Concentration inequalities for random fields via coupling

We present a new and simple approach to concentration inequalities in the context of dependent random processes and random fields. Our method is based on coupling and does not use information inequalities. In case one has a uniform control on the coupling, one obtains exponential concentration inequalities. If such a uniform control is no more possible, then one obtains polynomial or stretched-exponential concentration inequalities. Our abstract results apply to Gibbs random fields, both at high and low temperatures and in particular to the low-temperature Ising model which is a concrete example of non-uniformity of the coupling.      

切变模量和转动惯量实验的改进

设计了一种基于垂直轴定理的新型吊钩,对切变模量和转动惯量实验进行了改进,使之成为既可测定金属丝切变模量和环、柱等刚体的转动惯量,又可验证反映转动惯量重要性质的平行轴定理及垂直轴定理的多功能实验仪.     

Hawking Absorption and Planck Absolute Entropy of Kerr-Newman Black Hole

We find the existence of a quantum thermal effect, “Hawking absorption.” near the inner horizon of the Kerr–Newman black hole. Redefining the entropy, temperature, angular velocity, and electric potential of the black hole, we give a new formulation of the Bekenstein–Smarr formula. The redefined entropy vanishes for absolute zero temperature of the black hole and hence it is interpreted as the Planck absolute entropy of the KN black hole.     

On the Weak Invariance Principle for Stationary Sequences under Projective Criteria

In this paper, we study the central limit theorem and its weak invariance principle for sums of a stationary sequence of random variables, via a martingale decomposition. Our conditions involve the conditional expectation of sums of random variables with respect to the distant past. The results contribute to the clarification of the central limit question for stationary sequences. Magda Peligrad is supported in part by a Charles Phelps Taft research support grant at the Univeristy of Cincinnati and the NSA grant H98230-05-1-0066.     

Liouville theorem and coupling on negatively curved Riemannian manifolds

By using probabilistic approaches, Liouville theorems are proved for a class of Riemannian manifolds with Ricci curvatures bounded below by a negative function. Indeed, for these manifolds we prove that all harmonic functions (maps) with certain growth are constant. In particular, the well-known Liouville theorem due to Cheng for sublinear harmonic functions (maps) is generalized. Moreover, our results imply the Brownian coupling property for a class of negatively curved Riemannian manifolds. This leads to a negative answer to a question of Kendall concerning the Brownian coupling property.     

Multiple positive solutions for one-dimensional p-Laplacian boundary value problems

By means of the Leggett-Williams fixed-point theorem, criteria are developed for the existence of at least three positive solutions to the one-dimensional p-Laplacian boundary value problem, ((y′))′ + g(t)f(t,y) = 0, y(0) - B₀(y′(0)) = 0, y(1) + B₁(y′(1)) = 0, where (v) |v|^p−2v, p > 1.     

两类拟共形映射的掩盖定理

In this paper we define two classes of quasiconformal mappings,and study their covering properties by methods of module.We obtain some new results.In the meantime,we give new methods to prove Koebe 1/2 covering theorem on convex conformal mappings.     

A new trust region technique for the maximum weight clique problem

A new simple generalization of the Motzkin-Straus theorem for the maximum weight clique problem is formulated and directly proved. Within this framework a trust region heuristic is developed. In contrast to usual trust region methods, it regards not only the global optimum of a quadratic objective over a sphere, but also a set of other stationary points of the program. We formulate and prove a condition when a Motzkin-Straus optimum coincides with such a point. The developed method has complexity O(n³), where n is the number of vertices of the graph. It was implemented in a publicly available software package QUALEX-MS.Computational experiments indicate that the algorithm is exact on small graphs and very efficient on the DIMACS benchmark graphs and various random maximum weight clique problem instances.     

二阶非线性微分方程的斜周期边值问题

In this paper a uniqueness theorem for a skewperiodic boundary value problem is obtained. By using the optimal control method, we derive the best estimate for the integration mean ensuring that the results hold.     

Darboux transformation and solitons of Yang-Mills-Higgs equations in R2,1

The Darboux transformations for soliton equations are applied to the Yang-Mills-Higgs equations.New solutions can be obtained from a known one via universal and purely algebraic formulas. SU(N) soliton solutions are constructed with explicit formulas. The interaction of solitons is described by the splitting theorem:each p-soliton is splitting into p single solitons asymptotically as t →±∞.