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20 May 2010, Volume 30 Issue 3 Previous Issue    Next Issue

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PARAMETER ESTIMATION FOR A CLASS OF STOCHASTIC DIFFERENTIAL EQUATIONS DRIVEN BY SMALL STABLE NOISES FROM DISCRETE OBSERVATIONS Long Hongwei Acta mathematica scientia,Series B. 2010, 30 (3):  645-663.  DOI: 10.1016/S0252-9602(10)60067-7 Abstract ( 908 )   RICH HTML PDF (217KB) ( 1406 )   Save We study the least squares estimation of drift parameters for a class of stochastic differential equations driven by small α-stable noises, observed at n regularly spaced time points ti=i/n, i=1, …, n on [0,1]. Under some regularity conditions, we obtain the consistency and the rate of convergence of the least squares estimator(LSE) when a small dispersion parameter ε→0 and n → ∝simultaneously. The asymptotic distribution of the LSE in our setting is shown to be stable, which is completely different from the classical cases where asymptotic distributions are normal. References | Related Articles | Metrics

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THE JOINT DISTRIBUTIONS OF SOME ACTUARIAL DIAGNOSTICS FOR THE JUMP-DIFFUSION RISK PROCESS LV Yu-Hua, TUN Rong, XU Run Acta mathematica scientia,Series B. 2010, 30 (3):  664-676.  DOI: 10.1016/S0252-9602(10)60068-9 Abstract ( 937 )   RICH HTML PDF (183KB) ( 1057 )   Save In this article,  the joint distributions of several actuarial diagnostics which are important to insurers' running for the jump-diffusion risk process are examined. They include the ruin time, the time of the surplus process leaving zero ultimately (simply, the ultimately leaving-time), the surplus immediately prior to ruin, the supreme profits before ruin, the supreme profits and deficit until it leaves zero ultimately and so on. The explicit expressions for their distributions are obtained mainly by the various properties of Lévy process, such as the homogeneous strong Markov property and the spatial homogeneity property etc, moveover, the many properties for Brownian motion. References | Related Articles | Metrics

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ASYMPTOTIC PROPERTIES OF ESTIMATORS IN PARTIALLY LINEAR SINGLE-INDEX MODEL FOR LONGITUDINAL DATA TIAN Ping, YANG Lin, XUE Liu-Gen Acta mathematica scientia,Series B. 2010, 30 (3):  677-687.  DOI: 10.1016/S0252-9602(10)60069-0 Abstract ( 907 )   RICH HTML PDF (183KB) ( 1407 )   Save In this article, a partially linear single-index model for longitudinal data is investigated. The generalized penalized spline least squares estimates of the unknown parameters are suggested. All parameters can be estimated simultaneously by the proposed method while the feature of longitudinal data is considered. The existence, strong consistency and asymptotic normality of the estimators are proved under  suitable conditions. A simulation study is conducted to investigate the finite sample performance of the proposed method. Our approach can also be used to study the pure single-index model for longitudinal data. References | Related Articles | Metrics

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UNIFORM ESTIMATE ON FINITE TIME RUIN PROBABILITIES WITH RANDOM INTEREST RATE MING Rui-Xing, HE Xiao-Xia, HU Yi-Jun, LIU Juan Acta mathematica scientia,Series B. 2010, 30 (3):  688-700.  DOI: 10.1016/S0252-9602(10)60070-7 Abstract ( 916 )   RICH HTML PDF (185KB) ( 1320 )   Save We consider a discrete time risk model in which the net payout (insurance risk){Xk,, k=1,2, …} are assumed to take real values and belong to the heavy-tailed class L ∩ D and the discount factors (financial risk) {Yk, k=1, 2, …} concentrate on [θ, L], where 0<θ<1, L<∞, {Xk, k=1, 2, …}, and {Yk, k=1, 2, …} are assumed to be mutually independent. We investigate the asymptotic behavior of the ruin probability within a finite time horizon as the initial capital tends to infinity, and figure out that the convergence holds uniformly for all n≥1, which is different from Tang Q H and Tsitsiashvili G (Adv Appl Prob, 2004, 36: 1278--1299). References | Related Articles | Metrics

