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25 October 2011, Volume 31 Issue 5 Previous Issue    Next Issue

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Hedging Unit-linked Life Insurance Contracts under Mean-variance Criterion BI Jun-Na, GUO Jun-Yi Acta mathematica scientia,Series A. 2011, 31 (5):  1141-1149.  Abstract ( 1134 )   RICH HTML PDF (390KB) ( 969 )   Save In this paper, the authors try to hedge the life insurance claims under the mean-variance criterion. The hedging portfolio is constructed for unit-linked life insurance contracts with a term insurance payment. Premiums are supposed to be payed as single premium at the beginning. It is  assumed that the insurer can invest in a risk-free asset (bond) and a risky asset (stock). The price of the risky asset is described by a geometric Brownian motion. Using stochastic control theory, the efficient strategy (hedging strategy) and the efficient frontier are obtained. References | Related Articles | Metrics

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Exact Solutions to Hyperbolic Geometric Flows TU Jie, FU Lin, ZHOU Xin Acta mathematica scientia,Series A. 2011, 31 (5):  1150-1159.  Abstract ( 1058 )   RICH HTML PDF (452KB) ( 879 )   Save In this paper, the authors investigate the exact solutions to hyperbolic geometric flow. Some interesting properties and phenomena enjoyed by these solutions are  also  discovered and analyzed. These are useful to understand the Einstein equations and the hyperbolic geometric flow. References | Related Articles | Metrics

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Zero-sets of Clifford Analytic Functions with Real Coefficients YANG Yan, QIAN Tao Acta mathematica scientia,Series A. 2011, 31 (5):  1160-1166.  Abstract ( 1091 )   RICH HTML PDF (278KB) ( 747 )   Save In this note it is proved that the zero set of any Clifford analytic function f with real coefficients is the disjoint union of real isolated zeroes and the spherical conjugate ones. What is more, a technique for computing the zeroes is presented. The authors also find the preimages f-1(A) for any paravector A. References | Related Articles | Metrics

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Integral Equations to the Scattering Problem by a Mixed Crack YAN Guo-Zheng Acta mathematica scientia,Series A. 2011, 31 (5):  1167-1175.  Abstract ( 1333 )   RICH HTML PDF (348KB) ( 1106 )   Save Consider the scattering of an electro-magnetic time-harmonic plane wave by an infinite cylinder having a mixed open crack in R2 as the cross section. We assume that the crack is made of two parts, and one of which  is (possibly) coated on one side by a material with surface impedance λ. The problem can be reformulated as a boundary integral system (BIS) by using potential theory. We obtain the existence and uniqueness of the weak solution to the system by the Fredholm theory. References | Related Articles | Metrics

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A Remark on the Convexity of Hypersurface with Prescribed Curvature Equations XU Jin-Ju Acta mathematica scientia,Series A. 2011, 31 (5):  1176-1180.  Abstract ( 1190 )   RICH HTML PDF (269KB) ( 769 )   Save In this article, the author investigates the solution surface of the prescribed curvature equation Skλ{hij})(X),=\, f(X),\, \forall X∈M\subsetRn+1. It is proved that the solution surface M of the prescribed curvature equation in Rn+1 is convex under the condition that the second fundamental form hij of M is semi-positive definite on the boundary ∂M. The author  makes use of Hamilton tensor maximum principle to prove this result. As a consequence, the convexity for the solution surface of constant mean curvature in Rn+1 is easily obtained. References | Related Articles | Metrics

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A Class of Caffarelli-Kohn-Nirenberg Type Inequalities for Generalized Baouendi-Grushin Vector Fields HAN Ya-Zhou, ZHAO Qiong Acta mathematica scientia,Series A. 2011, 31 (5):  1181-1189.  Abstract ( 1085 )   RICH HTML PDF (298KB) ( 748 )   Save Inspired by the method of Caffarelli et al., which  establishes the CKN inequality on Rn, this paper is devoted to study the CKN type inequality for the generalized B-G vector fields. By using the polar coordinates transform of the generalized B-G vector fields, the necessity of the CKN type inequality is given by constructing suitable auxiliary functions. Combining the Hardy-Sobolev type inequality of the generalized B-G vector fields and some tools, such as interpolation method and H\"{o}lder inequality, etc., it is proved  that the condition of necessity is also that of  sufficiency for the case p=2. References | Related Articles | Metrics

