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25 August 2012, Volume 32 Issue 4 Previous Issue    Next Issue

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Levitin-Polyak Well-posedness of Generalized Mixed Variational Inequalities ZHU Li, XIA Fu-Quan Acta mathematica scientia,Series A. 2012, 32 (4):  633-643.  Abstract ( 965 )   RICH HTML PDF (325KB) ( 796 )   Save In this paper, we introduce the concepts of the Levitin-Polyak-α-approximating sequences and the  Levitin-Polyak-α-well-posedness to the generalized mixed variational inequalities. We also define the gap function of the generalized mixed variational inequalities and prove that the Levitin-Polyak well-posedness to the generalized mixed variational inequalities and the corresponding minimization problems are equivalent. After that, we investigate the Furi-Vignoli type metric characteristics of (generalized) Levitin-Polyak well-posedness to the generalized mixed variational inequalities. References | Related Articles | Metrics

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Liouville Theorems on Subelliptic Quasilinear Equations in Unbounded Exterior Domain ZHENG Shen-Zhou, LU Han-Fang Acta mathematica scientia,Series A. 2012, 32 (4):  644-653.  Abstract ( 765 )   RICH HTML PDF (332KB) ( 707 )   Save In this paper, the analytic properties is considered for a class of subelliptic quasilinear equations in unbounded exterior domian. we establish various Liuoville theorems in unbounded exterior domain under the different settings with n≥3. References | Related Articles | Metrics

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Quotient Categories and AR-triangles LIN Zeng-Qiang Acta mathematica scientia,Series A. 2012, 32 (4):  654-660.  Abstract ( 727 )   RICH HTML PDF (285KB) ( 796 )   Save Let D be a triangulated category and U be a triangulated subcategory of D. This paper mainly discusses the relationship between the AR-triangles of D and D/U. In particular, if D admits a recollement relative to D'  and D" , and D has AR-triangles, then D'  and D"  also have AR-triangles. Moreover, their AR-triangles are induced by the AR-triangles of D. References | Related Articles | Metrics

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Integral Average |of Philos Type for Second Order Nonlinear Oscillation LIN Quan-Wen, YU Yuan-Hong Acta mathematica scientia,Series A. 2012, 32 (4):  661-669.  Abstract ( 703 )   RICH HTML PDF (273KB) ( 677 )   Save The purpose of this paper is to study the oscillation of second order nonlinear differential equation (a(t)x'(t))'+p(t)x'(t)+q(t)x(t)=0.                              (E) Some new oscillation criteria are established under quite general assumptions. Our methodology is somewhat different from that of previous authors [1--4, 8--10, 13--15]. Our results extend and complement some earlier results of Philos[7] and Rogovchenko[9].  An example is also given to illustrate the results. References | Related Articles | Metrics

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Analysis of an Impulsive Epidemic Model with Time Delays and Nonlinear Incidence Rate JIANG Yu, MEI Li-Quan, SONG Xin-Yu, TIAN Wei-Jun, DING Xue-Mei Acta mathematica scientia,Series A. 2012, 32 (4):  670-684.  Abstract ( 1016 )   RICH HTML PDF (572KB) ( 771 )   Save The aim of this study is to introduce an impulsive SEIQRS epidemic model with time delays,  quarantine measure and nonlinear incidence rate. The total population size is varied. The global attractivity of an `infection-free' periodic solution, the existence, and the permanence of an endemic periodic solution are investigated. We obtain a sufficient condition for the permanence of the epidemic model with pulse vaccination. We show that time delay, pulse vaccination can bring different effects on the dynamic behavior of the model by numerical analysis. Our results also show a smaller pulse vaccination rate or a shorter latent period of the disease or a shorter immunity period of the recovered could cause global attractive `infection-free' periodic solution to lose and epidemic disease to be permanent. The main feature of this study is to introduce three time delays, nonlinear incidence rates and impulses into the SEIQRS epidemic model and give pulse vaccination strategies. References | Related Articles | Metrics

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Generalized Gradient of Set-valued Optimization Problems and Optimality Conditions of Strong-efficient Solutions YU Li, XU Xi-Hong Acta mathematica scientia,Series A. 2012, 32 (4):  685-690.  Abstract ( 814 )   RICH HTML PDF (298KB) ( 713 )   Save A kind of generalized gradient for set-valued map is introduced in ordered Banach spaces. Under the connected condition, its existence is proved by the separation theorem for convex sets. As an application, the optimality necessary and sufficient conditions of strong-efficient solution for set-valued optimization problem are established in terms of the generalized gradient. References | Related Articles | Metrics

