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26 February 2021, Volume 41 Issue 1 Previous Issue    Next Issue

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Properties and Applications of the Core Inverse of an Even-Order Tensor Hongxing Wang,Xiaoyan Zhang Acta mathematica scientia,Series A. 2021, 41 (1):  1-14.  Abstract ( 133 )   RICH HTML PDF (326KB) ( 169 )   Save Tensor generalized inverse is one of the important contents of tensor theory research. In this paper, based on the research of tensor generalized inverse in recent years, we obtain some properties of the core inverse of tensor with the Einstein product, a tensor partial ordering based on the core inverse and the least-squares solution of $ {{\cal A}} {*}{{\cal X}}={{\cal B}}$ under condition ${{\cal X}}\in{\Bbb {\cal R}}({{\cal A}}) $. References | Related Articles | Metrics

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Construction of the Planar Bodies with Constant Width Deyan Zhang,Botao Duan Acta mathematica scientia,Series A. 2021, 41 (1):  15-28.  Abstract ( 84 )   RICH HTML PDF (490KB) ( 156 )   Save Firstly, a class of planar curves "lever wheel" and their arm functions are defined, and the parameter representation of the lever wheel is established in this paper. Secondly, it is shown that the lever wheel is an equivalent characterization of the constant width curve. Finally, it is proven that the Reuleaux polygons are a class of lever wheels with piecewise constant arm functions, and Reuleaux polygons with even edges are constructed. Figures and Tables | References | Related Articles | Metrics

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Stabilities of K- Frames and Tight K- Frames Under the Operator Perturbation Dandan Du,Yucan Zhu Acta mathematica scientia,Series A. 2021, 41 (1):  29-38.  Abstract ( 73 )   RICH HTML PDF (311KB) ( 100 )   Save In this paper, we discuss the stabilities of K-frames and tight K-frames under the operator perturbation. Firstly, we provide an equivalent characterization of the operator perturbation for a K-frame by using a bounded linear operator $T $ from ${{\cal H}_1} $ to ${{\cal H}_2} $. We also give a simple way to construct new K-frames from two existing Bessel sequences. Meanwhile, we make a discussion on the construction for K-frames from given ones. In the end, we obtain a necessary and sufficient condition to generate tight K-frames from two old Bessel sequences. Our results generalize and improve the remarkable results which had been obtained by Casazza and Christensen. References | Related Articles | Metrics

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Nontrivial Solution of High Order Yamabe-Type Equation on Finite Graph Chungeng Liu,Yuyou Zhong Acta mathematica scientia,Series A. 2021, 41 (1):  39-45.  Abstract ( 59 )   RICH HTML PDF (310KB) ( 87 )   Save In this paper, we study the existence of nontrivial positive solution of the following high order Yamabe-type equation ${\cal L}_{m, p} u-g|u|^{p-2} u=\lambda f|u|^{\alpha-2} u $ on a finite graph $ G$, where $ {\cal L}_{m, p}$ is a $ 2m$-order difference operator which is a kind of $ p$-th $ (-\Delta)^m$ operator, $ \alpha \geq p \geq 2$, $g>0 $ and $f>0 $ are real functions defined on all vertices of $G $, $ m\ge 1$ is an integer. We show that the above equation always has a nontrivial solution $u\ge 0 $ for some constant λ∈ ${\Bbb R} $. References | Related Articles | Metrics

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Boundness of Riesz Transforms on Hardy Spaces Associated with Schrödinger Operators on the Heisenberg Group Xuan Chen Acta mathematica scientia,Series A. 2021, 41 (1):  46-62.  Abstract ( 74 )   RICH HTML PDF (359KB) ( 108 )   Save Let $L=-\Delta_{{\Bbb H}^{n}}+V $ be a Schrödinger operator on the Heisenberg group ${\Bbb H}^{n} $, where $V $ is a nonnegative potential belonging to the reverse Hölder class. By the molecular decomposition of the Hardy space $ H_{L}^{p}({\Bbb H}^{n})$, we obtain the $ H^p_L$-boundedness of the Riesz transform associated with $L $. References | Related Articles | Metrics

