod-></b> It means % in some programming languages, to explain how to obtain would be through:</span><br />
</b><br />
<div style="text-align: justify;">
<b><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b></div>
<b>
</b>
<br />
<div style="text-align: center;">
<b><span style="font-family: Arial, Helvetica, sans-serif;"> </span></b><span style="color: #0b5394; font-family: Arial, Helvetica, sans-serif;"><b>Asks 6% 5 or 6 mod 5. - This is equal to 6/5, if what comes out is an integer without decimals the result is 0 if not, grab the decimal part of the problem (6/5 = 1.2) and you multiply it by the value of the mod (in this case 5), 0.2 X 5 = 1 and what you round it out, what comes out will be the result (6% 5 = 1).</b></span></div>
<b>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">----------------------------------------------------------------------------------------------------------------------------------</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b><br />
<div>
<b><span style="font-family: Arial, Helvetica, sans-serif;">What is commissioned task was to choose two companions who would Alice and Bob, I chose to Alejandro Avendaño and </span><b><span style="font-family: Arial, Helvetica, sans-serif;">Eduardo </span></b><b></b></b><br />
<div style="display: inline !important;">
<b><b><span style="font-family: Arial, Helvetica, sans-serif;">Triana respectively and Eve I would be therefore have to find the values of 'x', 'y' and 'K '.</span></b></b></div>
<b><b>
</b></b></div>
<b>
</b><b></b>
<br />
<div>
<b><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b></div>
<b>
</b>
<br />
<div>
<b><span style="font-family: Arial, Helvetica, sans-serif;">Then I show the values of 'p', 'g', 'X' and 'Y' supplied by them.</span></b></div>
<b>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<br />
</b><br />
<div class="separator" style="clear: both; text-align: center;">
<b><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVLDNLVTCSlYavA6w4se5NGoAB5-Ixqwx4FTpa67Gmc5lpd5j9eGowCgnddxWXff4lqI7K2lCxeN4ya6xKvFSxbYhygzhB-MXGs6zBSnxKI2Z67S4yvRgZ8a-JSxc0OcGQ_UlX5PEHLbU/s1600/Pantallazo+del+2012-09-05+19:04:12.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="266" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhVLDNLVTCSlYavA6w4se5NGoAB5-Ixqwx4FTpa67Gmc5lpd5j9eGowCgnddxWXff4lqI7K2lCxeN4ya6xKvFSxbYhygzhB-MXGs6zBSnxKI2Z67S4yvRgZ8a-JSxc0OcGQ_UlX5PEHLbU/s320/Pantallazo+del+2012-09-05+19:04:12.png" width="320" /></span></a></b></div>
<b>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span><b><span style="font-family: Arial, Helvetica, sans-serif;">Basen in the image, we have:</span></b></b><br />
<div style="text-align: center;">
<b><b><span style="font-family: Arial, Helvetica, sans-serif;"><b><b><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;">p = 13</span></b></b></span></b></b></div>
<b><span style="font-family: Arial, Helvetica, sans-serif;">
</span></b><span style="color: #20124d;"></span>
<div style="text-align: center;">
<span style="color: #20124d;"><b><span style="color: #20124d;"><b><span style="font-family: Arial, Helvetica, sans-serif;">g = 7</span></b></span></b></span></div>
<span style="color: #20124d;">
<b><div style="text-align: center;">
<b><span style="color: #20124d;"><b><span style="font-family: Arial, Helvetica, sans-serif;">X = 9</span></b></span></b></div>
</b>
<b><div style="text-align: center;">
<b><span style="color: #20124d;"><b><span style="font-family: Arial, Helvetica, sans-serif;">Y = 12</span></b></span></b></div>
</b></span>
<b><span style="font-family: Arial, Helvetica, sans-serif;"><br />The next thing is to try to find x or y, I chose to try to find 'x' then 'y'.</span></b><br />
<div>
<b><b><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b></b></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgex852233Bmi6mmJYGn0IBYyjDS37X8a5g0J5oXButUxpon74vn-vfxBUMjfii-g0jJLJStAgQ5NkxUUCp5zYLOh_3IukpH6wgd_yLJzIXrEGkBb_PIjR2Ak_JZpgYMCaAVqp3ugm3r1E/s1600/IMG298.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgex852233Bmi6mmJYGn0IBYyjDS37X8a5g0J5oXButUxpon74vn-vfxBUMjfii-g0jJLJStAgQ5NkxUUCp5zYLOh_3IukpH6wgd_yLJzIXrEGkBb_PIjR2Ak_JZpgYMCaAVqp3ugm3r1E/s400/IMG298.jpg" width="311" /></a></div>
<div>
<br /></div>
<div>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>As seen in the image I tried x values that were under p, to find X and this compared with they gave me them, but was tried with another and so on until you find the correct X value.</b></span><br />
<b><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;">Then I did the same with to find Y.</span></b><br />
<div>
<b><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiq1sS0wfBFKzORSNrvqaK-BcCgnAgweJzdezjqcU9wFY8OmOVLkQXYrIHwP4iyC3SDou4NsnrVhWEQFQc62Ewh_BCap8WpFRWM2EX8c_H83OQrJuRyR6WbdEH_T9C-iODOXRtEqOlXE-Q/s1600/IMG300.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="400" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiq1sS0wfBFKzORSNrvqaK-BcCgnAgweJzdezjqcU9wFY8OmOVLkQXYrIHwP4iyC3SDou4NsnrVhWEQFQc62Ewh_BCap8WpFRWM2EX8c_H83OQrJuRyR6WbdEH_T9C-iODOXRtEqOlXE-Q/s400/IMG300.jpg" width="357" /></a></div>
<div>
<b><b><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b></b>
<b><span style="font-family: Arial, Helvetica, sans-serif;">Already with the data found kick K, so that the value is correct I did with the two equations that there.</span></b><br />