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LOCAL CENTRAL LIMIT THEOREM AND BERRY-ESSEEN THEOREM FOR SOME NONUNIFORMLY HYPERBOLIC DIFFEOMORPHISMS XIA Hong-Qiang Acta mathematica scientia,Series B. 2010, 30 (3):  701-712.  DOI: 10.1016/S0252-9602(10)60071-9 Abstract ( 721 )   RICH HTML PDF (206KB) ( 1443 )   Save We prove that, for non-uniformly hyperbolic diffeomorphisms in the sense of Young, the local central limit theorem holds, and the speed in the central limit theorem is O(1√n}). References | Related Articles | Metrics

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EXISTENCE AND NONEXISTENCE OF GLOBAL POSITIVE SOLUTIONS FOR DEGENERATE PARABOLIC#br# EQUATIONS IN EXTERIOR DOMAINS ZENG Xian-Zhong, LIU Zhen-Hai Acta mathematica scientia,Series B. 2010, 30 (3):  713-725.  DOI: 10.1016/S0252-9602(10)60072-0 Abstract ( 1028 )   RICH HTML PDF (203KB) ( 1305 )   Save This article deals with the degenerate parabolic equations in exterior domains and with  inhomogeneous Dirichlet boundary conditions. We obtain  that pc= (σ+m)n(n-σ-2) is its critical exponent provided {-1, [(1-m)n-2](n+1)} < σ < n-2. This critical exponent is not the same as that for the corresponding equations with the boundary value 0, but is more closely tied to the critical exponent of the  elliptic type degenerate equations. Furthermore, we demonstrate  that if max{1, σ + m} < p ≤ pc,  then every positive solution of the equations blows  up in finite time; whereas for p < pc, the equations admit global positive solutions for some boundary values  and initial data. Meantime, we also  demonstrate that its positive solutions blow  up in finite time provided n ≤ σ + 2. References | Related Articles | Metrics

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QUASILINEAR-ADDITIVE PROPERTIES AND APPLICATIONS ZHANG Xiao-Hui, WANG Gen-Di, CHU Yu-Ming Acta mathematica scientia,Series B. 2010, 30 (3):  726-732.  DOI: 10.1016/S0252-9602(10)60073-2 Abstract ( 594 )   RICH HTML PDF (145KB) ( 1054 )   Save In this article, the authors study some basic properties of the so-called quasilinear-additive functions, and some applications to the special functions of quasiconformal analysis are specified. References | Related Articles | Metrics

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THE CONSISTENCY AND ASYMPTOTIC NORMALITY OF NEAREST NEIGHBOR DENSITY ESTIMATOR UNDER α- |MIXING CONDITION LIU Yan-Yan, ZHANG Yan-Li Acta mathematica scientia,Series B. 2010, 30 (3):  733-738.  DOI: 10.1016/S0252-9602(10)60074-4 Abstract ( 907 )   RICH HTML PDF (145KB) ( 1263 )   Save We investigate the consistency and asymptotic normality of nearest-neighbor density estimator of a sample data process based on α-mixing assumption. We extend the correspondent result under independent identical cases. References | Related Articles | Metrics

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THE DUAL BRUNN-MINKOWSKI INEQUALITIES FOR STAR DUAL OF MIXED INTERSECTION BODIES ZHU Xian-Yang, SHEN Ya-Jun Acta mathematica scientia,Series B. 2010, 30 (3):  739-746.  DOI: 10.1016/S0252-9602(10)60075-6 Abstract ( 676 )   RICH HTML PDF (150KB) ( 1137 )   Save In this article, some dual Brunn-Minkowski inequalities are established for star dual of mixed intersection bodies with respect to the harmonic p-combination and p-radial linear combination. References | Related Articles | Metrics

