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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Liouville Properties on gradient shrinking Ricci solitons with constant scalar curvature
常标量 曲率梯度收缩 Ricci孤子 Liouville性质
2023/11/13
In this talk we show that bounded harmonic functions are constant on gradient shrinking Ricci solitons with CSC by frequency function method. As an application, we show that the space of harmonic func...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Recent Developments in Constant Mean Curvature Hypersurfaces
恒定 平均曲率 超曲面
2023/4/13
We will survey some recent existence theory of closed constant mean curvature hypersurfaces using the min-max method. We hope to discuss some old and new open problems on this topic as well.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The constant rank theorem and its applications
常秩定理 半线性方程组 规定曲率 克里斯托费尔-闵可夫斯基问题 魏因加滕曲率问题
2023/5/6
The constant rank theorem was initially developed by Caffarelli-Friedman in 1985 in two-dimensions for convex solutions of semilinear equations. Later, Korevaar-Lewis extended the result to higher dim...
The Asymptotic Minimax Constant for Sup-Norm Loss in Nonparametric Density Estimation
Density estimation exact constant optimal recovery uniform norm risk white noise
2015/8/25
We develop the exact constant of the risk asymptotics in the uniform norm for density estimation. This constant has first been found for nonparametric regression and for signal estimation in Gaussian ...
THE LOOPING CONSTANT OF Zd
LOOPING CONSTANT Zd
2015/8/14
The looping constant ξ(Zd) is the expected number of neighbors of the origin that lie on the infinite loop-erased random walk in Zd.Poghosyan, Priezzhev and Ruelle, and independently, Kenyon and Wilso...
A Constant Factor Approximation Algorithm for Event-Based Sampling
Event-Based Sampling Approximation Algorithm
2015/6/19
We consider a control system in which sensor data is transmitted from the plant to a receiver over a communication channel, and the receiver uses the data to estimate the state of the plant. Using a f...
We develop a nonlinear spectral graph theory, in which the Laplace
operator is replaced by the 1 Laplacian ∆1
. The eigenvalue problem is to
solve a nonlinear system, involving a set valued f...
An Explicit Harmonic Extension for the Constant-like Basis and Its Application to Domain Decompositions
domain decomposition coarse subspace constant-like basis nearly harmonic extension preconditioner inexact solvers condition number
2012/8/8
In this paper we are concerned with substructuring methods for the second-order
elliptic problems in three-dimensional domains. We 痳st design a simple and completely
explicit nearly harmonic extensi...
Consistent testing for a constant copula under strong mixing based on the tapered block multiplier technique
Change point test Copula Empirical copula process Nonparametric estimation Time series Strong mixing Multiplier central limit theorem
2012/6/29
Considering multivariate strongly mixing time series, nonparametric tests for a constant copula with specified or unspecified change point (candidate) are derived; the tests are consistent against gen...
On complete constant mean curvature vertical multigraphs in E(κ,τ)
multigraphs constant mean curvature homogeneous spaces
2012/6/29
We prove that any complete surface with constant mean curvature in a homogeneous space E(\kappa,\tau) which is transversal to the vertical Killing vector field is, in fact, a vertical graph. As a cons...
Multifractal analysis of some multiple ergodic averages for the systems with non-constant Lyapunov exponents
Multifractal analysis of some multiple ergodic averages non-constant Lyapunov exponents Dynamical Systems
2012/6/27
We study certain multiple ergodic averages of an iterated functions system generated by two contractions on the unit interval. By using the dynamical coding ${0,1}^{\mathbb{N}}$ of the attractor, we c...
The normality of digits in almost constant additive functions
Normal numbers additive function Selberg-Delange method
2012/6/21
We consider numbers formed by concatenating some of the base b digits from additive functions f(n) that closely resemble the prime counting function \Omega(n). If we concatenate the last
The Yamabe constant on noncompact manifolds
The Yamabe constant noncompact manifolds Differential Geometry
2012/6/19
We prove several facts about the Yamabe constant of Riemannian metrics on general noncompact manifolds and about S. Kim's closely related "Yamabe constant at infinity". In particular we show that the ...
Absolute continuity of the best Sobolev constant of a bounded domain
Absolute continuity Lipschitz continuity p-Laplacian Rayleigh quotient Sobolev best constants
2012/6/7
Let $\lambda_{q}:=\inf{\Vert\nabla u\Vert_{L^{p}(\Omega)}^{p}/\Vertu\Vert_{L^{q}(\Omega)}^{p}:u\in W_{0}^{1,p}(\Omega)\setminus{0}} $, where $\Omega$ is a bounded and smooth domain of $\mathbb{R}^{N},...
Quaternary Constant-Composition Codes with Weight Four and Distances Five or Six
Quaternary Constant-Composition Codes Weight Four Distances Five or Six
2012/3/1
The sizes of optimal constant-composition codes of weight three have been determined by Chee, Ge and Ling with four cases in doubt. Group divisible codes played an important role in their construction...