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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Arnold conjecture and advances in Floer theory
阿诺德猜想 弗洛尔理论 哈密顿微分同胚
2023/5/4
In 1960s, Arnold conjectured that the number of fixed points of a Hamiltonian diffeomorphism of a symplectic manifold should be (much) greater than its counterpart for a general diffeomorphism. This c...
A Differential Equation for Modeling Nesterov’s Accelerated Gradient Method:Theory and Insights
Differential Equation Modeling Nesterov’s Accelerated Gradient Method
2015/7/8
We derive a second-order ordinary differential equation (ODE), which is the limit of Nesterov’s accelerated gradient method. This ODE exhibits approximate equivalence to Nesterov’s scheme and thus can...
Analyzing Weighted $\ell_1$ Minimization for Sparse Recovery with Nonuniform Sparse Models\footnote{The results of this paper were presented in part at the International Symposium on Information Theory, ISIT 2009}
Analyzing Weighted $\ell_1$ Minimization Sparse Recovery International Symposium Information Theory
2010/12/8
In this paper we introduce a nonuniform sparsity model and analyze the performance of an optimized weighted ℓ1 minimization over that sparsity model. In particular, we focus on a model where the...
Intersection Theory for Generic Differential Polynomials and Differential Chow Form
Generic Differential Polynomials Differential Chow Form
2010/11/26
In this paper, an intersection theory for generic differential polynomials is presented. The intersection of an irreducible differential variety of dimension d and order h with a generic differential ...
This paper is an overview of our works which are related to investigations of the integrability of natural Hamiltonian systems with homogeneous potentials and Newton's equations with homogeneous veloc...
GROWTH AND OSCILLATION THEORY OF NON-HOMOGENEOUS COMPLEX DIFFERENTIAL EQUATIONS WITH ENTIRE COEFFICIENTS
Differential equations Order of growth Exponent of convergence of distinct zeros Wiman-Valiron theory
2008/11/26
In this paper, we investigate the growth and the complex oscillation theory of the
linear differential equation f (k)+Ak¡1 f (k¡1)+:::+A1 f 0 +A0 f =F, where A0;A1; :::;
Ak¡1;F 6&a...
GENERALIZED BOCHNER-HECKE THEOREMS AND APPLICATION TO HOMOGENEOUS DISTRIBUTIONS IN DUNKL’S THEORY
Dunkl transform Bochner-Hecke theorems Dunkl transform of homogeneous distributions
2008/11/25
In this paper we prove generalized Bochner-Hecke theorems for the Dunkl transform
on Rd, and we give an application of these theorems to homogeneous distributions .
C1 modules with respect to a hereditary torsion theory
Torsion theory C1-module closed submodule
2010/2/25
An R-module M is said to be a C1-module if every closed submodule of M is a direct summand. In this paper we introduce and investigate the concept of the t-C1 module for a hereditary torsion theory t ...