Dimensional reduction for Helmholtz's equation on a bounded domain

Summary. The dimensional reduction method for solving boundary value problems of Helmholtz's equation in domain by replacing them with systems of equations in dimensional space are investigated. It is proved that the existence and uniqueness for the exact solution and the dimensionally reduced solution of the boundary value problem if the input data on the faces are in some class of functions. In addition, the difference between and in is estimated as and are fixed. Finally, some numerical experiments in a domain are given in order to compare theretical results. Received April 2, 1996 / Revised version received July 30, 1990     

An evolutionary method for optimization of plate buckling resistance

Optimization of plate buckling resistance is very complicated, because the in-plane stress resultants in the prebuckled state of a plate are functions of thickness distribution. This paper discusses the problem of finding the optimum thickness distribution of isotropic plate structures, with a given volume and layout, that would maximise the buckling load. A simple numerical method using the finite-element analysis is presented to obtain the optimum thickness distribution. Optimum designs of compression-loaded rectangular plates with different boundary conditions and plate aspect ratios are obtained by using the proposed method. Optimum designs from earlier studies and the methods of buckling analysis used to attain these results are discussed and compared with the designs from the proposed method. This paper also examines the reliability of the optimality criterion generally used for plate buckling optimization, which is based on the uniform strain energy density.     

新显色剂2-(2-咪唑偶氮)-5-二甲氨基苯甲酸与镍(Ⅱ)的显色反应研究

研究了新显色剂2-(2-咪唑偶氮)-5-二甲氨基苯甲酸(IZDBA)与Ni(Ⅱ)的显色反应。结果表明,在pH 6.0的HAc-NaAc缓冲溶液中,IZDBA可与Ni(Ⅱ)形成一种配合比为2∶1的稳定红色配合物,其最大吸收波长位于580 nm处,而试剂的最大吸收波长为390nm,对比度为190 nm。配合物的表观摩尔吸光系数为2.95×104L.mol-1.cm-1;Ni(Ⅱ)量在0~0.8 mg/L范围内遵守比耳定律。在硫脲和氟化铵存在下,方法可直接用于测定镍催化剂和铸造铝合金中的微量镍。本法与原子吸收光谱法相对照,结果基本一致。     

Large-time behavior of perturbed diffusion markov processes with applications to the second eigenvalue problem for fokker-planck operators and simulated annealing

We study the large-time behavior and rate of convergence to the invariant measures of the processes dX (t)=b(X) (t)) dt + (X (t)) dB(t). A crucial constant appears naturally in our study. Heuristically, when the time is of the order exp( – )/² , the transition density has a good lower bound and when the process has run for about exp( – )/², it is very close to the invariant measure. LetL =(²/2) – U · be a second-order differential operator on ^d. Under suitable conditions,L ^z has the discrete spectrum

Cardinal hermite interpolation with box splines II

Summary In the present work we extent the results in [RS] on CHIP, i.e. Cardinal Hermite Interpolation by the span of translates of directional derivatives of a box spline. These directional derivatives are that ones which define the type of the Hermite Interpolation. We admit here several (linearly independent) directions with multiplicities instead of one direction as in [RS]. Under the same assumptions on the smoothness of the box spline and its defining matrixT we can prove as in [RS]: CHIP has a system of fundamental solutions which are inL L ² together with its directional derivatives mentioned above. Moreover, for data sequences inl ^p ( ^d ), 1p2, there is a spline function inL ^p, 1/p+1/p=1, which solves CHIP.Research supported in part by NSERC Canada under Grant # A7687. This research was completed while this author was supported by a grant from the Deutscher Akademischer Austauschdienst     

On a question of H. Kraljević

In this paper, assuming a certain set-theoretic hypothesis, a positive answer is given to a question of H. Kraljevi, namely it is shown that there exists a Lebesgue measurable subsetA of the real line such that the set {c R: A + cA contains an interval} is nonmeasurable. Here the setA + cA = {a + ca: a, a A}. Two other results about sets of the formA + cA are presented.     

The Binet-Pexider functional equation for rectangular matrices

IfK is a field of characteristic 0 then the following is shown. Iff, g, h: M _n (K) K are non-constant solutions of the Binet—Pexider functional equation

A new Pythagorean functional equation

The purpose of this paper is to solve the following Pythagorean functional equation:(e ^p(x,y) ) ² ) = q(x,y) ² + r(x, y) ², where each ofp(x,y), q(x, y) andr(x, y) is a real-valued unknown harmonic function of the real variablesx, y on the wholexy-planeR ².The result is as follows.     

Jacobi elliptic functions and change of variable in a convolution

We solve the functional equation