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25 February 2014, Volume 34 Issue 1 Previous Issue    Next Issue

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Strong Convergence Theorems of a Modified Mann Iterative Method for Nonexpansive Mappings in Banach Spaces CAI Gang, BU Shang-Quan Acta mathematica scientia,Series A. 2014, 34 (1):  1-8.  Abstract ( 621 )   RICH HTML PDF (257KB) ( 446 )   Save In this paper, we introduce a new modified Mann iterative algorithm for finding a common element of the set of common fixed points of infinite family of nonexpansive mappings in a real Banach space. Then we prove a strong convergence theorem under some suitable conditions. Our results improve and extend the corresponding results announced by many others in the literature. References | Related Articles | Metrics

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Bifurcation and Multiple Growth Paths in an Economic Growth Model with Demographic Transition CAI Dong-Han, YE Hui Acta mathematica scientia,Series A. 2014, 34 (1):  9-15.  Abstract ( 442 )   RICH HTML PDF (392KB) ( 359 )   Save In this paper, we make a further study of the model provided by Holger Sriulik[1]. It is proved that the dynamical system  which describes the model has no nonzero equilibrium  when α>α-, one nonzero equilibrium when α=α- and two equilibria, one saddle and one node when α>α- and α--α is small enough. So the dynamical system undergoes a saddle-node bifurcation at α=α-. By phase portrait analysis, we obtain that the first quadrant of y-k plane is divided into two regions by the stable manifold of the saddle point when there exists two equilibria and the economy has a Malthusian region in which all growth paths converge to the low level equilibrium and a non-Malthusian region in which the economy has normal growth path. Therefore, the economy can escape the “Malthusian poverty trap”by promoting the technological growth rate or by “big-push”which promotes the per capita income. References | Related Articles | Metrics

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S-asymptotically ω-periodic Solutions of Semi-linear Neutral Fractional Differential Equations SHU Xiao-Bao, DAI Bin-Xiang Acta mathematica scientia,Series A. 2014, 34 (1):  16-26.  Abstract ( 448 )   RICH HTML PDF (347KB) ( 471 )   Save This paper is concerned with the existence of the S-asymptotically ω-periodic solutions of the semilinear neutral Caputo fractional equation Dtα(x(t)+F(t, xt))+A x(t) =G(t, xt), t≥0,  x(0)=φ ∈B. considered in a Banach space X, where  0<α<1, -A is the infinitesimal generator of an analytic semigroup {T(t)}t≥0. References | Related Articles | Metrics

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Global Regularity for Very Weak Solutions to Obstacle Promlems Corresponding to a Class of A-Harmonic Equations ZHOU Shu-Qing, HU Zhen-Hua, PENG Dong-Yun Acta mathematica scientia,Series A. 2014, 34 (1):  27-38.  Abstract ( 393 )   RICH HTML PDF (389KB) ( 418 )   Save Using Hodge decomposition theorem, the local and the global W1, q(Ω)-regularity results for very weak solutions to the obstacle problems associated with the following non-homogeneous A-harmonic equations  -div(A(x, Du(x)))=f(x, u(x)) are obtained under certain conditions on A(x, Du(x)), f(x, u(x)) listed in the context. The results generalize the corresponding results in related literatures. The results can be widely applied to optimal control problems. References | Related Articles | Metrics

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Lie Derivable Maps on Operator Algebras AN Run-Ling, Kichi-Suke Saito Acta mathematica scientia,Series A. 2014, 34 (1):  39-48.  Abstract ( 393 )   RICH HTML PDF (296KB) ( 585 )   Save Let A be a unital algebra, and let M be an A-bimodule. We say δ: A→M is a Lie derivable map if it (with no assumption of additivity and continuity) satisfies δ([A, B])=[δ(A), B]+[A, δ(B)] for all A, B∈A. Under some condition, we show that δ is of the form δ(A)=τ(A)+f(A), where τ: A→M is an additive derivation and f is a map from A into the center of M with f([A, B])=0 for all A, B∈A. As its application, we characterize Lie derivable maps on factor von Neumann algebras and nest algebras. References | Related Articles | Metrics

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Littlewood-Paley g*λ-function Associated to Schr\"{o}dinger Operator HUANG Ji-Zheng Acta mathematica scientia,Series A. 2014, 34 (1):  49-61.  Abstract ( 414 )   RICH HTML PDF (319KB) ( 376 )   Save Let L=-Δ+V be a Schr\"{o}dinger operator, where Δ is the Laplacian on Rd and the nonnegative potential V belongs to the reverse H\"{o}lder class Bd/2. In this paper, we investigate the boundedness of Littlewood-Paley g*λ-function associated to Schr\"{o}dinger operator L. References | Related Articles | Metrics

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Existence and Uniqueness of |Common Fixed Point for Four Mappings on Partial Metric Spaces WANG Yun-Jie Acta mathematica scientia,Series A. 2014, 34 (1):  62-69.  Abstract ( 482 )   RICH HTML PDF (297KB) ( 353 )   Save In this work, we shall prove that a common fixed point theorem for four mappings satisfying a generalized nonlinear contraction type condition on partial metric spaces. Finally, we give two examples to show that our contractive conditions is real improvement for the contractive conditions used in the literature. References | Related Articles | Metrics

