Acta Mathematica Scientia

The Large Time Behavior of Inhomogeneous Burgers Equation with Periodic Initial Data

Kuang Jie,Wang Zejun

Acta mathematica scientia,Series A. 2015, 35 (1): 1-14.

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In this paper, we study the large time behavior of the Cauchy problem for inhomogeneous Burgers equation. The initial data is assumed to be periodic and the source term has several zero points. We show that under some assumptions on the initial data, the solution approaches to a traveling wave. The main method we used is the theory of generalized characteristics generated by Dafermos C M.

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Analysis of A Diffusive Predator-prey Model with Disease and Holling II Functional Response

WANG Fei, WANG Jing

Acta mathematica scientia,Series A. 2015, 35 (1): 15-28.

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This paper is concerned with the dynamical behaviors of a diffusive predator-prey system with disease and Holling II functional response. We discuss the stability of the nonnegative constant steady states by using the characteristic equation technique and Laypunov functional method. Priori estimates for the system is given by inequality technique and Maximum Principle. Furthermore, we derive some results for the non-existence and existence of non-constant positive solution.

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The Complexity of Entropy-Minimal Dynamical Systems

YIN Jian-Dong, ZHOU Zuo-Ling

Acta mathematica scientia,Series A. 2015, 35 (1): 29-35.

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Let X be a compact metric space and f: X $\100dpi \inline \rightarrow$ X be a continuous map. In this paper, we prove that f is strongly ergodic if f is entropy-minimal.In addition, we show that f has positive topological entropy and fⁿ is ergodically sensitive for any n $\100dpi \inline \geq$ 1 if there exists a proper (quasi) weakly almost periodic point of f , hence f is chaotic in the sense of Li-Yorke and Takens-Ruelle.The presented results improve and generalize some recent results.

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Bounds for Toader Mean by Quadratic and Harmonic Means

SUN Hui, CHU Yu-Meng

Acta mathematica scientia,Series A. 2015, 35 (1): 36-42.

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We prove that the double inequalities $\100dpi \inline $\alphaQ(a,b)+(1-\alpha)H(a,b)<T(a,b)<\beta Q(a,b)+(1-\beta)H(a,b)$$ and
$\100dpi \inline $\lambda/H(a,b)+(1-\lambda)/Q(a,b)<1/T(a,b)<\mu/H(a,b)+(1-\mu)/Q(a,b)$$ hold for all a,b>0 with $\100dpi \inline $a\neq b$$ if and only if $\100dpi \inline $\alpha\leq5/6$, $\beta\geq 2\sqrt{2}/\pi$, $\lambda\leq 0$$ and $\100dpi \inline $\mu\geq 1/6$$ .Here, $\100dpi \inline $Q(a,b)=\sqrt{(a^{2}+b^{2})/2}$, $H(a,b)=2ab/(a+b)$$ and
$\100dpi \inline $T(a,b)=\frac{2}{\pi}\int_{0}^{{\pi}/{2}}\sqrt{a^2{\cos^2{\theta}}+b^2{\sin^2{\theta}}}{\rm d}\theta$$ denote the quadratic, harmonic and Toader means of two positive
numbers $\100dpi \inline $a$$ and $\100dpi \inline $b$$ , respectively.

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Elliptic Boundary Value Problems on Compact Manifolds

HUANG Qin, RUAN Qi-Hua

Acta mathematica scientia,Series A. 2015, 35 (1): 43-49.

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A class of inhomogeneous nonlinear elliptic boundary value problem is discussed on compact manifolds with a smooth boundary.
The maximum principles are used to obtain the gradient estimates for the solution of the problem. As its application, we obtain the efficiency ratio estimate of the solution.

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Multiplicity Results for A Boundary Value Problem with Double Parameter

GAO Li-Meng

Acta mathematica scientia,Series A. 2015, 35 (1): 50-55.

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The aim of this note is to establish the existence of multiple solutions for Sturm-Liouville boundary value problems.Proofs are based on variational methods as developed in the important works of Bonanno. In particular, the existence of three solutions for a Sturm-Liouville problem, even under a perturbation of the nonlinearity, is established.

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Boundedness of Generalized Higher Order Commutators of Marcinkiewicz |Integrals with Variable Kernels on Herz-type Hardy Spaces

MO Hui-Xia, LU Shan-Zhen

Acta mathematica scientia,Series A. 2015, 35 (1): 56-67.

