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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Multiple solutions for a Kirchhoff-type fractional coupled problem with p-Laplacian
p-Laplacian算子 Kirchhoff型分数 耦合问题 多重解
2023/11/13
We discuss a class of two-parameters coupled Kirchhoff-type fractional differential equations. Two differentiated methods are used to prove the existence of two solutions to the equation. The fundamen...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A 1.344-approximation algorithm for the vertex cover problem
顶点覆盖问题 1.344 近似算法
2023/12/11
We present an algorithm for the vertex cover problem by combining the LP relaxation and the random edge-reductions. The algorithm has the expected approximation ratio of 1.344.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The Minkowski problem in Gaussian probability space
高斯概率空间 闵可夫斯基问题 广义相对论
2023/5/6
The classical Minkowski problem, which asks for the characterization of surface area measure in Euclidean space with Lebesgue measure, largely motivated the development of elliptic PDEs throughout the...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Boundary expansion in the Loewner-Nirenberg problem
Loewner-Nirenberg problem 边界展开 利玛窦曲率
2023/4/28
We first review some classical results of the Loewner-Nirenberg problem. Then we discuss the characteristics of boundary expansion and its applications in studying the negativity of Ricci curvatures o...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Solving hidden number problem with lattice sieving
晶格筛分 隐数问题 格约简算法
2023/4/28
Lattice reduction algorithms have been proved to be one of the most powerful and versatile tools in public key cryptanalysis. In this talk, we primarily concentrate on lattice attacks against (EC)DSA ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Multiple solutions for semilinear subelliptic Dirichlet problem
半线性 次椭圆 狄利克雷问题 多种解
2023/4/27
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Multiple solutions for semilinear subelliptic Dirichlet problem。
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...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Inverse problem for the harmonic measure
谐波测量 反问题 双曲群
2023/4/17
Sample paths of a random walk on a hyperbolic group are known to converge to the Gromov boundary. The distribution of the exit point is called the harmonic measure. I will discuss the following invers...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Some recent progress on the gradient estimates for the insulated conductivity problem
绝缘 电导率 梯度估计 椭圆偏微分方程
2023/4/17
In this talk, I will describe an elliptic PDE that models electric conduction, and the electric field concentration phenomenon between closely spaced inclusions of high contrast. In the first part, I ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Pandora Box Problem with Nonobligatory Inspection: Hardness and Approximation Scheme
潘多拉盒问题 非强制性检查 硬度 近似方案
2023/4/14
Weitzman (1979) introduced the Pandora Box problem as a model for sequential search with inspection costs, and gave an elegant index-based policy that attains provably optimal expected payoff. In vari...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Convexity, Uniqueness, and Stability of the Regular Shock Reflection-diffraction Problem
规则冲击 反射衍射问题 凸性 唯一性 稳定性
2023/4/17
We will talk about our recent results on the convexity, uniqueness, and stability of regular reflection solutions for the potential flow equation in a natural class of self-similar solutions. The appr...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stability conditions for a free boundary problem of 3-D compressible Euler equations coupled with a nonlinear Poisson equation
三维 可压缩欧拉方程 耦合 非线性泊松方程 自由边界问题 稳定性条件
2023/4/18
In this talk, I will discuss the stability conditions for a free boundary problem of compressible Euler equations coupled with a nonlinear Poisson equation of electric potential. Under those stability...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On Lehmer's problem
莱默问题 代数闭包 小Weil高度
2023/4/19
Let x be an algebraic number. Lehmer's problem predicts that the product of the degree of x and the Weil height of x is bounded by an absolute constant. The basic idea to tackle this problem is to stu...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：ENERGY, POINTWISE, AND FREE BOUNDARY APPROXIMATION OF THE OBSTACLE PROBLEM FOR NONLOCAL OPERATORS
非局部 算子障碍物 自由边界 近似
2023/4/28
We consider the obstacle problem for a nonlocal elliptic operator, like the integral fractional Laplacian of order $s \in (0,1)$. We derive regularity results in weighted Sobolev spaces, where the wei...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stokes phenomenon and isomonodromy deformation equations: Explicit solution to the Riemann-Hilbert problem and integrability of the isomonodromy equation
斯托克斯现象 等单向变形方程 黎曼-希尔伯特问题 显式解 单场方程 可积性
2023/5/6
Stokes phenomenon states that the asymptotic behavior of functions can differ in different regions of the complex plane, and that these differences can be described in a quantitative way. These quanti...