Table of Content

25 October 2014, Volume 34 Issue 5 Previous Issue    Next Issue

For Selected:

View Abstracts

Download Citations EndNote Reference Manager ProCite BibTeX RefWorks

Toggle Thumbnails

Articles

Select

Generalization Bounds of Compressed Regression Learning Algorithm ZHANG Yong-Quan, LI You-Mei, CAO Fei-Long, XU Zong-Ben Acta mathematica scientia,Series A. 2014, 34 (5):  1049-1060.  Abstract ( 293 )   RICH HTML PDF (374KB) ( 387 )   Save This article studies generalization performance of regularized learning algorithm with a general convex loss function and varying Gaussian kernels. Our goal is to give a satisfactory estimate of  generalization error for the learning algorithm. The generalization error is measured by regularization error and sample error. The regularization error is estimated by constructing a radial basis function (briefly denoted by RBF) neural network in view of the special structures of Gaussian kernels.  The sample error is obtained by using projection operator and covering number of reproducing kernel Hilbert spaces with Gaussian kernels. The obtained results demonstrate the  learning algorithm has good  generalization performance  with suitable choice of m and λ. References | Related Articles | Metrics

Select

Blow-up and Global Boundedness for a Degenerate Parabolic System with Positive Boundary Value Condition LING Zheng-Qiu, QIN Sai-Qan Acta mathematica scientia,Series A. 2014, 34 (5):  1061-1070.  Abstract ( 225 )   RICH HTML PDF (325KB) ( 343 )   Save This paper deals with a degenerate parabolic system coupled via nonlocal sources, subjecting to positive Dirichlet boundary value conditions. With the help of the super and sub-solution methods and the piecewise function, the blow-up criteria and global boundedness of nonnegative solutions are determined. The results show that the positive boundary value ε0 plays an important role in the case of blow-up. References | Related Articles | Metrics

Select

Resonance Theorems for Families of Pointwise Semi-bounded and Non-unbounded Linear Operators on F* Spaces SONG Ming-Liang Acta mathematica scientia,Series A. 2014, 34 (5):  1071-1082.  Abstract ( 232 )   RICH HTML PDF (367KB) ( 312 )   Save We prove that every F* space (i.e., Hausdorff topological vector space satisfying the first countable axiom) can be characterized by meams of its “standard generating family of pseudo-norms”. By using the standard generating family of pseudo-norms P, the concepts of P-bounded set, P-semi-bounded set and P-unbounded set in F* space are introduced. The resonance theorems for families of pointwise semi-bounded and pointwise non-unbounded linear operators on F* spaces are established. As their applications, the resonance theorems for families of pointwise probabilistically semi-bounded  and pointwise probabilistically non-unbounded linear operators in Menger probabilistic normed spaces are obtained. References | Related Articles | Metrics

Select

The Riemann Problem with Delta Initial Data for the Zero-Pressure Relativistic Euler Equations Hyperbolic Systems of Conservation Laws LI Jian-Ye, SHAO Zhi-Qiang Acta mathematica scientia,Series A. 2014, 34 (5):  1083-1092.  Abstract ( 273 )   RICH HTML PDF (328KB) ( 339 )   Save In this paper, we solve the Riemann problem with the initial data containing Dirac delta functions for the zero-pressure relativistic Euler hyperbolic systems of conservation laws. With characteristic analysis, under suitably generalized Rankine-Hugoniot relation and entropy condition, we constructively obtain the global generalized solutions that explicitly exhibit four kinds of different structure involving delta shock waves. References | Related Articles | Metrics