<b><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b>
<b><span style="font-family: Arial, Helvetica, sans-serif;">Once you do that wrote the values found in the publication:</span></b><br />
<b>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<br />
</b><br />
<div class="separator" style="clear: both; text-align: center;">
<b><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAcPV0pAH-S7TrbS58wSoiL-mbEdFRfx26twJ-aWoP58S_n3zlx1GcHRXa28XfDakM0RNVnPhUiTKC-wzIK0Z7OWYZaasjEqkZLcqvXffCl8PgR4oycUsLTHBnhP4wCiuDga2IZDm6Abk/s1600/Pantallazo+del+2012-09-05+19:15:58.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="254" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiAcPV0pAH-S7TrbS58wSoiL-mbEdFRfx26twJ-aWoP58S_n3zlx1GcHRXa28XfDakM0RNVnPhUiTKC-wzIK0Z7OWYZaasjEqkZLcqvXffCl8PgR4oycUsLTHBnhP4wCiuDga2IZDm6Abk/s320/Pantallazo+del+2012-09-05+19:15:58.png" width="320" /></a></b></div>
<b>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span><span style="font-family: Arial, Helvetica, sans-serif;"></span></b><br />
<b><span style="font-family: Arial, Helvetica, sans-serif;">To complement the above create a file in python to check if my results were correct.</span></b><br />
<b><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></b>
<b><span style="font-family: Arial, Helvetica, sans-serif;">And the result:</span></b><br />
<b>
<br />
</b><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEit3bt9kdkPU5xzwyoFK0imysqjFYhGB754OAb6f44yCHIad8TXCb6RGUXvMml27x4U2D5qzWCf_DxLZmj6PrXdc-7fBSv9m6Taf3ZMTXhVTXCfKvHzDN9pCoJONMTBocZh9k9cKLkXHvU/s1600/Pantallazo+del+2012-09-05+21:46:54.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="192" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEit3bt9kdkPU5xzwyoFK0imysqjFYhGB754OAb6f44yCHIad8TXCb6RGUXvMml27x4U2D5qzWCf_DxLZmj6PrXdc-7fBSv9m6Taf3ZMTXhVTXCfKvHzDN9pCoJONMTBocZh9k9cKLkXHvU/s400/Pantallazo+del+2012-09-05+21:46:54.png" width="400" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<b>
<span style="font-family: Arial, Helvetica, sans-serif;">References:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<a href="http://es.wikipedia.org/wiki/Diffie-Hellman"><span style="font-family: Arial, Helvetica, sans-serif;">http://es.wikipedia.org/wiki/Diffie-Hellman</span></a><br />
<a href="http://www.slideshare.net/fivefingers/protocolo-de-diffiehellman"><span style="font-family: Arial, Helvetica, sans-serif;">http://www.slideshare.net/fivefingers/protocolo-de-diffiehellman</span></a></b></div>
</div>
guelmi_rickhttp://www.blogger.com/profile/00075155021794486805noreply@blogger.com1tag:blogger.com,1999:blog-3668401867087218235.post-11005814116548144182012-08-30T08:29:00.003-07:002012-08-30T09:27:10.013-07:00Entrada # 3<div style="text-align: center;">
<span style="background-color: #20124d; color: white; font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>Análisis de Aleatoriedad de las llaves del One-Time Pad</b></span></div>
<br />
<div style="text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<span style="font-family: Arial, Helvetica, sans-serif;">
Para esta semana consistió en demostrar que las llaves generadas son realmente aleatorias.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br />La demostración de lo anterior se realizo de esto mediante la Prueba de Frecuencia de Bloques, la elección de esta se debió ya que en la clase de Modelado ( <b> </b><a href="http://modelado-p.blogspot.mx/2012/05/reporte-3.html"><b>http://modelado-p.blogspot.mx/2012/05/reporte-3.html</b></a>) ya había hecho uso de ella.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span><span style="font-family: Arial, Helvetica, sans-serif;">La Prueba de Frecuencia de Bloques verifica que la cantidad de unos y de ceros sea equitativa.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br />
Esta prueba hace uso de algunas variables, a continuación explicare el uso de cada una:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="background-color: white; font-size: 14px; line-height: 19px; text-align: justify;"><br /></span>
<span style="background-color: white; font-size: 14px; line-height: 19px; text-align: justify;"><b>n -> </b>Número de elementos, en el problema seria la cantidad de llaves generadas</span></span><br />
<span style="background-color: white; font-family: Arial, Helvetica, sans-serif; font-size: 14px; line-height: 19px; text-align: justify;"><b>m -> </b>Todos los números aleatorios generados por todas las llaves</span><br />
<span style="background-color: white; font-family: Arial, Helvetica, sans-serif; font-size: 14px; line-height: 19px; text-align: justify;"><b>N -> </b>Cantidad de números de por bloque, la cantidad de números con las cuenta cada llave</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /><b><span style="color: #660000;">Código realizado:</span></b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<script src="https://gist.github.com/3530728.js"> </script>
