组合计数与Huckel矩阵本征多项式

本文用组合理论方法讨论有机共轭分子,得出了几类分子的本征多项式公式。这些公式可用以研究这几类分子的结构和性能。本文实质上是文献[1]的第二部份。在该文中,我们用组合方法得到的直链多烯的本征多项式     

Characteristic polynomials of chemical graphs via symmetric function theory

The characteristic polynomial corresponding to the adjacency matrix of a graph is constructed by using the traces of the powers of the adjacency matrix to calculate the coefficients of the characteristic polynomial via Newton's identities connecting the power sum symmetric functions and the elementary symmetric functions of the eigenvalues. It is shown that Frame's method, very recently employed by Balasubramanian, is nothing but symmetric functions and Newton's identities.     

Generation of the eigenvectors of the topological matrix from graph theory

The technique of describing the characteristic polynomial of a graph is here extended to construction of the eigenvectors. Recurrence relations and path tracing are combined to generate eigenvector coefficients as polynomial functions of the eigenvalues. The polynomials are expressed as linear functions of Chebyshev polynomials in order to simplify the computational effort. Particular applications to the Hückel MO theory, including heteroatom effects, are shown.     

Equivalence of the microscopic and macroscopic models of chromatography: stochastic-dispersive versus lumped kinetic model

The microscopic model of chromatography is a stochastic model that consists of two fundamental processes: (i) the random migration of the molecules in the mobile phase, and (ii) the random adsorption-desorption of molecules on the stationary phase contained in a chromatographic column. The diffusion and drift of the molecules in the mobile phase is described with a simple one-dimensional random walk. The adsorption-desorption process is modeled by a Poisson process that assumes exponential sojourn times of the molecules in both the mobile and the stationary phases. The microscopic, or molecular model of chromatography studied here turns out to be identical to the macroscopic lumped kinetic model of chromatography, whose solution is well known in chromatography. A complete equivalence of the two models is established via the identical expressions they provide for the band profiles.     

A method of centers algorithm for certain minimax problems

An algorithm is presented for the numerical solution of nonlinear programming problems in which the objective function is to be minimized over feasiblex after having been maximized over feasibley. The vectorsx andy are subjected to separate nonlinear constraints. The algorithm is obtained as follows: One starts with an outer algorithm for the minimization overx, that algorithm being taken here to be a method of centers; then, one inserts into this algorithm an adaptive inner procedure, which is designed to compute a suitable approximation to the maximizery in a finite number of steps. The outer and inner algorithms are blended in such a way as to cause the inner one to converge more rapidly. The results on convergence and rate of convergence for the outer algorithm continue to hold (essentially) for the composite algorithm. Thus, what is considered here, for the first time for this type of problem, is the question of how one inserts an approximation procedure into an algorithm so as to preserve its convergence and its rate of convergence.     

Les classes de Chern des représentations galoisiennes complexes

Let F be a field, G _F its absolute Galois group, : G _FGL(C) a continuous complex representation of G _F and c _i() H_2i(F, Z) its Chern classes. We show, under a mild assumption on F. that c _i ()=0 for all i2. For general F, one has that 2c_i ()=0 for all i 2.

Cette dernière condition résulte en fait de la continuité de .     

Characteristic of composite functions of entire function with saturated defective number

In this article we solved some problems due to Yang concerning the characteristic function of the composite functions.     

The Characteristic Finite Volume Method for Nonlinear Convection-diffusion Problems

§ 1.Introduction　 The finite elementor finite difference methods along characteristics for convection-dif-fusion problems in an unbounded domain R have been developed by Douglas and Rus-sel[1 ] .In those problems with significant convection,the solution changes much lessrapidly in the characteristicτ direction than in time tdirection.Thus,the characteristic-type numerical methods will permitthe use of largertime steps,with corresponding im-provements in efficiency,at no cost in accuracy.　…     

Solutions with exponential character to a linear functional equation and roots of its characteristic equation

We study the connection between solutions of the functional equation φ(x)=S_∫φ(x+M(s))σ(ds) which are comparable at infinity with functions of the form xeλx, and real roots of the characteristic equation S_∫eλM(s)σ(ds)=1.