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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stable commutator length and linear programming
换向器长度 线性规划 曲面 拓扑优化
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2023/4/18
Several topological optimization problems involving surfaces can be turned into linear programming problems. In the case of stable commutator length, this was first discovered by Danny Calegari in the...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Topological optimization and the stable commutator length
拓扑优化 稳定换向器 长度
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2023/4/19
It is a relatively recent discovery in geometric topology that optimization problems of certain topological complexity are connected to important geometric and topological information. One example is ...
Odd-order Cayley graphs with commutator subgroup of order pq are hamiltonian
Cayley graph hamiltonian cycle commutator subgroup
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2012/5/9
We show that if G is a nontrivial, finite group of odd order, whose commutator subgroup [G,G] is cyclic of order p^m q^n, where p and q are prime, then every connected Cayley graph on G has a hamilton...
The poset of the nilpotent commutator of a nilpotent matrix
Jordan type nilpotent matrix commutator poset
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2012/2/29
Fix an n by n nilpotent matrix B with entries in an infinite field k. Assume that B is in Jordan canonical form with associated Jordan block partition P. It is well known that the nilpotent commutator...
Multiple Commutator Formulas
Multiple Commutator Formulas Rings and Algebras
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2011/9/9
Abstract: Let A be a quasi-finite R-algebra (i.e., a direct limit of module finite algebras) with identity. Let I_i, i=0,...,m, be two-sided ideals of A, \GL_n(A,I_i) the principal congruence subgroup...
Relative commutator calculus in Chevalley groups
Relative commutator calculus Chevalley groups Rings and Algebras
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2011/9/9
Abstract: We revisit localisation and patching method in the setting of Chevalley groups. Introducing certain subgroups of relative elementary Chevalley groups, we develop relative versions of the con...
The ternary commutator obstruction for internal crossed modules
cross-effect commutator internal crossed module semi-abelian category
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2011/8/25
Abstract: We study the notion of internal crossed module in terms of cross-effects of the identity functor. These cross-effects give rise to a concept of commutator which allows a description of inter...
Outer Commutator Multiplier and Capability of Finitely Generated Abelian Groups
Outer Commutator Multiplier Capability of Finitely Generated Abelian Groups
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2011/2/21
We present an explicit structure for the Baer invariant of a finitely generated abelian group with respect to the variety [Nc1 ,Nc2], for all c2 ≤ c1 ≤ 2c2.
Rescaled Mourre's commutator theory, application to Schrödinger operators with oscillating potential
Mourre’s commutator theory Mourre estimate limiting absorption principle
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2011/1/18
We present a variant of Mourre’s commutator theory. We apply it to prove the limiting absorption principle for Schr¨odinger operators with a perturbedWigner-Von Neumann potential at suitable energies....
A commutator method for the diagonalization of Hankel operators
Hankel operators spectrum and eigenfunctions explicit solutions
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2010/12/1
We present a method for the explicit diagonalization of some Han-kel operators. This method allows us to recover classical results on the diag-onalization of Hankel operators with the absolutely conti...
n-Commutator Groups
Commutator subgroup irreducible characters
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2010/3/1
A sufficient condition such that any element of G' (the commutator subgroup of G) can be represented as a product of n commutators, was studied in \cite{GAL62}. In this article we study a necessary an...