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<span style="color: #660000; font-family: Arial, Helvetica, sans-serif;"><b>Teniendo las llaves generadas:</b></span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjaPqEYg6_5nWGsD96rGd2IN0HPfGtHIYB8tcl0TwnVr9aDxXpbXXrb2KTppAiPuwdDdQ2eKbPHbChbkMfLHORfhJpuFUlCPFH3QLtmqxia81uE_VNojdS-4GEG-56pfakB_aY-MXfRiJ8/s1600/Pantallazo+del+2012-08-30+10:38:42.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="206" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjaPqEYg6_5nWGsD96rGd2IN0HPfGtHIYB8tcl0TwnVr9aDxXpbXXrb2KTppAiPuwdDdQ2eKbPHbChbkMfLHORfhJpuFUlCPFH3QLtmqxia81uE_VNojdS-4GEG-56pfakB_aY-MXfRiJ8/s320/Pantallazo+del+2012-08-30+10:38:42.png" width="320" /></span></a></div>
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<span style="color: #660000; font-family: Arial, Helvetica, sans-serif;"><b>Corriéndolo:</b></span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwwUPkXtjXiE15rAKYIxNzemVefuufnyAYV3-V6B_LKN03Dy7Ao4WZ2Aoj_-LJf_-lgwiI7wG9Z9uWWgqKoK_InPY6HqQLkwuIaLB9OymDVRgcuZrI1EZGEQIT62xmCeXnZ8LmJibWDic/s1600/Pantallazo+del+2012-08-30+11:07:28.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="116" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhwwUPkXtjXiE15rAKYIxNzemVefuufnyAYV3-V6B_LKN03Dy7Ao4WZ2Aoj_-LJf_-lgwiI7wG9Z9uWWgqKoK_InPY6HqQLkwuIaLB9OymDVRgcuZrI1EZGEQIT62xmCeXnZ8LmJibWDic/s640/Pantallazo+del+2012-08-30+11:07:28.png" width="640" /></a></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: #660000; font-family: Arial, Helvetica, sans-serif;"><b>Referencias:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<a href="http://es.wikipedia.org/wiki/Libreta_de_un_solo_uso"><span style="font-family: Arial, Helvetica, sans-serif;">http://es.wikipedia.org/wiki/Libreta_de_un_solo_uso</span></a><br />
<a href="http://scipy.org/Numpy_Example_List"><span style="font-family: Arial, Helvetica, sans-serif;">http://scipy.org/Numpy_Example_List</span></a><br />
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guelmi_rickhttp://www.blogger.com/profile/00075155021794486805noreply@blogger.com1tag:blogger.com,1999:blog-3668401867087218235.post-68189556856776189172012-08-22T18:56:00.001-07:002012-08-23T20:41:31.098-07:00Entrada # 1<div style="text-align: center;">
<b><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif; font-size: large;">Laboratorio de Automatización y Control de Sistemas </span></b><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>Dinámicos</b></span></div>
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<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif; font-size: large;"><b><br /></b></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Para esta semana hay que investigar acerca de unos temas que nos dieron la semana pasada.</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">A mi me toco acerca de la <b><span style="color: #660000;">función Escalón, Rampa e Impulso</span></b>; a continuación hablare de ellos:</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br />
<span style="color: #660000; font-size: large;"><b style="background-color: white;">Función Impulso:</b></span></span><br />
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<a href="https://encrypted-tbn0.google.com/images?q=tbn:ANd9GcQBZt6LK_b2G_KGk06x5ClhJSxO8qPE65yEE-o0zRcT4eqsoGHP" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="298" src="https://encrypted-tbn0.google.com/images?q=tbn:ANd9GcQBZt6LK_b2G_KGk06x5ClhJSxO8qPE65yEE-o0zRcT4eqsoGHP" width="400" /></span></a></div>
<span style="background-color: white; line-height: 18px; text-align: start;"><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><span aria-readonly="true" class="MathJax" role="textbox" style="background-color: white; border: 0px; cursor: pointer; direction: ltr; display: inline; float: none; margin: 0px; padding: 0px; text-align: left; white-space: nowrap; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-55" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 1.353em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.339em; width: 0px;">.</span></span></nobr></span>Conocida como Función Delta de Dirac y como Impulso Unitario.</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><span style="background-color: white; line-height: 18px; text-align: start;">La función del impulso usualmente se escribe como </span><span aria-readonly="true" class="MathJax" role="textbox" style="background-color: white; border: 0px; cursor: pointer; direction: ltr; display: inline; float: none; margin: 0px; padding: 0px; text-align: left; white-space: nowrap; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-55" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 1.543em;"><span style="border: 0px; clip: rect(1.854em 1000em 3.226em -0.52em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.79em; vertical-align: 0px;"><b><span class="mrow" id="MathJax-Span-56" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-57" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-58" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-59" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-60" style="border: 0px; display: inline; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">δ</span></span><span class="mo" id="MathJax-Span-61" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"></span><span class="mfenced" id="MathJax-Span-62" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mo" id="MathJax-Span-63" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">(</span></span><span class="mrow" id="MathJax-Span-64" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-65" style="border: 0px; display: inline; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">t</span></span><span class="mo" id="MathJax-Span-66" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">)</span></span></span></span></span></span><span style="border: 0px; display: inline-block; height: 2.79em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></b></span></span><b><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 1.353em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.339em; width: 0px;"></span></b></span></nobr></span></span><br />
