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We use Young’s raising operators to give short and uniform proofs
of several well known results about Schur polynomials and symmetric functions, starting from the Jacobi-Trudi identity.
An old friend revisited: Countable models of ω-stable theories
Countable models ω-stable theories
2015/9/25
We work in the context of ω-stable theories. We obtain a natural,
algebraic equivalent of ENI-NDOP and discuss recent joint proofs with
S. Shelah that if an ω-stable theory has either ENI-DOP or is ...
A Bahri-Lions Theorem and a Brezis-Nirenberg Problem Revisited
Bahri-Lions Theorem Brezis-Nirenberg
2015/4/3
A Bahri-Lions Theorem and a Brezis-Nirenberg Problem Revisited.
The homological finiteness length of a group G is the maximal length (counting from 0) of a partial resolution by finitely generated projective modules of the trivial ZG-module Z. It is closely relate...
Lowering topological entropy over subsets revisited
entropy principal extension lowerable hereditarily lowerable
2012/6/19
Let $(X, T)$ be a topological dynamical system. Denote by $h (T, K)$ and $h^B (T, K)$ the covering entropy and dimensional entropy of $K\subseteq X$, respectively. $(X, T)$ is called D-{\it lowerable}...
The main goal of this article is to put some known results in a common perspective and to simplify their proofs. We start with a simple proof of a result of Vereshchagin saying that $\limsup_n C(x|n)$...
"Spectral implies Tiling" for Three Intervals Revisited
Three Intervals Revisited Classical Analysis and ODEs Algebraic Geometry
2011/9/21
Abstract: In \cite{BCKM} it was shown that "Tiling implies Spectral" holds for a union of three intervals and the reverse implication was studied under certain restrictive hypotheses on the associated...
Bohr's inequality revisited
Bohr's inequality revisited Functional Analysis Operator Algebras
2011/8/26
Abstract: We survey several significant results on the Bohr inequality and presented its generalizations in some new approaches. These are some Bohr type inequalities of Hilbert space operators relate...
Proving the existence of an operator that connects non-perturbed states to perturbed states, an alternative derivation of the Dalgarno-Lewis method is given.To illustrate that the Dalgarno-Lewis metho...
Cohen-Macaulayness of bipartite graphs, revisited
edge ideal of a graph Cohen-Macaulay bipartite graph
2011/1/17
Cohen-Macaulayness of bipartite graphs is investigated by several mathematicians and has been characterized combinatorially. In this note, we give some different combi-natorial conditions for a bipart...
We introduce two new heuristic ideas concerning the spectrum of a Laplacian,and we give theorems and conjectures from the realms of manifolds, graphs and fractals that validate these heuristics.
Relations among tautological classes revisited
moduli spaces tautological algebra Abel–Jacobi map
2011/1/19
We give a simple generalisation of a theorem of Morita [6, 7], which leads to a great number of relations among tautological classes on moduli spaces of curves.
The AKNS Hierarchy Integrability Analysis Revisited: The Vertex Operator Approach and its Lie-Algebraic Structure
the AKNS hierarchy Lax type integrability Lie-algebraic approach
2011/3/2
A regular approach to studying the Lax type integrability of the AKNS hierarchy of nonlinear Lax type integrable dynamical systems in the vertex operator representation is devised.
The AKNS Hierarchy Integrability Analysis Revisited: The Vertex Operator Approach and its Lie-Algebraic Structure
the AKNS hierarchy Lax type integrability Lie-algebraic approach vertex operators
2010/12/28
A regular approach to studying the Lax type integrability of the AKNS hierarchy of nonlinear Lax type integrable dynamical systems in the vertex operator representation is devised.
Affine Bodies Revisited. Constraints, Symmetry, Analytical Methods and Some Perspectives
Affine Bodies Revisited Constraints Symmetry
2011/2/25
The purpose of this publication is to derive and discuss equations of mo-tion of affinely rigid (homogeneously deformable) body moving in Eu-clidean space of general dimension n. Our aim is to present...