Multiplicity of Solutions for Nonlinear Biharmonic Equation Involving Critical Parameter and Critical Exponent

WANG You-jun, SHEN Yao-tian

2011, 26(3): 317-324.

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By using variational method, the multiplicity of solutions for nonlinear biharmonic equation involving critical parameter and critical exponent are established.

Zeroes of the Bergman Kernels on Some New Hartogs Domains

WANG An, LIU Yu-lan

2011, 26(3): 325-334.

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We obtain the Bergman kernel for a new type of Hartogs domain. The corresponding LU Qi-Keng’s problem is considered.

An Operator Inequality for Three Operators

YANG Chang-sen, WANG Ya-qing

2011, 26(3): 335-342.

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As a generalization of grand Furuta inequality, recently Furuta obtain: If A≥ B≥0 with A>0, then for t∈[0,1] and p₁, p₂, p₃, p₄≥1, .... In this paper, we generalize this result for three operators as follow: If A≥B≥C≥0 with B>0, t∈[0,1] and p₁, p₂, ···, p_2n-1, p_2n≥1 for a natural number n. Then the following inequalities hold for r≥t, ..., where q_[2n]≡···.

The Extremal Problem on Cartan-egg Domain of the First Type

SU Jian-bing, LI Hai-tao

2011, 26(3): 343-349.

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In this paper, we study the extremal problem on Cartan-egg domain of the first type by using some inequalities. The extremal mapping and extremal value between the first type of Cartan-egg domain and the unit ball when k≤1 and k=2, m=2 are constructed.

Ergodicity of the IP P + M/M/c Queue

LI Xiao-hua, HOU Zhen-ting

2011, 26(3): 350-354.

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The IP P+M/M/c queueing system has been extensively used in the modern communication system. The existence and uniqueness of stationary distribution of the queue length L(t)for IP P+M/M/1 queue has been proved in [10]. In this paper, we shall give the suffcient and necessary conditions of l-ergodicity, geometric ergodicity, and prove that they are neither uniformly polynomial ergodicity nor strong ergodicity.

Cover a 3-regular Claw-free Graph by Induced Matchings

DONG Li, TANG Jing-yong, SONG Xin-yu

2011, 26(3): 355-359.

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The induced matching cover number of a graph G without isolated vertices, denoted by imc(G), is the minimum integer k such that G has k induced matchings {M₁,M₂,···,M_k} such that, V(M₁)∪V(M₂)∪···∪V(M_k) covers V(G). This paper shows that, if G is a 3-regular claw-free graph, then imc(G)∈{2,3}.

A Note on Normal Families of Meromorphic Functions and Sharing Set

XIAO Bing, WU Qi-feng, YUAN Wen-jun

2011, 26(3): 360-365.

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In the paper, we prove the main result: Let k(≥2) be an integer, and a, b and c be three distinct complex numbers. Let F be a family of functions holomorphic in a domain D in complex plane, all of whose zeros have multiplicity at least k. Suppose that for each f∈F, f(z) and f(k)(z) share the set {a,b,c}. Then F is a normal family in D.

Right pp Semigroups with Multiplicative Right Adequate Transversals

HU Yao-hua, GUO Xiao-jiang

2011, 26(3): 366-371.

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In this paper, the concept of right adequate transversals of rpp semigroups is introduced. We establish the structure of rpp semigroups with multiplicative right adequate transversals in terms of right normal bands and right adequate semigroups.In particular, some special cases are considered.

Solvability of Non-homogeneous Mixed Type Multi-point BVPs for Second Order Differential Equations with p-Laplacian

LIU Xing-yuan

2011, 26(3): 372-377.

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A class of multi-point boundary value problems are studied. Easily verified suffcient conditions to guarantee the existence of at least one solutions of above mentioned BVPs are established. The examples are presented to illustrate the main results.

A New Approach for Inverting the Pascal Matrix Plus a Scalar

YANG Sheng-liang, MA Cheng-ye

2011, 26(3): 378-382.

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In this paper, using the Jordan canonical form of the Pascal matrix P_n, we present a new approach for inverting the Pascal matrix plus a scalar P_n+aI_n for arbitrary real number a≠1.

