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 Select Uniqueness Problem for Meromorphic Maps Sharing Hyperplanes with Low Truncated Multiplicities Kai Zhou,Lu Jin Acta mathematica scientia,Series A    2019, 39 (1): 1-14.   Abstract （74）   HTML （2）    PDF（pc） （356KB）（89）       Save In this paper, we prove first some uniqueness theorems for two meromorphic maps sharing 2n + 2 hyperplanes with low truncated multiplicities. And in the last section, we give a simple proof of a uniqueness theorem under the assumption that f-1(Hj)⊆ g-1(Hj) and q ≥ 2n+3.
 Select 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 （72）   HTML （11）    PDF（pc） （322KB）（152）       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.
 Select Stability of Some Fractional Systems and Laplace Transform Chun Wang Acta mathematica scientia,Series A    2019, 39 (1): 49-58.   Abstract （50）   HTML （2）    PDF（pc） （304KB）（83）       Save This paper investigates the Hyers-Ulam-Rassias stability of a kind of fractional differential systems, and proves that this kind of fractional differential systems are Hyers-UlamRassias stable by the Laplace transform method. Two examples are given to illustrate the theoretical results.
 Select 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 （49）   HTML （1）    PDF（pc） （315KB）（104）       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.
 Select Covering Surface Inequality on the Ring and Its Applications Xiaojing Guo,Daochun Sun Acta mathematica scientia,Series A    2018, 38 (5): 833-841.   Abstract （48）   HTML （5）    PDF（pc） （315KB）（129）       Save The main purpose of this paper is to give the covering surface inequality for the meromorphic function on the ring, which studies the problem on ring sequence and promotes the classic Picard theorem. Furtherly, we use Valiron type function to obtain the Borel theorem for the finite positive meromorphic function on the infinite ring sequence.
 Select Generalized Kato Decomposition and Weyl Type Theorems Lihong Chen,Weigang Su Acta mathematica scientia,Series A    2019, 39 (3): 417-422.   Abstract （43）   HTML （3）    PDF（pc） （252KB）（90）       Save Using the character of generalized Kato decomposition, this paper discusses the sufficient and necessary conditions for which Browder's theorem and Weyl's theorem hold from the angle of generalized Kato spectrum for a bounded linear operator.
 Select Existence of Nontrivial Solutions for a Class of Relativistic Nonlinear Schrödinger Equations Wen Qiu,Yimin Zhang,Ahmed Adam Abdelgadir Acta mathematica scientia,Series A    2019, 39 (1): 95-104.   Abstract （42）   HTML （2）    PDF（pc） （330KB）（63）       Save Using the critical point theory, we consider a class of relativistic nonlinear Schrödinger equations. By introducing a change, we transform the relativistic nonlinear Schrödinger equations into the semilinear elliptic equations. First, we extend results of the classical field equation to the relativistic nonlinear Schrödinger equation. Then, the variational methods was used to obtain the existence of nontrivial solutions of the relativistic nonlinear Schrödinger equations with bounded potential. Moreover, we improved the general superlinear conditions which was used in [12-13].
 Select 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 （40）   HTML （6）    PDF（pc） （408KB）（40）       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.
 Select The Invariance of Two Subclasses of Biholomorphic Mappings Under the Roper-Suffridge Extension Operators Chaojun Wang,Yanyan Cui,Hao Liu Acta mathematica scientia,Series A    2019, 39 (2): 209-219.   Abstract （38）   HTML （4）    PDF（pc） （360KB）（60）       Save In this paper, we generalize the Roper-Suffridge operator on Bergman-Hartogs domains. Applying the geometric properties and the growth theorems of spirallike mappings of type β and order α as well as almost starlike mappings of complex order λ, we obtain that the generalized Roper-Suffridge operators preserve spirallikeness of type β and order α as well as almost starlikeness of complex order λ on Bergman-Hartogs domains which lead to some special cases. The conclusions provide new approaches to construct spirallike mappings of type β and order α and almost starlike mappings of complex order λ in several complex variables.
