Exploring inequality violations by classical hidden variables numerically

There are increasingly suggestions for computer simulations of quantum statistics which try to violate Bell type inequalities via classical, common cause correlations. The Clauser–Horne–Shimony–Holt (CHSH) inequality is very robust. However, we argue that with the Einstein–Podolsky–Rosen setup, the CHSH is inferior to the Bell inequality, although and because the latter must assume anti-correlation of entangled photon singlet states. We simulate how often quantum behavior violates both inequalities, depending on the number of photons. Violating Bell 99% of the time is argued to be an ideal benchmark. We present hidden variables that violate the Bell and CHSH inequalities with 50% probability, and ones which violate Bell 85% of the time when missing 13% anti-correlation. We discuss how to present the quantum correlations to a wide audience and conclude that, when defending against claims of hidden classicality, one should demand numerical simulations and insist on anti-correlation and the full amount of Bell violation.     

Convergence theorems for implicit iteration process for a finite family of continuous pseudocontractive mappings

In this paper, a necessary and sufficient conditions for the strong convergence to a common fixed point of a finite family of continuous pseudocontractive mappings are proved in an arbitrary real Banach space using an implicit iteration scheme recently introduced by Xu and Ori [H.K. Xu, R.G. Ori, An implicit iteration process for nonexpansive mappings, Numer. Fuct. Anal. Optim. 22 (2001) 767-773] in condition αn∈(0,1], and also strong and weak convergence theorem of a finite family of strictly pseudocontractive mappings of Browder-Petryshyn type is obtained. The results presented extend and improve the corresponding results of M.O. Osilike [M.O. Osilike, Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps, J. Math. Anal. Appl. 294 (2004) 73-81].     

母线含非圆曲线的超声变幅杆精确加工的研究

介绍在普通数控车床上准确加工母线含非圆曲线的超声变幅杆的两种通用程序的编制方法及应用。方法一以等弦长划分待加工曲线决定节点,以平均曲率半径作为插补圆半径,以C语言编制出加工代码生成软件。方法二采用VB6编程,使用双圆弧法进行插补,伸缩步长法进行误差控制和决定节点,可设定并控制插补误差理论值,运行时生成的NC代码指令条数少,适应任何超声变幅杆的加工,界面友好易用。上述两程序在进行切削加工前,均可全程模拟加工过程。两软件经分别在GSK-928和G-CNC6135A(G)数控车床上应用,效果良好。而第一软件较完善。     

Common fixed points for maps on cone metric space

The purpose of this paper is to generalize and to unify fixed point theorems of Das and Naik, ?iri?, Jungck, Huang and Zhang on complete cone metric space.     

Simple linear approximations to the likelihood equation for combining evidence in multiple 2×2 tables: A critique of conventional procedures

Summary The conventional procedures for a common odds ratio in multiple 2×2 tables are explored and critiqued. Three types of linear approximation to the likelihood equations under some models of common measures of association are used to derive the popular conventional estimators and test statistics. Some of them are derived using the model of the common standardized difference which is an unacceptable measure. The derivation provides us with some characteristics of the procedures. The advantages of procedures based on the conditional and unconditional likelihoods are discussed. The Institute of Statistical Mathematics     

Common knowledge,communication, and convergence of beliefs

The aim of this paper is to examine the adequacy of the so-called expected utility theory. It is concluded that the theory is inadequate when the decision-maker is decreasingly risk averse and his initial wealth is risky.     

On the Logic of Common Belief

We investigate an axiomatization of the notion of common belief (knowledge) that makes use of no rules of inference (apart from Modus Ponens and Necessitation) and highlight the property of the set of accessibility relations that characterizes each axiom. Mathematics Subject Classification: 03B45, 68T25.     

g-非扩张型FUZZY映象序列的公共FUZZY混合不动点

提出fuzzy映象序列的公共fuzzy混合不动点的概念，研究了g-非扩张型fuzzy映象序列的公共fuzzy混合不动点定理，我们所得的定理改进和推广了近期相关的重要结果．     

Existence and data dependence of fixed points for multivalued operators on gauge spaces

The purpose of this note is to present some fixed point and data dependence theorems in complete gauge spaces and in hyperconvex metric spaces for the so-called Meir-Keeler multivalued operators and admissible multivalued aα-contractions. Our results extend and generalize several theorems of Espínola and Kirk [R. Espínola, W.A. Kirk, Set-valued contractions and fixed points, Nonlinear Anal. 54 (2003) 485-494] and Rus, Petru?el, and Sînt?m?rian [I.A. Rus, A. Petru?el, A. Sînt?m?rian, Data dependence of the fixed point set of some multivalued weakly Picard operators, Nonlinear Anal. 52 (2003) 1947-1959].     

Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semigroups without Bochner integrals

In this paper, we prove Krasnoselskii and Mann's type convergence theorems for nonexpansive semigroups without using Bochner integral and without assuming the strict convexity of Banach spaces. One of our main results is the following: let C be a compact convex subset of a Banach space E and let be a one-parameter strongly continuous semigroup of nonexpansive mappings on C. Let {tn} be a sequence in [0,∞) satisfying