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26 December 2018, Volume 38 Issue 6 Previous Issue    Next Issue

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The Pointwise Multiplier on the Normal Weight Zygmund Space in the Unit Ball Yuting Guo,Qingli Shang,Xuejun Zhang Acta mathematica scientia,Series A. 2018, 38 (6):  1041-1048.  Abstract ( 119 )   RICH HTML PDF (322KB) ( 240 )   Save Let μ be a normal function on[0, 1). In this paper, the authors character the pointwise multipliers on the normal weight Zygmund space Zμ(B) in the unit ball of Cn. The necessary and sufficient conditions for the multiplier operator is bounded or compact are given. References | Related Articles | Metrics

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Some Properties and Inequalities for Chord-Integrals of Star Bodies Chunna Zeng,Ran Li,Baocheng Zhu Acta mathematica scientia,Series A. 2018, 38 (6):  1049-1057.  Abstract ( 136 )   RICH HTML PDF (315KB) ( 218 )   Save In this paper, we obtain some limit properties of chord-integrals in $\mathbb{R}$n, and establish some inequalities for chord-integrals of star bodies, including the inequalities between chord-integrals and dual quermass-integrals, the dual Blaschke-Santaló inequality and so on. References | Related Articles | Metrics

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New Simpson Type Inequalities for Generalized Convex Functions on Fractal Space and Its Applications Wenbing Sun,Qiong Liu Acta mathematica scientia,Series A. 2018, 38 (6):  1058-1066.  Abstract ( 129 )   RICH HTML PDF (283KB) ( 259 )   Save In the paper, the authors use local fractional calculus theory and the definition of generalized convex function on the α type set of the real line numbers $$\begin{document}$\mathbb{R}$\end{document}$$ α, some new Simpson-type inequalities involving local fractional integrals are established. Finally, some applications of our obtained inequalities to special means and numerical integration are given. References | Related Articles | Metrics

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Boundedness of Marcinkiewicz Integrals and Commutators with Variable Kernel on Morrey Spaces with Variable Exponents Xukui Shao,Shuangping Tao Acta mathematica scientia,Series A. 2018, 38 (6):  1067-1075.  Abstract ( 100 )   RICH HTML PDF (311KB) ( 171 )   Save In this paper, we using the boundednes results of Marcinkiewicz integrals with variable kernels μΩ and their commutators μΩb which generated by μΩ and BMO function b on Lebesgue spaces with variable exponents, the boundednes results are established on Morrey spaces with variable exponents.. References | Related Articles | Metrics

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Lagrange-Like Multiplier Rules for Weak Approximate Pareto Solutions of Multiobjective Constrained Vector Optimization Problems Runxin Li,Hui Huang,Zhenhong Shang,Yu Cao,Hongbin Wang,Jing Zhang Acta mathematica scientia,Series A. 2018, 38 (6):  1076-1094.  Abstract ( 113 )   RICH HTML PDF (408KB) ( 129 )   Save In real Hilbert space case, Zheng and Li[21] established a Lagrange multiplier rule for weak approximate Pareto solutions of constrained vector optimization problems with only one constrained multifunction. In this paper, we improve and extend their main results to multiobjective constrained vector optimization problems' cases. References | Related Articles | Metrics

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Complete Convergence for Weighted Sums for $φ$-Mixing Random Variables Zhihua Zhang,Pingyan Chen Acta mathematica scientia,Series A. 2018, 38 (6):  1095-1102.  Abstract ( 72 )   RICH HTML PDF (316KB) ( 148 )   Save The paper obtains the complete convergence for the maximun weighted sums, which improved and extended the result of Chen and Sung[1] from NA sequence to $φ$-mixing random variables. The main tool in Chen and Sung[1] is the exponent inequality of NA sequence, but no one knows wether the coresponding exponent inequality holds or not for $φ$-mixing random variables, so a different method is needed. In fact, we use only the maximun moment inequality and a new truncated method to prove the main result. References | Related Articles | Metrics

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Complete Moment Convergence for Sung's Type Weighted Sums Under END Setup Dehua Qiu, Juan Xiao Acta mathematica scientia,Series A. 2018, 38 (6):  1103-1111.  Abstract ( 87 )   RICH HTML PDF (302KB) ( 133 )   Save In this paper, the authors study a complete moment convergence result for Sung's type weighted sums of identically distributed END random variables by utilizing the Menshov-Rademacher's inequality of the partial sums of END random variables. The result extends and improves the corresponding theorems in series of previous papers. References | Related Articles | Metrics

