Table of Content

30 September 2012, Volume 27 Issue 3

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The Shock Solution for a Class of Quasilinear Singularly Perturbed Boundary Value Problems

CHEN Ting, YAO Jing-sun

2012, 27(3):  317-322. 

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The existence and asymptotic behavior of solution for a class of quasilinear singularly perturbed boundary value problems are discussed under suitable conditions by the theory of differential inequalities and matching principle.



One Note on the Convexity Radius of Holomorphic Mappings on the Unit Ball in Cⁿ 

XU Ji-jun, WANG Xiao-feng, LIU Hao

2012, 27(3):  323-327. 

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In this paper, we prove that: if M is a family which has convexity radius, then the convexity radius for M and the second order item coefficients of every mapping in M are closely related to each other. As an application, we show that the convexity radius of starlike mappings r(S*) < 2-√3.

Adjacent Vertex-distinguishing E-total Coloring on Some Join Graphs C_mVG_n

WANG Ji-shun

2012, 27(3):  328-336. 

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Let G(V, E) be a simple connected graph and k be positive integers. A mapping f from V∪E to {1, 2, ··· , k} is called an adjacent vertex-distinguishing E-total coloring of G(abbreviated to k-AVDETC), if for uv ∈ E(G), we have f(u) ≠ f(v), f(u) ≠ f(uv), f(v) ≠ f(uv), C(u) ≠C(v), where C(u) = {f(u)}∪{f(uv)|uv ∈ E(G)}. The least number of k colors required for which G admits a k-coloring is called the adjacent vertex-distinguishing E-total chromatic number of G is denoted by x^e_at(G). In this paper, the adjacent vertexdistinguishing E-total colorings of some join graphs C_m∨G_n are obtained, where G_n is one of a star S_n, a fan F_n, a wheel W_n and a complete graph Kn. As a consequence, the adjacent vertex-distinguishing E-total chromatic numbers of C_m∨G_n are confirmed. 

Positive Solutions for First-order PBVPs on Time Scales

SONG Chang-xiu

2012, 27(3):  337-343. 

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In this paper, the author studies the following nonlinear dynamic equation {x△(t) = r(t)x(σ(t)) + f(t, x(σ(t))), t ∈ [0, T ], x(0) = x(σ(T )). By applying and improving the generalized form of Leggett-Williams fixed point theorem, sufficient conditions are established for the existence of positive solutions.



Coefficient Multipliers on Some Analytic Function Spaces

YUE Xiu-kui

2012, 27(3):  344-351. 

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In this paper, we give some new results of the coefficient multiplier of some analytic function spaces, characterize the coefficient multiplier spaces (H_α,H_β) and (A^p,α), A^q,β) with 0 < p ≤ 1, p ≤ q ≤∞, 0 ≤α < β < ∞ and show (H_α, H_β) = H_β-α with 0 < α < β < ∞.



Composition-integral Type Operators from F(p, q, s) Spaces to Bloch-type Spaces

LV Xiao-fen, YING Shao-hong

2012, 27(3):  352-356. 

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Uniqueness Theorem of Algebroidal Function in the Unit Disc

ZHANG Xiao-mei, SUN Dao-chun

2012, 27(3):  357-363. 

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In this paper, discussed are the problems about uniqueness of algebroidal functions in the unit disc with share-values in a sector domain instead of the whole disk. Results are obtained extending some uniqueness theorems of meromorphic functions.



Coincidence Points and Almost-like Coincidence Points on Generalized Convex Spaces with Applications

PIAO Yong-jie, SHI Ren-shu

2012, 27(3):  364-370. 

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We introduce the concept of a weakly G-quasiconvex map with respect to a map on generalized convex spaces and use the concept to prove coincidence point theorems and almost-like coincidence point theorems. As applications of the above results, we derive almost fixed point theorems and fixed point theorem. These main results generalize and improve some known results in the literature.



Exact Travelling Wave Solutions for a Combined KdV and Schwarzian KdV Equation

LI Ling-xiao, LI Er-qiang

2012, 27(3):  371-374. 

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In this paper the (G’/G)-expansion method is used to find exact travelling wave solutions for a combined KdV and Schwarzian KdV equation. As a result, multiple travelling wave solutions with arbitrary parameters are obtained, which are expressed by hyperbolic functions, trigonometric functions and rational functions. When the parameters are taken as special values, the solitary waves are derived from the travelling waves. The (G’/G)-expansion method presents a wider applicability for handling nonlinear wave equations. 


The Properties of k-quasi-∗-A(n) Operator

ZUO Fei, SHEN Jun-li

2012, 27(3):  375-381. 

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An operator T is called k-quasi-*-A(n) operator, if T^*k|T¹⁺ⁿ|^2/(1+n)T^k≥T^*k|T^*|²T^k, k ∈ Z, which is a generalization of quasi-*-A(n) operator. In this paper we prove some properties of k-quasi-*-A(n) operator, such as, if T is a k-quasi-*-A(n) operator and N(T )N(T^*), then its point spectrum and joint point spectrum are identical. Using these results, we also prove that if T is a k-quasi-*-A(n) operator and N(T )N(T^*), then the spectral mapping theorem holds for the Weyl spectrum and for the essential approximate point spectrum. 

Global Existence for Thermoelastic Plates with Memory

MA Zhi-yong, ZHANG Ling-rui

2012, 27(3):  382-388. 

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In this paper, we shall establish some global existence results for the higherdimensional nonhomogeneous, linear, semilinear and nonlinear Thermoelastic plates with memory respectively by using semigroup approach. The existence and decay of solutions of homogeneous linear problem has been solved by Romero [1].


Notes on Strongly n-Gorenstein Projective, Injective and Flat Modules

SHANG Wen-liang

2012, 27(3):  389-396. 