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Some Properties of Tortken Superalgebras and Classification of Low Dimensional Tortken Superalgebras XU Li-Yuan, ZHANG Qiang-Cheng, MENG Dao-Ji Acta mathematica scientia,Series A. 2011, 31 (5):  1190-1208.  Abstract ( 937 )   RICH HTML PDF (323KB) ( 834 )   Save In this paper the authors give the definition of Tortken superalgebra first, then they classfy the 2-dimensional Tortken superalgebra while A1≠{0}; they give an equivalence for a 2-dimensional superalgebra to be tortken while A1={0}; they also discuss some properties on Tortken superalgebras and  get an identity with  degree 4  on Tortken superalgebra. References | Related Articles | Metrics

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Weak Associated |Primes over Ore Extension Rings OUYANG Lun-Qun Acta mathematica scientia,Series A. 2011, 31 (5):  1209-1219.  Abstract ( 1385 )   RICH HTML PDF (340KB) ( 896 )   Save As a generalization of annihilator and associated primes, in this paper, the author introduces the notions of weak annihilator and weak associated primes, and investigates the relationship between the weak associated primes of a ring R and those  of the Ore extension ring R[x; α, δ]. It is proved that if R is an (α, δ)-compatible reversible ring, then N Ass(R[x; α, δ])=P[x; α, δ]| P∈N Ass(R), where N Ass}(R[x; α, δ]) and N Ass}(R) stand for the set of all weak associated primes over R[x; α, δ] and that over R, respectively. So all associated primes over R[x; α, δ] can be described  in terms of the weak associated primes over R in a very straightforward way. Consequently, several results in [3], [5], [6] are generalized to a more general setting. References | Related Articles | Metrics

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Irregular Sampling Theorem of Hermite Type and Estimate of Aliasing Error TU Yan-Yan, ZHANG Ya-Lan, CHEN Guang-Gui Acta mathematica scientia,Series A. 2011, 31 (5):  1220-1229.  Abstract ( 1726 )   RICH HTML PDF (379KB) ( 753 )   Save In this paper, the authors prove a Marcinkiewicz-Zygmund type inequality for entire functions of exponential type with multiple sampling sequences f(λn) and f^(λn). And from this result, the authors establish an irregular Whittaker-Kotelnikov-Shannon type sampling theorem and determine the bound of its aliasing error on the Sobolev classes. References | Related Articles | Metrics

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Nontrivial Solutions of Superlinear Fredholm Integral Equations and Their Applications LI Zhi-Long Acta mathematica scientia,Series A. 2011, 31 (5):  1230-1238.  Abstract ( 1184 )   RICH HTML PDF (299KB) ( 833 )   Save By computation of topological degree the author establishes an existence theorem on nontrivial solutions for superlinear Fredholm  integral equations in which the nonlinearity is allowed to be sign-changed and unbounded below. Applying it, the author discusses the existence of solutions of Sturm-Liouville problems in which the coefficient function q(t) is admitted to be singular at t=0,1. References | Related Articles | Metrics

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Error Estimate of Parallel Two-step W-methods for Singular-perturbation Problems with Delays ZhAO Yong-Xiang, XIAO Ai-Guo Acta mathematica scientia,Series A. 2011, 31 (5):  1239-1252.  Abstract ( 1241 )   RICH HTML PDF (359KB) ( 760 )   Save In this paper, the authors study the error estimates of parallel two-step W-methods for singular-perturbation initial value problems with delays in variable stepsizes environment, and obtain the corresponding convergence results. These theoretical results are confirmed by some numerical examples. References | Related Articles | Metrics

