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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...
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.
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...
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
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...
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...
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 ...
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...
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...
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...
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...
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...
In this talk we will discuss a Steklov eigenvalue problem on an exterior Euclidean domain. We will present sharp lower and upper bounds for its first eigenvalue under various conditions on the domain....
A positive integer n is called a θ-congruent number if n sin θ is the area of a triangle with rational side lengths and with an angle θ. Markov chains play a key role in the study of the distribution ...

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