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SOME PROPERTIES OF HOLOMORPHIC CLIFFORDIAN FUNCTIONS |IN COMPLEX CLIFFORD ANALYSIS KU Min, DU Jin-Yuan, WANG Dao-Shun Acta mathematica scientia,Series B. 2010, 30 (3):  747-768.  DOI: 10.1016/S0252-9602(10)60076-8 Abstract ( 806 )   RICH HTML PDF (243KB) ( 1346 )   Save In this article, we mainly develop the foundation of a new function theory of several complex variables with values in a complex Clifford algebra defined on some subdomains of Cn+1, so-called complex holomorphic Cliffordian functions. We define the complex holomorphic Cliffordian functions, study polynomial and singular solutions of the equation D?mf=0, obtain the integral representation formula for the complex holomorphic Cliffordian functions with values in a complex Clifford algebra defined on some submanifolds of Cn+1, deduce the Taylor expansion and the Laurent expansion for them and prove an invariance under an action of Lie group for them. References | Related Articles | Metrics

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CONTACT PROCESS ON HEXAGONAL LATTICE YAO Qiang, LI Qun-Chang Acta mathematica scientia,Series B. 2010, 30 (3):  769-790.  DOI: 10.1016/S0252-9602(10)60077-X Abstract ( 827 )   RICH HTML PDF (258KB) ( 1081 )   Save In this article, we discuss several properties of the basic contact process on hexagonal lattice ${\Bbb H}$, showing that it behaves quite similar to the process on d-dimensional lattice Zd in many aspects. Firstly, we construct a coupling between the contact process on hexagonal lattice and the oriented percolation, and prove an equivalent finite space-time condition for the survival of the process. Secondly, we show the complete convergence theorem and the polynomial growth hold for the contact process on hexagonal lattice. Finally, we prove exponential bounds in the supercritical case and exponential decay rates in the subcritical case of the process. References | Related Articles | Metrics

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OPTIMAL PROPORTIONAL REINSURANCE WITH CONSTANT DIVIDEND BARRIER YUAN Hai-Li, HU Yi-Jun Acta mathematica scientia,Series B. 2010, 30 (3):  791-798.  DOI: 10.1016/S0252-9602(10)60078-1 Abstract ( 928 )   RICH HTML PDF (152KB) ( 1433 )   Save In this article, we consider an optimal proportional reinsurance with constant dividend barrier. First, we derive the Hamilton-Jacobi-Bellman equation satisfied by the expected discounted dividend payment, and then get the optimal stochastic control and the optimal constant barrier. Secondly, under the optimal constant dividend barrier strategy, we consider the moments of the discounted dividend payment and their explicit expressions are given. Finally, we discuss the Laplace transform of the time of ruin and its explicit expression is also given. References | Related Articles | Metrics

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STRONG SOLUTIONS FOR THE INCOMPRESSIBLE FLUID MODELS OF KORTEWEG TYPE TAN Zhong, WANG Yan-Jin Acta mathematica scientia,Series B. 2010, 30 (3):  799-809.  DOI: 10.1016/S0252-9602(10)60079-3 Abstract ( 1006 )   RICH HTML PDF (171KB) ( 1229 )   Save In this article, we are concerned with the strong solutions for the incompressible fluid models of Korteweg type in a bounded domain Ω ( R3 . We prove the existence and uniqueness of local strong solutions to the initial boundary value problem. We point out that  in this article we allow the existence of initial vacuum  provided initial data satisfy a compatibility condition. References | Related Articles | Metrics