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On Miranda's Normality Criterion ZENG Cui-Ping, LEI Chun-Lin, YANG De-Gui Acta mathematica scientia,Series A. 2012, 32 (4):  691-697.  Abstract ( 880 )   RICH HTML PDF (281KB) ( 680 )   Save Let F be a family of holomorphic functions in a domain D,  L(f)=akf (k)+ak-1f (k-1)+…+a1f'+a0f, where a0, a1, …, ak(≠0) are constants, and  a, b, c be complex numbers with c≠0, a0a≠b. If, for each f ∈F, f=a ↔L(f)=b, and f'=L'(f)=c whenever f =a, then F is normal in D. This improves Miranda's normality criterion. References | Related Articles | Metrics

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Gautschi-type Inequalities and Their Applications CHU Yu-Ming, ZHANG Xiao-Ming, SHI Huan-Nan Acta mathematica scientia,Series A. 2012, 32 (4):  698-708.  Abstract ( 1480 )   RICH HTML PDF (286KB) ( 782 )   Save We established two new Gautschi-type inequalities for the gamma function. As applications, we present the upper and lower bounds for Γ(x+1)/Γ(x+1/2) (x>0) and (2n-1)!!/(2n)!! . References | Related Articles | Metrics

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Wavelet Regularization Method for Determining Heat Flux of Non-standard Inverse Conduction Problem FENG Li-Xin, LI Yuan Acta mathematica scientia,Series A. 2012, 32 (4):  709-719.  Abstract ( 790 )   RICH HTML PDF (396KB) ( 757 )   Save We consider the non-standard inverse heat conduction problem of determiniting  the heat flux ux(x, t), 0<x<1 from a measured temperature at x=1 ut+ux=uxx,      x>0, t>0, u(1, t)=g(t), t ≥0, u(x, 0)=0, x≥0, u(x, t)|x→∞, bounded. This problem is severely ill-posed.  In this paper, we analyse the problem ill-posedness, give a wavelet regularization solution based on an application of Meyer wavelet.  And  error estimate with H\"{o}lder type between the exact solution and the regularized solution is given at (√2-√π/3)/√2<x<1.  The numerical experiment result shows that the regularization solution may converge to the exact solution for 0<x<1. References | Related Articles | Metrics

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Chinese Product of Cyclic Codes over Zk TANG Yong-Sheng, ZHU Shi-Xin, SHI Min-Jia Acta mathematica scientia,Series A. 2012, 32 (4):  720-728.  Abstract ( 1067 )   RICH HTML PDF (311KB) ( 836 )   Save In this paper, we describe the Chinese Remainder Theorem for studying cyclic and dual cyclic codes over the ring Zk, where k=(∏i=1spi)m,   the pi are distinct primes and m is a positive integer, also with the condition that the code length n cannot be divided by pi. A necessary and sufficient condition for the existence of nontrivial cyclic self-dual codes is given. The upper bound of minimum distance of such cyclic codes is also obtained. Furthermore, we determine the minimal generator set and the rank of such cyclic codes. References | Related Articles | Metrics

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Maximum Empirical Likelihood Estimators in Nonlinear Semiparametric EV Regression Models FENG San-Ying, XUE Liu-Gen Acta mathematica scientia,Series A. 2012, 32 (4):  729-743.  Abstract ( 859 )   RICH HTML PDF (424KB) ( 751 )   Save In this paper, we consider the nonlinear semiparametric models with measurement error in the nonparametric part. When the error is ordinarily smooth, we obtain the maximum empirical likelihood estimators of regression coefficient, smooth function and error variance by using the empirical likelihood method. The asymptotic normality and consistency of the proposed estimators are proved under some appropriate conditions. Finite sample performance of the proposed method is illustrated in a simulation study. References | Related Articles | Metrics

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Infinitely Many Solutions for the Resonant Quasi-linear Equation Without Landesman-Lazer Conditions RAO Ruo-Feng, WANG Xiong-Rui Acta mathematica scientia,Series A. 2012, 32 (4):  744-752.  Abstract ( 646 )   RICH HTML PDF (368KB) ( 662 )   Save The famous Landesman-Lazer conditions is used to be applied in solving the existent solution for elliptic resonant equations. In this paper, the author is by using the property of the space of the first eigenfunctions and the technique of genus to give an existence theorem for infinitely many solutions of the strong resonant equation -Δpu=λ1|u|p-2u+g(x, u) without any Landesman-Lazer conditions, which extends some recent results  from single or several solutions to infinitely many solutions. References | Related Articles | Metrics