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Let $\100dpi \inline $A$$ be a function with derivatives of order $\100dpi \inline $m$$ and $\100dpi \inline $D^{\gamma}A\in\dot{\Lambda}_{\beta}(0<\beta<1, |\gamma|=m).$$ The authors in the
paper prove that if $\100dpi \inline $\Omega(x,z)\in L^{\infty}({\Bbb R}^{n})\timesL^{s}(S^{n-1})(s\geq n/(n-\beta))$$ is homogenous of degree zero and satisfies the mean value zero condition about the variable $\100dpi \inline $z$$ , then both the generalized higher order Marcinkiewicz integral $\100dpi \inline $\mu_{\Omega}^{A}$$ and itsvariation $\100dpi \inline $\tilde{\mu}_{\Omega}^{A}$$ are bounded on Herz-type Hardy spaces.

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Global Existence of Solution of Cauchy Problem for A Generalized IMBq Equation with Weak Damping

CHEN Xiang-Ying

Acta mathematica scientia,Series A. 2015, 35 (1): 68-82.

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In this paper, we prove that the Cauchy problem for the generalized IMBq equations with weak damping, $\100dpi \inline $u_{tt}-u_{xx}-u_{xxtt}+\nu_0u_t=f(u)_{xx}$$ , $\100dpi \inline $x\in {\Bbb R}$,$t>0$$ , admits a unique global generalized solution in $\100dpi \inline $C^2([0,\infty);H^s({{\Bbb R}}))(s\geq 2$$ ~is~real~number) and a unique global classical solution in $\100dpi \inline $C^2([0,\infty);$$H^s({{\Bbb R}}))(s>\frac{7}{2})$$ . We give the sufficient conditionsof the blow up of the solution for the above mentioned Cauchy problem.

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Global Bifurcation of A Symmetric Cubic System

SHANG De-Sheng, ZHANG Yao-Ming

Acta mathematica scientia,Series A. 2015, 35 (1): 83-96.

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The number of limit cycles of a class of symmetric cubic near-Hamiltonian system under symmetric non-smooth perturbations are investigated in this paper. At least 19 limit cycles are found in this class of perturbed non-smooth cubic system by using the method of multi-parameter perturbation theory and qualitative analysis.

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Existence Results of Damped Second Order Impulsive Functional Differential Equations with Infinite Delay

XIE Sheng-Li

Acta mathematica scientia,Series A. 2015, 35 (1): 97-109.

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Using the Kuratowski measure of noncompactness and progressive estimation method, we study the existence and regularity of mild solutions for damped second order impulsive functional differential equations with infinite delay in Banach spaces. The compactness
condition on the impulsive term,some restrictive conditions on a priori estimation and noncompactness measure estimation have not been used, our results are different from the known results.As applications, some examples are provided to illustrate the obtained results.

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Some Series-Product Identities and Expansions on Dedekind's Eta Function

ZHU Jun-Ming, ZHANG Zhi-Zheng

Acta mathematica scientia,Series A. 2015, 35 (1): 110-117.

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We establish three series-product identities. Our tools are the Jacobi triple product identity and the method of series rearrangement. Several identities on Dedekind's eta function $\100dpi \inline $\eta(\tau)$$ are obtained.

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Fuzzy Pricing Formula for European Options with Jumps and Transaction Costs

XIAO Shuang, JIAN Ming, CHEN Ai-Xiang, JIAN Bei

Acta mathematica scientia,Series A. 2015, 35 (1): 118-130.

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In this paper, we consider the fuzzy pricing problems for European options with jumps and transaction costs, based on the Merton's jump diffusion model. First, we deduce the pricing formula for European call options with jumps and transactions,and then the fuzzy counterpart of it is given by applying the fuzzy mathematical theory. Also, we provid the disfuzzification method for the obtained European call option pricing formula with the help of fuzzy integration. In the end, some illustrative numerical analysis examples are executed with Sage codes.

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The Bisymmetric Least Squares Solutions of the General Coupled |Matrix Equations with A Submatrix Constraint

PENG Zhuo-Hua

Acta mathematica scientia,Series A. 2015, 35 (1): 131-150.

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The general coupled matrix equations $\100dpi \inline $\sum\limits_{j=1}^lA_{ij}X_jB_{ij}=C_i,\;\;i=1,2,\cdots,t$$ ,   have numerous applications in control and system theory.    In this paper, an algorithm is constructed   to solve the   general coupled matrix equations where   $\100dpi \inline $X_j\in R^{n_j\times n_j}\;(j=1,2,\cdots,l)$$ is a bisymmetric  matrix with a specified central  principal submatrix. The algorithm produces suitable
   $\100dpi \inline $[X_1,X_2,\cdots,X_l]$$ such that    $\100dpi \inline $\sum\limits_{i=1}^t\|\sum\limits_{j=1}^lA_{ij}X_jB_{ij}-C_i\|$$    is minimized within a finite iteration steps in the absence of roundoff errors.
The algorithm requires little storage capacity.    Numerical examples are given to show that the algorithm is efficient.

