Relaxation of Certain Integral Functionals Depending onStrain and Chemical Composition

The authors provide a relaxation result in BV×Lq, 1≤q<+∞ as the first step towards the analysis of thermochemical equilibria.     

A change of variables formula for mappings in

A change of variables formula for mappings in is obtained, where the usual jacobian is replaced by the determinant of the approximate differential.

     

On a result of Aumann and Shapley about values of non-atomic games

We focus our attention on the argument developed by R.J. Aumann and L.S. Shapley in a proposition used to prove the existence of a value on a certain class of games. Since we have found such an argument to be inexact, we have devised a supplementary construction which should be incorporated in the original proof to make it run in a satisfactory way.     

Characterization of Sobolev and BV spaces

The main results of this paper are new characterizations of W1,p(Ω), 1<p<∞, and BV(Ω) for Ω⊂RN an arbitrary open set. Using these results, we answer some open questions of Brezis (2002) [10] and Ponce (2004) [25].     

A new theory of regular functions of a quaternionic variable

In this paper we develop the fundamental elements and results of a new theory of regular functions of one quaternionic variable. The theory we describe follows a classical idea of Cullen, but we use a more geometric formulation to show that it is possible to build a rather complete theory. Our theory allows us to extend some important results for polynomials in the quaternionic variable to the case of power series.     

On a Characterization of the Gamma Distribution: The Independence of the Sample Mean and the Sample Coefficient of Variation

Let n 3 and let X ₁,...,X _n be positive i.i.d. random variables whose common distribution function f has a continuous p.d.f. Using earlier work of the present authors and a method due to Anosov for solving certain integro-functional equations, it is shown that the independence of the sample mean and the sample coefficient of variation is equivalent to that f is a gamma function. While the proof is of methodological interest, this conclusion can also be arrived at without any assumptions by appealing to the Laplace-Stieltjes transform, as in the Concluding Romark (Section 3).     

关于积和式差的一点注记

It is shown that for any two n×n complex valued matrices A, B the inequality |perA-perB|≤n‖A-B‖Fmax(‖A‖F,‖B‖F)n-1 or |perA-perB|≤‖A‖Fn ‖B‖Fn holds for where AH denotes the conjuagte transpose of the matrix A=(aij)n×n.     

Image Restoration and Decomposition via Bounded Total Variation and Negative Hilbert-Sobolev Spaces

We propose a new class of models for image restoration and decomposition by functional minimization. Following ideas of Y. Meyer in a total variation minimization framework of L. Rudin, S. Osher, and E. Fatemi, our model decomposes a given (degraded or textured) image u ₀ into a sum u+v. Here u∈BV is a function of bounded variation (a cartoon component), while the noisy (or textured) component v is modeled by tempered distributions belonging to the negative Hilbert-Sobolev space H ^−s . The proposed models can be seen as generalizations of a model proposed by S. Osher, A. Solé, L. Vese and have been also motivated by D. Mumford and B. Gidas. We present existence, uniqueness and two characterizations of minimizers using duality and the notion of convex functions of measures with linear growth, following I. Ekeland and R. Temam, F. Demengel and R. Temam. We also give a numerical algorithm for solving the minimization problem, and we present numerical results of denoising, deblurring, and decompositions of both synthetic and real images.     

Validation of Solutions of Construction Problems in Dynamic Geometry Environments

This paper discusses issues concerning the validation of solutions of construction problems in Dynamic Geometry Environments (DGEs) as compared to classic paper-and-pencil Euclidean geometry settings. We begin by comparing the validation criteria usually associated with solutions of construction problems in the two geometry worlds – the ‘drag test’ in DGEs and the use of only straightedge and compass in classic Euclidean geometry. We then demonstrate that the drag test criterion may permit constructions created using measurement tools to be considered valid; however, these constructions prove inconsistent with classical geometry. This inconsistency raises the question of whether dragging is an adequate test of validity, and the issue of measurement versus straightedge-and-compass. Without claiming that the inconsistency between what counts as valid solution of a construction problem in the two geometry worlds is necessarily problematic, we examine what would constitute the analogue of the straightedge-and-compass criterion in the domain of DGEs. Discovery of this analogue would enrich our understanding of DGEs with a mathematical idea that has been the distinguishing feature of Euclidean geometry since its genesis. To advance our goal, we introduce the compatibility criterion, a new but not necessarily superior criterion to the drag test criterion of validation of solutions of construction problems in DGEs. The discussion of the two criteria anatomizes the complexity characteristic of the relationship between DGEs and the paper-and-pencil Euclidean geometry environment, advances our understanding of the notion of geometrical constructions in DGEs, and raises the issue of validation practice maintaining the pace of ever-changing software.     

