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    25 June 2014, Volume 34 Issue 3 Previous Issue    Next Issue
    Articles
    Pointwise Estimates for the Solution to the Multi-Dimensional Generalized BBM-Burgers Equation
    ZHANG Dan-Dan
    Acta mathematica scientia,Series A. 2014, 34 (3):  473-486. 
    Abstract ( 351 )   RICH HTML PDF (365KB) ( 411 )   Save

    In this paper, the author focuses on the time-asymptotic behavior of solution for the scalar multi-dimensional generalized BBM-Burgers equation in the whole-space Rn. By using Green's function method combined with Fourier analysis method, the author yields the pointwise estimates of the solution when the initial data is a small perturbation around the constant state u*, (u*≠0). As a corollary, the optimal decay rate in Lp(Rn)(1≤p≤∞) space is obtained.

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    The Period of a Whirling Pendulum
    ZHANG Jun, DAI Dong
    Acta mathematica scientia,Series A. 2014, 34 (3):  487-494. 
    Abstract ( 293 )   RICH HTML PDF (413KB) ( 330 )   Save

    The authors considered a whirling pendulum system. The system has at most five periodic annuli. By calculating the elliptic integrals, The authors obtained the monotonicity of the period of those periodic annuli for various cases of the parameter. The analysis also provides a method to discuss the problem of the monotonicity of period, which is more
    fundamental than the one by using Abelian integrals. Finally, the authors given numerical simulations to demonstrate their conclusions.

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    Study on the Diabetic Population Development of Early Warning Modeling
    LIU Dan-Hong, XU Gen-Qi
    Acta mathematica scientia,Series A. 2014, 34 (3):  495-511. 
    Abstract ( 418 )   RICH HTML PDF (506KB) ( 305 )   Save

    The rapid development of diabetes has become a serious public health problem, diabetes can induce a variety of
    chronic complications, and enormous economic burden to society and individuals. In this paper, we setup a mathematical warning model to study the development of diabetes and prove that a system exists non-negative
    dynamic solution and steady-state solution  under the  assumption in the system model. We calculate dynamic solutions to  the probability of  time stages of diabetes, while the steady state solution can be the probability of diabetes stage when the time is full. Patients with diabetes in China are close to one hundred million people, nearly 150 million people in the pre-diabetes, diabetes is very serious form of development. The control of blood glucose is the key of the control of diabetes.  Through the different states of the blood sugar control  undervthe development of different states, this paper obtains steady-state solution validates the severe  form, and dynamic solutions  play a role in early warning to  the future development of the diabetes. Especially  the dynamic solution converges to  the steady-state  solution in the sense of norm. And the indices of the system determined by the steady-state solution are reliable.

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    The Triviality of Definitions of Probabilistic Inner Product Spaces
    ZHU Xing-Hua, XIAO Jian-Zhong
    Acta mathematica scientia,Series A. 2014, 34 (3):  512-520. 
    Abstract ( 342 )   RICH HTML PDF (316KB) ( 278 )   Save

    In the paper some properties concerning the quasi-inverses of distribution functions are studied. By means of these properties some relations among the families of semi-inner products are discussed. It is showed that the probabilistic inner product spaces under several definitions are usual inner product spaces in fact.

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    Attached Primes of Generalized Inverse Polynomial Modules
    OUYANG Lun-Qun, LIU Jin-Wang
    Acta mathematica scientia,Series A. 2014, 34 (3):  521-529. 
    Abstract ( 377 )   RICH HTML PDF (324KB) ( 306 )   Save

    Let R be an associative ring with  identity,  and (S, ≤) a strictly totally ordered monoid which is also artinian  and  MR  a right R-module. Attached primes of a generalized inverse polynomial module [MS, ] over a generalized power series ring [[RS, ]] are considered in this paper. Given a module MR, we write Att(MR) for the Attached primes of MR. It is shown that Att([MS, ][[RS, ≤]])=[[PS, ]]|PAtt(MR)} under some additional conditions. Thus all Attached primes of [MS, ][[RS, ]] can be described in terms of the Attached primes of MR in a very straightforward way. This result partially generalizes  the  S. Annin's recent work [1] on inverse polynomial modules over skew polynomial rings.

