A regular boundary element method for fluid flow

The Boundary Element Method is now well established as a valid numerical technique for the solution of field problems, equal to the Finite Element Method in generality and surpassing it in computational efficiency in some cases.¹ In this paper is presented a 'Regular Boundary Element Method' as applied to inviscid laminar fluid flow problems. It involves the formation of a system of regular integral equations obtained by moving the singularity outside the domain of the given problem. It is also shown that non-conforming elements may be used whereby freedoms are not defined at the geometric nodes under the boundary element discretization. A linear element is developed here; higher order variants could easily be defined. Satisfactory numerical results have been obtained using the proposed regular method with both conventional (continuous across the boundary) and non-conforming boundary elements for two-dimensional inviscid laminar fluid flow problems having regular and singular solutions.     

A hyperspatial representation of a particular set of fuzzy preference relations

In this paper we study a geometrical representation of a special class of fuzzy preference relations by establishing a one-one correspondence between the set of all these relations and a hypercube of an n(n?1)/2 dimensional space.Furthermore, we study some geometrical figures (called H-spheres) and properties of the points which represent the preference relations in the above mentioned euclidean space.     

一类递推关系式的解的计算公式

文献[1]给出了一个三项单指标的常系数齐次递推式的一般解公式。本文一类带双指标的变系数非齐次递推关系的解的结构。其结果，对双指标的相应递推关系式的解的求出，亦或在其有关理论的研究方面，皆有其作用。     

On the relation between particle velocity and shock wave speed for thermoelastic materials

Results of shock-wave experiments in solids often suggest a nearly-linear relation between the particle velocity behind the shock and the shock wave speed. The present note reconsiders the question of whether thermoelastic material models may be consistent with such observations. Emphasis is placed on the role played by the response of the material in severe compression, as distinguished from its response for small or moderate deformations. The details are illustrated for materials of Mie-Grüneisen type. Received 21 December 2001 / Accepted 22 April 2002 Published online 8 July 2002     

Numerical solution of the abel integral equation

A numerical method for the solution of the Abel integral equation is presented. The known function is approximated by a sum of Chebyshev polynomials. The solution can then be expressed as a sum of generalized hypergeometric functions, which can easily be evaluated, using a simple recurrence relation.     

相对性原理与惯性系的时空变换

依据相对性原理,要求粒子动量和能量对于粒子速度的依赖关系在不同惯性系中具有相同的函数形式,由此可证明惯性系之间的时空变换必须是线性变换,并建立了线性变换系数与粒子无量纲质速关系之间的联系。由相对性原理普遍证明了相对论能量必须正比于动质量而不依赖于具体的时空变换关系。无须利用光速不变假设和相互作用守恒定律求解粒子质速关系,确定了惯性系之间时空线性变换的广义洛伦兹变换公式;证明了光速不变假设以及动量守恒和能量守恒定律实际上都不是建立相对论的必要条件。     

The Directed Geodetic Structure of a Strong Digraph

By a ternary structure we mean an ordered pair (U ₀, T ₀), where U ₀is a finitenonempty set and T ₀is a ternary relation on U ₀. A ternary structure (U ₀, T ₀) is called here a directed geodetic structure if there exists a strong digraph Dwith the properties that V(D) = U ₀and T ₀ (u,v, w)if and only if d _D (u,v)+ d _D (v,w)= d _D (u, w) for all u, v, w U ₀, where d _Ddenotes the (directed) distance function in D. It is proved in this paper that there exists no sentence sof the language of the first-order logic such that a ternary structure is a directed geodetic structure if and only if it satisfies s.     

On a theorem of Chowla

Let be a finite field with q=p^felements, where p is a prime number and f is a positive integer. For a nonprincipal multiplicative character χ and a nontrivial additive character ψ on , it is well known that Gauss sum has absolute value . In this paper, we investigate when is a root of unity.