数学季刊

陈志勇, 刘婷婷, 王学军, 李晓琴

2014, 29(4): 475-485. doi:10.13371/j.cnki.chin.q.j.m.2014.04.001

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In this article, the strong laws of large numbers for array of rowwise asymptotically almost negatively associated(AANA) random variables are studied. Some sufficient conditions for strong laws of large numbers for array of rowwise AANA random variables are presented without assumption of identical distribution. Our results extend the corresponding ones for independent random variables to case of AANA random variables.

R⁷中的Laguerre等参超曲面

姬秀, 胡传峰

2014, 29(4): 486-500. doi:10.13371/j.cnki.chin.q.j.m.2014.04.002

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Let x : M → R ⁿ be an umbilical free hypersurface with non-zero principal curvatures, then x is associated with a Laguerre metric g, a Laguerre tensor L, a Laguerre form C, a Laguerre second fundamental form B, which are invariants of x under Laguerre transformation group. A classical theorem of Laguerre geometry states that M（n > 3） is characterized by g and B up to Laguerre equivalence. A Laguerre isopararmetric hypersurface is defined by satisfying the conditions that C = 0 and all the eigenvalues of B with respect to g are constant. It is easy to see that all Laguerre isopararmetric hypersurfaces are Dupin hypersurfaces. In this paper, we established a complete classification for all Laguerre isopararmetric hypersurfaces with three distinct principal curvatures in R⁷.

不可约集与Sober空间

陈东立, 张彦

2014, 29(4): 501-504. doi:10.13371/j.cnki.chin.q.j.m.2014.04.003

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This paper, using the monads theory in the topological space, gives a new characterization of irreducible sets in the nonstandard enlarged models. Further, the discretization expression of Sober topological spaces is presented.

关于强正则环

班秀和, 梁世健, 尹闯

2014, 29(4): 505-508. doi:10.13371/j.cnki.chin.q.j.m.2014.04.004

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In this paper we investigate strongly regular rings. In terms of W-ideals of rings some characterizations of strongly regular rings are given.

求等差数列多项式函数值的快速并行算法

卢健康, 陈海标, 敬瑞星

2014, 29(4): 509-515. doi:10.13371/j.cnki.chin.q.j.m.2014.04.005

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We present a fast method for polynomial evaluation at points in arithmetic progression. By dividing the progression into m new ones and evaluating the polynomial at each point of these new progressions recursively,this method saves most of the multiplications in the price of little increase of additions comparing to Horner’s method, while their accuracy are almost the same. We also introduce vector structure to the recursive process making it suitable for parallel applications.

单李代数的抛物子代数上的线性交换映射

陈正新, 汪冰

2014, 29(4): 516-522. doi:10.13371/j.cnki.chin.q.j.m.2014.04.006

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A map φ on a Lie algebra g is called to be commuting if [φ（x）, x] = 0 for all x ∈ g. Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0, P a parabolic subalgebra of L. In this paper, we prove that a linear mapφon P is commuting if and only if φ is a scalar multiplication map on P.

论定积分与不定积分的关系

孙宝法

2014, 29(4): 523-528. doi:10.13371/j.cnki.chin.q.j.m.2014.04.007

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Relation of definite integral and indefinite integral was discussed and an important result was gotten. If f（x） is bounded and has primary function, the formal definite integral \int^x_s \tilde{f}（t）dt is the indefinite integral of f（x）, where x is a self-variable, s is a parameter,\tilde{f}（x） is a function defined in（-∞, +∞）, which comes from f（x） by restriction and extension. In other words, the indefinite integral is a special form of definite integral, its lower integral limit and upper integral limit are all indefinite.

E-反演半环上的矩形环同余

程子强, 周媛兰, 潘是菊

2014, 29(4): 529-538. doi:10.13371/j.cnki.chin.q.j.m.2014.04.008

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In this paper, we discussed the property of rectangular band semiring congruence and ring congruence on a semiring and gave some characterizations and structure of rectangular ring congruence on an E-inversive semiring.