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    A General Class of Marginal Semiparametric Hazards Model with Multivariate Failure Time Data
    YANG Qing-Long, GUO Li-Sha, LIU Yan-Yan
    Acta mathematica scientia,Series A. 2014, 34 (3):  530-539. 
    Abstract ( 366 )   RICH HTML PDF (395KB) ( 320 )   Save

    Multivariate failure time data are frequently encountered in biomedical research. In this article,  we propose a general class of hazards regression model for multivariate failure time data. This general class includes some popular classes of models as subclasses,  such as marginal proportional hazards model, the marginal accelerated failure time model.
     Regression coefficients are estimated through estimating equation method. The proposed estimators for the  regression parameters are shown asymptotically to follow a multivariate normal distribution with a sandwich-type
    covariance matrix that can be consistently estimated. The estimated subject-specific cumulative baseline hazard process is  shown to converge weakly to a zero mean Gaussian random field.

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    Ur, t-module Algebra Structures on the Quantum Plane
    HONG Yan-Yong, WU Zhi-Xiang
    Acta mathematica scientia,Series A. 2014, 34 (3):  540-561. 
    Abstract ( 307 )   RICH HTML PDF (426KB) ( 298 )   Save

    When q is not the root of unity and the ground field is C, we give a complete list of Ur, t-module algebra structures on the quantum plane and describe these representations. Moreover, it is interesting to find that, in some cases, Cq[x, y]=\bigoplus\limitsn=0Cq[x, y]n, where Cq[x, y]n is the n-th homogeneous component and is isomorphic to the irreducible representation V1, nγ1n/2 for some γ1≠0.

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    Relation Between Small Functions with Differential Polynomials Generated by Solution of Periodic Differential Equations
    XIAO Li-Peng
    Acta mathematica scientia,Series A. 2014, 34 (3):  562-572. 
    Abstract ( 325 )   RICH HTML PDF (332KB) ( 425 )   Save

    In this paper, the existence of subnormal solution, the growth and the oscillation of solutions of certain second-order nonhomogeneous periodic differential equation are investigated. Also, the relationship between small functions and differential polynomials L(f)=d2f''+d1f'+d0f generated by solutions of the above equation, where d0(z), d1(z), d2(z) are entire functions that are not all equal to zero, is studied.

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    The Discreteness of Spectrum of a Class of Differential Operators with Coefficients of Power-exponential Product Functions
    ZHOU Li-Guang, WANG Wan-Yi
    Acta mathematica scientia,Series A. 2014, 34 (3):  573-580. 
    Abstract ( 274 )   RICH HTML PDF (308KB) ( 350 )   Save

    The discrete spectrum of a class of differential operators with coefficients of power-exponential product functions is
     discussed. Some sufficient conditions for considered differential operators are obtained to ensure that the spectrum is discrete with direct sum decomposition method of operators and comparison method of the corresponding quadratic forms.

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    Monotone Minkowski Functionals and Scalarizations of Henig Proper Efficiency
    ZHANG Shen-Yuan, QIU Jing-Hui
    Acta mathematica scientia,Series A. 2014, 34 (3):  581-592. 
    Abstract ( 288 )   RICH HTML PDF (364KB) ( 369 )   Save

    Without the closedness and the pointedness of convex cones, we consider monotone Minkowski functionals generated
    by general convex cones and investigate  properties of those Minkowski functionals. From this, in the framework of partially ordered locally convex spaces we obtain scalarizations of weakly efficient points of a general set and of a cone-bounded set by using a monotone continuous Minkowski functional and a monotone continuous semi-norm,
    respectively.  Using the scalarizations of weak efficiency, we deduce scalarizations of Henig properly efficient points of a
    general set and of a cone-bounded set, respectively. Moreover, when the ordering cone has a bounded base, we obtain some scalarization results on superefficiency in locally convex spaces. Finally we give some density results for Henig proper efficiency and superefficiency. These results generalize and improve the related known results.