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A Simplified and Stabilized Second |Order Mixed Finite Element Formulation Based on Bubble Functions for Plane Elasticity Problems AN Jing, SUN Ping, LUO Zhen-Dong Acta mathematica scientia,Series A. 2011, 31 (5):  1253-1265.  Abstract ( 1479 )   RICH HTML PDF (375KB) ( 882 )   Save In this paper, a stabilized second order mixed finite element formulation based on bubble functions for plane elasticity problems is studied, and a simplified second order mixed finite element formulation with less freedom degrees is obtained by eliminating all bubble functions. It is shown by analyzing error that the convergence of the simplified and stabilized second order mixed finite element formulation eliminated all bubble functions is the same as that of the stabilized second order mixed finite element formulation with bubble functions, but it can save 18Np freedom degrees (where Np is the number of vertices of triangularization). References | Related Articles | Metrics

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Algebraic Index of Eigenvalues of Infinite-dimensional Hamiltonian Operators WANG Hua, Alatancang, HUANG Jun-jie Acta mathematica scientia,Series A. 2011, 31 (5):  1266-1272.  Abstract ( 1558 )   RICH HTML PDF (342KB) ( 822 )   Save This paper deals with the algebraic index of eigenvalues of infinite-dimensional Hamiltonian operators with at least one diagonal elements to be invertible. Based on certain properties of their eigenvalues and eigenvectors, it is  obtained that the algebraic index of eigenvalue  of a class of infinite-dimensional Hamiltonian operators  is 1 or 2. Moreover, some applications are presented to illustrate these results. References | Related Articles | Metrics

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Existence of Travelling Wave Solutions for a Reaction-diffusion Equation with Nonlocal Delay LIANG Fei, GAO Hong-Jun Acta mathematica scientia,Series A. 2011, 31 (5):  1273-1281.  Abstract ( 1270 )   RICH HTML PDF (350KB) ( 995 )   Save This paper is concerned with the existence of a reaction-diffusion equation with nonlocal delay. For special kernels, by linear chain trick and geometric singular perturbation theory, the authors consider a natural connection between the existence of travelling wave solutions for the reaction-diffusion equation with nonlocal delay and the existence of travelling wave solutions for the corresponding undelayed reaction-diffusion equation. It is showed that if the corresponding undelayed reaction-diffusion equation has a travelling wave solution, then the reaction-diffusion with nonlocal delay also has a travelling wave solution for any sufficiently small delay. References | Related Articles | Metrics

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The Neuberg-Pedoe Inequality in the Spherical Space YANG Shi-Guo, QIAN Di, PAN Juan-Juan, WANG Wen Acta mathematica scientia,Series A. 2011, 31 (5):  1282-1289.  Abstract ( 1620 )   RICH HTML PDF (319KB) ( 832 )   Save In this paper, the authors  study the problem about geometric inequalities for two n-dimensional simplexes in the spherical space by the theory and method of distance geometry. The authors establish a form of the Neuberg-Pedoe inequality and a form of the Peng-Chang inequality in the spherical space. References | Related Articles | Metrics

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Normality Criterion of Meromorphic Functions Concerning Shared Set ZHANG Han, XIE Dong, ZHANG Qiang-De Acta mathematica scientia,Series A. 2011, 31 (5):  1290-1294.  Abstract ( 1175 )   RICH HTML PDF (294KB) ( 937 )   Save Let F be a family of meromorphic functions in a domain D and S be a set consisting of three distinct elements. Let a be a finite complex number and k(>2) be a positive integer. If each f ∈F satisfies that the zeros and poles of f-a are of multiplicity ≥k and \overline{E}(S, f)=\overline{E}(S, f(k), then F is normal in D. References | Related Articles | Metrics

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Dynamical Analysis of a Predator-prey System with Hassell-Varley-Holling Functional Response ZHONG Min-Ling, LIU Xiu-Xiang Acta mathematica scientia,Series A. 2011, 31 (5):  1295-1310.  Abstract ( 1702 )   RICH HTML PDF (678KB) ( 884 )   Save This paper deals with a non-autonomous predator-prey system with Hassell-Varley-Holling functional response. The permanence and extinction are considered for general non-autonomous case. For periodic (almost periodic) case, necessary and sufficient criteria for the existence of positive periodic (almost periodic) solutions are derived by a new estimation technique and the invariance property of homotopy, the dynamics of boundary periodic (almost periodic) solutions are also investigated. The authors end this paper with some numerical simulations and interesting problems remaining. References | Related Articles | Metrics

