On a Projection from One Co – Invariant Subspace onto Another in Character – Automorphic Hardy Space on a Multiply Connected Domain

In a case of a theory in a unit disk the solution of a problem on the invertibility of an orthogonal projection from one co–invariant subspace of the shift operator onto another turned out to be essential for the solution of the problem on the Riesz basis property of the reproducing kernels and in particular for the solution of the problem on the basis of exponentials in L₂ space on a segment. In the present paper we are dealing with the similar problems in harmonic analysis on a finitely connected domain. Namely we obtain necessary and sufficient conditions for the invertibility of an orthogonal projection from one co – invariant subspace of character – automorphic Hardy space in the domain onto another. The given condition has a form of a Muckenhoupt condition for a certain weight on the boundary of the domain, but essentially depends on a character. Namely, for two fixed character – automorphic inner functions, which define the co – invariant subspaces, the projection may be invertible for one character and not invertible for another.     

Flat Partial Connections on a Three Manifold Equipped with a Codimension One Foliation

Given a compact connected oriented three manifold, equipped with a codimension one foliation, such that the Bott connection on the normal bundle is flat, a 2-form on the space parametrizing flat partial connections on it has been constructed. This form is closed. In the special case where the foliated three manifold is a surface bundle over the circle, this 2-form is identified with a certain 2-form on the parameter space for a class of paths in the representation space for the surface group. The 2-form, in question, on the parameter space for paths is constructed from the natural symplectic form on the representation space for a surface group.     

圆柱壳中圆盘状晶体压力传感器的厚度剪切振动

以电弹性体中叠加于偏场之上的小增量场理论为基础,研究了固定在圆柱壳中的圆盘状晶体谐振器的厚度剪切振动问题,得到了环境压力所诱导的谐振器频率漂移的表达式,该表达式可用于指导压力传感器的优化设计．数值结果表明:频率漂移与环境压力成正比,并且外壳的刚度越小或者压电晶片与外壳厚度之比越小,则压力传感器的灵敏度越高．     

Poisson比为1/2材料中球形空穴突变和球形空穴萌生的分岔问题研究

研究Ｐｏｉｓｓｏｎ比为１／２的Ｈｏｏｋｅ材料中,空穴的突变和萌生现象·求解一个球对称几何非线性弹性力学的移动边界（ｍｏｖｉｎｇｂｏｕｎｄａｒｙ）问题,空穴为球形,远离空穴处为三向均匀拉伸应力状态,在当前构形上列控制方程;在当前构形边界上列边界条件·找到了这个自由边界问题的封闭解并得到空穴半径趋于零时的叉型分岔解·计算结果显示,在位移＿载荷曲线上存在一个切分岔型分岔点（或鞍结点型分岔点、极值型分岔点）,这个分岔点说明在外力作用下空穴会发生突变,即突然“长大”;当球腔半径趋于零时,这个切分岔转化为叉型分岔（或分枝型分岔）,这个叉型分岔可以解释实心球中的空穴萌生现象     

几何分析中的基本概念与原理

本文是根据作者在中国科学院“中德几何分析伙伴小组”成立仪式上的演讲整理而成，主要目的在于通过回顾几何分析中的基本概念及基本定理，了解现阶段的研究情况和将来的研究线路，主要描述黎曼几何与量子场论中的思想，特别特别是极化物理量与几何量产生的变分问题。     

Bolzano's Theorems for Holomorphic Mappings

The existence of a zero for a holomorphic functions on a ball or on a rectangle under some sign conditions on the boundary generalizing Bolzano's ones for real functions on an interval is deduced in a very simple way from Cauchy's theorem for holomorphic functions.A more complicated proof,using Cauchy's argument principle,provides uniqueness of the zero,when the sign conditions on the boundary are strict.Applications are given to corresponding Brouwer fixed point theorems for holomorphic functions.Extensions to holomorphic mappings from Cn to Cn are obtained using Brouwer degree.     

Sampling Schemes for Bayesian Variable Selection in Generalized Linear Models

Bayesian approaches to prediction and the assessment of predictive uncertainty in generalized linear models are often based on averaging predictions over different models, and this requires methods for accounting for model uncertainty. When there are linear dependencies among potential predictor variables in a generalized linear model, existing Markov chain Monte Carlo algorithms for sampling from the posterior distribution on the model and parameter space in Bayesian variable selection problems may not work well. This article describes a sampling algorithm based on the Swendsen-Wang algorithm for the Ising model, and which works well when the predictors are far from orthogonality. In problems of variable selection for generalized linear models we can index different models by a binary parameter vector, where each binary variable indicates whether or not a given predictor variable is included in the model. The posterior distribution on the model is a distribution on this collection of binary strings, and by thinking of this posterior distribution as a binary spatial field we apply a sampling scheme inspired by the Swendsen-Wang algorithm for the Ising model in order to sample from the model posterior distribution. The algorithm we describe extends a similar algorithm for variable selection problems in linear models. The benefits of the algorithm are demonstrated for both real and simulated data.     

