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 Select On Isoperimetric Inequality for Mixture of Convex and Star Bodies Changjian Zhao Acta mathematica scientia,Series A    2019, 39 (5): 993-1000.   Abstract （63）   HTML （5）    PDF（pc） （292KB）（89）       Save In this paper, we establish a new isoperimetric inequality for the mixture of convex and star bodies. Our result in special case yields the classical isoperimetric inequality, and which is an improvement and modification of a previous result.
 Select Reverse Order Law of the Drazin Inverse for Bounded Linear Operators Hua Wang,Jinfeng Li,Junjie Huang Acta mathematica scientia,Series A    2020, 40 (1): 1-9.   Abstract （60）   HTML （4）    PDF（pc） （268KB）（69）       Save In this paper, we discuss the Drazin invertibility and reverse order law of the Drazin inverse for the product of two bounded linear operators. Under the assumptions that P commutes with PQP and Q commutes with QPQ, respectively, we derive the Drazin invertibility of PQ and some equivalent conditions for the reverse order law (PQ)D=QDPD to hold by using space decomposition technique.
 Select Quasimöbius Maps and the Connectedness Properties of Quasi-Metric Spaces Hongjun Liu,Xiaojun Huang Acta mathematica scientia,Series A    2019, 39 (5): 1001-1010.   Abstract （59）   HTML （1）    PDF（pc） （263KB）（73）       Save This paper is to investigate the connectedness properties of quasi-metric space, and show that connectedness properties of quasi-metric space are preserved under quasimöbius maps.
 Select kUKK Property in Banach Spaces Liying Fan,Jingjing Song,Jianing Zhang Acta mathematica scientia,Series A    2019, 39 (4): 705-712.   Abstract （58）   HTML （17）    PDF（pc） （324KB）（212）       Save A new geometric property of Banach space kUKK is given, It is proved that Banach space with this property has weak Banach-saks property, Banach space X is kNUC if and only if it is reflexive and has kUKK property. considering the important role of geometric constants in Banach space geometric properties, The definition of the new constant R2(X) < k is given by the definition of kUKK and proved that when R2(X)< k, the Banach space X has a weak fixed point property. Finally, the specific values are calculated in the Cesaro sequence space.
 Select Equivalent Characterization of Several Quantities on Holomorphic Function Spaces Pengcheng Tang,Xuejun Zhang,Ruixin Lv Acta mathematica scientia,Series A    2019, 39 (6): 1291-1299.   Abstract （52）   HTML （2）    PDF（pc） （335KB）（59）       Save In this paper, the expression under the action of fractional derivative and fractional integral for a common function on the unit ball of several complex variables is improved. At the same time, the equivalent norms of the fractional differential on two holomorphic function spaces are improved, and the constraint conditions β=s+N for the fractional differential Rs, t and Rβ, t in the equivalent norms are removed, where N is a positive integer.
 Select An Estimate of Spectral Gap for Schrödinger Operators on Compact Manifolds Yue He,Hailong Her Acta mathematica scientia,Series A    2020, 40 (2): 257-270.   Abstract （52）   HTML （5）    PDF（pc） （433KB）（50）       Save Let $M$ be an $n$-dimensional compact Riemannian manifold with strictly convex boundary. Suppose that the Ricci curvature of $M$ is bounded below by $(n-1)K$ for some constant $K\geq0$ and the first eigenfunction $f_1$ of Dirichlet (or Robin) eigenvalue problem of a Schrödinger operator on $M$ is log-concave. Then we obtain a lower bound estimate of the gap between the first two Dirichlet (or Robin) eigenvalues of such Schrödinger operator. This generalizes a recent result by Andrews et al. ([4]) for Laplace operator on a bounded convex domain in $\mathbb{R} ^n$.
 Select System Capacity Optimization Design and Optimal Control Policy (N*, D*) for M/G/1 Queue with p-Entering Discipline and Min(N, D, V)-Policy Le Luo,Yinghui Tang Acta mathematica scientia,Series A    2019, 39 (5): 1228-1246.   Abstract （45）   HTML （0）    PDF（pc） （550KB）（29）       Save This paper considers a M/G/1 queueing system with p-entering discipline and Min(N, D, V)-policy, in which the customers who arrive during multiple vacations enter the system with probability p(0 < p ≤ 1). By using the total probability decomposition technique and the Laplace transform, we discuss the transient distribution of queue length at any time t which started from an arbitrary initial state, and obtain the expressions of the Laplace transform of transient queue-length distribution. Moreover, we obtain the recursion expressions of the steady-state queue length distribution. Meanwhile, we discuss the optimal capacity design by combining the steady-state queue length distribution and numerical example. Finally, the explicit expression of the long-run expected cost rate is derived under a given cost structure. And by through numerical calculation, we determine the optimal control policy (N*, D*) for minimizing the long-run expected cost per unit time.
