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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The regularity with respect to domains of the additive eigenvalues of super-quadratic Hamilton-Jacobi equation
超二次 哈密尔顿-雅可比方程 加性特征值域 规律性
2023/4/27
Viewingtheadditiveeigenvaluesasamapwithrespecttodomainperturbationbyscal- ing, we show that this map enjoys some regularity. Precisely, let c(λ) be the additive eigenvalue with respect to (1 + r(λ))Ω,...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A Landscape View of Eigenvalues Approximation
特征值近似 景观视图 无序系统
2023/4/24
Waves of all sorts, including electromagnetic waves, acoustic waves, and mechanical vibrations, play a role in shaping our world. In disordered systems, the transport of waves is hindered, resulting i...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Eigenvalues of boundary value problems with transmission conditions and eigenparameter-dependent boundary conditions
传输条件 本征参数 相关边界条件 边值问题 本征值
2023/5/16
In this talk, we mainly show some eigenvalue properties of second order Sturm-Liouville problems and third-order boundary value problems with both transmission conditions and eigenparameter-dependent ...
Eigenvalues of products of unitary matrices and Lagrangian involutions
Unitary representations Parabolic bundles Lagrangian involutions
2015/12/17
This paper introduces a submanifold of the moduli space of unitary representations of the fundamental group of a puncturedsphere with fixedlocal monodromy. The submanifoldis definedvia products of inv...
FIRST EIGENVALUES OF GEOMETRIC OPERATORS UNDER THE RICCI FLOW
GEOMETRIC OPERATORS UNDER FLOW
2015/8/17
In this paper, we prove that the first eigenvalues of
−∆ + cR (c ≥
1
4
) is nondecreasing under the Ricci flow. We also
prove the monotonicity under the normalized Ricci &...
Method of centers for minimizing generalized eigenvalues
quasiconvex nondifferentiable optimization generalized eigenvalue linear fractional programming analytic center method of centers interior point method logarithmic barrier Newton algorithm path-following method ellipsoidal approximations
2015/8/12
We consider the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices, each of which depends affinely on the decision variables. Although this problem may appear spe...
Convex optimization of graph Laplacian eigenvalues
Graph theory Laplacian matrix Convex optimization Semidefinite pro-gramming Markov chain Distributed averaging Effective resistance
2015/8/10
We consider the problem of choosing the edge weights of an undirected graph so as to maximize or minimize some function of the eigenvalues of the associated Laplacian matrix, subject to some constrain...
We develop bounds for the second largest eigenvalue and spectral gap
of a reversible Markov chain. The bounds depend on geometric quantities
such as the maximum degree, diameter and covering numbe...
On the Eigenvalues of Random Matrices.
New tests of the correspondence between unitary eigenvalues and the zeros of Riemann’s zeta function
Statistical tests random unitary matrix Riemann zeta function data set
2015/7/14
This paper presents some new statistical tests and new conjectures regarding
the correspondence between the eigenvalues of random unitary matrices and
the zeros of Riemann’s zeta function. Global fe...
Linear Functionals of Eigenvalues of Random Matrices
Random unitary matrix the calculation function
2015/7/14
.L.et 1% be a random r~x r~unitary matrix with distribution given
by Haar measure on the unitary group. Using explicit monlerlt calculations,
a general criterion is given for linear cornbinations of...
PATTERNS IN EIGENVALUES: THE 70TH JOSIAH WILLARD GIBBS LECTURE
Unitary matrix value distribution patterns telephone encryption function
2015/7/8
Typical large unitary matrices show remarkable patterns in their eigenvalue distribution. These same patterns appear in telephone encryption, the zeros of Riemann's zeta function, a variety of physics...
Semi-linear equations and principal eigenvalues in unbounded domains
Semi-linear equations principal eigenvalues unbounded domains
2015/4/3
Semi-linear equations and principal eigenvalues in unbounded domains.
Eigenvalues control for a Finsler--Laplace operator
Eigenvalues control Finsler--Laplace operator Differential Geometry
2012/6/27
Using the definition of a Finsler--Laplacian given by the first author, we show that two bi-Lipschitz Finsler metrics have a controlled spectrum. We deduce from that several generalizations of Riemann...
Homological eigenvalues of mapping classes and torsion homology growth for fibered 3--manifolds
Homological eigenvalues mapping classes torsion homology growth fibered 3--manifolds Group Theory
2012/5/9
Let S be an orientable surface with negative Euler characteristic, let \psi\in\Mod(S) be a mapping class of S, and let T_{\psi} be the mapping torus of \psi. We study the action of lifts of \psi on th...