罗特曼透镜独立设计参数探讨

介绍了罗特曼透镜的理论设计公式,探讨了独立设计参数的选取范围及各独立设计参数的变化对透镜性能的影响。实际制作的宽频带罗特曼透镜实测结果印证了独立设计参数选取范围的合理性。     

Critical Analysis of Hypothesis Tests in Federal Information Processing Standard (140-2)

This work presents an analysis of the existing dependencies between the tests of the FIPS 140-2 battery. Two main analytical approaches are utilized, the first being a study of correlations through the Pearson’s correlation coefficient that detects linear dependencies, and the second one being a novel application of the mutual information measure that allows detecting possible non-linear relationships. In order to carry out this study, the FIPS 140-2 battery is reimplemented to allow the user to obtain p-values and statistics that are essential for more rigorous end-user analysis of random number generators (RNG).     

A quasi‐static boundary value problem in multi‐surface elastoplasticity: Part 1—Analysis

The quasi‐static evolution of an elastoplastic body with a multi‐surface constitutive law of linear kinematic hardening type allows the modelling of curved stress–strain relations. It generalizes classical small‐strain elastoplasticity from one to various plastic phases. This paper presents the mathematical models and proves existence and uniqueness of the solution of the corresponding initial‐boundary value problem. The analysis involves an explicit estimate for the effective ellipticity constant. Copyright © 2004 John Wiley & Sons, Ltd.     

随机变量独立性判别方法注记

给出了随机变量 X1 ,X2 ,X3相互独立的一个判定方法 .并将此方法中推广到更一般情形.     

Mesh independent superlinear convergence estimates of the conjugate gradient method for some equivalent self-adjoint operators

A mesh independent bound is given for the superlinear convergence of the CGM for preconditioned self-adjoint linear elliptic problems using suitable equivalent operators. The results rely on K-condition numbers and related estimates for compact Hilbert-Schmidt operators in Hilbert space.This research was supported by the Hungarian National Research Fund OTKA under grant No. T043765.     

On αrγs(k)-perfect graphs

For some integer k0 and two graph parameters π and τ, a graph G is called πτ(k)-perfect, if π(H)−τ(H)k for every induced subgraph H of G. For r1 let α_r and γ_r denote the r-(distance)-independence and r-(distance)-domination number, respectively. In (J. Graph Theory 32 (1999) 303–310), I. Zverovich gave an ingenious complete characterization of α₁γ₁(k)-perfect graphs in terms of forbidden induced subgraphs. In this paper we study α_rγ_s(k)-perfect graphs for r,s1. We prove several properties of minimal α_rγ_s(k)-imperfect graphs. Generalizing Zverovich's main result in (J. Graph Theory 32 (1999) 303–310), we completely characterize α_2r−1γ_r(k)-perfect graphs for r1. Furthermore, we characterize claw-free α₂γ₂(k)-perfect graphs.     

Efficiency of the independence assumption in the combination of forecasts

In seeking to minimise the composite forecast error variance of a linear combination of forecasts, contradictory suggestions have been reported concerning the practice of making the assumption of independence between forecast errors. This assumption can introduce robustness though its avoidance of sampling errors in the estimation of correlation coefficient(s), although it does render the composite forecast theoretically suboptimal. By means of theory and experimental simulation, this paper examines the circumstances whereby the independence assumption may produce more efficient composite forecasts. Its applicability is shown to depend both upon the underlying correlation structure and relative size of forecast errors as well as the observation base available for estimation.     

An error analysis and the mesh independence principle for a nonlinear collocation problem

A nonlinear Dirichlet boundary value problem is approximated by an orthogonal spline collocation scheme using piecewise Hermite bicubic functions. Existence, local uniqueness, and error analysis of the collocation solution and convergence of Newton's method are studied. The mesh independence principle for the collocation problem is proved and used to develop an efficient multilevel solution method. Simple techniques are applied for estimating certain discretization and iteration constants that are used in the formulation of a mesh refinement strategy and an efficient multilevel method. Several mesh refinement strategies for solving a test problem are compared numerically. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2006     

Hybrid Approach with Active Set Identification for Mathematical Programs with Complementarity Constraints

We consider a mathematical program with complementarity constraints (MPCC). Our purpose is to develop methods that enable us to compute a solution or a point with some kind of stationarity to MPCC by solving a finite number of nonlinear programs. We apply an active set identification technique to a smoothing continuation method (Ref. 1) and propose a hybrid algorithm for solving MPCC. We develop also two modifications: one makes use of an index addition strategy; the other adopts an index subtraction strategy. We show that, under reasonable assumptions, all the proposed algorithms possess a finite termination property. Further discussions and numerical experience are given as well This work was supported in part by the Scientific Research Grant-in-Aid from the Ministry of Education, Science, Sports, and Culture of Japan. The authors are grateful to Professor Paul Tseng for helpful suggestions on an earlier version of the paper.     

Independent sets in tensor graph powers

The tensor product of two graphs, G and H, has a vertex set V(G) × V(H) and an edge between (u,v) and (u′,v′) iff both u u′ ∈ E(G) and v v′ ∈ E(H). Let A(G) denote the limit of the independence ratios of tensor powers of G, lim, α(Gⁿ)/|V(Gⁿ)|. This parameter was introduced in [Brown, Nowakowski, Rall, SIAM J Discrete Math 9 ( 5 ), 290–300], where it was shown that A(G) is lower bounded by the vertex expansion ratio of independent sets of G. In this article we study the relation between these parameters further, and ask whether they are in fact equal. We present several families of graphs where equality holds, and discuss the effect the above question has on various open problems related to tensor graph products. © 2006 Wiley Periodicals, Inc. J Graph Theory