<span aria-readonly="true" class="MathJax" role="textbox" style="background-color: white; border: 0px; cursor: pointer; direction: ltr; display: inline; float: none; margin: 0px; padding: 0px; text-align: left; white-space: nowrap; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></span></nobr></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="background-color: white; text-align: start;"><span style="line-height: 18px;">Esta es una función infinitamente angosta, infinitamente alta, cuya integral tiene un valor </span></span><dfn class="term" style="background-color: white; display: inline; font-style: normal; font-weight: bold; line-height: 18px; text-align: start;">unitario</dfn><span style="background-color: white; line-height: 18px; text-align: start;"> .</span></span><br />
<span style="background-color: white; line-height: 18px; text-align: start;"><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></span>
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<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEji-QvswLEs1dk6HXy1H34HERwaxkrePFfEHkXwqtjlbs9GRfr4bg0z8kvTRDVPvYKSQGZXHdtMief8CztTFodJOwCYAYFNOCOyDoPY5wpgZu6VrPOvZuU7qS5aQX-EqZMotSF0xFXDy5Q/s1600/Pantallazo+del+2012-08-23+01:53:50+%28otra+copia%29.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" height="125" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEji-QvswLEs1dk6HXy1H34HERwaxkrePFfEHkXwqtjlbs9GRfr4bg0z8kvTRDVPvYKSQGZXHdtMief8CztTFodJOwCYAYFNOCOyDoPY5wpgZu6VrPOvZuU7qS5aQX-EqZMotSF0xFXDy5Q/s320/Pantallazo+del+2012-08-23+01:53:50+%28otra+copia%29.png" width="320" /></span></a></div>
<span style="background-color: white; line-height: 18px; text-align: start;"><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></span>
<span style="background-color: white; line-height: 18px; text-align: start;"><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="background-color: white; text-align: start;"><span style="line-height: 18px;">La manera para ver como es la gráfica es usar un pulso rectangular que va de </span></span><span aria-readonly="true" class="MathJax" role="textbox" style="background-color: white; border: 0px; cursor: pointer; direction: ltr; display: inline; float: none; margin: 0px; padding: 0px; text-align: left; white-space: nowrap; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-14" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 2.284em;"><span style="border: 0px; clip: rect(1.843em 1000em 3.373em -0.523em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.79em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-15" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-16" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-17" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-18" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-19" style="border: 0px; display: inline; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">a</span></span><span class="mo" id="MathJax-Span-20" style="border: 0px; display: inline; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">−</span><span class="mfrac" id="MathJax-Span-21" style="border: 0px; display: inline; margin: 0px; padding: 0px 0.12em 0px 0.342em; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 0.49em;"><span style="border: 0px; clip: rect(2.285em 1000em 2.991em -0.536em); left: 50%; margin: 0px 0px 0px -0.154em; padding: 0px; position: absolute; top: -3.231em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-22" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-23" style="border: 0px; display: inline; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">ε</span></span><span style="border: 0px; display: inline-block; height: 2.79em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(2.134em 1000em 2.976em -0.521em); left: 50%; margin: 0px 0px 0px -0.185em; padding: 0px; position: absolute; top: -2.393em; vertical-align: 0px;"><span class="mn" id="MathJax-Span-24" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">2</span><span style="border: 0px; display: inline-block; height: 2.79em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(2.528em 1000em 2.975em -0.556em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -3.01em; vertical-align: 0px;"><span style="border-left-style: solid; border-width: 0px 0px 0px 0.49em; display: inline-block; height: 0.077em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0em; width: 0px;"></span><span style="border: 0px; display: inline-block; height: 2.79em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span></span></span></span></span><span style="border: 0px; display: inline-block; height: 2.79em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 1.565em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.536em; width: 0px;"></span></span></nobr></span><span style="background-color: white; line-height: 18px; text-align: start;"> a </span><span