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    Optimality Conditions for Approximate Solutions on Nonconvex Vector Equilibrium Problems in Asplund Spaces
    LONG Xian-Jun
    Acta mathematica scientia,Series A. 2014, 34 (3):  593-602. 
    Abstract ( 266 )   RICH HTML PDF (313KB) ( 322 )   Save

    The purpose of this paper is to study approximate solutions for the vector equilibrium problem in Asplund spaces without any convexity assumption. We obtain optimality conditions for εe-quasi weakly efficient solutions, εe-quasi Henig efficient solutions, εe-quasi globally efficient solutions and εe-quasi efficient solutions to vector equilibrium problems 
    by the Mordukhovich subdifferential. As applications of our results, we derive some optimality conditions for nonconvex vector optimization problems.

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    M2-Type Sharp Maximal Function Estimates and Boundedness for Toeplitz Type Operator Associated to Multiplier Operator
    TONG Li-Juan, LIU Lan-Zhe
    Acta mathematica scientia,Series A. 2014, 34 (3):  603-610. 
    Abstract ( 277 )   RICH HTML PDF (267KB) ( 569 )   Save

    In this paper, we establish the M2-type sharp maximal function estimates for the Toeplitz type operator associated to some multiplier operator. As an application, we obtain the boundedness of the operator on Lebesgue and Morrey spaces.

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    Asymptotic Properties of the Negative Extreme-value Index Estimator
    TAO Bao
    Acta mathematica scientia,Series A. 2014, 34 (3):  611-618. 
    Abstract ( 272 )   RICH HTML PDF (270KB) ( 284 )   Save

    As the extreme-value index is negative, the author proposes the negative extreme-value index estimator, whose weak and strong consistency are proved.  Under the second order regularly varying condition, the author obtains the rate of strong convergence, asymptotic expansion and proves asymptotic normality. Moreover, the optimal choice of the smoothing parameter is discussed.

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    The Core on a Real Module
    ZOU Qun, ZENG Guang-Xing, QI Zhi-Peng
    Acta mathematica scientia,Series A. 2014, 34 (3):  619-625. 
    Abstract ( 283 )   RICH HTML PDF (295KB) ( 430 )   Save

    The main aim of this paper is to obtain a sufficient and necessary condition for existent of orderings on a module through obtaining a real prime submodule corresponding the real prime ideal of a commutative ring with identity 1. Then, the intersection of all orderings on a module (It is intitule ``The Core on a Real Modul" in this paper) are characterized.
    The most important conclusion in this paper is a sufficient and necessary condition is obtained for judging a element of modul belongs to the core of modul.

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    Global Existence and Blow-up of Solutions to a Doubly Degenerate Parabolic System with Nonlinear Boundary Conditions
    MI Yong-Sheng, MU Chun-Lai, WU Yun-Long
    Acta mathematica scientia,Series A. 2014, 34 (3):  626-637. 
    Abstract ( 319 )   RICH HTML PDF (343KB) ( 388 )   Save

    This paper deals with interactions among three kinds of nonlinear mechanisms: nonlinear diffusion, nonlinear reaction and nonlinear boundary flux in a parabolic model with multiple nonlinearities. We obtain the critical global existence curve and critical Fujita curve by constructing various self-similar supersolutions and subsolu-tions.

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    A Note on the Finitistic Dimension of Crossed Product Group Algebras
    ZHANG Mian-Mian, CAO Hai-Jun
    Acta mathematica scientia,Series A. 2014, 34 (3):  638-642. 
    Abstract ( 321 )   RICH HTML PDF (256KB) ( 371 )   Save

    Let G be a finite group, k be an algebraically closed field whose characteristic does not divide the order of G, and
    ∧ be a  twisted kG-module algebra such that ∧*G exists as a crossed product algebra. We show that the finitistic
    dimensions of ∧*G and ∧ are same and ∧*G satisfies the finitistic dimension conjecture if and only if ∧ does.

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    Analysis of a Two-grid Method for Characteristic Finite Element Solutions of Nonlinear Convection-diffusion Equations
    CHEN Chuan-Jun, ZHAO Xin
    Acta mathematica scientia,Series A. 2014, 34 (3):  643-654. 
    Abstract ( 304 )   RICH HTML PDF (381KB) ( 427 )   Save

    A two-grid characteristic finite element approximation is presented and discussed for nonlinear convection-diffusion equations. Piecewise linear trial functions are used to develop the finite element scheme. In this two-grid scheme, the full nonlinear problem is solved only on a coarse grid with grid size H. The nonlinearities are expanded by one Newton-like iteration about the coarse grid solution on a fine gird of size h. The resulting linear system is solved only on the fine grid. A prior error estimates are derived with the L2-norm O(?t +h2+H4-d/2), where d≥1 is the spacial dimension.

