Table of Content

30 March 2018, Volume 33 Issue 1

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Common Fixed Point Results for Quasi-contractions Involving Altering Distance Functions in Ordered Cone Metric Spaces

SONG Ji-ping, WANG Mao-fa

2018, 33(1):  1-16.  doi:10.13371/j.cnki.chin.q.j.m.2018.01.001

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Some common fixed point results for mappings satisfying a quasi-contractive condition which involves altering distance functions are obtained in partially ordered complete cone metric spaces. A sufficient condition for the uniqueness of common fixed point is proved. Also, an example is given to support our results. 

Some Generalized Normal Subgroups and p-nilpotency of Finite Groups

ZHONG Guo, LIN Shi-Xun, CHEN Qi-le, QIN Li-hua

2018, 33(1):  17-24.  doi:10.13371/j.cnki.chin.q.j.m.2018.01.002

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In this paper, the influence of s-semipermutable, c^#-normal, subnormally embedded and ss-quasinormal subgroups on the p-nilpotency of finite groups is investigated and some recent results are generalized.

The Growth Order of Solutions of Systems Complex Difference Equations

LI Xiong-ying

2018, 33(1):  25-31.  doi:10.13371/j.cnki.chin.q.j.m.2018.01.003

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In this paper, using Nevanlinna theory of the value distribution of meromorphic functions, the problem of growth order of solutions of a class of system of complex difference equations is investigated, some results are improved and generalized. More precisely,some results of the growth order of solutions of system of differential equations to difference equations are extended. 

The {P; k + 1}-reflexive Solution to System of Matrix Equations AX = C; XB = D

CAO Nan-bin, ZHANG Yu-ping

2018, 33(1):  32-42.  doi:10.13371/j.cnki.chin.q.j.m.2018.01.004

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Let P ∈ C^n×n be a Hermitian and {k + 1}-potent matrix, i.e., P^k+1= P = P^*,where（·）^*stands for the conjugate transpose of a matrix. A matrix X ∈ Cn×nis called{P, k + 1}-reflexive（anti-reflexive） if PXP = X（P XP =-X）. The system of matrix equations AX = C, XB = D subject to {P, k + 1}-reflexive and anti-reflexive constraints are studied by converting into two simpler cases: k = 1 and k = 2, the least squares solution and the associated optimal approximation problem are also considered.

The Credibility Estimators under MLINEX Loss Function

ZHANG Qiang, CUI Qian-qian, CHEN Ping

2018, 33(1):  43-50.  doi:10.13371/j.cnki.chin.q.j.m.2018.01.005

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In this paper, MLINEX loss function was considered to solve the problem of high premium in credibility models. The Bayes premium and credibility premium were obtained under MLINEX loss function by using a symmetric quadratic loss function. A credibility model with multiple contracts was established and the corresponding credibility estimator was derived under MLINEX loss function. For this model the estimations of the structure parameters and a numerical example were also given. 

Implicative Pseudo Valuations on Hoops

WANG Mei, XIN Xiao-long, WANG Jun-tao

2018, 33(1):  51-60.  doi:10.13371/j.cnki.chin.q.j.m.2018.01.006

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The concept of implicative pseudo valuations on hoops is introduced and some related properties are investigated. As an application of properties of pseudo valuations, we find the relationship between a pseudo valuation and an implicative pseudo valuation and obtain some characterizations of implicative pseudo valuations. In particular, we show that a pseudo valuation on regular hoops is implicative if and only if it satisfies φ(x■x’) = 0.This result will provide a more general algebraic foundation for pseudo valuations theory on algebraic structures based on substructure logic. 

An Elliptic Gradient Estimate for A Non-homogeneous Heat Equation on Complete Noncompact Manifolds

JI Xiang

2018, 33(1):  61-67.  doi:10.13371/j.cnki.chin.q.j.m.2018.01.007

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Let M be an n-dimensional complete noncompact Riemannian manifold. In this paper, we will give the elliptic gradient estimate for positive smooth solutions to the non-homogeneous heat equation(?_t-△)u(x, t) = A(x, t)when the metric evolves under the Ricci flow. As applications, we get Harnack inequalities to compare solutions at the same time. 

A New Method for A Rank Subtractivity Formula

ZHANG Qian, YUAN Yong-xin

2018, 33(1):  68-72.  doi:10.13371/j.cnki.chin.q.j.m.2018.01.008

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Let A be an m by n matrix of rank l, and let M and N be m by k and n by q matrices, respectively, where k is not necessarily equal to q or rank(M AN) < min(k, q). In this paper, we provide some necessary and sufficient conditions for the validity of the rank subtractivity formula: rank(A-AN(M AN)-M A) = rank(A)-rank(AN(M AN)-M A)by applying the full rank decomposition of A = F G(F ∈ Rm×l, G ∈ Rl×n, rank(A) =rank(F) = rank(G) = l) and the product singular value decomposition of the matrix pair[F M, GN ]. This rank subtractivity formula along with the condition under which it holds is called the extended Wedderburn-Guttman theorem. 

On Approximation by Two Kinds Modified Durrmeyer Rational Interpolation Operators in  L_ω^M Spaces

ZHANG Xu, WU Ga-ridi

2018, 33(1):  73-78.  doi:10.13371/j.cnki.chin.q.j.m.2018.01.009

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This paper discusses the approximation problem of two kinds Durrmeyer rational interpolation operators in Orlicz spaces with weight functions,and gives a kind of Jackson type estimation of approximation order by means of continuous modulus, Hardy-Littlewood maximal function, convexity of N function and Jensen inequality. 

Strongly Ding projective modules with respect to a semidualizing module

ZHAO Liang

2018, 33(1):  79-92.  doi:10.13371/j.cnki.chin.q.j.m.2018.01.010

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This paper is a study of strongly Ding projective modules with respect to a semidualizing module. The class of strongly Ding flat modules with respect to a semidualizing module is also investigated, and the relationship between strongly Ding projective modules and strongly Ding flat modules with respect to a semidualizing module is characterized.Some well-known results on strongly Ding projective modules, n-strongly Ding projective modules and strongly D_C-projective modules are generalized and unified. 

The Proof of Structural Stability of Hyperbolic Fixed Points in Ordinary Di®erential Equations

WANG Qi, ZHANG Shuo

2018, 33(1):  93-97.  doi:10.13371/j.cnki.chin.q.j.m.2018.01.011

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In ordinary differential equations, structural stability of hyperbolic fixed points is a classical result, but the proof of this result in [2] has same small mistake. In this paper,we will correct the above mistake by using the Hartman theorem and its idea. 

On the Cofficient Inequality for A Subclass of Starlike Mappings in Several Complex Variables

GUO Sheng-ti, XU Qing-hua

2018, 33(1):  98-110.  doi:10.13371/j.cnki.chin.q.j.m.2018.01.012

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Let S^* be the familiar class of normalized univalent functions in the unit disk.In [9], Keogh and Merkes proved that for a function f（z） = z +∑k=2∞ a_kz^k in the class S^*,then |a₃-λa_2^2| ≤ max{1, |3-4λ|}, λ∈ C. In this article, we investigate the corresponding problem for the subclass of starlike mappings defined on the unit ball in a complex Banach space, on the unit polydisk in Cⁿand the bounded starlike circular domain in C^*, respectively.