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25 June 2013, Volume 33 Issue 3 Previous Issue    Next Issue

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On the Growth of Solutions of Some Higher Order Linear Differential Equations LONG Jian-Ren, ZHU Jun, LI Xiao-Man Acta mathematica scientia,Series A. 2013, 33 (3):  401-408.  Abstract ( 807 )   RICH HTML PDF (281KB) ( 693 )   Save In this paper, we shall involve the deficient value in investigating the growth of  solutions of the linear differential equation f (k)+Ak-1(z)f(k-1)+…+A1(z)f' +A0(z)f=0, where Aj(z) (j=0, 1, …, k-1) are entire functions, and we obtain some results which improves some earlier results. More specifically, we estimate the lower bounded of hyper-order of solutions of the equation if every solution f(≠0) of the equation is of infinite order. References | Related Articles | Metrics

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Uniform Convergence of the Fourier Spectral Method for the Zakharov Equations YANG Zheng, JI Yuan-Yuan, MA He-Ping Acta mathematica scientia,Series A. 2013, 33 (3):  409-423.  Abstract ( 688 )   RICH HTML PDF (402KB) ( 614 )   Save In this paper, the optimal H1 error estimate of the Fourier spectral method for the Zakharov equations with  periodic boundary conditions is obtained and, especially, the uniform convergence with respect to the parameter ε is proved. Also, some semi-implicit time advancing scheme is proposed for the Fourier spectral approximation to a class of relative equations, which is of good stability and can be implemented efficiently. At last, various numerical experiments are conducted to confirm the validity of the method. References | Related Articles | Metrics

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Local C1(Ω) -minimizers Versus W1, p(x)(Ω)-minimizers of Nonsmooth Functionals DAI Guo-Wei, DA Ting Acta mathematica scientia,Series A. 2013, 33 (3):  424-430.  Abstract ( 615 )   RICH HTML PDF (285KB) ( 441 )   Save In this paper, we study not necessarily differentiable functionals of the form J(u)=∫Ω1/p(x)(|∨u|p(x)+|u|p(x))dx+∫Ω j1(x, u)dx+∫∂Ωj2(x, γu)dσ, where p(x)∈ C0, β(Ω), with β∈(0,1),  and 1<p-≤p+<+∞, j1: Ω×R→R as well as j2: ∂Ω×R→R are locally Lipschitz functions. We prove that local C1(Ω)-minimizers of J must be local W1, p(x)(Ω)-minimizers of J. References | Related Articles | Metrics

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The Categorification of Quantum Affine Algebra Uq(sln) REN Lei, CHANG Wen-Jing, WANG Na, WANG Zhi-Xi, WU Ke, YANG Zi-Feng Acta mathematica scientia,Series A. 2013, 33 (3):  431-465.  Abstract ( 820 )   RICH HTML PDF (876KB) ( 514 )   Save We construct 2-categories U and U using string diagrams corresponding to Lusztig's quantum group U=Uq(sln). Here U is the Karoubi envelope of U. By constructing the 2-representation of U, we also prove that the Grothendieck ring K0(U) of U is isomorphic to the algebra AU, where U is the idempotented modification of U and AU is the integral form of U. We obtain that the category U could be considered as the categorification of quantum affine algebra Uq(sln). References | Related Articles | Metrics

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The Arf Invariant of Knots HAN You-Fa, SUN De-Zhi, SUN Sheng, YAN Shu Acta mathematica scientia,Series A. 2013, 33 (3):  466-474.  Abstract ( 601 )   RICH HTML PDF (344KB) ( 550 )   Save In this paper, we will show how to calculate the Arf invariant of some links or knots by using the numerical link type invariant I(L), and we will find some new formulas. By these formulas, we can get the Arf invariants of a link or a knot easily, instead of polynomials. And then the calculation Arf becomes not complicated. References | Related Articles | Metrics

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The Asymptotic Properties and Almost Sure Central Limit Theorems for the Products of a Class of Statistics QIU Jin, LU Chuan-Rong Acta mathematica scientia,Series A. 2013, 33 (3):  475-482.  Abstract ( 590 )   RICH HTML PDF (325KB) ( 515 )   Save Let {Xn, -∞<n<∞} be a sequence of independent and identically distributed, positive, square integrable random variables with μ=EX1, σ2=Var X1>0. The asymptotic properties for the products of a class of statistics (or random functions) expressed by Tn=anSn+Rn are discussed, where Sn=∑ni=1Xi, an>0 is a sequence of constants, Rn=o(an√n) a.s.. The results contain the almost sure central limit theorems, asymptotically lognormality and the weak invariance principles. Some examples such as U-statistics, Von-Mises statistics, error variance estimates in linear models are stated to illustrate the generality of the results. References | Related Articles | Metrics

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Weak Bases and the Compact-Covering Images of Metric Spaces LIN Shou, ZHANG Jing Acta mathematica scientia,Series A. 2013, 33 (3):  483-493.  Abstract ( 611 )   RICH HTML PDF (389KB) ( 466 )   Save In this paper some equivalent conditions of a space in which each compact subset is metrizable and has a countable weak base in the space are obtained by means of sn-networks, the spaces are characterized as images of metric spaces under 1-scc~(resp. scc) and quotient maps, and spaces in which each compact subset has a countable outer weak base are discussed, which generalized the classic result about compact-covering and open images of metric spaces by Michael and Nagami. References | Related Articles | Metrics