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On Operators Satisfying T*|T1+n|2/1+nT&ge|T*|T*|2T SHEN Jun-Li, ZUO Fei, YANG Chang-Sen Acta mathematica scientia,Series A. 2011, 31 (5):  1311-1316.  Abstract ( 953 )   RICH HTML PDF (249KB) ( 716 )   Save Let T ∈B(H) be a bounded linear operator on a complex Hilbert space H. In this paper the authors introduce a new class of operator--quasi-*-A(n) and prove some properties of these operators, such as, if T is quasi-*-A(n), then its point spectrum and joint point spectrum are identical. Using these results, the authors also prove that if T or T* is quasi-*-A(n), then the spectral mapping theorem holds for the weyl spectrum and for the essential approximate point spectrum. References | Related Articles | Metrics

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On a Special Class of Prescribed Scalar Curvature Problems with Volume Element Preserving Deformations QIU Liang-Hua Acta mathematica scientia,Series A. 2011, 31 (5):  1317-1322.  Abstract ( 1479 )   RICH HTML PDF (295KB) ( 713 )   Save In this paper, the author discusses a special class of prescribed scalar curvature problems with volume element preserving deformations by the help of variational method.  It is obtained that when the prescribed scalar curvature only depends on one of the two product manifolds and some extra condtions are satisfied, the volume element preserving deformation exists. References | Related Articles | Metrics

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Inequalities for Generalized Matrix Functions LIU Xiu-Sheng Acta mathematica scientia,Series A. 2011, 31 (5):  1323-1327.  Abstract ( 871 )   RICH HTML PDF (226KB) ( 834 )   Save Let Sm denote the symmetric group of degree m and G be a subgroup of Sm. Let χ be a character of degree 1 on G . Suppose A is an m-by-m matrix complex matrix with singular-values r1, r2,…, rm. Denote dχ(A)=∑σ∈G χ(σ)∏i=1ma1,σ(i). It is proved that |dχ(A)|≤(1/m∑mi=1r i2m)1/2. In particular, |dχ(A)|2≤1/m∑mi=1ri2m. References | Related Articles | Metrics

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Continuity |of Julia |Set Concerning Potts Models GAO Jun-Yang, YANG Cun-Ji Acta mathematica scientia,Series A. 2011, 31 (5):  1328-1334.  Abstract ( 1709 )   RICH HTML PDF (323KB) ( 870 )   Save For λ-state  Potts models on diamond-like hierarchical lattices, the zeros of the partition function  is condense to the  Julia sets J(Tnλ). In this paper, the authors discuss the continuity of J(Tnλ) about λ ∈R by the methods of complex dynamics. References | Related Articles | Metrics

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Uniqueness Theorems for Algebroid Functions Sharing Values with Their Derivatives LIU Hui-Fang, SUN Dao-Chun Acta mathematica scientia,Series A. 2011, 31 (5):  1335-1344.  Abstract ( 1152 )   RICH HTML PDF (300KB) ( 745 )   Save In this paper, the shared value of algebroid functions and their derivatives are defined. Some uniqueness theorems of algebroid functions sharing values with their derivatives are obtained. References | Related Articles | Metrics

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Integral Inequalities of Some Harmonic Maps ZHOU Zhen-Rong Acta mathematica scientia,Series A. 2011, 31 (5):  1345-1352.  Abstract ( 854 )   RICH HTML PDF (236KB) ( 794 )   Save In this paper, the author calculates the Laplacian of the second fundamental form of a harmonic map, and then uses it to establish integral inequalities on harmonic maps into space forms. References | Related Articles | Metrics

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Existence of Nonoscillatory Solutions for a New Higher-order Nonlinear Neutral Delay Differential Equation GUO Zhen-Yu Acta mathematica scientia,Series A. 2011, 31 (5):  1353-1358.  Abstract ( 1246 )   RICH HTML PDF (253KB) ( 887 )   Save A new higher-order nonlinear neutral delay differential equation is studied in this paper, and some sufficient conditions for existence of nonoscillatory solutions for this equation are established and expatiated through five theorems according as the range of value of function P(t). References | Related Articles | Metrics