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Optimality Conditions for Composite Optimization Problems with Conical Constraints Lingli Hu, Donghui Fang Acta mathematica scientia,Series A. 2018, 38 (6):  1112-1121.  Abstract ( 81 )   RICH HTML PDF (303KB) ( 132 )   Save By using the properties of subdifferentials, some new constraint qualifications are obtained, which characterize completely some optimality conditions for composite optimization problem with conical constraints. Moreover, saddle point theorems for the Lagrange function of this optimization problem are also given. Our results extend the corresponding results in the previous papers. References | Related Articles | Metrics

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A Kind of Efficient Difference Method for the Time Fractional Sub-Diffusion Equation Yadi Zhao, Lifei Wu, Xiaozhong Yang, Shuzhen Sun Acta mathematica scientia,Series A. 2018, 38 (6):  1122-1134.  Abstract ( 92 )   RICH HTML PDF (706KB) ( 146 )   Save In this paper, a kind of numerical difference method of explicit-implicit(E-I) scheme and implicit-explicit(I-E) scheme was constructed for solving the time fractional sub-diffusion equation. It is based on the combination of the explicit scheme and implicit scheme. Theoretical analyses have shown that the solution of E-I(I-E) scheme is uniquely solvable. At the same time the stability and convergence of the scheme were proved by the Fourier method. Numerical experiments verified the theoretical analyses and showed the computational efficiency of E-I scheme is 75% higher than the implicit scheme under the premise of unconditional stability and having better accuracy. Therefore it is feasible to use the scheme for solving the time fractional diffusion equation. Figures and Tables | References | Related Articles | Metrics

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Attracting and Quasi-Invariant Sets of Second-Order Neutral Stochastic Partial Differential Equations Yingfei Fan, Guopeng Zhang, Xinguo Jiang, jian Ma Acta mathematica scientia,Series A. 2018, 38 (6):  1135-1143.  Abstract ( 79 )   RICH HTML PDF (329KB) ( 123 )   Save This paper is concerned with the second-order neutral stochastic partial differential equations. By using stochastic analysis and inequality techniques, sufficient conditions for the existence of attracting and quasi invariant sets are obtained. Some existing related results are generalized. References | Related Articles | Metrics

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Solvability of Directional Perturbed Generalized Mixed Variational Inequalities in Reflexive Banach Spaces Xueping Luo, Mengtian Cui Acta mathematica scientia,Series A. 2018, 38 (6):  1144-1152.  Abstract ( 94 )   RICH HTML PDF (331KB) ( 134 )   Save Solvability of directional perturbed generalized mixed variational inequalities is discussed in reflexive Banach spaces, under a coercivity condition. In particular, the result we present that the set is directional perturbed is new. Our results generalize and extend some known results in this area (Acta Math Sci, 2016, 36A(3):473-480). References | Related Articles | Metrics

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Two Solutions for Quasilinear Elliptic Equation with Hardy Potential on RN Wenjuan Tang, Zhengjie Zhang Acta mathematica scientia,Series A. 2018, 38 (6):  1153-1161.  Abstract ( 82 )   RICH HTML PDF (299KB) ( 127 )   Save In the paper, we used variational method to consider the following quasilinear elliptic equation $-\sum\limits_{i=1}^{N}\frac{\partial}{\partial x_i}\left(|\triangledown u|^{p-2}\frac{\partial u}{\partial x_i}\right)-\mu\frac{|u|^{p-2}u}{|x|^p}=|u|^{p^*-2}u+\lambda g(x)\quad u\in {\cal D}^{1, p}(\mathbb{R} ^N),$ we show that there exists two nontrivial solutions for our problem, one solution is a local minimum and the other is of mountain pass type. References | Related Articles | Metrics

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Existence and Uniqueness of Solutions to a Class of Anti-Periodic Boundary Value Problem of Fractional Differential Equations with p-Laplacian Operator Yongzhen Yun,Youhui Su,Weimin Hu Acta mathematica scientia,Series A. 2018, 38 (6):  1162-1172.  Abstract ( 109 )   RICH HTML PDF (380KB) ( 147 )   Save In this paper, we investigate the existence and uniqueness of solutions to a class of anti-periodic boundary value problem of nonlinear Caputo fractional differential equations with p-Laplacian operator. First, the Green function of the fractional boundary value problem is given. By using the properties of p-Laplacian operator and the Banach contraction mapping principle, some new results on the existence and uniqueness of solutions to the fractional boundary value problem are obtained. As an application, two examples are given to illustrate our main results. In particular, the boundary value conditions of fractional differential equation which is studied in this paper contains the Caputo fractional differentiation. References | Related Articles | Metrics

