Euler-Seidel method for certain combinatorial numbers and a new characterization of Fibonacci sequence

In this paper we use the Euler-Seidel method for deriving new identities for hyperharmonic and r-Stirling numbers. The exponential generating function is determined for hyperharmonic numbers, which result is a generalization of Gosper’s identity. A classification of second order recurrence sequences is also given with the help of this method.      

Hyperpolarizability of donor-acceptor azines subject to push-pull character and steric hindrance

The push-pull character of two series of donor-acceptor azines has been quantified by ¹³C, ¹⁵N chemical shift differences of the partial C(1)N(1) and N(2)C(2) double bonds in the central linking C(1)N(1)-N(2)C(2) unit and by the quotient of the occupations of the bonding π and anti-bonding π^∗ orbitals of these bonds. Excellent correlation of the latter push-pull parameter with the corresponding bond lengths d_CN strongly recommend both the occupation quotients π^∗/π and the corresponding bond lengths as reasonable sensors for quantifying the push, pull character along the CN-NC linking unit, for the donor-acceptor quality of the two series of azines and for the molecular hyperpolarizability ß₀ of these compounds. Within this context, reasonable conclusions concerning the interplay of steric hindrance in the chromophore, push-pull character and hyperpolarizability of the azines and their application as NLO materials will be drawn.     

色散方程两组三阶恒稳显格式

采用组合差商法对色散方程ut=auxxx(a为常数)的初边值问题,构造了两组互为对称带参数的三层显式差分格式.它们空间宽度为4,其局部截断误差为O(τ+h3),绝对稳定.而且计算时无方向性的约束,即不管a的符号如何,每一组格式均可以计算.最后给出了数值例子,数值结果表明了理论分析的正确性.     

Reducing Subspaces of Toeplitz Operators on N_φ-type Quotient Modules on the Torus

In this paper, we prove that the Toeplitz operator with finite Blaschke product symbol Sψ（z） on Nφ has at least m non-trivial minimal reducing subspaces, where m is the dimension of H^2（Гω）⊙φ（ω）H^2（Гω）. Moreover, the restriction of Sψ（z） on any of these minimal reducing subspaces is unitary equivalent to the Bergman shift Mz.     

Generalized Rayleigh quotient and finite element two-grid discretization schemes

This study discusses generalized Rayleigh quotient and high efficiency finite element discretization schemes. Some results are as follows: 1) Rayleigh quotient accelerate technique is extended to nonselfadjoint problems. Generalized Rayleigh quotients of operator form and weak form are defined and the basic relationship between approximate eigenfunction and its generalized Rayleigh quotient is established. 2) New error estimates are obtained by replacing the ascent of exact eigenvalue with the ascent of fin...     

A Property Satisfying Reducedness over Centers

This article concerns a ring property called pseudo-reduced-over-center that is satisfied by free algebras over commutative reduced rings.The properties of radicals of pseudo-reduced-over-center rings are investigated,especially related to polynomial rings.It is proved that for pseudo-reduced-over-center rings of nonzero characteristic,the centers and the pseudo-reduced-over-center property are preserved through factor rings modulo nil ideals.For a locally finite ring R,it is proved that if R is pseudo-reduced-over-center,then R is commutative and R/J(R) is a commutative regular ring with J(R) nil,where J(R) is the Jacobson radical of R.     

对称环的扩张

本文首先考虑了对称环的性质和基本的扩张．其次讨论了几种多项式环的对称性,且证明了:如果R是约化环,则R[x]／(xn)是对称环,其中(xn)是由xn生成的理想,n是一个正整数．最后证明了:对一个右Ore环R,R是对称环当且仅当R的古典右商环Q是对称环．