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25 February 2013, Volume 33 Issue 1 Previous Issue    Next Issue

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Hilbert-type Integral Inequalities in Normed Linear Spaces KUANG Ji-Chang Acta mathematica scientia,Series A. 2013, 33 (1):  1-5.  Abstract ( 710 )   RICH HTML PDF (267KB) ( 670 )   Save In this paper we employ a new technique based on an integral identity to study some new Hilbert-type integral inequalities in normed linear spaces. These new results include the corresponding multiple Hilbert-type integral inequalities in Rn as special cases. References | Related Articles | Metrics

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The Weighted Norm for Some Mercer Kernel SHENG Bao-Huai Acta mathematica scientia,Series A. 2013, 33 (1):  6-15.  Abstract ( 779 )   RICH HTML PDF (365KB) ( 624 )   Save In the present paper, the  upper and lower bounds  of  the  weighted  norm for the Mercer kernel matrix  produced by the generalized translation of an entire function defined on  the infinite interval  are investigated, the weighted norm  is  estimated by the Fourier-Bessel of the entire function. References | Related Articles | Metrics

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Stationary Patterns of a Leslie-Gower Type Three Species Model with Cross-Diffusions HU Guang-Ping, LI Xiao-Ling Acta mathematica scientia,Series A. 2013, 33 (1):  16-27.  Abstract ( 1079 )   RICH HTML PDF (381KB) ( 590 )   Save This paper is concerned with a Leslie-Gower type three species model subject to the homogeneous Neumann boundary condition. We will show that under certain hypotheses, even though the unique positive equilibrium is asymptotically stable for the dynamics with diffusion, Turing instability can produce due to the presence of the cross-diffusion. In particular, we establish the existence of non-constant positive steady states of this system. The results indicate that cross-diffusion can create  stationary patterns. References | Related Articles | Metrics

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Low Dimensional Cohomology Groups for Even Parts of Special Odd Hamiltonian Lie Superalgebras BAI Wei, LIU Wen-De, YUAN Ji-Xia Acta mathematica scientia,Series A. 2013, 33 (1):  28-36.  Abstract ( 627 )   RICH HTML PDF (338KB) ( 650 )   Save Derivation spaces for even parts of finite-dimensional special odd Hamiltonian superalgebras into even parts of generalized Witt superalgebras are completely determined by means of weight space decompositions with respect to suitable tori. Moreover, the corresponding dimension formulas of low dimensional cohomology groups are determined. References | Related Articles | Metrics

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Structured Matrix Nearness Problem with Least Square Spectra Constraint and Its Perturbation Analysis XIE Dong-Xiu, ZHANG Zhong-Zhi Acta mathematica scientia,Series A. 2013, 33 (1):  37-45.  Abstract ( 627 )   RICH HTML PDF (356KB) ( 562 )   Save A nearness matrix problem is considered with two constraints—least square spectra constraint, symmetric and skew-Hamiltonian structure. It discusses two problems: (I) the set L of symmetric and skew-Hamiltonian real n × n matrices A to minimize the Frobenius norm of AX − X∧, where X, ∧ are eigenvector and eigenvalue matrices, respectively, and (II) find Â ∈ L such that C − Â = min A∈L ||C −A||, where || ·|| is the Frobenius norm. A general form of elements in L is given and an explicit expression of the minimizer Â is derived. Perturbation theory of the nearest matrix is analyzed. A numerical example is reported. References | Related Articles | Metrics

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On the Growth of Solutions of f''+Af'+Bf=0, Where A is a Solution of a Second Order Linear Differential Equation WU Xiu-Bi, WU Peng-Cheng Acta mathematica scientia,Series A. 2013, 33 (1):  46-52.  Abstract ( 754 )   RICH HTML PDF (306KB) ( 1117 )   Save Let  A(z) be  a nontrivial solution of f''+P(z)f=0, where P(z) is a polynomial and let B(z) be a transcendental  entire function of  order ρ≤1/2. Then every nontrivial solution of f''+A(z)f'+B(z)f=0 is of infinite order. Moreover, the exponent of convergence of zero-sequence of the product of two linearly independent solutions of f''+A(z)f=0 is of infinite. References | Related Articles | Metrics

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Multiplicity of |Solutions for a Singular Biharmonic Equation PENG Yan-Fang, GUO Jie Acta mathematica scientia,Series A. 2013, 33 (1):  53-61.  Abstract ( 569 )   RICH HTML PDF (288KB) ( 494 )   Save In this paper, by virtue of fibering method and theory of genus,we prove the existence and multiple solutions for a singular Biharmonic equation under  two different cases. References | Related Articles | Metrics

