Asymptotic properties of solutions of nonlinear difference equations

Using discrete inequalities and Schauder's fixed point theorem we study the problem of asymptotic equilibrium for difference equations.     

Asymptotic formulae of Mehler–Heine-type for certain classical polyorthogonal polynomials

The purpose of this article is to give some asymptotic formulae of polyorthogonal polynomials with respect to some classical measures. The formulae are analogous to the Mehler–Heine formulae for Jacobi and Laguerre polynomials.     

Mass formulae for Λ-hypernuclei

Simple considerations regarding the Hamiltonian and the ground state wavefunctions of Λ-hypernuclei are used to derive several mass formulae. The parameters that occur in the mass formulae are determined by fitting the experimental binding energies. Information regarding the various interactions in hypernuclal is deduced from the values of these parameters. The ‘best’ mass formula is further used to predict energies of other light hypernuclei. Relationship between binding energies are also suggested and checked with observed data.     

Meromorphic continuation of dynamical zeta functions via transfer operators

We describe a method to prove meromorphic continuation of dynamical zeta functions to the entire complex plane under the condition that the corresponding partition functions are given via a dynamical trace formula from a family of transfer operators. Further we give general conditions for the partition functions associated with general spin chains to be of this type and provide various families of examples for which these conditions are satisfied.     

Implicit summation formulae for Hermite and related polynomials

In this article, we derive some implicit summation formulae for Hermite and related polynomials by using different analytical means on their respective generating functions.     

Boolean formulae, hypergraphs and combinatorial topology

With a view toward studying the homotopy type of spaces of Boolean formulae, we introduce a simplicial complex, called the theta complex, associated to any hypergraph, which is the Alexander dual of the more well-known independence complex. In particular, the set of satisfiable formulae in k-conjunctive normal form with ?n variables has the homotopy type of Θ(Cube(n,n−k)), where Cube(n,n−k) is a hypergraph associated to the (n−k)-skeleton of an n-cube. We make partial progress in calculating the homotopy type of theta for these cubical hypergraphs, and we also give calculations and examples for other hypergraphs as well. Indeed studying the theta complex of hypergraphs is an interesting problem in its own right.     

一种新的二维区域上嵌入式数值积分公式构造方法

The purpose of this paper is to study a new strategy to construct embedded cubature formulae over two-dimensional regions.A new kind of embedded cubature formulae with some nodes along the selected algebraic curve is constructed.Some examples on the unit disk are presented to illustrate the validity of this strategy.     

On a spatial generalization of the Kolosov–Muskhelishvili formulae

The main goal of this paper is to construct a spatial analog to the Kolosov–Muskhelishvili formulae using the framework of the hypercomplex function theory. We prove a generalization of Goursat's representation theorem for solutions of the biharmonic equation in three dimensions. On the basis of this result, we construct explicitly hypercomplex displacement and stress formulae in terms of two monogenic functions. Copyright © 2008 John Wiley & Sons, Ltd.