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Local Classical Solutions of 3D Fluid-Particle Interaction Model: The Flowing Regime Lin Zheng,Shu Wang,Linrui Li Acta mathematica scientia,Series A. 2018, 38 (6):  1173-1192.  Abstract ( 91 )   RICH HTML PDF (378KB) ( 143 )   Save In this paper, we concerned with the Cauchy problem for 3D fluid-particle interaction model in the so-called Flowing regime with vacuum in ${{\mathbb{R}}^{3}}$. We prove both existence and uniqueness of the local strong solution, and then obtain a local classical solution by deriving the smooth effect of the strong solution for t > 0. References | Related Articles | Metrics

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New Multiple Periodic-Soliton Solutions for the -Dimensional Potential-YTSF Equation Huan Wei,Lianwu Yang,Jianguo Liu Acta mathematica scientia,Series A. 2018, 38 (6):  1193-1204.  Abstract ( 115 )   RICH HTML PDF (2840KB) ( 130 )   Save By using the Hirota's bilinear form and generalized three-wave approach, we construct multiple periodic-soliton solutions of (3+1)-dimensional potential-YTSF equation. Some entirely new periodic-soliton solutions are presented including periodic cross-kink wave, periodic two-solitary wave and breather type of two-solitary wave solutions. With the aid of symbolic computation, propagation characteristics and interactions of breathers and solitons are shown with some figures. Figures and Tables | References | Related Articles | Metrics

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Global Attractor in H1（Rn) x Lu2(R+;H1(Rn)) for the Nonclassical Diffusion Equations with Fading Memory Xuan Wang, Ying Han, Chenghua Gao Acta mathematica scientia,Series A. 2018, 38 (6):  1205-1223.  Abstract ( 89 )   RICH HTML PDF (439KB) ( 145 )   Save In this paper, we are concerned with the dynamical behavior of the nonclassical diffusion equations with fading memory and supercritical nonlinearity on unbounded domain ${{\mathbb{R}}^{n}}$. By applying semigroup theory and method of contractive function, we obtain the existence of global attractors in ${{H}^{1}}\left( {{\mathbb{R}}^{n}} \right)\times L_{\mu }^{2}\left( {{\mathbb{R}}^{+}};{{H}^{1}}\left( {{\mathbb{R}}^{n}} \right) \right)$, when the external forcing term g merely belongs to H-1(${{\mathbb{R}}^{n}}$). References | Related Articles | Metrics

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Maximal Global Estimate for Solution to Generalized Dispersive Equation Yaoming Niu,Yong Ding Acta mathematica scientia,Series A. 2018, 38 (6):  1224-1238.  Abstract ( 96 )   RICH HTML PDF (363KB) ( 143 )   Save We consider maximal estimates for solution to the generalized dispersive equation $\left\{ \begin{align} & \text{i}{{\partial }_{t}}u+\phi (\sqrt{-\Delta })u=0,\ \ \ \ \ (x,t)\in {{\mathbb{R}}^{n}}\times \mathbb{R}, \\ & u(x,0)=f(x),\ \ \ \ \ \ \ \ \ \ \ \ \ f\in {\cal S}({{\mathbb{R}}^{n}}), \\ \end{align} \right.\ \ \ \ \ \ \ (*)$ where $\phi(\sqrt{-\Delta})$ is a pseudo-differential operator with symbol $\phi(|\xi|)$. When $\phi$ satisfies suitable growth conditions and the initial data $f$ belong to the Sobolev space $H^{s}({\Bbb R}^{n})$, we obtain the global estimate for the maximal operator $S_{\phi}^*$ generated by the operators family $\{S_{t, \phi}\}_{0 <t <1},$ where $S_{\phi}^*$ is defined by $S^{\ast}_{\phi}f(x)=\displaystyle\sup_{0 <t <1}|S_{t, \phi}f(x)|,$ and $S_{t, \phi}f$ is a formal solution of the equation $(\ast)$. These estimates are apparently good extensions to the current results for the fractional Schrödinger equation and these estimates were obtained in a general unified way. References | Related Articles | Metrics

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Finite Time Blow up of Solutions for Nonlinear Wave Equation with General Nonlinearity for Arbitrarily Positive Initial Energy Yanbing Yang,Wei Lian,Shaobin Huang,Runzhang Xu Acta mathematica scientia,Series A. 2018, 38 (6):  1239-1244.  Abstract ( 129 )   RICH HTML PDF (312KB) ( 159 )   Save This paper investigates the finite time blow up of solutions for the initial boundary value problem of a class of some nonlinear wave equations with general nonlinearity at high initial energy level. By employing the classical concavity method, we establish some new sufficient conditions on initial data such that the solution with arbitrarily positive initial energy blows up in finite time. References | Related Articles | Metrics