带有分数阶边界条件的离散分数阶边值问题

黄忠敏, 谢作诗, 侯成敏

2014, 29(4): 539-552. doi:10.13371/j.cnki.chin.q.j.m.2014.04.009

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In this paper, we investigate the nonlinear fractional difference equation with nonlocal fractional boundary conditions. We derive the Green’s function for this problem and show that it satisfies certain properties. Some existence results are obtained by means of nonlinear alternative of Leray-Schauder type theorem and Krasnosel-skii’s fixed point theorem.

n-强Gorenstein投射和内射和平坦模

杨晓燕

2014, 29(4): 553-564. doi:10.13371/j.cnki.chin.q.j.m.2014.04.010

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In this paper, we study some properties of n-strongly Gorenstein projective,injective and flat modules, and discuss some connections between n-strongly Gorenstein injective, projective and flat modules. Some applications are given.

单位群Z_n*上的迭代图的圈结构

居腾霞, 吴美云

2014, 29(4): 565-572. doi:10.13371/j.cnki.chin.q.j.m.2014.04.011

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In this paper, we consider the properties of iteration graphs over the unit group Z_n^*of the residue ring Z _n associated with the maps x → x ^p and compute the average values of tails and cycles of those iteration graphs.

一类含有q-二项式系数倒数乘积的恒等式

杨继真, 王云鹏

2014, 29(4): 573-582. doi:10.13371/j.cnki.chin.q.j.m.2014.04.012

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The purpose of this paper is to establish some identities with products of qHermite polynomials, q-ultraspherical polynomials and reciprocals of q-binomial coefficients.

Hom-Leibniz超代数

沈振军, 魏竹, 张庆成

2014, 29(4): 583-591. doi:10.13371/j.cnki.chin.q.j.m.2014.04.013

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We gived the definition of Hom-Leibniz superalgebra and studied its basic properties. In particular, the derivations of Hom-Leibniz Superalgebras are portrayed in detail.

END随机阵列的强收敛性

郑璐璐, 徐陈, 黄旭峰, 王学军

2014, 29(4): 592-601. doi:10.13371/j.cnki.chin.q.j.m.2014.04.014

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A general result on the strong convergence rate and complete convergence for arrays of rowwise extended negatively dependent random variables is established. As applications, some well-known results on negatively dependent random variables can be easily extended to the case of arrays of rowwise extended negatively dependent random variables.

关于G锥度量空间的一些注解

曹小双, 许绍元

2014, 29(4): 602-611. doi:10.13371/j.cnki.chin.q.j.m.2014.04.015

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In this paper, we introduce a G metric on the G-cone metric space and then prove that a complete G-cone metric space is always a complete G metric space and verify that a contractive mapping on the G-cone metric space is a contractive mapping on the G metric space. At last, we also give a new way to obtain the unique fixed point on G-cone metric space.

环面结和二桥结Jones多项式的零点

韩友发, 张容玮, 王琳琳, 马晓莎

2014, 29(4): 612-619. doi:10.13371/j.cnki.chin.q.j.m.2014.04.016

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We study zeros of the Jones polynomial and their distributions for torus knots and 2-bridge knots. We prove that e^{（2m+1）πi/2}and e^{（2m+1）πi/4}（m is a positive integer）can not be the zeros of Jones polynomial for torus knots T p,q by the knowledge of the trigonometric function. We elicit the normal form of Jones polynomials of the 2-bridge knot C（-2, 2, ···,（-1）^r2） by the recursive form and discuss the distribution of their zeros.

一类具有csc（τ-θ）核的卷积型奇异积分方程

李平润

2014, 29(4): 620-626. doi:10.13371/j.cnki.chin.q.j.m.2014.04.017

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In this paper, we propose and discuss a class of singular integral equation of convolution type with csc（τ- θ） kernel in class L₂[-π, π]. Using discrete Fourier transform and the lemma, this kind of equations is transformed to discrete system of equations, and then we obtain the solvable conditions and the explicit solutions in class L₂[-π, π].

解Zakharov方程的Jacobi椭圆函数法

王庆

2014, 29(4): 627-632. doi:10.13371/j.cnki.chin.q.j.m.2014.04.018

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The Zakharov equation to describe the laser plasma interaction process has very important sense, this paper gives the solitary wave solutions for Zakharov equation by using Jacobi elliptic function method.

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