On the Convergence of Bernstein-Stancu Polynomials in the Variation Seminorm

This article studies the variation detracting property and rate of approximation of the Bernstein-Stancu polynomials in the space of functions of bounded variation with respect to the variation seminorm. Moreover, we will present Voronovskaya-type theorems for Bernstein-Stancu polynomials B_{n, α, β}f and for the first derivative of these polynomials. Finally we include some graphical examples.     

Some critical minimization problems for functions of bounded variations

Using a new elementary method, we prove the existence of minimizers for various critical problems in BV(Ω) and also in W1,p(Ω), 1<p<∞.     

On the subdifferential of a submodular function

The author recently introduced a concept of a subdifferential of a submodular function defined on a distributive lattice. Each subdifferential is an unbounded polyhedron. In the present paper we determine the set of all the extreme points and rays of each subdifferential and show the relationship between subdifferentials of a submodular function and subdifferentials, in an ordinary sense of convex analysis, of Lovász's extension of the submodular function. Furthermore, for a modular function on a distributive lattice we give an algorithm for determining which subdifferential contains a given vector and finding a nonnegative linear combination of extreme vectors of the subdifferential which expresses the given vector minus the unique extreme point of the subdifferential.     

On the Unavoidable Uncertainty of Truth in Dynamic Geometry Proving

The aim of this note is to discuss some issues posed by the emergency of universal interfaces able to decide on the truth of geometric statements. More specifically, we consider a recent GeoGebra module allowing general users to verify standard geometric theorems. Working with this module in the context of Varignon’s theorem, we were driven—by the characteristics of the GeoGebra interface—to perform a quite detailed study of the very diverse fate of attempting to automatically prove this statement, when using two different construction procedures. We highlight the relevance—for the theorem proving output—of expression power of the dynamic geometry interface, and we show that the algorithm deciding about the truth of some—even quite simple—statements can fall into a not true and not false situation, providing a source of confusion for a standard user and an interesting benchmark for geometers interested in discovering new geometric facts.     

Omniscience Principles and Functions of Bounded Variation

A very weak omniscience principle is formulated, related omniscience principlesare considered, and the theorem that a function of bounded variation is the difference of two increasing functions is shown to be equivalent to the omniscience principle WLPO. It is a so shown that an arbitrary function (not necessarily strongly extensional) with located variation on an interval is the difference of two increasing functions.     

The landscape: Through a Different Lens A New Angle on the Price Spiral in Higher Education

Abstract

“Academic institutions now find themselves confronting hard questions about whether their spending patterns match their priorities and about how to communicate the choices they have made to the public.”

The College Cost Crisis: A Congressional Analysis of College Costs and Implications for America's Higher Education System     

带合作行为的平均场模型的依全变差稳定性

该文考虑一个带合作行为的平均场模型的稳定性问题. 应用耦合方法, 建立了相应于这个平均场模型的扩散过程的依全变差稳定性.     

Characterizations and Examples of Hidden Regular Variation

Random vectors on the positive orthant whose distributions possess hidden regular variation are a subclass of those whose distributions are multivariate regularly varying. The concept is an elaboration of the coefficient of tail dependence of Ledford and Tawn (1996, 1997). We provide characterizations and examples of such distribution in terms of mixture models and product models.Sidney Resnicks research was partially supported by NSF grant DMS-0303493 and NSA grant MSPF-02G-183 at Cornell University.This revised version was published online in March 2005 with corrections to the cover date.     

On the Rate of Convergence of Fourier Series of Functions of Bounded Variation

Mathematical Notes -     

基于差异系数的多元过程能力指数

过程能力指数表示过程能力满足产品质量标准的程度的评价指标，最普遍使用的过程能力指数有Cp、Cpk、Cpm、Cpkm等，它们已在各大工业部门得到了广泛的应用，但是多元质量特性的过程能力指数尚未得到很好的解决。许多学试图以不同的方式、方法计算多元质量特性的过程能力指数，但存在局限性。本以多元正态分布为基础，比较分析了每个质量特征的差异系数，给出了多元过程能力指数的计算公式。最后的一个算例表明，该方法是有效且符合实际的。