Select

λ-Center BMO Estimates for the Toeplitz Operator Related to Singular Integral Operator with Non-smooth Kernels CHEN Dong-Xiang, FANG Yu-Da Acta mathematica scientia,Series A. 2014, 34 (5):  1093-1103.  Abstract ( 291 )   RICH HTML PDF (317KB) ( 343 )   Save Let L be the infinitesimal generator of analytic semigroup on L2(Rn) with Gaussian kernel bounds, and L-α/2 be the general fractional integrals generated by L for 0<α<n. Let Tj,1 be the singular integral with non smooth kernel related to L, or Tj,1=I,Tj,2,Tj,4 be the linner operators, which are bounded on Lp(Rn) for 1<p<∞, and Tj,3=±I(j=1,2…, m), where I is the identity operator, Mb is a multiplication operator.  the authors prove that when  b∈CBMOp2,λ2, the Toeplitz-type operator  θbα is bounded from Bp1, λ1 to Bp1, λ1. As applications, the boundedness of the general fractional integral commutator [b , L-α/2] on center Morrey space and that of the commutator of singular integral operator with non-smooth kernel [b, T] on center Morrey space are established. References | Related Articles | Metrics

Select

Asymptotic Solution for Second-order Semilinear Singularly Perturbed Boundary Value Problems LIU Shuai, CHEN Jian-He, ZHOU Zhe-Yan Acta mathematica scientia,Series A. 2014, 34 (5):  1104-1110.  Abstract ( 270 )   RICH HTML PDF (340KB) ( 313 )   Save This paper considers second-order semi-linear non-autonomous singularly perturbed boundary value problem under the non-hyperbolic condition. Firstly, we construct the algebraic decay boundary layers by using the method of boundary layer functions. Hence, we obtain the uniformly valid asymptotic solution. Then, based on the obtained asymptotic solution, we define a couple of upper and lower solutions suitably, and prove the existence of solutions, the uniform validity of the asymptotic solution as well as the error estimate between the asymptotic and the exact solutions. Finally, a typical example is performed to verify the correctness of the theoretical result. References | Related Articles | Metrics

Select

The Global Solutions of the Compressible Euler Equations With Nonlinear Damping in 3-Dimensions ZHU Xu-Sheng, LI Fang-E Acta mathematica scientia,Series A. 2014, 34 (5):  1111-1122.  Abstract ( 284 )   RICH HTML PDF (360KB) ( 302 )   Save The Cauchy problem for the compressible isentropic Euler equations with nonlinear damping in three space dimensions is investigated in this paper. The global classic solution is obtained provided the initial data is a small perturbation in H3∩L1 of a constant state by utilizing energy estimates, the L2, L∞ decays rates of the global solution are also obtained by using Fourier transform method, they are t-3/4, t-3/2 respectively. Here we have generalized the linear damping case to nonlinear damping case. References | Related Articles | Metrics

Select

Strong Convergence of an General Iterative Method for a Finite Family of Pseudo-Contractive and Monotone Mappings WEN Dao-Jun Acta mathematica scientia,Series A. 2014, 34 (5):  1123-1132.  Abstract ( 246 )   RICH HTML PDF (307KB) ( 349 )   Save In Hilbert space, a general approximation method is proposed for finding a common element of the set of fixed points of a finite family of continuous pseudo-contractive mappings and solutions of variational inequalities for monotone mappings. Strong convergence of iterative sequences generated by the method are obtained under some more general conditions. References | Related Articles | Metrics

Select

Inequalities for Lower Order Eigenvalues of the Folland-Stein Operator and Quadratic Polynomial Operator of the Kohn Laplacian SUN He-Jun Acta mathematica scientia,Series A. 2014, 34 (5):  1133-1143.  Abstract ( 286 )   RICH HTML PDF (299KB) ( 290 )   Save In this paper, we investigate the Dirichlet eigenvalue problems of the Folland-Stein operator and quadratic polynomial operator of the Kohn Laplacian on the Heisenberg group. We establish some inequalities for their lower order eigenvalues. References | Related Articles | Metrics

Select

Existence of Positive Solutions to Semilinear Elliptic Equations with Bi-Parameter and a Threshold Result YAO Xian-Zhong, MU Chun-Lai, ZHANG Fu-Chen Acta mathematica scientia,Series A. 2014, 34 (5):  1144-1150.  Abstract ( 218 )   RICH HTML PDF (304KB) ( 452 )   Save We investigate the existence and nonexistence of the positive solution to a semilinear elliptic problem with bi-parameter under Robin condition. More precisely, we admit that there exists a λ*=λ*(c)<∞, for  any given boundary parameter 0<c<∞),  such that the problem has a minimum solutions for 0<λ≤λ*, whereas, any other solution is an initial datum threshold for the existence and nonexistence of global solution to the parabolic version. References | Related Articles | Metrics