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Existence and Multiplicity of Nontrivial Solutions for Kirchhoff-Type Problem in R^N

WEI Mei-Chun, TANG Chun-Lei

Acta mathematica scientia,Series A. 2015, 35 (1): 151-162.

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The existence and multiplicity of nontrivial solutions are
obtained for the Kirchhoff-type problem
$$
\left\{
   \begin{array}{ll}
\disp -\left(a+b\int_{{\Bbb R}^N}|\nabla u|^2 {\rm d}x\right)
\Delta {u}+{V(x)u}={f(x,u)}\qq \mbox{in}\q {\Bbb R}^N,\\
u\in H^1({\Bbb R}^N)
   \end{array}
   \right.
$$
by using the Mountain Pass Lemma, the Fountain Theorem and the
Symmetric Mountain Pass Lemma.

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The Limit Theorems for Function of Markov Chains in Random Environments

WAN Cheng-Gao

Acta mathematica scientia,Series A. 2015, 35 (1): 163-171.

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In this paper, the limit theorems for function of Markov Chains in random environments are investigated. Moreover, some sufficient conditions for the strong convergence of the weighted sums to hold for function of Markov Chains in random environments are obtained, which extend and improve the related known works for weighted sums of random variables in the literature.

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Unique Common Fixed Points for Four Mappings on |TVS-Valued Cone Metric Spaces

PIAO Yong-Jie, JIN Hai-Lan, JIN Yuan-Feng

Acta mathematica scientia,Series A. 2015, 35 (1): 172-181.

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New unique common fixed point results for four mappings satisfying certain Lipschitz type conditions on a non-complete topological vector space-valued cone metric space are obtained, and their corollaries are given. Our main results generalize and improve some well-known recent results in the literatures.

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Generalized Cesaro Operator Between Different Dirichlet-type Spaces in the Unit Ball of |Cⁿ

LIU Jing-Cheng, LI Jun-Feng, ZHANG Xua-Jun

Acta mathematica scientia,Series A. 2015, 35 (1): 182-193.

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In this paper, we study the generalized $\100dpi \inline Ces\`{a}ro$ operator $\100dpi \inline $T_{\psi}:D_\alpha^p\rightarrow D_\beta^q$$ between different Dirichlet type spaces. For $\100dpi \inline $0<p\leq 1$$ 、 $\100dpi \inline $1<p<\alpha+1$$ or $\100dpi \inline $p>n+1+\alpha$$ , we provide sufficient and necessary conditons for $\100dpi \inline $T_{\psi}$$ to be bounded or compact. Moreover, for other $p$, we also discuss the sufficient conditions or the necessary conditons for $\100dpi \inline $T_{\psi}$$ to be bounded or compact.

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Energy Decay Estimates for the Weakly Coupled Systems with Local Memory Damping

ZHANG Chun-Guo, ZHANG Hai-Yan, GU Shang-Wu

Acta mathematica scientia,Series A. 2015, 35 (1): 194-209.

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This paper studies the weakly coupled beam-string systems with local memory damping. First, under the appropriate hypothesis, we proved that the well-posedness of the system by using the theory of linear operator semigroup. And then, we show that the energy of the weakly coupled beam-string system with local memory damping is uniform exponential decay by applying the frequence domain
result on Hilbert space.

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On Volterra-type Composition Operators from Mixed Norm Spaces |to Little Zygmund Spaces

LIU Yong-Min, YU Yan-Yan

Acta mathematica scientia,Series A. 2015, 35 (1): 210-217.

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In this paper, using the estimate of the higher order derivative of the function in mixed norm spaces, the properties of the analytic function andoperator theory, the authorscharacterize the boundedness and compactness of the Volterra-type composition operator from mixed norm spaces $\100dpi \inline $H(p,\, q,\, \phi)$$ to little Zygmund spaces. Some necessary and sufficient conditions of the Volterra-type composition operatorsto be bounded and compact are obtained.

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Complex Oscillation of Meromorphic Solutions of Some Difference Equations

ZHANG Ke, WANG Jun

Acta mathematica scientia,Series A. 2015, 35 (1): 218-224.

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In this paper, the authors study the properties of some complex difference equations, such as the growth, the distribution of zeros and poles of the soultions, and the possible reduced form of the equations. The authors generalize the previous result of Zheng X M and Chen Z X.

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