 Select SDE Driven by Fractional Brown Motion and Their Coefficients are Locally Linear Growth Qikang Ran Acta mathematica scientia,Series A    2020, 40 (1): 200-211.   Abstract （41）   HTML （1）    PDF（pc） （390KB）（25）       Save In this paper, we discuss the existence and uniqueness of a class of stochastic differential equations driven by fractional Brown motion with Hurst parameter H ∈ ($\frac{1}{2}$, 1) and their coefficients are local linear growth. So far, there are several ways to define stochastic integrals with respect to FBM. In this paper, we define stochastic integrals with respect to FBM as a generalized Stieltjes integral. We give the existence and uniqueness theorems respectively for SDEs driven by fractional Brown motion and their coefficients are local linear growth.
 Select COVID-19 Transmission Model in an Enclosed Space: A Case Study of Japan Diamond Princess Cruises Xinxin Cheng,Yaqing Rao,Gang Huang Acta mathematica scientia,Series A    2020, 40 (2): 540-544.   Abstract （41）   HTML （2）    PDF（pc） （491KB）（51）       Save In this paper, we study the transmission of a novel coronavirus pneumonia (COVID-19) on Japan Diamond Princess Cruises as an example. By establishing a simple susceptible-infected epidemic model, the transmission mechanism of NCP in an enclosed space is established. Dynamic analysis and numerical fitting predict the disease transmission process and the final results, we estimate the infection rate and evaluate the effect of quarantine, and some suggestions for prevention and control strategies are given.
 Select Pricing European Lookback Option in a Special Kind of Mixed Jump-Diffusion Black-Scholes Model Zhaoqiang Yang Acta mathematica scientia,Series A    2019, 39 (6): 1514-1531.   Abstract （35）   HTML （0）    PDF（pc） （504KB）（53）       Save This article considers the pricing problem of European fixed strike lookback options under the environment of mixed jump-diffusion fractional Brownian motion. Under the conditions of Merton assumptions, we analyze the Cauchy initial problem of stochastic parabolic partial differential equations which the risky asset satisfied, by using the perturbation method of multiscale-parameter, the approximate pricing formulae of European lookback options are given by solving stochastic parabolic partial differential equations. Then the error estimates of the approximate solutions are given by using Feynman-Kac formula. Numerical simulation illustrate that the European lookback options have exact solutions when the volatilities are constant, and as the order of simulation increases, the approximate solutions are gradually approximates the exact solutions.
 Select The Generalized Riemann Problem for Chromatography Equations with Delta Shock Wave Lijun Pan,Xinli Han,Tong Li Acta mathematica scientia,Series A    2019, 39 (6): 1300-1313.   Abstract （34）   HTML （1）    PDF（pc） （643KB）（52）       Save This paper is concerned with the generalized Riemann problem for the nonlinear chromatography equations, where the delta shock wave occurs in the corresponding Riemann solution. It is quite different from the previous generalized Riemann problems which focus on classical elementary waves. We constructively solve the generalized Riemann problem in a neighborhood of the origin on the x-t plane. In solutions, we find that the generalized Riemann solutions have a structure similar to the solution of the corresponding Riemann problem for most of cases. However, a delta shock wave in the corresponding Riemann solution may turn into a shock wave followed by a contact discontinuity, which provides us with a detailed method for analyzing the internal mechanism of a delta shock wave.
 Select The Dynamics of an SEIR Epidemic Model with Time-Periodic Latent Period Shuangming Wang,Xingman Fan,Mingjun Zhang,Junrong Liang Acta mathematica scientia,Series A    2020, 40 (2): 527-539.   Abstract （34）   HTML （0）    PDF（pc） （608KB）（35）       Save A SEIR ordinary differential epidemic model with time-periodic latent period is studied. Firstly, the model is derived by means of the distribution function of infected ages. Next, the basic reproduction ratio $\mathcal R_0$ is introduced, and it is shown that $\mathcal R_0$ is a threshold index for determining whether the epidemic will go extinction or become endemic using the theory of dissipative dynamic systems. Finally, numerical methods are carried out to validate the analytical results and further to invetigate the effects on evaluating the propagation of disease owning to the neglect of the periodicity of the incubation period.
 Select Three Types of Solutions for a Class of Nonlinear Schrödinger Equations Yanfang Mei,Youjun Wang Acta mathematica scientia,Series A    2019, 39 (5): 1087-1093.   Abstract （33）   HTML （0）    PDF（pc） （296KB）（39）       Save In this paper, the existence of ground state, oscillation solution and soliton solution of a class of nonlinear Schrödinger equations in plasma are considered.
 Select Property (H) and Perturbations Lihong Chen,Weigang Su Acta mathematica scientia,Series A    2019, 39 (6): 1281-1290.   Abstract （32）   HTML （4）    PDF（pc） （300KB）（104）       Save This paper introduces two new spectral properties (H) and (gH), and investigates the two properties in connection with Weyl type theorems. Also the preservation of the two properties are studied under commuting nilpotent, quasi-nilpotent, finite rank or Riesz perturbation.
 Select The Squared Eigenfunction Symmetries and Miura Transformations for the KP and mKP Hierarchies Lumin Geng,Huizhan Chen,Na Li,Jipeng Cheng Acta mathematica scientia,Series A    2020, 40 (1): 10-19.   Abstract （31）   HTML （0）    PDF（pc） （271KB）（50）       Save In this paper, we discuss the relations of the squared eigenfunction symmetry and the Miura and auti-Miura transformations for the KP and mKP hierarchies and their constrained cases.