Select

Strong Convergence Theorems of Modified Halpern-mann-type Iterations for Quasi-Φ-asymptotically Nonexpansive Mappings and Applications TANG Yong-Kun, ZHANG Shi-Sheng, WANG Lin, XU Yu-Guang, WANG Gang Acta mathematica scientia,Series A. 2014, 34 (5):  1151-1160.  Abstract ( 230 )   RICH HTML PDF (309KB) ( 307 )   Save The purpose of this article is to modify the Halpern-Mann-type iteration algorithm for quasi-Φ-asymptotically nonexpansive mapping to have the strong convergence under a limit condition only in the framework of Banach spaces. The results presented in the paper improve and extend the corresponding recent results of [4, 6--7, 11--13] and others. References | Related Articles | Metrics

Select

Optimal Investment and Proportional Reinsurance under Exponential Premium Calculation CHEN Mi, GUO Jun-Yi Acta mathematica scientia,Series A. 2014, 34 (5):  1161-1172.  Abstract ( 286 )   RICH HTML PDF (412KB) ( 568 )   Save This paper studies the optimal investment and proportional reinsurance policies of an insurer whose insurance business follows a diffusion perturbed classical risk process. It is assumed that the reinsurance premium is calculated according to the exponential premium principle which makes the stochastic control problems to be nonlinear. The problems of maximizing the adjustment coefficient and the expected exponential utility of terminal wealth are considered. In both of the problems, explicit expressions for their optimal value functions and the corresponding optimal strategies are obtained. Furthermore, the influences of the risk aversion of the reinsurance company and the uncertainty of the insurance company on the optimal strategies are analyzed. References | Related Articles | Metrics

Select

Global Well-posedness of Cauchy Problem for Damped Multidimensional Generalized Boussinesq Equations SHEN Ji-Hong, ZHANG Ming-You, YANG Yan-Bing, LIU Bo-Wei, XU Run-Zhang Acta mathematica scientia,Series A. 2014, 34 (5):  1173-1187.  Abstract ( 393 )   RICH HTML PDF (390KB) ( 448 )   Save We study the Cauchy problem for a class of  damped multidimensional generalized Boussinesq equations utt-Δu-Δutt+Δ2 u- kΔut=Δf(u), where k>0. By using potential well method, we analyze the relation between the coefficient k of damping term and the initial data as well as the depth of potential well and obtain the existence and nonexistence of global weak solution without establishing the local existence theory. References | Related Articles | Metrics

Select

Invertibility of Formal Hamiltonian Operators with Unbounded Entries Qi Ya-Ru, HUANG Jun-Jie, Alatancang Acta mathematica scientia,Series A. 2014, 34 (5):  1188-1195.  Abstract ( 333 )   RICH HTML PDF (317KB) ( 587 )   Save Using the operator block technique, we investigate the invertibility and the invertible completion of formal Hamiltonian operators (not necessarily bounded) with natural domain. Also, the analogous results for Hamiltonian operators are further presented. References | Related Articles | Metrics

Select

Coincident Point Theorem for Non-self Hybrid Mappings in Convex Metric Space MAN Zhi-Xin, SONG Mei-Mei Acta mathematica scientia,Series A. 2014, 34 (5):  1196-1202.  Abstract ( 239 )   RICH HTML PDF (230KB) ( 316 )   Save We establish some results on coincident points for hybrid maps in convex metric spaces. Our theorems generalize recent results of Ciric et al[3]. References | Related Articles | Metrics

Select

Compact Kernel Sections and Kolmogorov Entropy for the Lattice Zakharov Equations with a Quantum Correction LIANG Yun-Yun, LI Chu-Jin, HAO Cai-Di Acta mathematica scientia,Series A. 2014, 34 (5):  1203-1218.  Abstract ( 290 )   RICH HTML PDF (410KB) ( 322 )   Save This work discusses the asymptotic behavior of solutions of the modified Zakharov equations with a quantum correction on infinite lattices. The authors use the technique of truncation function to derive the existence of compact kernel sections and give an upper bound for the Kolmogorov ε-entropy of the obtained compact kernel sections. References | Related Articles | Metrics