Inverses and Powers of Matrices over an Incline

DUAN Jun-sheng, GUO Ai-ping, YUN Wen-zai

2011, 26(3): 383-387.

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Invertible conditions, indices and periods of matrices over an incline are considered. In all proofs multiplicative commutativity is not used. Some results about invertibility, indices and periods in a commutative incline are proved to be correct also for any incline.

The Energy-orthogonal Tetrahedral Finite Element for Fourth Order Elliptic Equations

LIU Ming-fang, CAO Ji-wei, CHEN Shao-chun

2011, 26(3): 388-393.

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In this paper, the 16-parameter nonconforming tetrahedral element which has an energy-orthogonal shape function space is presented for the discretization of fourth order elliptic partial differential operators in three spatial dimensions. The newly constructed element is proved to be convergent for a model biharmonic equation.

Normal Families of Holomorphic Functions Concerning Shared a Polynomial

LIU Zhi-hong, LI Ying-chun, HUANG Bin

2011, 26(3): 394-399.

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In this paper, we study normal families of holomorphic function concerning shared a polynomial. Let F be a family of holomorphic functions in a domain D, k(2) be a positive integer, K be a positive number and α(z) be a polynomial of degree p(p>1). For each f∈F and z∈D, if f and f sharedα(z)CM and |f^(k)(z)|<K whenever f(z)-α(z)=0 in D, then F is normal in D.

Approximation Theorems of Bernstein-Durrmeyer Operators in L^Ba_M Spaces

Approximation Theorems of Bernstein-Durrmeyer Operators in L Ba M Spaces SUN Zhi-ling

2011, 26(3): 400-404.

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With the weighted modulus of smoothness as a metric, we prove the direct and the inverse theorems of approximation by Bernstein-Durrmeyer operators in LBa M spaces. Especially an approximation equivalent theorem of the operators is also obtained.

The Semi-implicit Euler Method for Stochastic Pantograph Equations with Jumps

MAO Wei, HAN Xiu-jing, CHEN Bo

2011, 26(3): 405-409.

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In this paper, we present the semi-implicit Euler(SIE) numerical solution for stochastic pantograph equations with jumps and prove that the SIE approximation solution converges to the exact solution in the mean-square sense under the Local Lipschitz condition.

A Note on Totally Real Riemannian Foliations with Parallelized Mean Curvature Vectors in a Complex Projective Space

PENG Hui-chun

2011, 26(3): 410-414.

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We discussed a totally real Riemannian foliations with parallel mean curvature on a complex projective space. We carried out the divergence of a vector field on it and obtained a formula of Simons’type.

Higher-order Optimality Conditions for Henig Eﬃcient Solution in Set-valued Optimization under Cone-convexlike Maps

ZHANG Jian, WANG Qi-lin

2011, 26(3): 415-419.

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This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems. By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for Henig effcient solutions of set-valued optimization problems whose constraint condition is determined by a fixed set.

An Analytical Study of Leibniz’s Secant and Tangent on the Logical Basis of Mathematical Inﬁnity

ZHU Wu-jia, GONG Ning-sheng, DU Guo-ping

2011, 26(3): 420-425.

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Refs 1 and 2 provide the definition of the concepts of ‘potential infinity’(poi) and actual infinity(aci); Ref 3 discusses and verifies that poi and aci are a pair of contradictory opposites without intermediate (p,-p).The second part of this paper, i.e., §2, further discusses the manners in which a variable x approaches infinitely to its limit x0 using the poi and aci methods and concludes that, in any system compatible with both poi and aci, the two approaching manners are also a pair of contradictory opposites without intermediate (A,-A). Finally, on the basis of this conclusion, we reexamine the fundamental question of Leibniz’s Secant and Tangent Lines in calculus and the limit theory and offer our analysis and raise new questions.

Finite-time Control of Fuzzy Discrete-time Nonlinear System with Exogenous Disturbance

ZHANG Ying-qi, MU Xiao-wu, LIU Cai-xia

2011, 26(3): 426-433.

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This paper give criterions on finite-time control of fuzzy discrete-time nonlinear system subject to exogenous disturbance. Employing the Lyapunov function theory, several suffcient conditions including relaxed ones are presented for finite-time stability via fuzzy controller laws. An illustrative example is given to demonstrate the effectiveness of the proposed method.