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Properties of E-Bayesian Estimation for the Reliability Derived form Binomial Distribution HAN Ming Acta mathematica scientia,Series A. 2013, 33 (1):  62-70.  Abstract ( 666 )   RICH HTML PDF (312KB) ( 517 )   Save Previously, the author introduces a new parameter estimation method---E-Bayesian estimation method, to estimate the reliability derived form Binomial distribution, the definition of E-Bayesian estimation of the reliability is provided; moreover, formulas of E-Bayesian estimation and hierarchical Bayesian estimation for the reliability are also provided, but the author did not provide propertiy of E-Bayesian estimation. This paper, properties of E-Bayesian estimation are provided. References | Related Articles | Metrics

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Spectral Problem of |Transport Equations with a Proliferating Cell Population WANG Sheng-Hua, CHENG Guo-Fei Acta mathematica scientia,Series A. 2013, 33 (1):  71-77.  Abstract ( 682 )   RICH HTML PDF (290KB) ( 553 )   Save This paper is to research the transport equations of an age structured proliferating cell population with infinite cycle length in Lp-space (1≤p<+∞). It is discussed the spectral prblem of the transport operators, and it is to prove that the spectrum of the transport operators consists of  countable isolate eigenvalues with finite algebraic mutiplicities in half plane. References | Related Articles | Metrics

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A New Nonmonotone Spectral Conjugate Gradient Algorithm HU Chao-Ming, WAN Zhong, WANG Xu Acta mathematica scientia,Series A. 2013, 33 (1):  78-88.  Abstract ( 727 )   RICH HTML PDF (360KB) ( 662 )   Save In this paper, a new spectral conjugate gradient method is proposed. By introducing a hybrid coefficient, the conjugacy parameter is determined based on the combination of PRP and HS methods. Then, a spectral parameter is appropriately chosen such that each search direction is a sufficiently descent direction independent of the employed line search techniques. On the other hand, the  nonmonotone line search technique proposed by Zhang and Hager is modified, and under more mild assumptions, the global convergence of the developed algorithm is proved. Numerical experiments are  employed to demonstrate the efficiency of the algorithm. References | Related Articles | Metrics

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A Note on Wavelet Frames for Affine Subspaces of L2(Rd) ZHOU Feng-Ying, LI Yun-Zhang Acta mathematica scientia,Series A. 2013, 33 (1):  89-97.  Abstract ( 632 )   RICH HTML PDF (341KB) ( 544 )   Save This paper addresses the construction of wavelet frames in the setting of finitely generated affine subspaces of L2(Rd). It is proved that an arbitrary finitely generated affine subspace admits a Parseval wavelet frame with finitely many generators. A sufficient condition is obtained for an affine subspace to be a reducing subspace. For a class of affine subspaces generated by a single function whose Fourier transform is a characteristic function, we derive an explicit Fourier-domain expression of the projection operators related to the construction of wavelet frames. Some examples are also provided. References | Related Articles | Metrics

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Bounded Oscillation for Second-order Nonlinear Neutral Delay Dynamic Equations with Oscillating Coefficients CHEN Da-Xue Acta mathematica scientia,Series A. 2013, 33 (1):  98-113.  Abstract ( 1198 )   RICH HTML PDF (419KB) ( 521 )   Save In this paper, we investigate the oscillation of bounded solutions of second-order nonlinear neutral delay dynamic equation with oscillating coefficients of the form (r(t)([y(t)+p(t)y(τ(t))]Δ)α)Δ+f(t, y(δ(t)))=0 on an arbitrary time scale T, where p is an oscillating function defined on T and α>0 is a quotient of odd positive integers. We get some sufficient conditions for the oscillation of all bounded solutions of the equation by developing a Riccati transformation technique. The obtained results extend and complement some known results in which p(t)≥0 for t∈T is required. Several examples are presented to illustrate our main results. References | Related Articles | Metrics

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Strong Convergence Theorems for Solving EquilibriumProblems and Fixed Point Problems of a Finite Family of ξ-Strict Pseudo-Contraction Mappings by Two Hybrid Projection Methods LI Na, LI Jun Acta mathematica scientia,Series A. 2013, 33 (1):  114-122.  Abstract ( 737 )   RICH HTML PDF (301KB) ( 699 )   Save In this paper, we introduce an iterative scheme by using the hybrid projection methods for finding a common element of the set solutions of an equilibrium problem and the set of fixed points of a finite family of ξ-strict pseudo-contraction mappings in Hilbert space. We obtain two strong convergence theorems under mild assumptions on parameters for the sequences generated by these processes. References | Related Articles | Metrics

