A purely algebraic characterization of the hyperreal numbers

The hyperreal numbers of nonstandard analysis are characterized in purely algebraic terms as homomorphic images of a suitable class of rings of functions.

     

大耦合孔同轴输出腔的3维解析分析

 在高功率微波器件中，通常采用大耦合孔的同轴微波输出腔，该腔为3维结构。采用场等效原理将腔体、耦合孔及其输出负载(行波边界)进行分区,每个区域中的场由界面上的磁流密度决定。采用格林函数积分法可得每个区域中的3维场,再由各个区域的场匹配方程求得腔体的谐振频率、特性阻抗、有载品质因数、模式分布等参数。为腔体的计算和设计提供一种计算模型。     

微分多项式的值分布

文[2-6]讨论了亚纯函数或代数体函数的微分多项式ω‘(z)-αω^n(z)及ω（z)ω^n(z)的例外值问题。本文利用代数体函数的Nevanlinna值分布理论方法，研究了代数体函数的微分多项式P（ω^(k)(z))-aΠk=1^s(ω(z)-ak)^pk,及a(w^(k)(z)^tw^n(t)的Picard值问题，推广了他们的结果。     

Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting

In this paper we discuss Sobolev bounds on functions that vanish at scattered points in a bounded, Lipschitz domain that satisfies a uniform interior cone condition. The Sobolev spaces involved may have fractional as well as integer order. We then apply these results to obtain estimates for continuous and discrete least squares surface fits via radial basis functions (RBFs). These estimates include situations in which the target function does not belong to the native space of the RBF.

     

A new summation identity for the Srivastava-Singhal polynomials

In his recent investigations involving differential operators for some generalizations of the classical Laguerre polynomials, H. Bavinck [J. Phys. A Math. Gen. 29 (1996) L277-L279] encountered and proved a certain summation identity for the classical Laguerre polynomials. The main object of this sequel to Bavinck's work is to prove a generalization of this summation identity for the Srivastava-Singhal polynomials. The demonstration, which is presented here in the general case, differs markedly from the earlier proof given for the known special case. It is also indicated how the general summation identity can be applied to derive the corresponding result for one class of the Konhauser biorthogonal polynomials.     

Relationship between the 2-body Parameters of the Biswas-Hamann and the Bauer-Maysenholder-Seeger Potential Functions

A theoretical relation between the Bauer-Maysenholder-Seeger (BMS) and the Biswas-Hamann (BH) potential function has been developed herein for the case of 2-body interaction. By equating derivatives of these two potential functions for the 2-body part, a loose form of BMS is expressed in terms of BH parameters with a scaling factor. The validity of the developed parametric relationships has been graphically demonstrated, and the suitability discussed with reference to the extent and direction of bond distortion.     

Two-function upward-downward minimax theorems

Two-function upward-downward minimax theorems are derived which contain Simons upward-downward minimax theorem as well as Domokos minimax theorem as special cases. Here the convexity assumptions on two functions are given by mixing up their values as means proposed by Lin and Quan.     

SCDA for 3D lattice gases with repulsive interaction

The selfconsistent diagram approximation (SCDA) is generalized for three-dimensional lattice gases with nearest neighbor repulsive interactions. The free energy is represented in a closed form through elementary functions. Thermodynamical (phase diagrams, chemical potential and mean square fluctuations), structural (order parameter, distribution functions) as well as diffusional characteristics are investigated. The calculation results are compared with the Monte Carlo simulation data to demonstrate high precision of the SCDA in reproducing the equilibrium lattice gas characteristics. It is shown that similarly to two-dimensional systems the specific statistical memory effects strongly influence the lattice gas diffusion in the ordered states. Received 7 August 2002 / Received in final form 22 January 2003 Published online 24 April 2003     

Moment vanishing properties of harmonic Bergman functions

We show that Poisson integrals belonging to certain weighted harmonic Bergman spaces b_δ^p on the upper half-space must have the moment vanishing properties. As an application, we show that b₀^p, p?1, contains a dense subspace whose members have the horizontal moment vanishing properties. Also, we derive related weighted norm inequalities for Poisson integrals. As a consequence, we obtain a characterization for Poisson integrals of continuous functions with compact support in order to belong to b_δ^p.     

Some families of hypergeometric polynomials and associated integral representations

The main object of this paper is to investigate several general families of hypergeometric polynomials and their associated single-, double-, and triple-integral representations. Some known or new consequences of the general results presented here, involving such classical orthogonal polynomials as the Jacobi, Laguerre, Hermite, and Bessel polynomials, and various other relatively less familiar hypergeometric polynomials, are also considered. Each of the integral representations, which are derived in this paper, may be viewed also as a linearization relationship for the product of two different members of the associated family of hypergeometric polynomials.