Mutual information, variation, and Fano’s inequality

Some upper and lower bounds are obtained for the maximum of the absolute value of the difference between the mutual information |I(X; Y) ? I(X′; Y′)| of two pairs of discrete random variables (X, Y) and (X′, Y′) via the variational distance between the probability distributions of these pairs. In particular, the upper bound obtained here substantially generalizes and improves the upper bound of [1]. In some special cases, our upper and lower bounds coincide or are rather close. It is also proved that the lower bound is asymptotically tight in the case where the variational distance between (X, Y) and (X′ Y′) tends to zero.     

A forbidden subposet characterization of an order — dimension inequality

Dushnik and Miller defined the dimension of a partially ordered setX, DimX, as the minimum number of linear extensions ofX whose intersection is the partial ordering onX. The concept of dimension for a partially ordered set has applications to preference structures and the theory of measurement. Hiraguchi proved that DimX [|X|/2] when |X| 4. Bogart, Trotter, and Kimble gave a forbidden subposet characterization of Hiraguchi's inequality by constructing for eachn 2 the minimum collection _n of posets such that if [|X|/2] =n 2, then DimX < n unlessX contains one of the posets in _n . Recently Trotter gave a simple proof of Hiraguchi's inequality based on the following theorem. IfA is an antichain ofX and |X – A| =n 2, then DimX n. In this paper we give a forbidden subposet characterization of this last inequality.     

Saddle point criteria and Wolfe duality in nonsmooth (Φ, ρ)-invex vector optimization problems with inequality and equality constraints

In this paper, saddle point criteria and Wolfe duality theorems are established for a new class of nondifferentiable vector optimization problems with inequality and equality constraints. The results are proved under nondifferentiable (Φ, ρ)-invexity and related scalar and vector-valued Lagrangians defined for the considered nonsmooth multiobjective programming problem. It turns out that the results are established for such vector optimization problems in which not all functions constituting a vector optimization problem possess the fundamental property of invexity and the most of generalized invexity notions previously defined in the literature.     

Boundary variational ‘principles’ for inequality structural analysis problems and numerical applications

The aim of the present paper is the derivation of boundary variational ‘principles’ for inequality problems i.e. for problems having as variational formulations variational or hemivariational inequalities. Using first the principles of minimum potential and complementary energy we derive first saddle point formulations for the problems using appropriate Lagrangians. Then we eliminate by an appropriate elimination technique the internal degrees of freedom and we obtain two minimum ‘principles’ having as unknowns the normal displacements and reactions of the boundary region respectively. Analogously we treat the case of hemivariational inequalities. The theory is applied to the inclusion and inhomogeneity problem and is illustrated by numerical examples solved both by the F.E.M. and the B.E.M.     

Looking for the best constant in a Sobolev inequality: a numerical approach

A numerical method for the computation of the best constant in a Sobolev inequality involving the spaces H ²(Ω) and C⁰([`(W)])C^{0}(\overline{\Omega}) is presented. Green’s functions corresponding to the solution of Poisson problems are used to express the solution. This (kind of) non-smooth eigenvalue problem is then formulated as a constrained optimization problem and solved with two different strategies: an augmented Lagrangian method, together with finite element approximations, and a Green’s functions based approach. Numerical experiments show the ability of the methods in computing this best constant for various two-dimensional domains, and the remarkable convergence properties of the augmented Lagrangian based iterative method.     

On stabilization for a class of nonlinear stochastic time-delay systems： a matrix inequality approach

This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.     

S,T,A,L,K,E,R,： Clear Sky潜行者--明朗天空

《潜行者——切尔诺贝利的阴影》是乌克兰的游戏公司GSC Game World花费6年多时间打造的大作,很早就因为可以与《半条命2》相媲美的游戏画面和独特的风格而备受期待,可是游戏接二连三地跳票,最后终于在2007年推出。虽然因为多次推迟,游戏画面已不再是顶尖的水准,但游戏中假设再次发生了核泄漏的切尔诺贝利核电站周围隔离区独特的气氛和加入RPG元素自由开发的游戏设计,还是给很多玩过该游戏的玩家留下了难以磨灭的印象。《潜行者——明朗天空》是其最新的资料片,或者说是前传。故事同样是发生在切尔诺贝利核电站周围的那片地区,但时间却是在前作中所发生事件一年以前的2011年。     

Spam,Spam, Spam,Spam…

Many Monty Python fans remember fondly the infamous musical sketch celebrating the versatility of the meat product Spam. However, others of us are less favourably disposed to the modern day, information society version of ‘spam’: junk E-mail. For many users of the Internet, junk E-mail is becoming a significant nuisance that existing laws do not prevent, but regulations will soon be introduced to make it more difficult for people to send.     

Comments on “Wirtinger-based integral inequality: Application to time-delay systems [Automatica 49 (2013) 2860–2866]”

In a recent paper (Automatica 49 (2013) 2860–2866), the Wirtinger-based inequality has been introduced to derive tractable stability conditions for time-delay or sampled-data systems. We point out that there exist two errors in Theorem 8 for the stability analysis of sampled-data systems, and the correct theorem is presented.     

更高,更快,更好

当今社会已步人信息社会,人们对电子商务、电子邮件的认识已达到“日益临近并不可离弃的”程度。信息通信被公认为是新的经济增长点和企业生存发展的生     

MDA,CGA,EGA,VGA,TVGA显示系统的异同

本文从六个方面比较了目前流行于我国PC机上的几种显示系统之异同,对广大用户选购适合自己需求的计算机系统,以及对高级程序员进行图形程序设计均有所帮助。     

张恩勤,施颂椒,徐立鸿

针对一类不确定非线性系统提出一种新的模糊自适应控制方法。用模糊逻辑系统逼近未知函数,并根据前一步参考误差来修正模糊逻辑系统的输入,以此对逼近误差进行补偿。该方法不但能保证闭环系统稳定,而且可使跟踪误差收敛于原点或原点的一个小领域内。仿真结果验证了此方法的有效性。     

基金,基金,一网打尽

我是河北省正定职中的一名数学教师,与CFan结缘是在学校于1995年购进第一批电脑后,因为要学电脑,便对电脑类书籍留上了心,在学校阅览室看到《电脑爱好者》后,便对其爱不释手了。后来为了方便阅读,便每期自己购买,至今,家里已存了各年的CFan杂志两大箱。回想起来,CFan伴我从一个电脑的门外汉成了一个电脑行家。