Deformations of functionals and bifurcations of extremals

We study homology characteristics of critical values and extremals of Lipschitz functionals defined on bounded closed convex subsets of a reflexive space that are invariant under deformations. Sufficient conditions for the existence of a bifurcation point of a multivalued potential operator (the switch principle for the typical number of an extremal) are established.     

Optimal reconstruction of the solution of the wave equation from inaccurate initial data

In the present paper, we consider the problem of the optimal reconstruction of the solution of the wave equation from the approximate values of the Fourier coefficients of the function specifying the initial form of the string. For an operator defined on the weight space of vectors from l ₂, we present the solution of the more general problem of reconstruction from the approximate values of the coordinates of these vectors.     

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.      

The Generalized West Decomposition of Operators and Other Compact Perturbation Problems

This paper introduces the concept of the generalized Riesz operators and the concept of the generalized West decomposition of a general operator which generalizes the definition of the West decomposition of Riesz operators, and proves that the following three statements are equivalent on a general Banach space： （a） Every generalized Riesz operator has the generalized West decomposition; （b） Every operator makes strong Stampfli theorem true; Every operator has Apostol＇s compact correction.     

About Regularity of Collections of Sets

The paper continues investigations of stationarity and regularity properties of collections of sets in normed spaces. It contains a summary of different characterizations (both primal and dual) of regularity and a list of sufficient conditions for a collection of sets to be regular.     

Isomorphisms of fiber spaces over Teichmüller spaces

We will be mainly concerned with some important fiber spaces over Teichmuller spaces, including the Bers fiber space and Teichmuller curve, establishing an isomorphism theorem between "punctured" Teichmuller curves and determining the biholomorphic isomorphisms of these fiber spaces.     

Nonlinear Time Series Analysis Since 1990:Some Personal Reflections

Abstract I reflect upon the development of nonlinear time series analysis since 1990 by focusing on five majorareas of development. These areas include the interface between nonlinear time series analysis and chaos,thenonparametric/semiparametric approach,nonlinear state space modelling,financial time series and nonlinearmodelling of panels of time series.     

一类多线性积分算子的端点有界性

本文对一类相关于非卷积型算子的多线性算子,证明了其在端点情形上的有界性,该算子包括Littlewood-Paley算子和Marcinkiewicz算子．     

微型热驱动热声热机热端换热器的优化设计

该文基于热声环境,采用厘米级扁管和deltaE数值计算对微型热声换热器进行了优化设计。