{"title":"The Musical Work as a “Manifold”","authors":"","doi":"10.2307/j.ctv4s7jp2.24","DOIUrl":"https://doi.org/10.2307/j.ctv4s7jp2.24","url":null,"abstract":"","PeriodicalId":212444,"journal":{"name":"Powers of Divergence","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117106864","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Derivative IX:","authors":"","doi":"10.2307/j.ctv4s7jp2.25","DOIUrl":"https://doi.org/10.2307/j.ctv4s7jp2.25","url":null,"abstract":"","PeriodicalId":212444,"journal":{"name":"Powers of Divergence","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129614905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Index","authors":"","doi":"10.2307/j.ctv4s7jp2.37","DOIUrl":"https://doi.org/10.2307/j.ctv4s7jp2.37","url":null,"abstract":"","PeriodicalId":212444,"journal":{"name":"Powers of Divergence","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116781153","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Vectors of the Body","authors":"","doi":"10.2307/j.ctv4s7jp2.22","DOIUrl":"https://doi.org/10.2307/j.ctv4s7jp2.22","url":null,"abstract":"","PeriodicalId":212444,"journal":{"name":"Powers of Divergence","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125153824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Derivative VIII:","authors":"","doi":"10.2307/j.ctv4s7jp2.23","DOIUrl":"https://doi.org/10.2307/j.ctv4s7jp2.23","url":null,"abstract":"","PeriodicalId":212444,"journal":{"name":"Powers of Divergence","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133735270","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Derivative IV:","authors":"","doi":"10.2307/j.ctv4s7jp2.14","DOIUrl":"https://doi.org/10.2307/j.ctv4s7jp2.14","url":null,"abstract":"","PeriodicalId":212444,"journal":{"name":"Powers of Divergence","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134522621","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Derivative III:","authors":"","doi":"10.2307/j.ctv4s7jp2.13","DOIUrl":"https://doi.org/10.2307/j.ctv4s7jp2.13","url":null,"abstract":"","PeriodicalId":212444,"journal":{"name":"Powers of Divergence","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128750442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Problem of Resemblance","authors":"","doi":"10.2307/j.ctv4s7jp2.7","DOIUrl":"https://doi.org/10.2307/j.ctv4s7jp2.7","url":null,"abstract":"","PeriodicalId":212444,"journal":{"name":"Powers of Divergence","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126527253","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Continuation of About Derivatives, this module will teach properties so one could find the derivative of more complicated functions
关于导数的延续，这个模块将教授一些性质，以便人们可以找到更复杂函数的导数
{"title":"Derivative II:","authors":"S. Crane","doi":"10.2307/j.ctv4s7jp2.10","DOIUrl":"https://doi.org/10.2307/j.ctv4s7jp2.10","url":null,"abstract":"Continuation of About Derivatives, this module will teach properties so one could find the derivative of more complicated functions","PeriodicalId":212444,"journal":{"name":"Powers of Divergence","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132245341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let Λ γ denote the Dirichlet-to-Neumann map for an electrical network with conductivity γ. By way of the Kirchhoff matrix K = (κ ij), consider the space of conductivities to be a subset of R N ×N , where N is the number of vertices, We donote the map from γ to Λ γ by L. In this note we compute the directional derivative D L of L. A direction in this context is represented by a matrix , with arbitrary real entries, which is symmetric and has row sum 0. where is symmetric, has row sum 0, and K is a Kirchhoff matrix. Let K(t) = A + tt A B + tt B B T + tt T B C + tt C , and Λ(t) = A + tt A − (B + tt B)(C + tt C) −1 (B T + tt T B). Then D L = Λ (0) = A − B C −1 B T − BC −1 T B + BC −1 C C −1 B T. Proof. Let C(t) = C + tt C. Notice C(t)(C(t)) −1 = I. By the product rule C (t)C(t) + C(t)(C(t) −1) = 0, hence (C −1) (0) = −C −1 C C −1. Using the product rule again
设Λ γ表示电导率为γ的电网络的Dirichlet-to-Neumann映射。通过Kirchhoff矩阵K = (κ ij)，考虑电导率空间是R N ×N的一个子集，其中N是顶点数，我们用L表示从γ到Λ γ的映射。在本文中，我们计算L的方向导数D L。在这种情况下，方向由一个矩阵表示，具有任意实数项，它是对称的，行和为0。其中是对称的，行和为0,K是基尔霍夫矩阵。设K(t) = A + tt A B + tt B B t + tt t BC + tt C， Λ(t) = A + tt A - (B + tt B)(C + tt C) - 1 (B t + tt B)，则dl = Λ(0) = A - BC - 1 B t - BC - 1 t B + BC - 1 C C - 1 B t证明。设C(t) = C + tt C，注意C(t)(C(t))−1 = i，根据乘法法则C(t) C(t) + C(t)(C(t)−1)= 0，因此(C−1)(0)= - C−1 C C−1。再次使用乘法法则
{"title":"Derivative I:","authors":"Lemma, Let K = A B B T C","doi":"10.2307/j.ctv4s7jp2.8","DOIUrl":"https://doi.org/10.2307/j.ctv4s7jp2.8","url":null,"abstract":"Let Λ γ denote the Dirichlet-to-Neumann map for an electrical network with conductivity γ. By way of the Kirchhoff matrix K = (κ ij), consider the space of conductivities to be a subset of R N ×N , where N is the number of vertices, We donote the map from γ to Λ γ by L. In this note we compute the directional derivative D L of L. A direction in this context is represented by a matrix , with arbitrary real entries, which is symmetric and has row sum 0. where is symmetric, has row sum 0, and K is a Kirchhoff matrix. Let K(t) = A + tt A B + tt B B T + tt T B C + tt C , and Λ(t) = A + tt A − (B + tt B)(C + tt C) −1 (B T + tt T B). Then D L = Λ (0) = A − B C −1 B T − BC −1 T B + BC −1 C C −1 B T. Proof. Let C(t) = C + tt C. Notice C(t)(C(t)) −1 = I. By the product rule C (t)C(t) + C(t)(C(t) −1) = 0, hence (C −1) (0) = −C −1 C C −1. Using the product rule again","PeriodicalId":212444,"journal":{"name":"Powers of Divergence","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2018-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116985181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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