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THE LARGEST SOLUTION OF LINEAR EQUATION OVER THE COMPLETE HEYTING ALGEBRA ZHOU Jing-Lei, LI Qiang-Guo Acta mathematica scientia,Series B. 2010, 30 (3):  810-818.  DOI: 10.1016/S0252-9602(10)60080-X Abstract ( 669 )   RICH HTML PDF (157KB) ( 1118 )   Save Let (L, ≤, ∨, ∧) be a complete Heyting algebra. In this article, the linear system Ax=b over a complete Heyting algebra, where classical addition and multiplication operations are replaced by ∨ and ∧ respectively, is studied. We obtain: (i) the necessary and sufficient conditions for S(A, b)≠Ø; (ii) the necessary conditions for |S(A, b)| =1. We also obtain the vector x ∈ Ln and prove that it is the largest element of S(A, b) if S(A, b)≠Ø. References | Related Articles | Metrics

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MANIFOLDS WITH POINTWISE PINCHED RICCI CURVATURE GU Hui-Ling Acta mathematica scientia,Series B. 2010, 30 (3):  819-829.  DOI: 10.1016/S0252-9602(10)60081-1 Abstract ( 836 )   RICH HTML PDF (167KB) ( 1400 )   Save In this article, the author proves a compactness result about Riemannian manifolds with an arbitrary pointwisely pinched Ricci curvature tensor. References | Related Articles | Metrics

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INFINITELY MANY SOLUTIONS FOR A SINGULAR ELLIPTIC EQUATION INVOLVING CRITICAL SOBOLEV-HARDY EXPONENTS IN RN HE Xiao-Ming, ZOU Wen-Ming Acta mathematica scientia,Series B. 2010, 30 (3):  830-840.  DOI: 10.1016/S0252-9602(10)60082-3 Abstract ( 981 )   RICH HTML PDF (192KB) ( 2074 )   Save In this article, we study the existence of multiple solutions for the singular semilinear elliptic equation involving critical Sobolev-Hardy exponents   -?u-u u/|x|2=α |u|2*(s)-2u/|x|s + βa(x)|u|r-2 u,   x ∈ RN. By means of the concentration-compactness principle and minimax  methods, we obtain infinitely many solutions which tend to zero for suitable positive parameters α, β. References | Related Articles | Metrics

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A RIGOROUS DERIVATION OF THE GROSS-PITAEVSKII HIERARCHY FOR WEAKLY COUPLED TWO-DIMENSIONAL BOSONS LIU Chuang-Ye Acta mathematica scientia,Series B. 2010, 30 (3):  841-856.  DOI: 10.1016/S0252-9602(10)60083-5 Abstract ( 925 )   RICH HTML PDF (223KB) ( 1128 )   Save In this article, we consider the dynamics of N two-dimensional boson systems interacting through a pair potential N-1Va(xi-xj) where Va(x)=a-2V(x/a). It is well known that the Gross-Pitaevskii (GP) equation is a nonlinear Schrodinger equation and the GP hierarchy is an infinite BBGKY hierarchy of equations so that if ut solves the GP equation, then the family of k-particle density matrices {   kut, k ≥1} solves the GP hierarchy. Denote by ψN, t the solution to the N-particle Schr\"odinger equation. Under the assumption that a =N-ε for 0< ε<3/4, we prove that as N → ∞ the limit points of the k-particle density matrices of ψN, t are solutions of the GP hierarchy with the coupling constant in the nonlinear term of the GP equation given by ∫V(x)dx. References | Related Articles | Metrics

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POLAR SETS OF MULTIPARAMETER BIFRACTIONAL BROWNIAN SHEETS CHEN Zhen-Long, LI Hui-Qiong Acta mathematica scientia,Series B. 2010, 30 (3):  857-872.  DOI: 10.1016/S0252-9602(10)60084-7 Abstract ( 835 )   RICH HTML PDF (228KB) ( 1122 )   Save Let BH, K=BH, K(t), t ∈ RN+ } be an (N, d)-bifractional Brownian sheet with Hurst indices H=(H1,…, HN)  ∈ (0, 1)N and K=(K1, …, KN) ∈ (0, 1]N. The properties of the polar sets of BH, K are discussed. The sufficient conditions and necessary conditions for a compact set to be polar for BH, K are proved. The infimum of Hausdorff dimensions of its non-polar sets are obtained by means of constructing a Cantor-type set to connect its Hausdorff dimension and capacity. References | Related Articles | Metrics