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The Existence of Global Solution of the Ginzburg-Landau Equations for Atomic Fermi Gases Near the BCS-BEC Crossover CHEN Shu-Hong, GUO Bo-Ling Acta mathematica scientia,Series A. 2011, 31 (5):  1359-1368.  Abstract ( 1472 )   RICH HTML PDF (327KB) ( 812 )   Save In this paper the authors investigate a time-dependent Ginzburg-Landau equations come from the superfluid atomic Fermi-gases near the Feshbach resonance from the fermion-boson model. By matrix theory and Galerkin method, the global existence and uniqueness of solution to the equations are obtained. References | Related Articles | Metrics

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A Note on a Rellich-Sobolev Inequality LUO Guang-Zhou Acta mathematica scientia,Series A. 2011, 31 (5):  1369-1376.  Abstract ( 960 )   RICH HTML PDF (243KB) ( 733 )   Save The author  proves a Rellich-Sobolev inequality and obtains the corresponding sharp constant. The procedure is based on decomposition into spherical harmonics and the best constant of Hardy-Sobolev inequality given by Adimurthi et al. References | Related Articles | Metrics

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Optimal Inequalities Related to the Power, Harmonic and Identric Means SHI Ming-Yu, CHU Yu-Ming, JIANG Yue-Ping Acta mathematica scientia,Series A. 2011, 31 (5):  1377-1384.  Abstract ( 1814 )   RICH HTML PDF (258KB) ( 1012 )   Save For any a, b>0 , the authors present the following two optimal inequalities: Hα(a, b)I1-α(a, b)≥M2-5α/3(a, b) for α∈(2/5,1), and Hα(a, b)I1-α(a, b)≤M2-5α/3(a, b) for α∈(1/25, 4/25). Here, H(a, b), I(a, b) and Mp(a, b) denote the harmonic, identric and power means of order of p of two positive numbers a and b, respectively. References | Related Articles | Metrics

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Singular Value Inequalities for Finite Sum of Products of Operators on Hilbert Space FANG Li, ZHANG Hai-Yan Acta mathematica scientia,Series A. 2011, 31 (5):  1385-1392.  Abstract ( 1449 )   RICH HTML PDF (252KB) ( 881 )   Save Let $A_k,B_k,X_{kl}\ (k=1,2,\cdots,n,\mbox{ and }l=1,2,\cdots,n)$ be bounded linear operators on a complex separable Hilbert space ${\mathcal H}.$ In the present paper, it is shown that if $X_{kl}\ (k,l=1,2,\cdots,n)$ are compact, then $$s_j\Big(\sum\limits_{k,l=1}^nA_kX_{kl}B_l\Big)\leqslant \sqrt{\Big\|\sum\limits_{k=1}^n|A_k^*|^2\Big\|}\cdot\sqrt{\Big\|\sum\limits_{l=1}^n|B_k|^2\Big\|} s_j(( X_{kl})_{n\times n})$$ for $j=1,2,\cdots,$ where $\|\cdot\|$ is the usual operator norm and $( X_{kl})_{n\times n}$ is the operator defined on $\oplus_{k=1}^n{\mathcal H}$ by $( X_{kl})_{n\times n} =\left(\begin{array}{ccc}X_{11}&~~\cdots~~ &X_{1n}\\\vdots&\ddots&\vdots\\X_{n1}&\cdots &X_{nn}\end{array}\right). References | Related Articles | Metrics

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Hypothesis Testing for Fractional Ornstein-Uhleneck Model ZHAO Shou-Jiang Acta mathematica scientia,Series A. 2011, 31 (5):  1393-1402.  Abstract ( 1046 )   RICH HTML PDF (279KB) ( 740 )   Save The goal of this article is to  study the large deviations and moderate deviations for the log-likelihood ratio processes of the fractional Ornstein-Uhleneck model. With the help of them, negative regions in testing fractional Ornstein-Uhleneck model and  the decay rates of the error probabilities of the first kind and the second kind are obtained. References | Related Articles | Metrics