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In this paper, we mainly investigate some properties of strongly n-Gorenstein projective, injective and flat modules under the extension of rings, which mainly including excellent extensions, morita equivalences, polynomial extensions and localizations.



The Credibility Models under LINEX Loss Functions

WEN Li-min, ZHANG Xian-kun, ZHENG Dan, FANG Jing

2012, 27(3):  397-402. 

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LINEX(linear and exponential) loss function is a useful asymmetric loss function. The purpose of using a LINEX loss function in credibility models is to solve the problem of very high premium by suing a symmetric quadratic loss function in most of classical credibility models. The Bayes premium and the credibility premium are derived under LINEX loss function. The consistency of Bayes premium and credibility premium were also checked. Finally, the simulation was introduced to show the differences between the credibility estimator we derived and the classical one. 


Approximate Analytic Solution for a Class of Generalized Nonlinear Singularly Perturbed Time-delay Model in the Critical Case 

WANG Na

2012, 27(3):  403-408. 

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Based on the boundary layer corrective method, a class of generalized nonlinear perturbed model in the critical case is studied. The asymptotic solution for the original equation is constructed. And the method is of significance to seek approximate solutions to other nonlinear models.



Sufficient Optimality Conditions for Multiobjective Programming Involving (V,ρ)h,φ-type I Functions

ZHANG Qing-xiang, JIANG Yan, KANG Rui-rui

2012, 27(3):  409-416. 

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New classes of functions namely (V, ρ)_h,φ-type I, quasi (V, ρ)h,φ-type I and pseudo (V, ρ)_h,φ-type I functions are defined for multiobjective programming problem by using BenTal’s generalized algebraic operation. The examples of (V, ρ)_h,φ-type I functions are given. The sufficient optimality conditions are obtained for multi-objective programming problem involving above new generalized convexity.



Diophantine Approximation with Two Primes and One Square of Prime

LI Wei-ping, WANG Tian-ze

2012, 27(3):  417-423. 

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We show that if λ₁, λ₂, λ₃ are non-zero real numbers, not all of the same sign, η is real and λ₁/λ₂ is irrational, then there are infinitely many ordered triples of primes (p₁, p₂, p₃) for which |λ₁p₁+λ₂p₂+λ₃p²₃₊η| < (maxp_j )- 1/40 (logmaxp_j)⁴.



On Utility Maximization with Random Interval Payoffs

YOU Su-rong, PENG Yu-zheng, ZHAO Fei-fei

2012, 27(3):  424-431. 

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This article discusses the problem of utility maximization in a market with random-interval payoffs without short-selling prohibition. A novel expected utility model is given to measure an investor’s subjective view toward random interval wealth. Some techniques are proposed to transfer a complex programming involving interval numbers into a simple non-linear programming. Under the existence of the optimal strategy, relations between the optimal strategy and assets’ prices are discussed. Some properties of the maximal utility function with respect to the endowment are given. 


Pseudo-umbilical Biharmonic Submanifolds in Constant Curvature Spaces

DU Li, ZHANG Juan

2012, 27(3):  432-438. 

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The conjecture [1] asserts that any biharmonic submanifold in sphere has constant mean curvature. In this paper, we first prove that this conjecture is true for pseudo-umbilical biharmonic submanifolds M n in constant curvature spaces S n+p (c)(c > 0), generalizing the result in [1]. Secondly, some sufficient conditions for pseudo-umbilical proper biharmonic submanifolds M n to be totally umbilical ones are obtained.



The Smoothing Newton Method for Solving the Extended Linear Complementarity Problem

TANG Jia, MA Chang-feng

2012, 27(3):  439-446. 

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The extended linear complementarity problem(denoted by ELCP) can be reformulated as the solution of a nonsmooth system of equations. By the symmetrically perturbed CHKS smoothing function, the ELCP is approximated by a family of parameterized smooth equations. A one-step smoothing Newton method is designed for solving the ELCP. The proposed algorithm is proved to be globally convergent under suitable assumptions.



On AP-property of Function Spaces 

SHEN Rong-xin

2012, 27(3):  447-451. 

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In this paper, it is discussed the AP-property of function spaces. We prove that for any compact network α for a space X which is closed under finite unions, (1) if Cα(X) is an AP-space and X is paracompact, then X is a Hurewicz space; (2) if Cα(X) is an AP-space which has countable tightness, then Cα(X) is discretely generated.





The Generalized Roper-suffridge Operator in Banach Spaces 

WANG Xiao-feng, RUAN Lin-yao, ZHANG Fang-fang

2012, 27(3):  452-457. 

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In this paper, by the definition of spirallike mapping of type β and order α ,we discuss that the generalized Roper-Suffridge extension operator preserves spirallikeness of type β and order α in complex Banach spaces.



Existence of Sign-changing Solution for Three-point Boundary Value Problems

LI Chun-yan, SU Ya-juan

2012, 27(3):  458-466. 

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In this paper, by using the fixed-point index theory, we study the existence of sign-changing solution of some three-point boundary value problems {y ’’(t) + f(y) = 0, t ∈ [0, 1], y’ (0) = 0, y(1) = αy(η), where 0 < α < 1, 0 < η < 1, f : R → R is continuous, strictly increasing and f(0) = 0.






Spreading Speed for a Periodic Reaction-diffusion Model with Nonmonotone Birth Function 

HUANG Ye-hui, WENG Pei-xuan

2012, 27(3):  467-474. 

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A reaction-diffusion model for a single species with age structure and nonlocal reaction for periodic time t is derived. Some results about the model with monotone birth function are firstly introduced, and then by constructing two auxiliary equations and squeezing method, the spreading speed for the system with nonmonotone birth function is obtained.