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NATURAL FROBENIUS SUBMANIFOLDS LIN Jie-Zhu Acta mathematica scientia,Series B. 2010, 30 (3):  873-889.  DOI: 10.1016/S0252-9602(10)60085-9 Abstract ( 618 )   RICH HTML PDF (201KB) ( 951 )   Save I.A.B. Strachan introduced the notion of a natural Frobenius submanifold of a Frobenius manifold and gave a sufficient but not necessary condition for a submanifold to be a natural Frobenius submanifold. This article will give a necessary and sufficient condition and classify the natural Frobenius hypersurfaces. References | Related Articles | Metrics

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RIGIDITY THEOREMS OF CLIFFORD TORUS ZHANG Yun-Tao Acta mathematica scientia,Series B. 2010, 30 (3):  890-896.  DOI: 10.1016/S0252-9602(10)60086-0 Abstract ( 872 )   RICH HTML PDF (147KB) ( 1498 )   Save In this article, we prove that the Clifford torus S1(√1-r2) ×Sn-1(r) is the only closed hypersurface in the  unit sphere Sn+1(1) with infinite fundamental group, which satisfy r2≥(n-1)/n, RicM ≤ C-(H), and S ≤ S+(H). Moreover, we give a  characterization of Clifford torus S1(√1-r2) ×Sn-1(r) with  r2 ={2(n-1)+nH2±|H|√n2H2+4(n-1)/2n(1+H2}. References | Related Articles | Metrics

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COMMUTATORS OF GENERALIZED HARDY OPERATORS ON HOMOGENEOUS GROUPS MO Hui-Xia Acta mathematica scientia,Series B. 2010, 30 (3):  897-906.  DOI: 10.1016/S0252-9602(10)60087-2 Abstract ( 711 )   RICH HTML PDF (167KB) ( 1241 )   Save Let G be a homogeneous group. The author considers the boundedness of commutators generated by the generalized Hardy operators and CMO(G) functions on Herz spaces in the setting of homogeneous group. This article extends some known results. References | Related Articles | Metrics

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DISPERSION COMPARISONS OF TWO PROBABILITY VECTORS UNDER MULTINOMIAL SAMPLING XIONG Shi-Feng, LI Guo-Ying Acta mathematica scientia,Series B. 2010, 30 (3):  907-918.  DOI: 10.1016/S0252-9602(10)60088-4 Abstract ( 745 )   RICH HTML PDF (196KB) ( 1234 )   Save We consider testing hypotheses concerning comparing dispersions between two parameter vectors of multinomial distributions in both one-sample and two-sample cases. The comparison criterion is the concept of Schur majorization. A new dispersion index is proposed for testing the hypotheses. The corresponding test for the one-sample problem is an exact test. For the two-sample problem, the bootstrap is used to approximate the null distribution of the test statistic and the p-value. We prove that the bootstrap test is asymptotically correct and consistent. Simulation studies for the bootstrap test are reported and a real life example is presented. References | Related Articles | Metrics

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CALCULATIONS OF RUIN PROBABILITIES CONCERNING WITH CLAIM OCCURRENCES WANG Shan-Shan, ZHANG Chun-Sheng, WU Rong Acta mathematica scientia,Series B. 2010, 30 (3):  919-931.  DOI: 10.1016/S0252-9602(10)60089-6 Abstract ( 809 )   RICH HTML PDF (436KB) ( 1193 )   Save In this article, we consider the perturbed classical surplus model. We study the probability that ruin occurs at each instant of claims, the probability that ruin occurs between two consecutive claims occurrences, as well as the distribution of the ruin time that lies in between two consecutive claims. We give some finite expressions depending on derivatives for Laplace transforms, which can allow computation of the probabilities concerning with claim occurrences. Further, we present some insight on the shapes of probability functions involved. References | Related Articles | Metrics

