正交小波包的构造

本文给出尺度因子ａ＝４时正交小波包的构造，推广了［２，４］引入的正交小波包，并给出相应的分解与再构造算法．本文引入的正交小波包具有保持信号ｆ∈Ｌ^２的线性相位，也讨论了尺度因子ａ＝ｋ（ｋ∈Ｚ，ｋ≥２）正交小波的构造     

Cyclic reduction and FACR methods for piecewise hermite bicubic orthogonal spline collocation

Cyclic reduction and Fourier analysis-cyclic reduction (FACR) methods are presented for the solution of the linear systems which arise when orthogonal spline collocation with piecewise Hermite bicubics is applied to boundary value problems for certain separable partial differential equations on a rectangle. On anN×N uniform partition, the cyclic reduction and Fourier analysis-cyclic reduction methods requireO(N ²log₂ N) andO(N ²log₂log₂ N) arithmetic operations, respectively.     

Radical copolymerization of 2‐trifluoromethylacrylic monomers. II. Kinetics,monomer reactivities,and penultimate effect in their copolymerization with norbornenes and vinyl ethers

Radical copolymerizations of electron‐deficient 2‐trifluoromethylacrylic (TFMA) monomers, such as 2‐trifluoromethylacrylic acid and t‐butyl 2‐trifluoromethylacrylate (TBTFMA), with electron‐rich norbornene derivatives and vinyl ethers with 2,2′‐azobisisobutyronitrile as the initiator were investigated in detail through the analysis of the kinetics in situ with ¹H NMR and through the determination of the monomer reactivity ratios. The norbornene derivatives used in this study included bicyclo[2.2.1]hept‐2‐ene (norbornene) and 5‐(2‐trifluoromethyl‐1,1,1‐trifluoro‐2‐hydroxylpropyl)‐2‐norbornene. The vinyl ether monomers were ethyl vinyl ether, t‐butyl vinyl ether, and 3,4‐dihydro‐2‐H‐pyran. Vinylene carbonate was found to copolymerize with TBTFMA. Although none of the monomers underwent radical homopolymerization under normal conditions, they copolymerized readily, producing a copolymer containing 60–70 mol % TFMA. The copolymerization of the TFMA monomer with norbornenes and vinyl ethers deviated from the terminal model and could be described by the penultimate model. The copolymers of TFMA reported in this article were evaluated as chemical amplification resist polymers for the emerging field of 157‐nm lithography. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 1478–1505, 2004     

Semidefinite optimization models for limit and shakedown analysis problems involving matrix spreads

Limit and shakedown analysis problems of Computational Mechanics lead to convex optimization problems, characterized by linear objective functions, linear equality constraints and constraints expressing the restrictions imposed by the material strength. It is shown that two important strength criteria, the Mohr–Coulomb and the Tresca criterion, can be represented as systems of semidefinite constraints, leading this way to semidefinite programming problems.     

Closed solution to electromagnetic scattering of a plane wave by an eccentric cylinder coated with metamaterials

Closed series solution of electromagnetic scattering by an eccentric coated cylinder is achieved in matrix form. Diffracted field patterns are examined for an incident plane transverse magnetic (TM) wave. The solution is found by the classical separation of variables technique and the translational addition theorems. Wave transformation and orthogonality of the complex exponentials are employed to produce an infinite series. Numerical results are then shown by shortening the infinite series to a limited number of terms. Solutions are discussed for a dielectric or a metamaterial coating.     

The harmonic consistency index for the analytic hierarchy process

A new consistency measure, the harmonic consistency index, is obtained for any positive reciprocal matrix in the analytic hierarchy process. We show how this index varies with changes in any matrix element. A tight upper bound is provided for this new consistency measure when the entries of matrix are at most 9, as is often recommended. Using simulation, the harmonic consistency index is shown to give numerical values similar to the standard consistency index but it is easier to compute and interpret. In addition, new properties of the column sums of reciprocal matrices are obtained.     

一个数学建模问题的简单解法

银行利率给出了一个简单计算方法 ,这种方法更符合中学生思维的习惯 .     

基于模糊方法的多人合作对策的研究

多人合作对策模型中联盟的收入和总体的收入常常出现相互矛盾的情况 ,此时核是空集 .由于不存在核 ,无法用 Nash-Harsanyi谈判模型求解 .采用模糊数学方法 ,调整模型中线性约束的右端系数 ,使核在一定程度上是非空集合 ,得到模糊意义下的 Nash平衡解 .该方法一定程度上解决了各联盟收入与总体收入的矛盾 .最后通过一个算例说明该方法的可行性 .     

The effect of multiple optima on the simple GA run-time complexity

Genetic algorithms are stochastic search algorithms that have been applied to optimization problems. In this paper we analyze the run-time complexity of a genetic algorithm when we are interested in one of a set of distinguished solutions. One such case occurs when multiple optima exist. We define the worst case scenario and derive a probabilistic worst case bound on the number of iterations required to find one of these multiple solutions of interest.