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On the Commutators of Multilinear Fractional Integrals with Weighted Lipschitz Functions LIAN Jia-Li, MA Bo-Lin, WU Huo-Xiong Acta mathematica scientia,Series A. 2013, 33 (3):  494-509.  Abstract ( 779 )   RICH HTML PDF (385KB) ( 530 )   Save In this paper, two types of commutators generated by the multilinear fractional integrals with the weighted Lipschitz functions are studied in products of weighted Lebesgue spaces. The strong type weighted norm estimates,  which extend and generalize some previous results, are obtained for such operators. References | Related Articles | Metrics

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Global Existence and Asymptotic Behavior of Smooth Solutions to the IBVP for the 3D Bipolar Euler-Poisson System MAO Jian-Feng, LI Ye-Ping Acta mathematica scientia,Series A. 2013, 33 (3):  510-522.  Abstract ( 737 )   RICH HTML PDF (385KB) ( 502 )   Save In this paper, we study a three-dimensional (3D) bipolar Euler-Poisson system (hydrodynamic model) from semiconductors and plasmas. This system takes the form of Euler-Poisson with electric field and frictional damping added to the momentum equations. We first proved global existence and uniqueness of classical solutions to the initial boundary value problem (IBVP) with slip boundary condition and Nemann boundary condition when the initial data is near its equilibrium. As the by-product, we also show asymptotic behavior of IBVP for the three-dimensional bipolar Euler-Poisson system. That is, the density of two particles (electron and hole or positive and negative ion) is verified to satisfy the porous medium equation and the current momentums obey to the classical Darcy's law. References | Related Articles | Metrics

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Testing for Autocorrelation and Random Effects in Mixed Effect Linear Models Based on M-estimation SUN Hui-Hui, LIN Jin-Guan Acta mathematica scientia,Series A. 2013, 33 (3):  523-534.  Abstract ( 638 )   RICH HTML PDF (436KB) ( 467 )   Save In this paper, the Fisher scoring method is applied to get M-estimator(robust estimator)in the mixed effects linear model for longitudinal data. And its asymptotic property is given later. Then tests for autocorrelation and presence of random effects in the models are studied based on M-estimation. The score test statistics are obtained and illustrated by the grape sugar data example. References | Related Articles | Metrics

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A Mixed Covolume Method for Pseudo-Hyperbolic Equation FANG Zhi-Chao, LI Hong, LUO Zhen-Dong Acta mathematica scientia,Series A. 2013, 33 (3):  535-550.  Abstract ( 704 )   RICH HTML PDF (1088KB) ( 630 )   Save The mixed covolume method is analyzed for a class of second-order pseudo-hyperbolic equations on triangular grids. Semi-discrete and fully-discrete mixed covolume schemes are constructed by using the lowest order Raviart-Thomas mixed finite element space and introducing a transfer operator γh that maps the trial function space into the test function space. According to the characteristics of the pseudo-hyperbolic equation, generalized mixed covolume projection is introduced, then optimal error estimates are derived by using the properties of the transfer operator and generalized mixed covolume projection. Finally, numerical experiments are given to verify the theoretical results and the effectiveness of the proposed method. References | Related Articles | Metrics

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Existence of Solutions of Nonlocal Terminal Value Problems for Nonlinear Mixed Integro-Differential Equations in Banach Spaces XIE Sheng-Li, GE Ci-Shui Acta mathematica scientia,Series A. 2013, 33 (3):  550-560.  Abstract ( 770 )   RICH HTML PDF (327KB) ( 495 )   Save Using M\"{o}nch fixed point theorem, this article proves the existence of solution of nonlocal terminal value problems for first order nonlinear mixed integro-differential equations in Banach spaces, the restricted conditions on noncompactness measure estimation hasn't used and our result generalizes and improves the corresponding result of Guo Wei [Guo Wei. A generalization and application of Ascoli--Arzela theorem.  Journal of Systems Science and Mathematical Sciences (in Chinese), 2002, 22(1): 115--122]. References | Related Articles | Metrics

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Some Further Results on Montel's Criterion LV Feng Acta mathematica scientia,Series A. 2013, 33 (3):  561-587.  Abstract ( 750 )   RICH HTML PDF (272KB) ( 507 )   Save In this paper, we study the problems of normal families and obtain a theorem, which improves and generalizes the classical normality results obtained by Fang and Xu[3], Pang[7] and Xu and Qiu[13]. References | Related Articles | Metrics

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Sharp Bounds for the first Seiffert and Logarithmic Means in Terms of Generalized Heronian Mean GAO Hong-Ya, GUO Jian-Ling, LI Meng-Hua Acta mathematica scientia,Series A. 2013, 33 (3):  568-572.  Abstract ( 727 )   RICH HTML PDF (212KB) ( 495 )   Save We find the least values α, γ and the greatest values β, τ, such that the inequalities Hα(a, b)<P(a, b)<Hβ (a, b) ; 和Hγ(a, b)<L(a, b)<Hτ(a, b) hold for all a, b>0 with a≠b. Here, Hω(a, b), P(a, b), and L(a, b) be the generalized Heronian, the first Seiffert and the logarithmic means of two positive numbers a and b, respectively. References | Related Articles | Metrics

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AL-space of Positive b-AM-compact Operators on Banach Lattice CHENG Na Acta mathematica scientia,Series A. 2013, 33 (3):  573-576.  Abstract ( 607 )   RICH HTML PDF (211KB) ( 487 )   Save Kb-AMr(E, F), the space of all positive b-AM-compact operators from E into F, is an AL-space under the ||•||b-AM-norm if and only if E is an AM-space and F is an AL-space; Kb-AMr(E, F) under the ||•||b-AM-norm is isomorphic to an AL-space if and only if E is an AM-space and F is an AL-space. References | Related Articles | Metrics