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    Solvability of Solutions for a Class of Nonlinear Fractional Multi-Point Boundary Value Problems
    HAO Xiao-Hong, CHENG Zhi-Long, ZHOU Zong-Fu
    Acta mathematica scientia,Series A. 2014, 34 (3):  655-668. 
    Abstract ( 288 )   RICH HTML PDF (349KB) ( 316 )   Save

    This paper is concerned with the following nonlinear fractional differential equations multi-point boundary value problem
    Dα0+u(t) = f(t, u(t), Dα-10+u(t), Dα-20+u(t), Dα-30+u(t)), t ∈(0,1),  

    u(0) = 0, Dα-10+u(0)=∑mi=1αiDα-10+ui),
    Dα-20+u(1)=∑j=1nβjDα-20+uj), Dα-30+u(1)-Dα-30+u(0)=Dα-20+u(1) 1/2Dα-10+u(0).
    By applying Mawhin coincidence degree theory, we obtain the existence of the solutions for the problem. The results expand the previous ones in the field.

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    Remarks of Convergence Theorems of Mann Iterative Process with Errors for Φ-Hemicontractive Mappings in Uniformly Smooth Real Banach Spaces
    XUE Zhi-Qun, LV Gui-Wen
    Acta mathematica scientia,Series A. 2014, 34 (3):  669-673. 
    Abstract ( 286 )   RICH HTML PDF (264KB) ( 336 )   Save

    In this paper, we obtain the convergence of Mann iterative process with errors for generalized Lipschitz  Φ-hemicontractive mappings in uniformly smooth real Banach spaces. Our results improve and extend the corresponding results of [1, 7, 10--12].

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    Chover´s Law of Iterated Logarithm for Weighted Partial Sums of NA Random Variables Sequences
    QIU De-Hua, CHEN Ping-Yan
    Acta mathematica scientia,Series A. 2014, 34 (3):  674-683. 
    Abstract ( 282 )   RICH HTML PDF (320KB) ( 526 )   Save

    We establish the integral test for the weighted partial sums of identically distributed NA random variables with heavy-tailed distribution assumption by using the exponential inequality, and obtain the Chover's law of iterated logarithm as a corollary. As applications, the corresponding limit results for some classical summable methods are also established. These results in this paper extend the related known works in the literature.

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    Optimal Harvest Rate for a Population System Modeling Periodic Environment and Body Size
    HE Ze-Rong, LIU Rong, LIU Li-Li
    Acta mathematica scientia,Series A. 2014, 34 (3):  684-690. 
    Abstract ( 319 )   RICH HTML PDF (362KB) ( 327 )   Save

    This paper is concerned with the optimal harvesting for a size-structured population model in a periodic environment.
    Applying a functional approach, we demonstrate the existence of the optimal strategies, and derive the structure of the optimal controls by means of tangent and normal cones. The results pave the way for practical applications of the
    model.

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    Characterizations of the Hardy Space H1(R) in Terms of |Tight Wavelet Frame Coefficients
    LU Da-Yong, LIU Zhan-Wei, WU Guo-Chang
    Acta mathematica scientia,Series A. 2014, 34 (3):  691-699. 
    Abstract ( 318 )   RICH HTML PDF (354KB) ( 286 )   Save

    To characterize the Hardy spaces H1(R) in terms of orthonormal basis coefficients have been verified successfully. In this paper, we give a characterization of H1(R) in terms of tight wavelet frame coefficients by means of properties of tight wavelet frames and the relationships between them and orthonormal bases.

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    Common Fixed Points for a Pare of Mappings Satisfying Contractive Conditions with Variable Coefficients |on Metric Spaces
    YAN Jin-Shi, PIAO Yong-Jie
    Acta mathematica scientia,Series A. 2014, 34 (3):  700-707. 
    Abstract ( 311 )   RICH HTML PDF (277KB) ( 355 )   Save

    In this paper, we use a pare of mappings satisfying contractive condition with some variable coefficients or Φ-contractive condition to construct a convergent sequence, and  prove that the unique limit of the sequence is the common fixed point of the two mappings and give  sufficient conditions that the pare of mappings have an unique common fixed point, and then give several particular conclusions. The obtained results in this paper generalize and improve some known results.