Select

On the Fundamental Theorems for Reducible Algebroid Functions WANG Song-Min Acta mathematica scientia,Series A. 2014, 34 (5):  1219-1227.  Abstract ( 219 )   RICH HTML PDF (345KB) ( 343 )   Save Algebroid functions are generally determined by the irreducible equations. Recently, Sun and Gao[1-2] have removed the request when they investigated the arithmetic operations of algebroid functions. In this paper, we study the algeroid functions determined by the reducible euqations. First, we discuss its single-valued branches and branch points, then show that the logarithmic derivative lemma, the first and second fundamental theorems of algeboird functions also apply to the reducible algeboid functions. References | Related Articles | Metrics

Select

Existence of Solutions for Fractional Laplace Equation with Concave-Convex Term LI Ben-Niao, CHEN Xiao-Li Acta mathematica scientia,Series A. 2014, 34 (5):  1228-1235.  Abstract ( 266 )   RICH HTML PDF (319KB) ( 367 )   Save In this paper, we investigate the existence of solutions for  the following equation with the fractional Laplacian (-Δ)s and concave-convex nonlinearities, {(-Δ)s u=λa(x)|u|q-2u+b(x)|u|p-2u    inΩ, u=0                                                      inRn\Ω. where s∈ (0,1), q∈(1,2), p∈(2,2s*] and 2s*=2n/n-2s, n>2s, λ>0, Ω is a bounded domain of Rn, a(x) and b(x) are bounded continuous with b(x)≥0 and a(x) changes signs. We not only prove the existence of nontrivial nonnegative solutions by the Mountain Pass Lemma when p is subcritical and critical, but also, by using Fountain Theorem, we obtain infinitely many solutions for the subcritical case. References | Related Articles | Metrics

Select

On Logarithmic Order and Logarithmic Proximate Order of the Analytic Function |Defined by Laplace-Stieltjes Transformations LU Wan-Chun, YI Cai-Feng Acta mathematica scientia,Series A. 2014, 34 (5):  1236-1244.  Abstract ( 272 )   RICH HTML PDF (286KB) ( 280 )   Save In the present paper, we study the growth and regular growth of analytic functions defined by infinite order Laplace-Stieltjes transformation converging in right plane. The characterizations of the growth and regular growth of the analytic functions are obtained in terms of some new growth parameters. References | Related Articles | Metrics

Select

Approximation Formulas for the Landau Constants CHEN Chao-Ping, CHENG Jun-Xiang Acta mathematica scientia,Series A. 2014, 34 (5):  1245-1253.  Abstract ( 274 )   RICH HTML PDF (268KB) ( 293 )   Save The Landau constants  are defined for all integers n ≥0 by Gn=∑k=0n 1/16k(2k k)2. We establish new approximation formulas for the Landau constants. Relevant connections of the results presented here with those derived in earlier work are also pointed out. References | Related Articles | Metrics

Select

Viscosity Method for Hierarchical Fixed Point Approach to Hierarchical Variational Inclusion Problems DENG Wei-Qi Acta mathematica scientia,Series A. 2014, 34 (5):  1254-1263.  Abstract ( 260 )   RICH HTML PDF (297KB) ( 297 )   Save Based on an original technique, i.e., a special way of choosing the indexes of involved mappings, we utilize a viscosity method for hierarchically approximating common fixed points of a kind of countable families of nonlinear mappings; under suitable conditions, a strong convergence theorem is obtained for solving the hierarchical variational inclusion problems in the setting of Hilbert spaces. References | Related Articles | Metrics

Select

Multiplicity of Positive Solutions for a (p, q-Laplacian Elliptic Systems in RN ZHANG Wen-Li, ZHONG Li-Nan Acta mathematica scientia,Series A. 2014, 34 (5):  1264-1274.  Abstract ( 216 )   RICH HTML PDF (340KB) ( 355 )   Save In the paper, by using Nehari manifold and Ljusternik-Schnirelmann theory, we investigate how the shape of the graph of f(x) affects the number of positive solutions of a class of (p, q)-Laplacian systems. References | Related Articles | Metrics

