Laguerre expansion on the Heisenberg group and Fourier-Bessel transform on ?n

Given a principal value convolution on the Heisenberg group H _n = ℂ ⁿ × ℝ, we study the relation between its Laguerre expansion and the Fourier-Bessel expansion of its limit on ℂ ⁿ . We also calculate the Dirichlet kernel for the Laguerre expansion on the group H _n . Dedicated to Professor Sheng GONG on the occasion of his 75th birthday     

An Improved Extra-Gradient Method for Minimizing a Sum of p-norms—A Variational Inequality Approach

This paper presents a variational inequality (VI) approach to the problem of minimizing a sum of p-norms. First the original problem is reformulated as an equivalent linear VI. Then an improved extra-gradient method is presented to solve the linear VI. Applications to the problem of p-norm Steiner Minimum Trees (SMT) shows that the proposed method is effective. Comparison with the general extra-gradient method is also provided to show the improvements of the new method.     

用三个关系式与Mathematica软件求第二类自然数幂和公式

首先介绍三个第二类自然数幂和关系式并对其中的两式给出证明,接着利用这些关系式与数学软件M athem atica4.0,给出求解第二类自然数幂和公式的若干机械计算方法.     

Laguerre expansion on the Heisenberg group and Fourier-Bessel transform on C~n Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

Given a principal value convolution on the Heisenberg group Hn = Cn×R, we study the relation between its Laguerre expansion and the Fourier-Bessel expansion of its limit on Cn. We also calculate the Dirichlet kernel for the Laguerre expansion on the group Hn.     

On Polynomials of Special Form over a Finite Field of Odd Characteristic Attaining the Weil Bound

An explicit construction of polynomials over a finite field of odd characteristic, for which the absolute value of trigonometric sums attains the Weil bound, is based on the construction of cyclic matrices of given rank. Dickson polynomials of the second kind play an essential role in the study of such matrices.__________Translated from Matematicheskie Zametki, vol. 78, no. 1, 2005, pp. 16–25.Original Russian Text Copyright © 2005 by L. A. Bassalygo, V. A. Zinov’ev.     

Pollaczek polynomials and hypergeometric representation

The Pfaff-Euler Transform for hypergeometric ₂ F ₁-series is applied to provide a direct and elementary proof that the hypergeometric representation with algebraic parameters of Pollaczek polynomials are indeed polynomials. Dedicated to Richard Askey on the occasion of his 70th birthday. 2000 Mathematics Subject Classification Primary—33C45; Secondary—33C05     

A degree sum condition for long cycles passing through a linear forest

Let G be a (k+m)-connected graph and F be a linear forest in G such that |E(F)|=m and F has at most k-2 components of order 1, where k?2 and m?0. In this paper, we prove that if every independent set S of G with |S|=k+1 contains two vertices whose degree sum is at least d, then G has a cycle C of length at least min{d-m,|V(G)|} which contains all the vertices and edges of F.     

On RSA moduli with almost half of the bits prescribed

We show that using character sum estimates due to H. Iwaniec leads to an improvement of recent results about the distribution and finding RSA moduli M=pl, where p and l are primes, with prescribed bit patterns. We are now able to specify about n bits instead of about n/2 bits as in the previous work. We also show that the same result of H. Iwaniec can be used to obtain an unconditional version of a combinatorial result of W. de Launey and D. Gordon that was originally derived under the Extended Riemann Hypothesis.     

关于多元幂级数

引入了多元函数项级数的概念,给出了其收敛域及和函数的定义;通过详实的例子讨论了多元幂级数的收敛域、和函数及多元函数展开为多元幂级数的计算方法.     

Comparison principles for viscosity solutions of elliptic equations via fuzzy sum rule

A comparison principle for viscosity sub- and super-solutions of second order elliptic partial differential equations is derived using the “fuzzy sum rule” of non-smooth calculus. This method allows us to weaken the assumptions made on the function F when the equation F(x,u,Du,D²u)=0 is under consideration.