样条边界元法分析圆形基础板非线性非光滑接触

本文用样条边界元法分析轴对称圆形基础板的非线性非光滑接触。除事先给出外力与地基表面位移的对应关系外,地基的模型、板的厚薄(Reissner/Kirchhoff型)和外荷载沿径向的分布均可是任意的。文中将地基反力看作板的外载,对变量沿径向采用不等距祥条插值,并用无地基效应的板基本解。算例表明本文方法只要用少量自由度,便可得到令人满意的结果。     

用功的互等定理求解矩形薄板的自然频率

从虚功原理出发，证明了薄板小挠度弯曲问题的功的互等定理，并由此推出了求解矩形薄板自然频率的公式．算例表明，该公式计算简便，精度较高．     

ContributionsTriangular embeddings of Kn−Km with unboundedly large m

The author has proposed methods of constructing index 2 and 3 current graphs generating triangular embeddings of graphs K_n−K_m with unboundedly large m (as n increases). As a result, triangular embeddings of graphs of many families of graphs K_n−K_m with unboundedly large m were constructed. The paper gives a survey of these results and a short explanation of the methods.     

Half Space and Quarter Space Dirichlet Problems for the Partial Differential Equation

A customary, heuristic, method, by which the Poisson integral formula for the Dirichlet problem, for the half space, for Laplace's equation is obtained, involves Green's function, and Kelvin's method of images. Although this heuristic method leads one to guess the correct result, this Poisson formula still has to be verified directly, independently of the method by which it was arrived at, in order to be absolutely certain that a solution of the Dirichlet problem for the half space, for Laplace's equation, has been actually obtained. A similar heuristic method, as seems to be generally known, could be followed in solving the Dirichlet problem, for the half space, for the equation where is a real constant. However, in Part 1, a different, labor-saving, method is used to study Dirichlet problems for the equation. This method is essentially based on what Hadamard called the method of descent. Indeed, it is shown that he who has solved the half space Dirichlet problem for Laplace's equation has already solved the half space Dirichlet problem for the equation In Part 2, the solution formula for the quarter space Dirichlet problem for Laplace's equation is obtained from the Poisson integral formula for the half space Dirichlet problem for Laplace's equation. A representation theorem for harmonic functions in the quarter space is deduced. The method of descent is used, in Part 3, to obtain the solution formula for the quarter space Dirichlet problem for the equation by means of the solution formula for the quarter space Dirichlet problem for Laplace's equation. So that, indeed, it is also shown that he who has solved the quarter space Dirichlet problem for Laplace's equation has already solved the quarter space Dirichlet problem for the " equation" For the sake of completeness and clarity, and for the convenience of the reader, the appendix, at the end of Part 3, contains a detailed proof that the Poisson integral formula solves the half space Dirichlet problem for Laplace's equation. The Bibliography for Parts 1,2, 3 is to be found at the end of Part 1.     

Full analogy of Sharkovsky's theorem for lower semicontinuous maps

A full analogy of the celebrated Sharkovsky cycle coexistence theorem is established for lower semicontinuous (multivalued) maps on metrizable linear continua. This result is further extended to triangular maps.     

On the resolution and optimization of a system of fuzzy relational equations with sup-T composition

This paper provides a thorough investigation on the resolution of a finite system of fuzzy relational equations with sup-T composition, where T is a continuous triangular norm. When such a system is consistent, although we know that the solution set can be characterized by a maximum solution and finitely many minimal solutions, it is still a challenging task to find all minimal solutions in an efficient manner. Using the representation theorem of continuous triangular norms, we show that the systems of sup-T equations can be divided into two categories depending on the involved triangular norm. When the triangular norm is Archimedean, the minimal solutions correspond one-to-one to the irredundant coverings of a set covering problem. When it is non-Archimedean, they only correspond to a subset of constrained irredundant coverings of a set covering problem. We then show that the problem of minimizing a linear objective function subject to a system of sup-T equations can be reduced into a 0–1 integer programming problem in polynomial time. This work generalizes most, if not all, known results and provides a unified framework to deal with the problem of resolution and optimization of a system of sup-T equations. Further generalizations and related issues are also included for discussion.     

Construction of triangular DP surface and its application

In this paper, a new type of bivariate basis on a triangle is presented, which is constructed by extending the univariate NTP basis proposed by Delgado and Peña. Some algebraic properties and its recursive formulae are given. Then a new type of surfaces that is called triangular DP surface is defined, and its recursive evaluation algorithm is obtained. Also, in the case of low degree, its subdivision algorithm and degree elevation algorithm are derived. It is shown that this type of surfaces is obviously more advantageous than triangular Bézier surface, and hence extremely useful for geometric design, especially for the situation in which the surface needs to be evaluated quickly.     

Numerical analysis for factorial data analysis. Part II: Special purpose hardware—the programmable systolic array SARDA

The second part of this paper deals with the systolic implementation of the computational kernel for factorial data analysis, defined in Part I, on special-purpose hardware. The framework of the study is that a sequence of different algorithms has to be performed on a unique hardware array. This fact has led us to the design of the programmable systolic array SARDA: this is a triangular array which consists of programmable nodes with local memory and programmable orthogonal connections.     

Exact Equilibrium Solutions for Linearly Elastic Plate-Like Bodies

A three-dimensional, explicit and exact, equilibrium solution is derived for transversely isotropic, linearly elastic bodies in the form of a right cylinder simply supported over its lateral boundary and loaded over its end faces. This solution, which generalizes an earlier proposal of Levinson in various respects, is to serve as a benchmark for the corresponding plate theories. This revised version was published online in August 2006 with corrections to the Cover Date.     

Applications of the Poincaré sphere in polarization metrology

The Poincaré sphere representation of polarization states is used to derive two auxiliary equations for phase retardance measurements. These equations, in addition to another two previously derived equations, allow for extending the range of validity of a model for calibrating phase plates in pairs. In another application, the sphere is used to explain a new method for identifying the principal axes of two birefringent phase plates during their calibration.