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Convergence Analysis for Countable Family of Weak Bregman Relatively Nonexpansive Mappings CHEN Jia-Wei, WAN Zhong-Peng, ZHAO Lie-Ji Acta mathematica scientia,Series A. 2014, 34 (1):  70-79.  Abstract ( 640 )   RICH HTML PDF (312KB) ( 386 )   Save A notion of countable family of weak Bregman relatively nonexpansive mappings is introduced in reflexive Banach space. We construct two iterative algorithms for finding a common fixed point of a countable family of weak Bregman relatively nonexpansive mappings in Banach spaces. Finally, the strong convergence of the proposed algorithms are also proved under appropriate conditions. References | Related Articles | Metrics

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H-Exponent of the Homogeneous Space SU(2n)/Sp(n) ZHAO Hao, YU Hai-Bo, SHEN Wen-Huai Acta mathematica scientia,Series A. 2014, 34 (1):  80-85.  Abstract ( 466 )   RICH HTML PDF (302KB) ( 336 )   Save Let p be a prime greater than 3. Under certain dimensional restriction we obtain an upper bound for the p-primary H-homotopy exponent of the homogeneous space SU(2n)/Sp(n) by decomposing it as the product of some homotopy associative, homotopy commutatice H-spaces. References | Related Articles | Metrics

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Multiple Solutions for Semilinear Elliptic Robin Boundary Value Problems with a Discontinuous Nonlinear Term ZHANG Jing Acta mathematica scientia,Series A. 2014, 34 (1):  86-94.  Abstract ( 364 )   RICH HTML PDF (283KB) ( 368 )   Save In this paper, we consider the Robin boundary value problem in a Banach space for semilinear elliptic equation on a bounded domain whose nonlinear term is discontinuous by using nonsmooth local linking methods. References | Related Articles | Metrics

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The Equivalence of the Smooth Modulus with Weights and a K-Functional in Orlicz Spaces and it's Application HAN Ling-Xiong, Wu Garidi, LIU Guo-Feng Acta mathematica scientia,Series A. 2014, 34 (1):  95-108.  Abstract ( 401 )   RICH HTML PDF (377KB) ( 336 )   Save First, the Orlicz space L*Φ[0, ∞) corresponding to the Young function Φ(x) is introduced. Then by the inductive assumption and the decomposition method, the equivalence theorem between K-functional and r-th modulus of smoothness in Orlicz space L*Φ[0, ∞) is given. Finally, as an application of the modulus, a strong converse inequality of B type for the Gamma operators is obtained. References | Related Articles | Metrics

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Spectral Analysis on Some Discrete Systems From Maxwell Equations Wu Shi-Liang, LI Cui-Xia Acta mathematica scientia,Series A. 2014, 34 (1):  109-114.  Abstract ( 490 )   RICH HTML PDF (308KB) ( 399 )   Save In this paper, spectral analysis on the saddle point linear systems from the finite element discretization of the mixed formulation of the time-harmonic Maxwell equations are presented. Theoretical analysis shows that all the eigenvalues of the relational coefficient matrix are strongly clustered under certain conditions. References | Related Articles | Metrics

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B\"acklund Transformations on Surfaces Swept out by Moving Curves with Constant Torsion CAO Xi-Fang, XU Chuan-You Acta mathematica scientia,Series A. 2014, 34 (1):  115-125.  Abstract ( 375 )   RICH HTML PDF (1080KB) ( 372 )   Save We give B\"acklund transformations on surfaces which are swept out by moving curves with constant torsion. The curvature of the moving curve discussed in this paper is governed by the modified KdV equation. Our result can be regarded as a geometric realization of the well-known B\"acklund transformation for the modified KdV equation. As applications, by taking the circular cylinder as a seed surface, we construct some novel surfaces which are swept out by moving periodic curves whose projections to the xy-plane are closed. References | Related Articles | Metrics

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Generalized Homoclinic Solutions for the Stationary Extended Fisher-Kolmogorov Equation LI Xiao-Pei Acta mathematica scientia,Series A. 2014, 34 (1):  126-138.  Abstract ( 416 )   RICH HTML PDF (369KB) ( 438 )   Save This paper investigates the stationary extended Fisher-Kolmogorov equation u''''-βu''+ u3-u=0,  β>0, which has a saddle-center equilibrium u = 0 (two nonzero real and two nonzero imaginary eigenvalues). Applying a perturbation method and adjusting some phase shift constants, we prove that it has a homoclinic solution connecting a periodic solution (called generalized homoclinic solution, thereafter) near the origin for each positive constant β. References | Related Articles | Metrics

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On Non-autonomous Multivalued Partial Integro-Differential Equations with State-Dependent Delay LI Wen-Sheng Acta mathematica scientia,Series A. 2014, 34 (1):  139-149.  Abstract ( 563 )   RICH HTML PDF (330KB) ( 309 )   Save This paper is mainly concerned with the existence of mild solutions for a first order non-autonomous multivalued partial integro-differential equations with state-dependent delay. The results are obtained by using theories of resolvent operators combined with the fixed point theorem for nonlinear alternatives of Leray-Schauder type for multivalued version. Finally, we present an example to illustrate the main theorem. References | Related Articles | Metrics