 Select Complex Dynamics of an Intraguild Predation Model Xiaomin Yang,Zhipeng Qiu,Ling Ding Acta mathematica scientia,Series A    2019, 39 (4): 963-970.   Abstract （31）   HTML （1）    PDF（pc） （1816KB）（46）       Save The complex dynamics of an intraguild predation (IGP) model is investigated in this paper, and the model incorporates the Holling-Ⅱ functional response functions. The sufficient conditions are obtained for the existence and local stability of boundary equilibria. Then, the numerical simulations are applied to the model under the given values of parameters. The numerical results show that the system may have an attracting invariant torus but no positive equilibrium. Furthermore, the Poincaré map and Fourier transform spectrum analysis are performed to study the complex dynamics of the system on the invariant torus. The results suggest that the dynamics on the invariant torus is almost periodic.
 Select An Lp Inhomogeneous Polyharmonic Neumann Problem on Lipschitz Domains in $\mathbb{R} ^{2}$ Zhihua Du,Yumei Li Acta mathematica scientia,Series A    2020, 40 (2): 271-287.   Abstract （29）   HTML （1）    PDF（pc） （432KB）（19）       Save In this paper, we study an inhomogeneous polyharmonic Neumann problem with $L^{p}$ boundary data on Lipschitz domains in $\mathbb{R} ^{2}$ by the method of layer potentials. Applying multi-layer ${\cal S}$-potentials, which are higher order analogues of the classical singular layer potential and defined in terms of polyharmonic fundamental solutions, the unique integral representation solution is given for the inhomogeneous polyharmonic Neumann problem on Lipschitz domains in $\mathbb{R} ^{2}$ when the boundary data are in some $L^{p}$ spaces.
 Select Traveling Waves in a Nonlocal Dispersal SIR Epidemic Model with Treatment Dong Deng,Yan Li Acta mathematica scientia,Series A    2020, 40 (1): 72-102.   Abstract （29）   HTML （0）    PDF（pc） （897KB）（27）       Save This paper is concerned with the existence and nonexistence of traveling wave solutions of a nonlocal dispersal epidemic model with treatment. The existence of traveling wave solutions is established by Schauder's fixed point theorem as well as a limiting argument, while the nonexistence of traveling wave solutions is proved by two-sided Laplace transform and Fubini's theorem. From the results, we conclude that the minimal wave speed is an important threshold to predict how fast the disease invades.
 Select Global Existence and Stability to a Prey-Taxis Model with Porous Medium Diffusion and Indirect Signal Production Limin Zhang,Haiyan Xu,Chunhua Jin Acta mathematica scientia,Series A    2019, 39 (6): 1381-1404.   Abstract （29）   HTML （0）    PDF（pc） （441KB）（33）       Save In this paper, we consider the following prey-taxis model with nonlinear diffusion and indirect signal production $\left\{ \begin{array}{l}{u_t} = \Delta {u^{{m_1}}} - \chi \nabla \cdot \left( {u\nabla w} \right),\\{w_t} = \Delta w - \mu w + \alpha v{F_0}\left( u \right),\\{v_t} = \Delta {v^{{m_2}}} + \lambda v\left( {1 - \frac{v}{k}} \right) - v{F_0}\left( u \right)\end{array} \right.$ in a bounded domain of ${{\mathbb{R}}^{3}}$ withzero-flux boundary condition. It is shown that for any m1>1, m2>1, there exists a global bounded weak solution for any large initial datum. Based on the uniform boundedness property, we also studied the large time behavior of solutions, and the global asymptotically stability of the constant steady states are established. More precisely, we showed that when λ=0, α ≥ 0, the global weak solution converges to (ū0, 0, 0) in the large time limit; when λ>0, α=0, the global weak solution converges to (ū0, 0, 0) if λ < F0(ū), and the global weak solution converges to $\left( {{{\bar u}_0}, 0, k\left( {1 - \frac{{{F_0}(\bar u)}}{\lambda }} \right)} \right)$ if λ > F0(ū).
 Select The Solvability of Dual Minkowski Problem in $\mathbb{R}$2 Na Wei Acta mathematica scientia,Series A    2019, 39 (6): 1314-1322.   Abstract （29）   HTML （0）    PDF（pc） （306KB）（32）       Save In this paper, we study the existence of minimum of a constrained variational problem in the Sobolev space W1, 4($\mathbb{S}$). If ∫$_\mathbb{S}$g(θ)dθ>0, the minimum is a positive solution to the related Euler-Lagrange equation ${u^{\prime \prime }} + u = \frac{{g(\theta )}}{{u\left( {{u^2} + {u^{\prime 2}}} \right)}}, \theta \in {\rm{\mathbb{S}}}$ Based on this, we prove the solvability of the dual Minkowski problem in $\mathbb{R}$2 posed by Huang-Lutwak-Yang-Zhang[Acta Math, 2016, 216(2):325-338].
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