aria-readonly="true" class="MathJax" role="textbox" style="background-color: white; border: 0px; cursor: pointer; direction: ltr; display: inline; float: none; margin: 0px; padding: 0px; text-align: left; white-space: nowrap; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-25" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 2.284em;"><span style="border: 0px; clip: rect(1.843em 1000em 3.373em -0.523em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.79em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-26" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-27" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-28" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-29" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-30" style="border: 0px; display: inline; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">a</span></span><span class="mo" id="MathJax-Span-31" style="border: 0px; display: inline; margin: 0px; padding: 0px 0px 0px 0.222em; position: static; vertical-align: 0px;">+</span><span class="mfrac" id="MathJax-Span-32" style="border: 0px; display: inline; margin: 0px; padding: 0px 0.12em 0px 0.342em; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 0.49em;"><span style="border: 0px; clip: rect(2.285em 1000em 2.991em -0.536em); left: 50%; margin: 0px 0px 0px -0.154em; padding: 0px; position: absolute; top: -3.231em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-33" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-34" style="border: 0px; display: inline; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">ε</span></span><span style="border: 0px; display: inline-block; height: 2.79em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(2.134em 1000em 2.976em -0.521em); left: 50%; margin: 0px 0px 0px -0.185em; padding: 0px; position: absolute; top: -2.393em; vertical-align: 0px;"><span class="mn" id="MathJax-Span-35" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">2</span><span style="border: 0px; display: inline-block; height: 2.79em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(2.528em 1000em 2.975em -0.556em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -3.01em; vertical-align: 0px;"><span style="border-left-style: solid; border-width: 0px 0px 0px 0.49em; display: inline-block; height: 0.077em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0em; width: 0px;"></span><span style="border: 0px; display: inline-block; height: 2.79em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span></span></span></span></span><span style="border: 0px; display: inline-block; height: 2.79em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 1.565em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.536em; width: 0px;"></span></span></nobr></span><span style="background-color: white; line-height: 18px; text-align: start;"> con una altura de </span><span aria-readonly="true" class="MathJax" role="textbox" style="background-color: white; border: 0px; cursor: pointer; direction: ltr; display: inline; float: none; margin: 0px; padding: 0px; text-align: left; white-space: nowrap; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-36" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 0.617em;"><span style="border: 0px; clip: rect(1.708em 1000em 3.336em -0.436em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.79em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-37" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-38" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mfrac" id="MathJax-Span-39" style="border: 0px; display: inline; margin: 0px; padding: 0px 0.12em; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 0.49em;"><span style="border: 0px; clip: rect(2.134em 1000em 2.975em -0.497em); left: 50%; margin: 0px 0px 0px -0.185em; padding: 0px; position: absolute; top: -3.216em; vertical-align: 0px;"><span class="mn" id="MathJax-Span-40" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">1</span><span style="border: 0px; display: inline-block; height: 2.79em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(2.285em 1000em 2.991em -0.536em); left: 50%; margin: 0px 0px 0px -0.154em; padding: 0px; position: absolute; top: -2.445em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-41" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-42" style="border: 0px; display: inline; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">ε</span></span><span style="border: 0px; display: inline-block; height: 2.79em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(2.528em 1000em 2.975em -0.556em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -3.01em; vertical-align: 0px;"><span style="border-left-style: solid; border-width: 0px 0px 0px 0.49em; display: inline-block; height: 0.077em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: 0em; width: 0px;"></span><span style="border: 0px; display: inline-block; height: 2.79em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span></span></span></span><span style="border: 0px; display: inline-block; height: 2.79em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 1.697em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -0.487em; width: 0px;"></span></span></nobr></span><span style="background-color: white; line-height: 18px; text-align: start;">. </span></span><br />