On a Generalized Dirichlet Problem for Analytic Family

In this paper, we give the Silov boundary for an analytic family on a bounded strictly pseudoconvex domain or an analytic polyhedron in Cn, and get a necessary and sufficient condition for a generalized Dirichlet problem to be solvable for an analytic family on a bounded holomorphic domain. Especially, we derive that this condition is just that the continuous real boundary value is prescribed on and only on the Silov boundary for an analytic family on a bounded strictly pseudoconvex domain or an analytic polyhedron.     

An iterative procedure for solving integral equations related to optimal stopping problems

We present an iterative algorithm for computing values of optimal stopping problems for one-dimensional diffusions on finite time intervals. The method is based on a time discretization of the initial model and a construction of discretized analogues of the associated integral equation for the value function. The proposed iterative procedure converges in a finite number of steps and delivers in each step a lower or an upper bound for the discretized value function on the whole time interval. We also give remarks on applications of the method for solving the integral equations related to several optimal stopping problems.     

An Extension of Set-Valued Contraction Principle for Mappings on a Metric Space with a Graph and Application

In this paper, we obtain an existence theorem for fixed points of contractive set-valued mappings on a metric space endowed with a graph. This theorem unifies and extends several fixed point theorems for mappings on metric spaces and for mappings on metric spaces endowed with a graph. As an application, we obtain a theorem on the convergence of successive approximations for some linear operators on an arbitrary Banach space. This result yields the well-known Kelisky–Rivlin theorem on iterates of the Bernstein operators on C[0,1].     

Riemannian Foliations and Eigenvalue Comparison

Eigenvalue comparison theorems for the Laplacian on a Riemannian manifold generally give bounds for the first Dirichlet eigenvalue on balls in the manifold in terms of an eigenvalue arising from a geometrically or analytically simpler situation. Cheng's eigenvalue comparison theory assumes bounds on the curvature of the manifold and then compares this eigenvalue to the eigenvalue of a ball in a constant curvature space form. In this paper we examine the basic Laplacian – the appropriate Laplacian on functions that are constant on the leaves of the foliation. The main theorems generalize Cheng's eigenvalue comparison theorem and other eigenvalue comparison theorems to the category of Riemannian foliations by estimating the first Dirichlet eigenvalue for the basic Laplacian on a metric tubular neighborhood of a leaf closure. Several other facts about the the first eigenvalue of such foliated tubes as well as some needed facts about the tubes themselves are established. This comparison theory, like Cheng's theorem, remains valid for large tubes that are not homotopic to the middle leaf closure and that may have irregular boundaries. We apply these results to obtain upper bounds for the eigenvalues of the basic Laplacian on a closed manifold in terms of curvature bounds and the transverse diameter of the foliation.     

On the number of cusps on cuspidal curves on Hirzebruch surfaces

In this article we give an upper bound for the number of cusps on a cuspidal curve on a Hirzebruch surface. We adapt the results that have been found for a similar question asked for cuspidal curves on the projective plane, and restate the results in this new setting.     

A Lagrangian relax-and-cut approach for the sequential ordering problem with precedence relationships

The sequential ordering problem with precedence relationships was introduced in Escudero [7]. It has a broad range of applications, mainly in production planning for manufacturing systems. The problem consists of finding a minimum weight Hamiltonian path on a directed graph with weights on the arcs, subject to precedence relationships among nodes. Nodes represent jobs (to be processed on a single machine), arcs represent sequencing of the jobs, and the weights are sums of processing and setup times. We introduce a formulation for the constrained minimum weight Hamiltonian path problem. We also define Lagrangian relaxation for obtaining strong lower bounds on the makespan, and valid cuts for further tightening of the lower bounds. Computational experience is given for real-life cases already reported in the literature.     