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THE GROWTH OF SOLUTIONS OF SYSTEMS OF COMPLEX NONLINEAR ALGEBRAIC DIFFERENTIAL EQUATIONS GAO Ling-Yun Acta mathematica scientia,Series B. 2010, 30 (3):  932-938.  DOI: 10.1016/S0252-9602(10)60090-2 Abstract ( 779 )   RICH HTML PDF (153KB) ( 1460 )   Save We investigate the problem of growth order of solutions of a type of systems of non-linear algebraic differential equations, and extend some results of the growth order of solutions of algebraic differential equations to systems of algebraic differential equations. References | Related Articles | Metrics

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UNIVERSAL BOUNDS FOR EIGENVALUES OF LAPLACIAN OPERATOR WITH ANY ORDER HUANG Guang-Yue, CHEN Wen-Yi Acta mathematica scientia,Series B. 2010, 30 (3):  939-948.  DOI: 10.1016/S0252-9602(10)60091-4 Abstract ( 691 )   RICH HTML PDF (155KB) ( 1206 )   Save Let Ω be a connected bounded domain in Rn. Denote by λi the i-th eigenvalue of the Laplacian operator with any order p: {(-?)p u=λu    in Ω,  u=∂u /∂n =…=∂p-1u / ∂n p-1=0   on  ∂Ω. In this article, we give some expressions for upper bound of the (k+1)-th eigenvalue λk+1 in terms of the first k eigenvalues. References | Related Articles | Metrics

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VORTEX DYNAMICS OF THE ANISOTROPIC GINZBURG-LANDAU EQUATION WEN Huan-Yao, DING Shi-Jin Acta mathematica scientia,Series B. 2010, 30 (3):  949-962.  DOI: 10.1016/S0252-9602(10)60092-6 Abstract ( 825 )   RICH HTML PDF (201KB) ( 887 )   Save In this article, using coordinate transformation and Gronwall inequality, we study the vortex motion law of the anisotropic Ginzburg-Landau equation in a smooth bounded domain $\Omega\subset{\bf R}^2$, that is, $ {\partial_tu_\varepsilon=\sum\limits_{j,k=1}^2(a_{jk}\partial_{x_k}u_\varepsilon)_{x_j}+\frac{b(x)(1-| u_\varepsilon| ^2)u_\varepsilon}{\varepsilon^2},x\in\Omega}$, and conclude that each vortex $ {b_j(t)~(j=1,2,\cdots ,N)}$ satisfies $ \frac{{\rm d}b_j(t)}{{\rm d}t}=-\big(\frac{a_{1k}(b_j(t))\partial_{x_k}a(b_j(t))}{a(b_j(t))},$ $ \frac{a_{2k}(b_j(t))\partial_{x_k}a(b_j(t))}{a(b_j(t))}\big),$ where $ {a(x)=\sqrt{a_{11}a_{22}-a_{12}^2}}$. We prove that all the vortices are pinned together to the critical points of $a(x)$. Furthermore, we prove that these critical points can not be the maximum points. References | Related Articles | Metrics

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A REMARK ON THE REGULARITY OF VECTOR-VALUED MAPPINGS DEPENDING ON TWO VARIABLES WHICH MINIMIZE SPLITTING-TYPE VARIATIONAL INTEGRALS M. Bildhauer, M. Fuchs Acta mathematica scientia,Series B. 2010, 30 (3):  963-967.  DOI: 10.1016/S0252-9602(10)60093-8 Abstract ( 743 )   RICH HTML PDF (139KB) ( 972 )   Save We combine the maximum principle for vector-valued mappings established by D'Ottavio, Leonetti and Musciano [7] with regularity results from [5] and prove the Holder continuity of the first derivatives for local minimizers u: Ω→RN of splitting-type variational integrals provided Ω is a domain in R2. References | Related Articles | Metrics