<span style="background-color: white; line-height: 18px; text-align: start;"><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="background-color: white; line-height: 18px; text-align: start;">Al momento de tomar su límite, </span><span aria-readonly="true" class="MathJax" role="textbox" style="background-color: white; border: 0px; cursor: pointer; direction: ltr; display: inline; float: none; margin: 0px; padding: 0px; text-align: left; white-space: nowrap; word-wrap: normal;"><nobr style="border: 0px; margin: 0px; max-height: none; max-width: none; padding: 0px; vertical-align: 0px;"><span class="math" id="MathJax-Span-43" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 2.407em;"><span style="border: 0px; clip: rect(1.911em 1000em 3.738em -0.53em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.79em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-44" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-45" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-46" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="munder" id="MathJax-Span-47" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span style="border: 0px; display: inline-block; height: 0px; margin: 0px; padding: 0px; position: relative; vertical-align: 0px; width: 2.407em;"><span style="border: 0px; clip: rect(1.911em 1000em 2.985em -0.53em); left: 0em; margin: 0px; padding: 0px; position: absolute; top: -2.79em; vertical-align: 0px;"><span class="mi" id="MathJax-Span-48" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">limit </span><span style="border: 0px; display: inline-block; height: 2.79em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span><span style="border: 0px; clip: rect(2.134em 1000em 3.091em -0.536em); left: 0.525em; margin: 0px; padding: 0px; position: absolute; top: -2.143em; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-49" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-50" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mrow" id="MathJax-Span-51" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;"><span class="mi" id="MathJax-Span-52" style="border: 0px; display: inline; font-style: italic; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">ε</span></span><span class="mo" id="MathJax-Span-53" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">→</span><span class="mn" id="MathJax-Span-54" style="border: 0px; display: inline; margin: 0px; padding: 0px; position: static; vertical-align: 0px;">0</span></span></span><span style="border: 0px; display: inline-block; height: 2.79em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span></span></span></span></span><span style="border: 0px; display: inline-block; height: 2.79em; margin: 0px; padding: 0px; position: static; vertical-align: 0px; width: 0px;"></span></span></span><span style="border-left-style: solid; border-width: 0px 0px 0px 0em; display: inline-block; height: 1.967em; margin: 0px; overflow: hidden; padding: 0px; position: static; vertical-align: -1.03em; width: 0px;"></span></span></nobr></span><span style="background-color: white; line-height: 18px; text-align: start;">, podemos observar que su ancho tiende a ser cero y su altura tiende a infinito (Llegando a parecerse a una línea recta como la imagen al principio) conforme su área total permanece constante con un valor de uno.</span></span><br />
<span style="background-color: white; line-height: 18px; text-align: start;"><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></span>
<span style="background-color: white; line-height: 18px; text-align: start;"><span style="font-family: Arial, Helvetica, sans-serif;">La forma del movimiento de la función se muestra abajo.</span></span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><img height="400" src="http://upload.wikimedia.org/wikipedia/commons/b/b4/Dirac_function_approximation.gif" width="238" /></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><b>Vídeo acerca de la explicación de esta función:</b></span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/KtUaWdjmiw8?feature=player_embedded' frameborder='0'></iframe></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><b>Referencias:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<a href="http://es.wikipedia.org/wiki/Delta_de_Dirac"><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;">http://es.wikipedia.org/wiki/Delta_de_Dirac</span></a><br />
<a href="http://en.wikipedia.org/wiki/Dirac_delta_function"><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;">http://en.wikipedia.org/wiki/Dirac_delta_function</span></a><br />
<a href="http://cnx.org/content/m12824/latest/"><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;">http://cnx.org/content/m12824/latest</span></a><br />
<a href="http://mathworld.wolfram.com/DeltaFunction.html"><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;">http://mathworld.wolfram.com/DeltaFunction.html</span></a><br />
<a href="http://www.wikimatematica.org/index.php?title=Funci%C3%B3n_Delta_de_Dirac"><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;">http://www.wikimatematica.org/index.php?title=Funci%C3%B3n_Delta_de_Dirac</span></a><br />