N-soliton Solution for Two Multidimensional Analogues of the m-KdV Equation

MA Yun-ling

2011, 26(3): 434-439.

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Using the Hirota’s bilinear method, some new N-soliton solution are presented for two multidimensional analogues of the m-KdV equation w_t+w_{xxx ...}=0 in view of a different treatment.

F-Rough Integrals and Its Measurements

YU Xiu-qing, XU Feng-sheng, HAN Zhong-yue

2011, 26(3): 440-444.

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F-rough integrals is defined on the basis of the dual of function one direction S-rough sets, which has dynamic characteristics. Using F-rough integrals, the concepts of expansion measurement-expansion degree and expansion ratio are given. By expansion degree and expansion ratio the changing extent can be expressed with numbers, and the recognition principle of attribute effect on function equivalences is got.

A Property of Claw-free Graphs

LU Xiao-xu, LI Jing, WU Min

2011, 26(3): 445-447.

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In this paper we consider a property of claw-free graphs. We show that if d(u)+ d(v)≥ν(G)+2k+3, for every two nonadjacent vertices u and v, then G is 2k-vertex-deletable IM-extendable, where ν(G)=|V(G)|. And the bound is tight.

Further Results of Meromorphic Functions that Share a Polynomial

QIU Hui-ling

2011, 26(3): 448-452.

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In this paper, we use the theory of value distribution and study the uniqueness of meromorphic functions. We will prove the following result: Let f(z) and g(z) be two transcendental meromorphic functions, p(z) a polynomial of degree k, n≥max{11, k+1} a positive integer. If fⁿ(z)f(z) and gⁿ(z)g(z) share p(z)CM, then either f(z)=c_1e^cp(z)dz, g(z)=c₂e^cp(z)dz ,where c₁, c₂ and c are three constants satisfying (c₁c₂)ⁿ⁺¹c₂₌-1 or f(z)≡tg(z) for a constant t such that tⁿ⁺¹=1.

Local S_β-compactness of L-topological Spaces

HAN Hong-xia, MENG Guang-wu, ZHANG An-ying

2011, 26(3): 453-456.

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In this paper, the notion of local S_β-compactness of L-topological spaces is introduced. It is proved that the local S_β-compactness is an L-good extension, which is inherited by a closed subspace, multiplicative and invariable under the continuous open surjective L-valued Zadeh function.

Components Admissible Solution of Algebraic Diﬀerential Equations Systems

LI Guo-wang, GAO Ling-yun

2011, 26(3): 457-461.

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Using the Nevanlinna value distribution theory of meromorphic function, we investigate the existence problem of admissible solutions of higher-order algebraic differential equations systems, and obtain a result concerning admissible components of solution.

Further Extension of the Relations between Two Operator Inequalities

GAO Fu-gen, ZUO Hong-liang

2011, 26(3): 462-465.

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In this paper, we give out a further extension of the relations between two famous inequalities (B^r/2A^pB^r/2) ^r/(p+r)≥B^r and A^p≥(A^p/2B^rA^{p/2) p/(p+r)}, which can yield the result of Yamazaki and Yanagida’s.

Forced Oscillation of Neutral Advanced Dynamic Equations with Positive and Negative Coeﬃcients on Time Scales

YANG Jun, WU Hui-ning

2011, 26(3): 466-469.

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In this paper, we consider the forced neutral advanced dynamic equations with positive and negative coeffcients [x(t)-R(t)x(t+r)]+P(t)x(t+τ)△Q(t)x(t+δ)= f(t), t≥t₀ on a time scale T.S everal suffcient conditions are obtained for the oscillation of the dynamic equations. The main result is illustrated by an example.

The Existence of Global Attractor for Zakharov Equations Arising from Ion-acoustic Modes

FANG Shao-mei, QIU Hua, GUO Bo-ling

2011, 26(3): 470-474.

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In this paper, we consider the initial-boundary problem for Zakharov equations arising from ion-acoustic modes and obtain the existence of global attractor for the initial-boundary problem for Zakharov equations.

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