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Qualitative Analysis of a Modified Leslie-Gower Predator-Prey System with Diffusion SHI Hong-Bo, LI Wan-Tong, LIN Guo Acta mathematica scientia,Series A. 2011, 31 (5):  1403-1415.  Abstract ( 1494 )   RICH HTML PDF (416KB) ( 759 )   Save This paper is concerned with a modified Leslie-Gower predator-prey system with Robin boundary conditions. The existence/nonexistence and stability of coexistence solutions are obtained. Furthermore, the long-time behavior of parabolic system is also investigated. The results show that the intrinsic growth rates and the principle eigenvalues of the corresponding elliptic problems with respect to the Robin boundary conditions play more important roles than other parameters for the existence/nonexistence of nonconstant positive steady-state solutions and the extinction of the species. References | Related Articles | Metrics

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H1-uniform Attractor for 2D Navier-Stokes Equations ZHAO Cai-De Acta mathematica scientia,Series A. 2011, 31 (5):  1416-1430.  Abstract ( 1240 )   RICH HTML PDF (394KB) ( 892 )   Save This paper is concerned with the existence of uniform attractor and asymptotic smoothing effect of solutions for two-dimensional (2D) nonautonomous Navier-Stokes equations in 2D domains (bounded or not). The author uses the enstrophy equation to obtain the asymptotic compactness of the family of processes associated with the Navier-Stokes equations and establishes the existence of H1-uniform attractor and thus reveal the asymptotic smoothing effect of the solutions in the sense that the solutions become eventually more regular than the initial data. References | Related Articles | Metrics

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Multiple Solutions for a p(x)}-Kirchhoff-type Equation with Nonsmooth Potential GE Bin, XUE Xiao-Ping, ZHOU Qing-Mei Acta mathematica scientia,Series A. 2011, 31 (5):  1431-1438.  Abstract ( 1202 )   RICH HTML PDF (317KB) ( 958 )   Save In this paper the authors  consider the differential inclusion problem involving the p(x)-Kirchhoff-type. Using Weierstrass Theorem and Mountain Pass Theorem, they obtain the existence of at least two nontrivial solutions of the problem in W01, p(x)(Ω). References | Related Articles | Metrics

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Controllability of a Nonlinear Parabolic Equation with Maximal Monotone Graph ZHANG Liang, YAO Xiao-Hua Acta mathematica scientia,Series A. 2011, 31 (5):  1439-1446.  Abstract ( 1009 )   RICH HTML PDF (306KB) ( 815 )   Save In this paper, the authors establish null controllability of a nonlinear parabolic equation with a maximal monotone graph. References | Related Articles | Metrics

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Commutators Generated by Multilinear Fractional Integrals and Lipschitz Functions MO Hui-Xia, ZHANG Zhi-Ying Acta mathematica scientia,Series A. 2011, 31 (5):  1447-1458.  Abstract ( 1088 )   RICH HTML PDF (311KB) ( 827 )   Save Let $m\in{\Bbb N}$, $\vec{b}=(b_{1},\cdots ,b_{m})$ whose components are of locally integrable functions, and $\vec{f}=(f_{1},\cdots ,f_{m})$ where $f_{1},\cdots ,f_{m}\in L_{c}^{\infty}({\mathbf{R}}^{n}).$ Let $x\notin\bigcap\limits_{i=1}^{m}\mbox{supp}f_{i},$ then the commutator generated by the multilinear fractional integral is given by $$I_{\alpha,m}^{\vec{b}}(\vec{f})(x) =\dint_{({\mathbf{R}}^{n})^{m}}K(x,y_{1},\cdots ,y_{m})\prod\limits_{i=1}^{m}(b_{i}(x)-b_{i}(y_{i}))f_{i}(y_i){\rm d}y_1\cdots {\rm d}y_m.$$ When $b_{j}\in\dot{\Lambda}_{\beta_{j}}({{\mathbf{R}}}^{n})~(1\leq j\leq m)$, the authors  establish the boundedness of $I_{\alpha,m}^{\vec{b}}$ on product Lebeasgue spaces, Triebel-Lizorkin spaces and Lipschitz spaces. References | Related Articles | Metrics