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<span style="color: #660000; font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>Función Escalón:</b></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><img height="300" src="http://upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Dirac_distribution_CDF.svg/250px-Dirac_distribution_CDF.svg.png" width="400" /></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Conocida como Función Escalón de<b style="background-color: white; line-height: 19.200000762939453px;"> Heaviside</b><span style="background-color: white; line-height: 19.200000762939453px;">, también conocida como F</span><b style="background-color: white; line-height: 19.200000762939453px;">unción Escalón Unitario.</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><b style="background-color: white; line-height: 19.200000762939453px;"><br /></b>
<span style="background-color: white;"><span style="line-height: 19.200000762939453px; text-align: start;">Esta función se utiliza en </span>ingeniería de control<span style="line-height: 19.200000762939453px; text-align: start;"> y </span>procesamiento de señales<span style="line-height: 19.200000762939453px; text-align: start;">, representando una </span>señal<span style="line-height: 19.200000762939453px; text-align: start;"> que se enciende en un tiempo específico, y se queda encendida indefinidamente.</span></span></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><span style="background-color: white; line-height: 19.200000762939453px; text-align: start;"><br /></span>
<span style="background-color: white; color: #161618; line-height: 16px; text-align: left;">O sea el representar el caso de un interruptor que permanece abierto hasta que en un instante se apaga, estableciendo el máximo voltaje a una carga.</span></span></div>
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</span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;"><img alt="funcion escalon" height="217" src="http://ejerciciosdefunciones.com/wp-content/uploads/2012/06/funcion-escalon-300x163.gif" width="400" /></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">El valor de salida de esta función es 1 cuando los argumentos (el valor de la variable) de la función son Positivos y es 0 cuando los argumentos son negativos.</span></div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTpjp2pvBgcRuR6tUg66wB4388vbm_t1v9OVeFyKl6CmSCq770Q4_4L2ui0FtoGnMZ35veGV-MfwKCsL91dyhISvHegAG4rE145ivgosCL6EN_nyY-rusDZyLWjUzwfuRObZchyJHLj24/s1600/Pantallazo+del+2012-08-22+22:29:04.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><span style="font-family: Arial, Helvetica, sans-serif;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTpjp2pvBgcRuR6tUg66wB4388vbm_t1v9OVeFyKl6CmSCq770Q4_4L2ui0FtoGnMZ35veGV-MfwKCsL91dyhISvHegAG4rE145ivgosCL6EN_nyY-rusDZyLWjUzwfuRObZchyJHLj24/s1600/Pantallazo+del+2012-08-22+22:29:04.png" /></span></a></div>
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<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif; font-size: x-small;"><b>H(x) = Nombre con el que se conoce a la Función Escalón</b></span></div>
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<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif; font-size: x-small;"><b>u(x) = Función a evaluar</b></span></div>
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<span style="color: #20124d; font-family: Arial, Helvetica, sans-serif; font-size: x-small;"><b>Si el valor de X es menor a 0 o negativo el valor de salida es 0; si el valor de X es mayor a 0, el valor de salida es 1.</b></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">La unica duda con lo anterior es si x = 0, este dato no esta bien definido ya que algunos le dan el valor de 1 y otros le dan el valor de 1/2 para que le de un parecido a la grafica que puse al principio.</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">A continuación pongo los valores de salida que tendria la Escalón si se respetara lo anterior.</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><img alt=" H(x) =
\begin{cases} 0, & x < 0
\\ \frac{1}{2}, & x = 0
\\ 1, & x > 0
\end{cases}
" height="157" src="http://upload.wikimedia.org/wikipedia/es/math/9/4/b/94ba7c2c0126ef1e22835a81837ead70.png" width="320" /></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
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<span style="font-family: Arial, Helvetica, sans-serif;"><b>Ejemplo de la Función Escalón:</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span><span style="font-family: Arial, Helvetica, sans-serif;">Se tiene una función (Cualquiera que desees) y después se tiene una tabla con valores de X (Como para resolver las ecuaciones; teníamos los valores de x y sacábamos lo de y, estos valores de x se compararían con lo anterior, así que todo los valores de x que sean mayores a 0 el valor de y sería 1 y así hasta encontrar todos los valores de la tabla.</span><span style="font-family: Arial, Helvetica, sans-serif;"> )</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br />
Una vez hecho lo anterior solo seria el Graficar los valores de X y de Y y la gráfica daría la estructura de la función Escalón.</span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><b>Ya por ultimo</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">En términos sencillos esta Función es la integral definida desde -Infinito hasta el valor de la variable (x) de la Función Impulso.</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;">Para terminar este punto anexo un video donde explican esta función:</span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
