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AI-discovered tuning laws explain neuronal population code geometry
Tilbury R +8 more
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CHARACTERIZATION OF SOLVABLE GROUPS AND SOLVABLE RADICAL
International Journal of Algebra and Computation, 2013We give a survey of new characterizations of finite solvable groups and the solvable radical of an arbitrary finite group which were obtained over the past decade. We also discuss generalizations of these results to some classes of infinite groups and their analogues for Lie algebras. Some open problems are discussed as well.
Fritz Grunewald +2 more
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Solvability and approximate solvability of fuzzy relation equations*
International Journal of General Systems, 2003We give here a discussion of approximate solvability of a system of fuzzy relation equations. We demonstrate how problems of interpolation and approximation of fuzzy functions are connected with solvability of systems of fuzzy relation equations. First we explain the general framework, and later on we prove some particular results related to the ...
Irina Perfilieva, Siegfried Gottwald
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Reachability Analysis for Solvable Dynamical Systems
IEEE Transactions on Automatic Control, 2018The reachability problem is one of the most important issues in the verification of hybrid systems. But unfortunately the reachable sets for most of hybrid systems are not computable.
Ting Gan +4 more
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Journal of Group Theory, 2003
A group \(G\) is called \(R^*\)-group if for all \(n>0\) and elements \(g\) and \(x_1,\dots,x_n\) the equation \(g^{x_1 }\cdots g^{x_n }=1\) implies \(g=1\). The following results are proved: (1) if \(G\) is an Abelian-by-nilpotent as well as nilpotent-by-Abelian \(R^*\)-group, then every partial order on \(G\) can be extented to a linear order; (2) if
LONGOBARDI, Patrizia +2 more
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A group \(G\) is called \(R^*\)-group if for all \(n>0\) and elements \(g\) and \(x_1,\dots,x_n\) the equation \(g^{x_1 }\cdots g^{x_n }=1\) implies \(g=1\). The following results are proved: (1) if \(G\) is an Abelian-by-nilpotent as well as nilpotent-by-Abelian \(R^*\)-group, then every partial order on \(G\) can be extented to a linear order; (2) if
LONGOBARDI, Patrizia +2 more
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Applicable Algebra in Engineering, Communication and Computing, 2003
This paper deals with the problem of determining whether a quintic polynomial is solvable, i.e. whether its roots are expressible by repeated radicals. Every irreducible quintic \(f(x)\) can be transformed, by two applications of Tschirnhausen transformations, into a so-called Brioschi quintic or Brioschi resolvent, with a parameter \(Z\) in the ...
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This paper deals with the problem of determining whether a quintic polynomial is solvable, i.e. whether its roots are expressible by repeated radicals. Every irreducible quintic \(f(x)\) can be transformed, by two applications of Tschirnhausen transformations, into a so-called Brioschi quintic or Brioschi resolvent, with a parameter \(Z\) in the ...
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On π-Solvable and Locally π-Solvable Groups with Factorization
Ukrainian Mathematical Journal, 2001Summary: We prove that in a locally \(\pi\)-solvable group \(G=AB\) with locally normal subgroups \(A\) and \(B\) there exist pairwise permutable Sylow \(\pi'\)- and \(p\)-subgroups \(A_{\pi'}\), \(A_p\) and \(B_{\pi'}\), \(B_p\), \(p\in\pi\), of the subgroups \(A\) and \(B\), respectively, such that \(A_{\pi'}B_{\pi'}\) is a Sylow \(\pi'\)-subgroup of
Chernikov, N. S., Putilov, S. V.
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