Displaying similar documents to “An explicit solution of coupled viscous Burgers' equation by the decomposition method.”

The generalized equations of Riccati and their applications to the theory of linear differential equations

T. Iwiński

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CONTENTSIntroduction.............................................................................................................................. 31. Definition of the Riccati equation of the n-th order....................................................... 62. Theorems on the existence of solutions of R equations. Relations between the solutions of linear differential equations and the solutions of the corresponding R equations..................................................................................................

Conservation Rules of Direct Sum Decomposition of Groups

Kazuhisa Nakasho, Hiroshi Yamazaki, Hiroyuki Okazaki, Yasunari Shidama (2016)

Formalized Mathematics

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In this article, conservation rules of the direct sum decomposition of groups are mainly discussed. In the first section, we prepare miscellaneous definitions and theorems for further formalization in Mizar [5]. In the next three sections, we formalized the fact that the property of direct sum decomposition is preserved against the substitutions of the subscript set, flattening of direct sum, and layering of direct sum, respectively. We referred to [14], [13] [6] and [11] in the formalization. ...