<div class="separator" style="clear: both; text-align: center;">
<span style="font-family: Arial, Helvetica, sans-serif;"><iframe allowfullscreen='allowfullscreen' webkitallowfullscreen='webkitallowfullscreen' mozallowfullscreen='mozallowfullscreen' width='320' height='266' src='https://www.youtube.com/embed/83flWdX9vgw?feature=player_embedded' frameborder='0'></iframe></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div>
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<span style="font-family: Arial, Helvetica, sans-serif;"><b>Referencias</b></span><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /><a href="http://es.wikipedia.org/wiki/Funci%C3%B3n_unitaria_de_Heaviside"><span style="color: #20124d;">http://es.wikipedia.org/wiki/Funci%C3%B3n_unitaria_de_Heaviside</span></a></span><br />
<a href="http://ejerciciosdefunciones.com/ejemplo-de-funcion-escalon/"><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;">http://ejerciciosdefunciones.com/ejemplo-de-funcion-escalon/</span></a><br />
<a href="http://mathworld.wolfram.com/HeavisideStepFunction.html"><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;">http://mathworld.wolfram.com/HeavisideStepFunction.html</span></a><br />
<a href="http://www.wikimatematica.org/index.php?title=Funci%C3%B3n_Heaviside"><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;">http://www.wikimatematica.org/index.php?title=Funci%C3%B3n_Heaviside</span></a><br />
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="color: #660000; font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>Función Rampa</b></span><br />
<div style="text-align: center;">
<img height="226" src="https://encrypted-tbn0.google.com/images?q=tbn:ANd9GcSoP_BFElGuYITAiDMXZLolcsNIzhaa2j-oRFCA8njP1qaNgsY-9w" width="400" /></div>
<span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>
<span style="background-color: white; line-height: 19.200000762939453px; text-align: start;"><span style="font-family: Arial, Helvetica, sans-serif;">Se la da el nombre de "función rampa" gracias a la forma de su gráfica.</span></span><br />
<span style="background-color: white; line-height: 19.200000762939453px; text-align: start;"><span style="font-family: Arial, Helvetica, sans-serif;">w</span></span><br />
<span style="background-color: white; line-height: 19.200000762939453px; text-align: start;"><span style="font-family: Arial, Helvetica, sans-serif;">La Función '<b>r(t)</b>' se define como<span style="color: #20124d;"><b> 'El valor de r(t) es igual a t si t es mayor o igual a 0 y r(t) es igual a 0 si t es menor que 0'</b></span>:</span></span><br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhP5lP4gbzpQW0CEdIjPZyBgvZgKblkMe_vpEuVo1lr_lIQ7yVJqtuWq5lpSmuAvhzFgUl2SC4XqDQeY8d5FMpAzLnz85s80DbZytx5sD3THw2yb4i1ii6L6-_kS4ewuIMhOa7UE_bjtE/s1600/Pantallazo+del+2012-08-23+02:27:06.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="95" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjhP5lP4gbzpQW0CEdIjPZyBgvZgKblkMe_vpEuVo1lr_lIQ7yVJqtuWq5lpSmuAvhzFgUl2SC4XqDQeY8d5FMpAzLnz85s80DbZytx5sD3THw2yb4i1ii6L6-_kS4ewuIMhOa7UE_bjtE/s320/Pantallazo+del+2012-08-23+02:27:06.png" width="320" /></a></div>
<span style="font-family: Arial, Helvetica, sans-serif;">La derivada de esta función es igual a la de la Función Escalón.</span><br />
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<span style="background-color: white; font-family: sans-serif; line-height: 19.200000762939453px; text-align: start;"><b>Referencias</b></span><br />
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<a href="http://es.wikipedia.org/wiki/Funci%C3%B3n_rampa"><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;">http://es.wikipedia.org/wiki/Funci%C3%B3n_rampa</span></a><br />
<a href="http://ingeniedia.blogspot.mx/2010/10/funcion-rampa.html"><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;">http://ingeniedia.blogspot.mx/2010/10/funcion-rampa.html</span></a><br />
<a href="http://www.scribd.com/doc/22359951/GRAFICO-DE-UNA-FUNCION-UTILIZANDO-SENALES-ELEMENTALES"><span style="color: #20124d; font-family: Arial, Helvetica, sans-serif;">http://www.scribd.com/doc/22359951/GRAFICO-DE-UNA-FUNCION-UTILIZANDO-SENALES-ELEMENTALES</span></a><br />
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<span style="background-color: white; line-height: 19.200000762939453px; text-align: start;"><span style="color: #660000; font-family: Arial, Helvetica, sans-serif; font-size: large;"><b>En General</b></span></span><br />
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<span style="font-family: Arial, Helvetica, sans-serif;">En base a todo lo anterior tenemos que la Función Escalón es la Integral de la de Impulso y la de Rampa es la Integral de la de Escalón, por lo tanto estas Funciones y en pocas palabras cada función depende de otra, la única que no depende de ninguna es la de Impulso.</span></div>
guelmi_rickhttp://www.blogger.com/profile/00075155021794486805noreply@blogger.com1tag:blogger.com,1999:blog-3668401867087218235.post-71343922032650976232012-08-12T22:24:00.003-07:002012-08-22T18:52:50.346-07:00Entrada # 1 Cripto<span style="font-family: Arial, Helvetica, sans-serif;"><b>Hay les va lo mio, una pista es parte de la letra de una canción.</b></span><br />
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