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Table of Content
30 December 2014, Volume 29 Issue 4
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Strong Law of Large Numbers for Array of Rowwise AANA Random Variables
CHEN Zhi-yong, LIU Ting-ting, WANG Xue-jun, LI Xiao-qin
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.
On Laguerre Isopararmetric Hypersurfaces in R
7
JI Xiu, HU Chuan-feng
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 R
7
.
Observations on Irreducible Sets and Sober Spaces
CHEN Dong-li, ZHANG Yan
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.
On Strongly Regular Rings
BAN Xiu-he, LIANG Shi-jian, YIN Chuang
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.
Fast Parallel Method for Polynomial Evaluation at Points in Arithmetic Progression
LU Jian-kang, CHEN Hai-biao, JING Rui-xing
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.
Linear Commuting Maps on Parabolic Subalgebras of Finite-dimensional Simple Lie Algebras
CHEN Zheng-xin, WANG Bing
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.
Study on the Relation of Definite Integral and Indefinite Integral
SUN Bao-fa
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.
Rectangular Ring Congruences on an E-inversive Semiring
CHENG Zi-qiang, ZHOU Yuan-lan, PAN Shi-ju
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.
On a Discrete Fractional Boundary Value Problem with Nonlocal Fractional Boundary Conditions
HUANG Zhong-min, XIE Zuo-shi, HOU Cheng-min
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-strongly Gorenstein Projective and Injective and Flat Modules
YANG Xiao-yan
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.
On the Cycle Structure of Iteration Graphs over the Unit Group Z
n
*
JU Teng-xia, WU Mei-yun
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.
A Kind of Identities for Products Reciprocals of q-binomial Coefficients
YANG Ji-zhen, WANG Yun-peng
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 Superalgebras
SHEN Zhen-jun, WEI Zhu, ZHANG Qing-cheng
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.
On the Strong Rates of Convergence for Arrays of Rowwise Extended Negatively Dependent Random Variables
ZHENG Lu-lu, XU Chen, HUANG Xu-feng, WANG Xue-jun
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.
Some Notes on G-cone Metric Spaces
CAO Xiao-shuang, XU Shao-yuan
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.
Zeros of the Jones Polynomial for Torus Knots and 2-bridge Knots
HAN You-fa, ZHANG Rong-wei, WANG Lin-lin, MA Xiao-sha
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）
r
2） by the recursive form and discuss the distribution of their zeros.
A Class of Singular Integral Equation of Convolution Type with csc
（τ-θ）
Kernel
LI Ping-run
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 L
2
[-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 L
2
[-π, π].
The Jacobi Elliptic Function Method for Solving Zakharov Equation
WANG Qing
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.