Select

Quadratic Perturbations of a Quadratic Reversible Lotka-Volterra System of Genus One with Two Centers WU Kui-Lin, SHAO Yi Acta mathematica scientia,Series A. 2014, 34 (5):  1275-1286.  Abstract ( 305 )   RICH HTML PDF (342KB) ( 289 )   Save This paper is concerned with limit cycles which bifurcate from period annulus of a quadratic reversible Lotka-Volterra system of genus one with two centers. We prove that the number of limit cycles of two period annulus of the quadratic reversible Lotka-Volterra system(rlv5) under quadratic perturbations is less or equal to three. References | Related Articles | Metrics

Select

The Bargmann Symmetry Constraint and Binary Nonlinearization of the Super Li System ZHANG Ling, ZHU Hong-Ling Acta mathematica scientia,Series A. 2014, 34 (5):  1287-1295.  Abstract ( 234 )   RICH HTML PDF (301KB) ( 286 )   Save An explicit Bargmann symmetry constraint and the binary nonlinearization of Lax pairs for the super Li hierarchy are established. Under the symmetry constraint, the n-th  flow of  the super Li hierarchy is decomposed into two super finite-dimensional integrable Hamilton systems over the supersymmetric manifold. References | Related Articles | Metrics

Select

On the Uniqueness of Algebroid Functions and Their Derivatives LIU Hui-Fang Acta mathematica scientia,Series A. 2014, 34 (5):  1296-1303.  Abstract ( 249 )   RICH HTML PDF (279KB) ( 318 )   Save In this paper, from considering the relationship between the shared values and the branch points of algebroid functions, we obtain some uniqueness theorem of algebroid functions sharing values with their derivatives, which extend some shared value theorem of meromorphic functions and their derivatives obtained by Gundersen and Mues-Steinmetz. References | Related Articles | Metrics

Select

Two Integrable Systems and Reductions GUO Xiu-Rong, HU Mei-Yan Acta mathematica scientia,Series A. 2014, 34 (5):  1304-1312.  Abstract ( 245 )   RICH HTML PDF (285KB) ( 363 )   Save A Lie algebra is presented whose two corresponding loop algebras are followed to obtained, which are used to introduce two kinds of isospectral problems whose compatibility leads to two integrable dynamics. Some interesting nonlinear evolution equations are produced by reduction of the two dynamics, including the well-known Burgers equation, a generalized combined KdV-MKdV equation and the Kuramoto-Sivashinsky equation and a generalized form of the KdV equation. Then with the help of Bell polynomials we investigate some integrable properties of the generalized form of the KdV equation, such as bilinear representation, Lax pair, B"{a}cklund transformation, infinite conservation laws, and so on. References | Related Articles | Metrics

Select

Existence of |Solutions for Two-point Boundary Value Problem of a Coupled Fractional Differential Equations at Resonance HU Lei, ZHANG Shu-Qin, SHI Ai-Ling Acta mathematica scientia,Series A. 2014, 34 (5):  1313-1326.  Abstract ( 287 )   RICH HTML PDF (338KB) ( 331 )   Save In this article, we establish the existence results for two-point boundary value problem of a coupled fractional differential equations at resonance by means of the coincidence degree theory. Furthermore, a result on the uniqueness of solution is obtained. We give an example to demonstrate our results. References | Related Articles | Metrics

Select

An Improved Regularity Criterion for the 3D Navier-Stokes Equations in Terms of Two Entries of the Velocity Gradient ZHANG Zu-Jin Acta mathematica scientia,Series A. 2014, 34 (5):  1327-1335.  Abstract ( 296 )   RICH HTML PDF (282KB) ( 300 )   Save We consider the Cauchy problem for the three-dimensional Navier-Stokes equations. An improved anisotropic regularity  criterion via any two entries of the velocity gradient is given. This improves the result of [24]. References | Related Articles | Metrics