On the balancing principle for some problems of Numerical Analysis

We discuss a choice of weight in penalization methods. The motivation for the use of penalization in computational mathematics is to improve the conditioning of the numerical solution. One example of such improvement is a regularization, where a penalization substitutes an ill-posed problem for a well-posed one. In modern numerical methods for PDEs a penalization is used, for example, to enforce a continuity of an approximate solution on non-matching grids. A choice of penalty weight should provide a balance between error components related with convergence and stability, which are usually unknown. In this paper we propose and analyze a simple adaptive strategy for the choice of penalty weight which does not rely on a priori estimates of above mentioned components. It is shown that under natural assumptions the accuracy provided by our adaptive strategy is worse only by a constant factor than one could achieve in the case of known stability and convergence rates. Finally, we successfully apply our strategy for self-regularization of Volterra-type severely ill-posed problems, such as the sideways heat equation, and for the choice of a weight in interior penalty discontinuous approximation on non-matching grids. Numerical experiments on a series of model problems support theoretical results.     

A new class of operators and a description of adjoints of composition operators

Starting with a general formula, precise but difficult to use, for the adjoint of a composition operator on a functional Hilbert space, we compute an explicit formula on the classical Hardy Hilbert space for the adjoint of a composition operator with rational symbol. To provide a foundation for this formula, we study an extension to the definitions of composition, weighted composition, and Toeplitz operators to include symbols that are multiple-valued functions. These definitions can be made on any Banach space of analytic functions on a plane domain, but in this work, our attention is focused on the basic properties needed for the application to operators on the standard Hardy and Bergman Hilbert spaces on the unit disk.     

Local convergence analysis of iterative aggregation-disaggregation methods with polynomial correction

The paper introduces some new results on local convergence analysis of one class of iterative aggregation-disaggregation methods for computing a stationary probability distribution vector of an irreducible stochastic matrix. We focus on methods, where the basic iteration on the fine level corresponds to a multiplication by a polynomial of order one with nonnegative coefficients in the original matrix. We show that this process is locally convergent for matrices with positive diagonals or when the coefficients of the polynomial are positive. On the other hand there are examples for which the process may diverge in a local sense for higher degree polynomials even if it converges for a polynomial of a lower degree for the same matrix.     

The impact of digital channel distribution on the experience goods industry

We explore the impact of a digital channel for experience goods on the profitability and behavior of players in the supply chain and on piracy. We consider a firm which can sell an experience good in physical form, in digitized form, or both. We analyze different pricing schemes – price for whole album on the retail channel and linear and nonlinear pricing for songs on the digital channel. Consumers are divided into a retail-captive segment whose consumers are limited to the retail channel and a hybrid segment whose consumers have access to both retail and digital channels.     

零误差计算

研究采用有误差的数值计算来获得无误差的准确值具有重要的理论价值和应用价值.这种通过近似的数值方法获得准确结果的计算被称为零误差计算.本文首先指出,只有一致离散集合中的数才能够开展零误差计算,即有非零隔离界的数集,这也是"数"可以进行零误差计算的一个充要条件.以此为基本出发点,本文分析代数数零误差计算的最低理论精度,该精度对应于恢复近似代数数的准确值时必要的误差控制条件,但由于所采用恢复算法的局限性,这一理论精度往往不能保证成功恢复出代数数的准确值.为此,本文给出采用PSLQ (partial-sum-LQ-decomposition)算法进行代数数零误差计算所需的精度控制条件,与基于LLL (Lenstra-Lenstra-Lovász)算法相比,该精度控制条件关于代数数次数的依赖程度由二次降为拟线性,从而可降低相应算法的复杂度.最后探讨零误差计算未来的发展趋势.     

Numerical solution of an inverse initial boundary-value problem for the full time-dependent Maxwell's equations in the presence of imperfections of small volume

We consider the numerical solution, in a three-dimensional bounded domain, of the inverse problem for identifying the location of small electromagnetic imperfections in a medium with homogeneous background. Our numerical algorithm is based on the coupling of a discontinuous Galerkin method for the time-dependent Maxwell's equations, on the exact controllability method and on a Fourier inversion. Several numerical results are given with one and two imperfections and the robustness and accuracy of the numerical method used for the dynamic detection problem are shown.     

Recessively Compact Sets: Properties and Uses

We develop the concept of recessive compactness recently introduced by Luc and Penot. Then we employ this idea to extend some important results of functional analysis such as closed image criteria, a theorem on a family of unbounded sets having a finite intersection property, an existence condition for a variational inequality problem on a noncompact set, a fixed point theorem for nonexpansive maps on unbounded sets, and an existence result for periodic solutions of a nonlinear differential equation in a Hilbert space without a-priori estimates for the solutions of the equation to stay in a bounded region.