 Select Almost Contact Lagrangian Submanifolds of Nearly Kaehler $\mathbb{S}$3×$\mathbb{S}$3 Biaogui Yang,Jing Chen Acta mathematica scientia,Series A    2019, 39 (1): 29-37.   Abstract （36）   HTML （0）    PDF（pc） （303KB）（38）       Save For a Lagrangian submanifold of the nearly Kaehler ${\Bbb S}^3\times {\Bbb S}^3$, we provide conditions for a canonically induced almost contact metric structure by a unit vector field, to be $\alpha$-Sasakian, $\beta$-Kenmotsu and cosymplectic. Furthermore, assuming the almost contact metric structure to be normal, we show the conditions when the contact metric structure is $\frac{\sqrt{3}}{3}$-Sasakian, $\frac{\sqrt{3}}{3}$-Kenmotsu or cosymplectic.
 Select On Some Product-Type Operators From Mixed Norm Space to Zygmund-Type Spaces Yongmin Liu,Yanyan Yu Acta mathematica scientia,Series A    2019, 39 (1): 15-28.   Abstract （34）   HTML （2）    PDF（pc） （345KB）（66）       Save Let $H({\Bbb D})$ denote the space of all analytic functions on the unit disk ${\Bbb D}$ in the complex plane ${\Bbb C}$, $\psi_1, \psi_2\in H({\Bbb D}),$ $n$ be a nonnegative integer, $\varphi$ an analytic self-map of ${\Bbb D}$ and $\mu$ a weight. We study the boundedness and compactness of a product-type operator which is defined by $T^n_{\psi_{1},\psi_{2},\varphi}f(z)=\psi_1(z)f^{(n)}(\varphi(z))+\psi_2(z)f^{(n+1)}(\varphi(z)), f\in H({\Bbb D}),$ from the mixed norm space to Zygmund-type spaces.
 Select Integrating Factors and Conserved Quantities for Constrained Hamilton Systems and Its Applications in Field Theory Jingrun Zhou,Jingli Fu Acta mathematica scientia,Series A    2019, 39 (1): 38-48.   Abstract （34）   HTML （2）    PDF（pc） （405KB）（48）       Save Field theory is the most important and difficult part in the study of constrained Hamiltonian systems. In recent years, it has became a hot research area. In this paper, a general method that to construct the conservation laws of field theory system based on the integral factor method is presented. Firstly, the general Hamilton canonical equation of constrained Hamiltonian system is structured. Secondly, the definition about integrating factors is given and the conservation theorem for constrained Hamiltonian systems is established. Thirdly, the general Killing equation of constrained Hamiltonian system is deduced, then the integrating factors of constrained Hamiltonian systems are obtained. Finally, two examples are used to demonstrate the effectiveness of this method. Obviously, compared with Noether symmetry method and Lie symmetry method, the integrating factor method of constrained Hamiltonian system has the advantages of clearing calculation step, lessening restrictive conditions and simplifying operation and so on.
 Select 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 （33）   HTML （4）    PDF（pc） （380KB）（56）       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.
 Select 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 （31）   HTML （0）    PDF（pc） （311KB）（80）       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..
 Select The Farkas Lemmas for Fractional Optimization Problem with Composite Functions Donghui Fang,Weilin Liu Acta mathematica scientia,Series A    2018, 38 (5): 842-854.   Abstract （30）   HTML （0）    PDF（pc） （332KB）（43）       Save In this paper, the fractional optimization problem with composite functions is turned into a constraint optimization problem by using the previous method. By introducing some news constraint qualifications, some duality results for the constraint optimization problem are established and some Farkas type lemmas for the fractional optimization problem with composite functions are then given.
 Select 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 （30）   HTML （0）    PDF（pc） （299KB）（40）       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.
 Select 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 （29）   HTML （0）    PDF（pc） （283KB）（42）       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.
 Select 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 （29）   HTML （0）    PDF（pc） （316KB）（43）       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.
 Select 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 （29）   HTML （0）    PDF（pc） （331KB）（41）       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).
 Select Bionomics Dynamic System for Epidemic Virus Transmission Xianglin Han,Weigang Wang,Jiaqi Mo Acta mathematica scientia,Series A    2019, 39 (1): 200-208.   Abstract （29）   HTML （1）    PDF（pc） （368KB）（85）       Save A nonlinear dynamic system of the epidemic contagion transmission is studied by using the asymptotic theory in modern mathematical physics. Firstly, a dynamic model of the epidemic contagion transmission is established, which is a system of differential equation. Next, a set of functional analytic homotopic mapping is led. Then the solution of dynamic system model for a power series with a artificial parameter is substituted. Their asymptotic solutions of the dynamic system are solved successively. Finely, the importance of solution for the original dynamic model is related.