Stokes drag on axially symmetric bodies: a new approach

In this paper a new approach to evaluate the drag force in a simple way on a restricted axially symmetric body placed in a uniform stream (i) parallel to its axis, (ii) transverse to its axis, is advanced when the flow is governed by the Stokes equations. The method exploits the well-known integral for evaluating the drag on a sphere. The method not only provides the value of the drag on prolate and oblate spheroids and a deformed sphere in axial flow which already exists in literature but also new results for a cycloidal body, an egg shaped body and a deformed sphere in transverse flow. The salient results are exhibited graphically. The limitations imposed on the analysis because of the lack of fore and aft symmetry in the case of an eggshaped body is also indicated. It is also seen that the analysis can be extended to calculate the couple on a body rotating about its axis of symmetry.     

n维单形的Erd“非汉字符号”-Mordell型不等式

本文利用距离几何的理论和方法证明了 En( n≥ 2 )中 n维单形几内任一点到 n- 1维界面的距离与它到顶点的距离的一个带权的 Erdos- Mordell型不等式 ,并由此导出了涉及 n维单形的内任一点的一组儿何不等式 ,其中包括三角形中著名的 Child不等式的高维推广     

Stereology of Extremes; Shape Factor of Spheroids

In the stereological unfolding problem of size and shape factor of spheroidal particles the extremal shape factor is investigated. The transformation of particle parameters is shown to be stable with respect to the domain of attraction in three situations: (a) Conditional distribution of shape factor given particle size. (b) Conditional distribution of shape factor given particle section size. (c) Marginal distribution of shape factor. In situation (a) the normalizing constants are derived in a parametric model, which enables prediction of extreme shape factor after a preliminary solution of the size unfolding problem. In both situations (b) and (c) obtaining a similar procedure is still an open problem. The uniformity conditions necessary for (b) and (c) are shown to be mild.     

NATURAL BOUNDARY ELEMENT METHOD FOR THREE DIMENSIONAL EXTERIOR HARMONIC PROBLEM WITH AN INNER PROLATE SPHEROID BOUNDARY

In this paper, we study natural boundary reduction for Laplace equation with Dirichletor Neumann boundary condition in a three-dimensional unbounded domain, which is theoutside domain of a prolate spheroid. We express the Poisson integral formula and naturalintegral operator in a series form explicitly. Thus the original problem is reduced to aboundary integral equation on a prolate spheroid. The variational formula for the reducedproblem and its well-posedness are discussed. Boundary element approximation for thevariational problem and its error estimates, which have relation to the mesh size andthe terms after the series is truncated, are also presented. Two numerical examples arepresented to demonstrate the effectiveness and error estimates of this method.     

Numerical investigation of the acoustic scattering problem from penetrable prolate spheroidal structures using the Vekua transformation and arbitrary precision arithmetic

A complete set of radiating “outwards” eigensolutions of the Helmholtz equation, obtained by transforming appropriately through the Vekua mapping the kernel of Laplace equation, is applied to the investigation of the acoustic scattering by penetrable prolate spheroidal scatterers. The scattered field is expanded in terms of the aforementioned set, detouring so the standard spheroidal wave functions along with their inherent numerical deficiencies. The coefficients of the expansion are provided by the solution of linear systems, the conditioning of which calls for arbitrary precision arithmetic. Its integration enables the polyparametric investigation of the convergence of the current approach to the solution of the direct scattering problem. Finally, far‐field pattern visualization in the 3D space clarifies the preferred scattering directions for several frequencies of the incident wave, ranging from the “low” to the “resonance” region.     

三维斯托克斯流动在扁球坐标系中的基本解及其应用

通过把Lamb基本解中的调和函数转换为扁球坐标系下的表达式,这项研究成功地得到了一个新的Stokes流动三维基本解.此基本解可用于解决任意多个扁椭球处于任意位置和方向时的流动问题.应用最小二乘法,三维流动问题中常遇到的收敛性差的困难在此得以完全克服.结果表明该方法具有准确度高,收敛性好和计算量小的特点.由于扁球可用于模拟从圆盘到圆球的多种物体形状,此基本解被用于系统地分析了各种几何因素对两个扁球所受力和力矩的影响.为了显示此方法的通用性,该基本解还用于研究了两例三个扁球的问题.     

三维非定常/定常不可压缩流动N-S方程基于人工压缩性方法的数值模拟

基于人工压缩性方法提出—中心与迎风混合的算法,以数值模拟N-S方程的定常/非定常解．对半离散方程的左端采用中心差分, 方程右端数值流量采用迎风Roe近似算法,其精度可达三阶．湍流模式利用Baldwin-Lomax代数模式．计算例子包括二维平板、机翼剖面、扁椭球、颅动脉瘤等．计算结果表明,压力和摩擦系数与实验符合,在分离涡旋区计算值与实验有差别,这或许是由于湍流模式不够精确的缘故．     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].     

Acta Mathematica Sinica EnglishSeries Instructions for Authors

<正>Submission Authors must use LaTeX for typewriting,and visit our website www.actamath.com to submit your paper.Our address is Editorial Office of Acta Mathematica Sinica,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,P.R.China.     

SUBJECT INDEX TO VOLUME 57(2014)

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Erratum to: Remarks on lines and minimal rational curves

<正>Erratum to:Science in China Series A:Mathematics,April 2009 Vol.52 No.4:617–630doi:10.1007/s11425-009-0038-2There is a mistake in the proof of[1,Lemma 2.2],which occurs in 4-th line at[1,p.619],