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On Lp-Intersection Body and Lp-Mixed Intersection Body MA Tong-Yi Acta mathematica scientia,Series A. 2012, 32 (4):  753-767.  Abstract ( 685 )   RICH HTML PDF (371KB) ( 685 )   Save For p<1and p≠0, Haberl and Ludwig introduced an Lp-intersection body IpK of a star body K. In this paper we study extreme nature of the Lp-intersection body, and Lp-type Busemann-Petty intersection inequality is established. Meanwhile, we further expand the concept of  Lp-intersection body to Lp-mixed intersection body is put forward. As an application, we  establish Aleksandrov-Fenchel type inequalities for Lp-mixed intersection body and its polar body. These results are the dual form of some known results. References | Related Articles | Metrics

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A One-step Smoothing Newton Method for Second-order Cone Programming TANG Jing-Yong, HE Guo-Ping Acta mathematica scientia,Series A. 2012, 32 (4):  768-778.  Abstract ( 1243 )   RICH HTML PDF (409KB) ( 669 )   Save In this paper,  a new one-step smoothing Newton method is investigated for solving the second-order cone programming (SOCP). Based on a new smoothing function of the vector minimum function, the proposed algorithm reformulates the SOCP as a nonlinear system of equations and then applies Newton's method to the system. This algorithm does not require the initial point and iteration points to be in the sets of strictly feasible solutions, and solves only one linear system of equations and performs only one line search at each iteration. Without strict complementarity, it is proved that the proposed algorithm is globally and locally quadratically convergent. Numerical experiments demonstrate the feasibility and efficiency of our algorithm. References | Related Articles | Metrics

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The Fixed Points of Solutions of Some Second Order Differential Equation WU Zhao-Jun, CHEN Yu-Xian Acta mathematica scientia,Series A. 2012, 32 (4):  779-784.  Abstract ( 953 )   RICH HTML PDF (276KB) ( 751 )   Save In this paper, we investigate the problem on the fixed-points of solutions of some second order differential equation with transcendental entire function coefficients. References | Related Articles | Metrics

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Multiple Solutions for the Nonlinear Hénon Equation Under Perturbations ZHU Hong-Bo, WANG Zheng-Ping, GUO Yuan-Bin Acta mathematica scientia,Series A. 2012, 32 (4):  785-796.  Abstract ( 692 )   RICH HTML PDF (358KB) ( 621 )   Save In this paper,  we are concerned with the following nonlinear elliptic problem u(x)=|x|α|u|p-2u+h(x),    x∈B, u=0,                                 x∈∂B Here Ω( RN, N>4 is smooth and bounded. Applying the perturbation method introduced by Bahari-Berestycki[3], for any h(x)=h(y, z)=h(|y|, |z|)L2B, x=(y, z)∈ Rl×RN-l, when α> N+2, we show that there exists pN, l>2 such that for any p∈(2, pN, l), problem (P) has infinity many distinct solutions. References | Related Articles | Metrics

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A Semiparametric Smooth Transition Regression Model and Its Series Estimator WANG Cheng-Yong Acta mathematica scientia,Series A. 2012, 32 (4):  797-807.  Abstract ( 1141 )   RICH HTML PDF (462KB) ( 827 )   Save An unknown smooth function is substituted into the traditional smooth transition regression model and a semiparametric smooth transition regression model has been proposed in this paper. Based on the i.i.d. data assumption, we estimate the unknown smooth transition function by series estimator, the consistency and asymptotic normality properties of parameters are proved applying Nonlinear Least Square regression theory. The bootstrapping consistent confidence interval and hypothesis testing problem are also discussed briefly. The simulation results shows that, compared to traditional STR type model, our new model and estimating method are more flexible and have comprehensive applicability. References | Related Articles | Metrics

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Growth of Dirichlet Series of Infinite Order in the Plane LIU Wei-Qun, SUN Dao-Chun Acta mathematica scientia,Series A. 2012, 32 (4):  808-815.  Abstract ( 833 )   RICH HTML PDF (288KB) ( 638 )   Save In this article, we study the growth of Dirichlet series of infinte order in the plane. Its order and low order by the type-function of Xiong Kin-lai and the method of Knopp-Kojima are defined, The relation between the low order of Dirichlet series and its coefficients is obtained by using the Newton polygon. References | Related Articles | Metrics