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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：2-representations and 2-vector bundles
2 向量丛 群论
2023/4/13
In this talk I will introduce some basic concepts in higher category and some details of the construction in the first talk. I will introduce crossed modules and the example of strict 2-representation...
On an arbitrary compact Riemann surface, necessary and sufficient conditions are found for the existence of semistable vector bundles with slope between zero and one and a prescribed number of linearl...
Leibniz algebras on symplectic plane and cohomological vector fields
Leibniz algebras symplectic-Poisson geometry anti-cyclic operads Quantum Algebra
2011/9/16
Abstract: By using help of algebraic operad theory, Leibniz algebra theory and symplectic-Poisson geometry are connected. We introduce the notion of cohomological vector field defined on nongraded sym...
Nonsmooth Formulation of the Support Vector Machine for a Neural Decoding Problem
Nonsmooth Formulation Support Vector Machine Neural Decoding Problem
2011/1/18
This paper formulates a generalized classification algorithm with an applica-tion to classifying (or ‘decoding’) neural activity in the brain. Medical doctors and researchers have long been interested...
Vector Groupoids
Brandt groupoid vector groupoid
2011/2/24
The main purpose of this paper is to study the vector groupoids.This is an algebraic structure which combines the concepts of Brandt groupoid and vector space such that these are compatible. The new c...
Semi-stable vector bundles on elliptic curves and the associative Yang-Baxter equation
elliptic curves the associative Yang-Baxter equation
2010/11/23
In this paper we study unitary solutions of the associative Yang--Baxter equation (AYBE) with spectral parameters. We show that to each point $\tau$ from the upper half-plane and an invertible $n \tim...
Multivariate Rogers-Szegö polynomials and flags in finite vector spaces
Multivariate Rogers-Szegö polynomials flags in finite vector spaces
2010/11/9
We give a recursion for the multivariate Rogers-Szeg\"o polynomials, along with another recursive functional equation, and apply them to compute special values. We also consider the sum of all $q$-mu...
A vector minmax problem for controlled Markov chains
A vector minmax problem controlled Markov chains
2010/11/9
The problem of controlling a finite state Markov chain in the presence of an adversary so as to ensure desired performance levels for a vector of objectives is cast in the framework of Blackwell appro...
Subspaces of a para-quaternionic Hermitian vector space
Subspaces para-quaternionic Hermitian vector space
2010/11/19
Let $(\tilde Q,g) $ be a para-quaternionic Hermitian structure on the real vector space $V$. By referring to the tensorial presentation $(V, \tilde{Q},g) \simeq (H^2 \otimes E^{2n}, \mathfrak{sl}(H),\...
Extremal maps in best constants vector theory - Part I: Duality and Compactness
Extremal maps constants vector theory - Part I
2010/11/11
We develop a comprehensive study on sharp potential type Riemannian Sobolev inequalities of order 2 by means of a local geometric Sobolev inequality of same kind and suitable De Giorgi-Nash-Moser est...
The endomorphisms monoid of a homogeneous vector bundle
endomorphisms monoid homogeneous vector bundle
2010/12/14
In this paper we give some properties of the algebraic and geometric structure of the endomorphisms monoid of a homogeneous vector bundle.
These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of one or more complex variables, and so ...
Loss of derivatives for systems of complex vector fields and sums of squares
Loss of derivatives for systems complex vector fields sums of squares
2010/11/29
We discuss, both for systems of complex vector fields and for sums of squares, the phenomenon discovered by Kohn of hypoellipticity with loss of derivatives.MSC: 32W05, 32W25, 32T25
On the Fourier coefficients of 2-dimensional vector-valued modular forms
Fourier coefficients 2-dimensional vector-valued modular forms
2010/11/30
Let : SL(2,Z) → GL(2,C) be an irreducible representation of the modular group such that (T) has finite order N. We study holomorphic vector-valued modular forms F( ) of integral weight associated ...
On the flag f-vector of a graded lattice with nontrivial homology
Flag f-vector graded lattice M¨obius function order complex homology
2011/1/19
It is proved that the Boolean algebra of rank n minimizes the flag f-vector among all graded lattices of rank n, whose proper part has nontrivial top-dimensional homology. The analogous statement for ...