Concerning Difference Matrices

Several new constructions for difference matrices are given. One classof constructions uses pairwise balanced designs to develop newdifference matrices over the additive group of GF (q). A second class of constructions gives difference matrices overgroups whose orders are not (necessarily) prime powers.     

Adams完备化与局部化的等价性

本文在一般的范畴上考虑了幂等对与Ａｄａｍｓ完备化的关系，证明了它们是等价的     

Incomplete Orthogonal Distance Regression

A common method of fitting curves and surfaces to data is to minimize the sum of squares of the orthogonal distances from the data points to the curve or surface, a process known as orthogonal distance regression. Here we consider fitting geometrical objects to data when some orthogonal distances are not available. Methods based on the Gauss–Newton method are developed, analyzed and illustrated by examples. AMS subject classification (2000) 65D10, 65K05.     

Parameter Inequalities for Orthogonal Arrays with Mixed Levels

An important question in the construction of orthogonal arrays is what the minimal size of an array is when all other parameters are fixed. In this paper, we will provide a generalization of an inequality developed by Bierbrauer for symmetric orthogonal arrays. We will utilize his algebraic approach to provide an analogous inequality for orthogonal arrays having mixed levels and show that the bound obtained in this fashion is often sharper than Raos bounds. We will also provide a new proof of Raos inequalities for arbitrary orthogonal arrays with mixed levels based on the same method.     

A Class of Orthogonal Polynomials Suggested by a Trigonometric Hamiltonian: Symmetric States

A new subclass of the Jacobi polynomials arising in the exact analytical solution of the one-dimensional Schrödinger equation with a trigonometric potential has been introduced. The polynomials which consist of a free parameter are not ultraspherical polynomials and have been simply named the -polynomials since they are generated by a trigonometric Hamiltonian. In certain sense, it is shown that the -polynomials can be regarded as a generalisation of the airfoil polynomials or the Chebyshev polynomials of the third kind. This paper is intended to discuss the basic properties of the polynomials so defined.     

Janossy Densities. I. Determinantal Ensembles

We derive an elementary formula for Janossy densities for determinantal point processes with a finite rank projection-type kernel. In particular, for =2 polynomial ensembles of random matrices we show that the Janossy densities on an interval I can be expressed in terms of the Christoffel–Darboux kernel for the orthogonal polynomials on the complement of I.     

Characterizations of Bochner–Krall Orthogonal Polynomials of Jacobi Type

Let $\{P_n(x) \}_{n=0}^\infty$ be an orthogonal polynomial system relative to a compactly supported measure. We find characterizations for $\{P_n(x) \}_{n=0}^\infty$ to be a Bochner--Krall orthogonal polynomial system, that is, $\{P_n(x) \}_{n=0}^\infty$ are polynomial eigenfunctions of a linear differential operator of finite order. In particular, we show that $\{P_n(x) \}_{n=0}^\infty$ must be generalized Jacobi polynomials which are orthogonal relative to a Jacobi weight plus two point masses.     

Detecting Mass Points of Representing Measures

We discuss a possibility of deciding whether measures representing a moment sequence or realizing orthogonality of polynomials have atoms. This is done on the real line and in several variables.     

On the Bochner theorem on orthogonal operators

We prove the following theorem. Any isometric operator , that acts from the Hilbert space with nonnegative weight to the Hilbert space with nonnegative weight , allows for the integral representation

where the kernels and satisfy certain conditions that are necessary and sufficient for these kernels to generate the corresponding isometric operators.