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    A Hilbert Type Series Inequality with Transferable Variable Kernel
    HONG Yong, KONG Yin-Ying
    Acta mathematica scientia,Series A. 2014, 34 (3):  708-715. 
    Abstract ( 313 )   RICH HTML PDF (267KB) ( 385 )   Save

    If λ1, λ2≠0, t>0, K(x, y)= K(tx, y)=K(x, tλ1/λ2y),   K(x, ty)=K(tλ1/λ2x, y). Then K(x, y) is called transferable variable           function with parameters λ1 and λ2. In this paper, let λ1λ2<0, Hilbert type series inequality with transferable variable kernel is studied. The equivalent form and the best constant factor are considered.

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    A Optimal Uniformly Convergent Discontinuous Galerkin Finite Element Method for Singularly Perturbed Problem
    YANG Yu-Bo, ZHU Peng, YIN Yun-Hui
    Acta mathematica scientia,Series A. 2014, 34 (3):  716-726. 
    Abstract ( 309 )   RICH HTML PDF (373KB) ( 377 )   Save

    A nonsymmetric discontinuous Galerkin finite element method with interior penalties is considered for one-dimensional
    singularly perturbed convection-diffusion problem. On a Bakhvalov-Shishkin mesh with Lagrange linear elements, the method is shown to be convergent, uniformly in the perturbation parameter ε, of optimal error O(N-1) in the energy
    norm, where N is the number of mesh. Finally, through numerical experiments, the authers verified the theoretical result.

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    The Singular Perturbation of Boundary Value Problem on Infinite Interval for a Class Nonlinear Vector Differential Equation
    LIN Su-Rong
    Acta mathematica scientia,Series A. 2014, 34 (3):  727-737. 
    Abstract ( 292 )   RICH HTML PDF (373KB) ( 269 )   Save

    The paper discuss the singular perturbation of boundary value problem on infinite interval for a class nonlinear vector differential equation. Although, the boundary problem on the finite interval had been treated extensiverly, but on the infinite interval it has not been studied using the diagonalization method. Under appropriate assumptions, we use new method to prove the existence of solution and the uniformly valid asymptotice expansion of arbitrary order and the error
    estimation are given as well.

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    On Fixed Points Theorems of a Class of Decreasing Operator and Applications
    LI Xing-Chang, TIAN Shi-Qin
    Acta mathematica scientia,Series A. 2014, 34 (3):  738-743. 
    Abstract ( 338 )   RICH HTML PDF (288KB) ( 311 )   Save

    The paper obtains a fixed point theorem for decreasing operators. The result is applied to singular boundary value problems which has the decreasing nonlinearity on u, and the nonlinearity may be singular at t = 0 and/or 1 and u = 0.

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    Martingale Transforms between Orlicz-Hardy and BMO Spaces
    ZHUANG Dan, YU Lin
    Acta mathematica scientia,Series A. 2014, 34 (3):  744-754. 
    Abstract ( 296 )   RICH HTML PDF (375KB) ( 312 )   Save

    Using the technique of Burkholder's martingale transforms, the relations between "predictable'' martingale Orlicz-Hardy spaces and BMO spaces are investigated. Let Φ be a Young function with finite index, it is proved that a martingale is in HΦ∈{PΦ, QΦ}, if and only if it is the transform of a martingale from BMO∈{BMO1, BMO2}.

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    An Iterative Sequence with Norm Convergence for Accretive Operators in Banach Spaces
    CUI Huan-Huan
    Acta mathematica scientia,Series A. 2014, 34 (3):  755-759. 
    Abstract ( 229 )   RICH HTML PDF (246KB) ( 414 )   Save

    This paper deals with the problem: find x so that 0∈Ax, where A is an accretive operator. One algorithm solving this problem has the following scheme: xn+1nu+(1-αn)((1-λ)xn+λJrnxn), where u is a fixed element, λ(0,1),  {rn} and αn are real sequences, and Jrn denotes the resolvent of  A. The algorithm is known to converge provided that (rn) is a convergent sequence. In this paper we show that such a condition can be relaxed as limn→∞|11-rn+1/rn|=0.

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