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Hadamard Product of Finitely Order of Certain Class of Analytic Functions Defined by Subordination XIONG Liang-Peng, LIU Xiao-Li Acta mathematica scientia,Series A. 2014, 34 (1):  150-156.  Abstract ( 676 )   RICH HTML PDF (308KB) ( 589 )   Save Let P(A, B) denote a class of analytic functions subordinated to the function 1+Az/1-Bz, where A+B≠0, |B|≤1. The Hadamard product of finitely order of certain classes H 1, H2, …, Hn is defined by H1*H2*H3*…*Hn(z)={f1*f2*f3*… fn(z): fi ∈Hi, i =1, 2, …, n, n ∈Z+}. It obtains the necessary and sufficient conditions for equality P(A1, B1)*P(A2, B2)*P(A3, B3)*…*P(An, Bn)=P(X, Y), which extends the corresponding earlier results. References | Related Articles | Metrics

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A New Description of Self-adjoint Domains of Singular Linear Hamiltonian Operators ZHENG Zhao-Wen, XU Yan-Li Acta mathematica scientia,Series A. 2014, 34 (1):  157-170.  Abstract ( 385 )   RICH HTML PDF (377KB) ( 335 )   Save In this paper, the self-adjoint extension of the  minimal Hamiltonian operator  h with equal deficiency index (d, d) is considered. Since  Im(h* y, y) can be represented as a quadratic form with rank  being 2d, the new characterization of the domains of self-adjoint extensions of  h is obtained by the representation matrix. References | Related Articles | Metrics

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The Univalent Radius of Harmonic Mappings Under Complex-Operator ZHU Jian-Feng, HUANG Xin-Zhong Acta mathematica scientia,Series A. 2014, 34 (1):  171-178.  Abstract ( 462 )   RICH HTML PDF (285KB) ( 339 )   Save Assume f(z) is a harmonic mapping defined in the unit disk D, denote complex-operator L:=z∂/∂z-z∂/∂z. In this paper, assume f satisfys coefficient condition (1.7), we obtained the univalent radius ρ0 of L(f). Here ρ0 is defined by (1.9). Moreover, if f is a harmonic K-quasiconformal mapping, we also obtained the univalent radium ρK of L(f). References | Related Articles | Metrics

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A Generalization of Hilbert-type Integral Inequality LIU Qiong, LONG Shun-Chao Acta mathematica scientia,Series A. 2014, 34 (1):  179-185.  Abstract ( 481 )   RICH HTML PDF (277KB) ( 351 )   Save By introducing Γ-function and ζ-function, and using the way of weight function and the method of real analysis, a generalized Hilbert-type integral inequality is given. The equivalent form is considered and their constant factors are proved being the best possible. By taking the special parameter values, some meaningful results are obtained. References | Related Articles | Metrics

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A Modified Tikhonov Regularization Method for Identifying an Unknown Source in the Heat Equation ZHAO Zhen-Yu, YOU Lei Acta mathematica scientia,Series A. 2014, 34 (1):  186-192.  Abstract ( 417 )   RICH HTML PDF (385KB) ( 386 )   Save In this paper, we consider the problem for determining the unknown source in the heat equation. A modified Tikhonov regularization method is presented to deal with the illposedness of the problem and error estimates are obtained with an a priori strategy and an a posteriori choice rule to find the regularization parameter. Numerical tests show that the proposed method is effective and stable. References | Related Articles | Metrics

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First and Second Order Optimality Conditions for Strict Minimality in Set-valued Optimization CHAI Yan-Fei, LIU San-Yang, LI Jun Acta mathematica scientia,Series A. 2014, 34 (1):  193-206.  Abstract ( 453 )   RICH HTML PDF (355KB) ( 327 )   Save In this paper, the notion of local strict minimum of order m (m≥1) for vector optimization problems is extended from single-valued maps to set-valued maps. Some properties and characterizations are then investigated in normed spaces. Furthermore, necessary and sufficient conditions for strict minimum of orders m≥1 are established by using Dini derivatives and support functions. References | Related Articles | Metrics

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Empirical Analysis of Lottery Data Based on Non-stationarity Measure TAN Qiu-Heng, DING Yi-Ming Acta mathematica scientia,Series A. 2014, 34 (1):  207-216.  Abstract ( 470 )   RICH HTML PDF (692KB) ( 374 )   Save Based on the ideas of nonstationarity measure (NS), we study historical data of three lotteries: “Pailie 50” and “7 stars”in China, and “Pick 30”in Arizona state (USA). The stability of frequencies of numbers in different digits and the uniformity of the distributions in different digits for each lottery are investigated carefully. Some empirical evidences are obtained: the occurrences of numbers in 0…9 at each digit admit stable probability, the distribution of numbers in different digits are di erent from the i.i.d uniform distribution on 0…9, and the nonstationarity measures NS(7 stars)< NS(Pick 3)<NS(Pailie 5). References | Related Articles | Metrics