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πnFrattini Subgroups and  πcFrattini Subgroups of Amalgamated Free Products of Groups ZHANG Zhi-Rang, DENG Li-Ping, HE Pei-Pei Acta mathematica scientia,Series A. 2013, 33 (1):  123-126.  Abstract ( 672 )   RICH HTML PDF (241KB) ( 710 )   Save Azarian M K  generalizes the theorem on Frattini subgroups of amalgamated free products of two subgroups proposed by Tang C Y  to the case of the free product of any set of subgroups with amalgamated subgroup. We consider πnFrattini subgroups and πcFrattini subgroups of the free product of any set of subgroups with amalgmated subgroup being a cyclic group and obtain similar results. References | Related Articles | Metrics

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Lr Convergence Properties for Mixing Random Arrays under Condition of h-Integrability HU Xue-Ping Acta mathematica scientia,Series A. 2013, 33 (1):  127-133.  Abstract ( 625 )   RICH HTML PDF (270KB) ( 549 )   Save By using the  moment inequality for ρ、φ mixing random sequence  and truncated method we investigate the Lr convergence for ρ、φ mixing random arrays under condition of h-integrability, some results in related literature were extended. References | Related Articles | Metrics

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An Active Set Method for Nonnegativity Constrained Image Deblurring Problem PANG Zhi-Feng, YANG Yu-Fei, DING Li-Xin, XIE De-Xuan Acta mathematica scientia,Series A. 2013, 33 (1):  134-144.  Abstract ( 711 )   RICH HTML PDF (394KB) ( 674 )   Save In this paper we investigate the total variation image deblurring problem with the non-negativity constraint.  An active set strategy based on the augmented Lagrangian method is presented and its convergence in finitely many steps is proved. Furthermore, we deduce that this active set strategy can be regarded as a semismooth Newton method for solving a  system of nonsmooth equations. References | Related Articles | Metrics

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A New Problem on Integer Sets Without 3AP YAO Bing, CHEN Xiang-En Acta mathematica scientia,Series A. 2013, 33 (1):  145-151.  Abstract ( 578 )   RICH HTML PDF (281KB) ( 568 )   Save For each integer k≥3, an anti-average k-set  is a set with k nonnegative integers that contains zero and has no three terms in arithmetic progression. We wish to find λ*(k)=min{maxS: S is an anti-average k-set} for every integer k≥3. Some properties and bounds of λ*(k) are shown, and the method of constructing larger anti-average sets are provided. References | Related Articles | Metrics

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The Boundedness of Commutators with the Weighted Lipschitz Functions KONG Xiang-Bo, JIANG Yin-Sheng, ZHANG Lin Acta mathematica scientia,Series A. 2013, 33 (1):  152-164.  Abstract ( 652 )   RICH HTML PDF (326KB) ( 536 )   Save Let Tb be commutator of the weighted Lipschitz function b and the Calder'{o}n-Zygmund singular integral operator T. In this paper, we study the boundedness properties of Tb on some weighted spaces: weighted Hardy space, weighted Herz spaces and weighted Herz-type Hardy spaces. In addition,  we also obtain its corresponding endpoint estimates. References | Related Articles | Metrics

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Nontrivial Solutions for p-Laplacian Dirichlet Problem PEI Rui-Chang Acta mathematica scientia,Series A. 2013, 33 (1):  165-173.  Abstract ( 652 )   RICH HTML PDF (314KB) ( 610 )   Save A class of particular p-Laplacian Dirichlet problem is studied. When the nonlinear term is superlinear at the positive infinity but asymptotically linear at the negative infinity, the existence of nontrivial solutions is obtained by using minimax methods. References | Related Articles | Metrics

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Existence and Multiplicity of Nonnegative Solutions for a Quasilinear System in RN ZHANG Wen-Li, ZHONG Li-Nan Acta mathematica scientia,Series A. 2013, 33 (1):  174-184.  Abstract ( 740 )   RICH HTML PDF (351KB) ( 563 )   Save In this paper, we consider a class of quasilinear elliptic equations in RN by the minimax theorems and the Ljusternik-Schnirelmann theory. When 2≤p, q<N, α≥0 and β≥0 satisfy the conditions of α+β+2>max{p, q} and α+1/p*+β+1/q* ≤1, the quasilinear system has at least catMδ(M)  nonnegative solutions by relating the number of solutions with the topology of the set where V and W attain its minimum. References | Related Articles | Metrics