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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On the Riemann-Hilbert problem of confluent hypergeometric systems and Seiberg-Witten curves
超几何系统 塞伯格-维滕曲线 黎曼-希尔伯特问题
2023/4/21
This talk first solves explicitly a Riemann-Hilbert problem of confluent hypergeometric systems. It then conjectures and proves a special case that the WKB approximation of the monodromy data of confl...
The planar circular restricted three body problem in the lunar case
The planar circular restricted three body problem lunar case
2015/3/18
The course is a short introduction to some aspects of the simplest non-integrable three body problem, the study of which goes back to the seminal works of Hill, Poincar′e and Birkhoff. After Goursat (...
On the Muskat problem: global in time results in 2D and 3D
Porous media incompressible ows uid interface global existence.
2014/4/3
This paper considers the three dimensional Muskat problem in the stable regime.We obtain a conservation law which provides an L2 maximum principle for the uid interface. We also show global in time ex...
On the Complexity of 2D Discrete Fixed Point Problem
Complexity 2D Discrete Fixed Point Problem
2012/12/3
While the 3-dimensional analogue of Sperner’s problem in the plane was known to be complete in class PPAD, the complexity of 2D-SPERNER itself is not known to be PPAD-complete or not. In this paper, w...
On the contact equivalence problem of second order ODEs which are quadratic with respect to the second order derivative
On the contact equivalence problem of second order ODEs quadratic second order derivative Differential Geometry
2012/6/19
In the present paper we establish the necessary and sufficient conditions for two ordinary differential equations of the form $y"{}^2+A(x,y,y') y"+B(x,y,y')=0$ to be equivalent under the action of the...
Bifurcation and local rigidity of homogeneous solutions to the Yamabe problem on spheres
homogeneous solutions Yamabe problem spheres Differential Geometry
2011/9/21
Abstract: We study existence and non existence of constant scalar curvature metrics conformal and arbitrarily close to homogeneous metrics on spheres, using variational techniques. This describes all ...
Local Equivalence Problem for Sub-Riemannian Structures
Sub-Riemannian Structures Differential Geometry
2011/9/15
Abstract: We solve the local equivalence problem for sub-Riemannian structures on (2n + 1)-dimensional manifolds. We show that two sub-Riemannian structures are locally equivalent if and only if? thei...
On Arnold's Problem on the Classifications of Convex Lattice Polytopes
Arnold's Problem Classifications of Convex Lattice Polytopes Metric Geometry
2011/9/9
Abstract: In 1980, V.I. Arnold studied the classification problem for convex lattice polygons of given area. Since then this problem and its analogues have been studied by B'ar'any, Pach, Vershik, Liu...
Calabi-Yau Problem for Legendrian curves in C^3 and applications
Calabi-Yau Problem Legendrian curves C^3 and applications
2011/8/22
Abstract: We construct a complete, bounded Legendrian immersion in C^3. As direct applications of it, we show the first examples of a weakly complete bounded flat front in hyperbolic 3-space, a weakly...
Positive solutions of singularly perturbed nonlinear elliptic problem on Riemannian manifolds with boundary
Positive solutions of singularly perturbed nonlinear elliptic Riemannian manifolds boundary
2011/2/28
Let (M, g) be a smooth connected compact Riemannian manifold of finite dimension n ≥ 2 with a smooth boundary @M. We consider the problem −"2gu + u = |u|p−2u, u > 0 on M, @u @= 0 on @M w...
On the eigenvalue problem for a particular class of finite Jacobi matrices
the eigenvalue problem finite Jacobi matrices
2010/11/11
A function $\mathfrak{F}$ with simple and nice algebraic properties is defined on a subset of the space of complex sequences. Some special functions are expressible in terms of $\mathfrak{F}$, first ...
Optimal anisotropic three-phase conducting composites: Plane problem
multimaterial composites optimal microstructures bounds for effective properties
2010/12/7
The paper establishes tight lower bound for effective conductivity tensor K∗ of two-imensional
three-phase conducting anisotropic composites and defines optimal microstructures. It is assumed t...
The covering radius problem for sets of perfect matchings
Perfect matchings Lovasz local lemma
2010/11/30
Consider the family of all perfect matchings of the complete graph K2n with 2n vertices.Given any collection M of perfect matchings of size s, there exists a maximum number f(n; x) such that if s f(...
Hardness of k-Vertex-Connected Subgraph Augmentation Problem
Network survivability Graph connectivity
2012/12/3
Given a k-connected graph G = (V ,E) and V 伡 V , k-Vertex-Connected Subgraph Augmentation Problem (k-VCSAP) is to find S 伡 V \ V with minimum
cardinality such that the subgraph induced by V 伨 S ...
Worm Problem 的一个新上界
碰触 凸覆盖 递减区
2007/12/13
1966 年, Leo Moser 提出了一个基本的几何问题,即Worm Problem.该问题是指：在平面上寻找一个面积最小的(凸)区域, 使得任何一条长为1的平面曲线都能够通过旋转和平移完全放入该(凸)区域之中.对于要寻找的区域是凸的情形,本文将把目前所知道的最小的上界由0.