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LARGE TIME BEHAVIOR OF SOLUTIONS TO NEWTONIAN FILTRATION EQUATIONS WITH SOURCES WANG Lu-Sheng, YIN Jing-Xue, WANG Ze-Jia Acta mathematica scientia,Series B. 2010, 30 (3):  968-974.  DOI: 10.1016/S0252-9602(10)60094-X Abstract ( 783 )   RICH HTML PDF (157KB) ( 1061 )   Save This article is concerned with large time behavior of solutions to the Neumann or Dirichlet problem for a class of Newtonian filtration equations |x|λ+k ∂u / ∂t =div(|x|k \nabla um)+|x|λ+kup with 0<m<1, p>1, λ ≥0, k ∈ R. An interesting phenomenon is that there exist two thresholds k∞ and k1 for the exponent k, such that the critical Fujita exponent pc for p exists and is finite if k ∈ (k∞, k1), otherwise, pc is infinite or does not exist. References | Related Articles | Metrics

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CONVERGENCE RATE OF AN APPROXIMATION TO MULTIPLE INTEGRAL OF FBM HU Yao-Zhong, WANG Bao-Bin Acta mathematica scientia,Series B. 2010, 30 (3):  975-992.  DOI: 10.1016/S0252-9602(10)60095-1 Abstract ( 864 )   RICH HTML PDF (202KB) ( 1404 )   Save In this article, we study the rate of convergence of the polygonal approximation to multiple stochastic integral Sp(f) of fractional Brownian motion of Hurst parameter H<1/2 when the fractional Brownian motion is replaced by its polygonal approximation. Under different conditions on f and for different p, we obtain different rates. References | Related Articles | Metrics

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THREE-SPHERE INEQUALITIES FOR SECOND ORDER SINGULAR PARTIAL DIFFERENTIAL EQUATIONS ZHANG Song-Yan Acta mathematica scientia,Series B. 2010, 30 (3):  993-1003.  DOI: 10.1016/S0252-9602(10)60096-3 Abstract ( 771 )   RICH HTML PDF (189KB) ( 1533 )   Save In this article, we give the three-sphere inequalities and three-ball inequalities for the singular elliptic equation div(A\nabla u)-Vu=0, and the three-ball inequalities on the characteristic plane and the three-cylinder inequalities for the singular parabolic equation ∂tu-div(A\nabla u)+Vu=0, where the singular potential V belonging to the Kato-Fefferman-Phong's class. Some applications are also discussed. References | Related Articles | Metrics

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ON SETS OF ZEROES OF CLIFFORD ALGEBRA-VALUED POLYNOMIALS YANG Yan, QIAN Tao Acta mathematica scientia,Series B. 2010, 30 (3):  1004-1012.  DOI: 10.1016/S0252-9602(10)60097-5 Abstract ( 782 )   RICH HTML PDF (148KB) ( 1319 )   Save In this note, we study zeroes of Clifford algebra-valued polynomials. We prove that if such a polynomial has only real coefficients, then it has two types of zeroes: the real isolated zeroes  and the spherical conjugate ones. The total number of zeroes does not exceed the degree of the polynomial. We also present a technique for computing the zeroes. References | Related Articles | Metrics

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COMPOSITION OPERATORS FROM p-BLOCH SPACES TO LITTLE q-BLOCH SPACES |ON THE UNIT BALL OF Cn LI Jun-Feng Acta mathematica scientia,Series B. 2010, 30 (3):  1013-1020.  DOI: 10.1016/S0252-9602(10)60098-7 Abstract ( 847 )   RICH HTML PDF (158KB) ( 1058 )   Save For all 0<p, q<∞,  let Cφ denote the composition operator from q-Bloch  spaces βp to  little p-Bloch  spaces β0q on the unit ball of Cn. In this article,  necessary and sufficient conditions for Cφ to be a bounded or compact operator are given. References | Related Articles | Metrics