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Multiplicity of Radial Solutions of $ k$-Hessian Equations Zaitao Liang,Xuemeng Shan Acta mathematica scientia,Series A. 2021, 41 (1):  63-68.  Abstract ( 57 )   RICH HTML PDF (269KB) ( 84 )   Save This paper concerns with a Dirichlet problem of the $ k$-Hessian equation. By using the Leggett-Williams fixed point theorem, we get some results on the existence of triple and arbitrarily many nontrivial radial solutions. References | Related Articles | Metrics

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The Non-Existence of Solutions of a Certain type of Nonlinear Complex Differential-Difference Equations Shuqing Lin,Junfan Chen Acta mathematica scientia,Series A. 2021, 41 (1):  69-80.  Abstract ( 65 )   RICH HTML PDF (334KB) ( 122 )   Save In this paper, we study transcendental entire solutions of a certain type of complex differential-difference equations $\left[f(z)f'(z)\right]^{n}+f^{m}(z+\eta)=1,$ $\left[f(z)f'(z)\right]^{n}+[f(z+\eta)-f(z)]^{m}=1,$ $\left[f(z)f'(z)\right]^{2}+P^{2}(z)f^{2}(z+\eta)=Q(z)e^{\alpha(z)},$ where $P(z) $ and $Q(z) $ are non-zero polynomials, $\alpha(z) $ is polynomial, $ m$ and $n $ are positive integers, $ \eta\in{\Bbb C}\setminus\{0\}$. Several sufficient conditions on the non-existence of transcendental entire solutions of such equations are supplied. References | Related Articles | Metrics

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Homogenization of the Oscillating Robin Mixed Boundary Value Problems Juan Wang,Jie Zhao Acta mathematica scientia,Series A. 2021, 41 (1):  81-90.  Abstract ( 52 )   RICH HTML PDF (346KB) ( 64 )   Save In this paper, we study the convergence rates of solutions for homogenization of the oscillating Robin mixed boundary value problems. The main difficulty of this work is due to the oscillating factor on the Robin boundary as well as boundary discrepancies. Thanks to the duality approach, we could handle the oscillatory integral. As a consequence, we establish the rates of convergence in $H^{1} $ and $L^{2} $, which depends on the dimension explicitly. This work may be regarded as an extension of the duality approach as well as smoothing operators for oscillating Robin mixed boundary value problems. References | Related Articles | Metrics

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Research on the Inviscid Limit for Boussinesq Equations Lianhong Guo Acta mathematica scientia,Series A. 2021, 41 (1):  91-99.  Abstract ( 52 )   RICH HTML PDF (324KB) ( 97 )   Save In this paper, we investigate the inviscid limit of the 3D viscous Boussinesq equations with slip boundary condition. We establish the local well-posedness of the strong solutions for initial boundary value problems for such systems. Furthermore, we establish the vanishing viscosity limit process and obtain a strong rate of convergence as the boundary of the domain is flat. In addition, the key observation is that the boundary term as $θ$ can be estimated by the part of high order of energy through the trace formula. References | Related Articles | Metrics

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Local well-Posedness for the Cauchy Problem of 2D Nonhomogeneous Incompressible and Non-Resistive MHD Equations with Vacuum Mingtao Chen,Wenhuo Su,Aibin Zang Acta mathematica scientia,Series A. 2021, 41 (1):  100-125.  Abstract ( 56 )   RICH HTML PDF (495KB) ( 91 )   Save In this paper, we investigate the Cauchy problem of the nonhomogeneous incompressible and non-resistive MHD on ${\Bbb R}$2 with vacuum as far field density and prove that the 2D Cauchy problem has a unique local strong solution provided that the initial density and magnetic field decay not too slow at infinity. Furthermore, if the initial data satisfy some additional regularity and compatibility conditions, the strong solution becomes a classical one. Moreover, we also establish a blowup criterion which depends only on the Magnetic fields. References | Related Articles | Metrics

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A Formal Analysis on the Large Ericksen Number Limit for the Incompressible Hyperbolic Ericksen-Leslie System of Liquid Crystals Feng Cheng Acta mathematica scientia,Series A. 2021, 41 (1):  126-141.  Abstract ( 66 )   RICH HTML PDF (428KB) ( 60 )   Save In this paper, we consider the parameterized incompressible hyperbolic Ericksen-Leslie system of liquid crystals. Formally, letting the parameter vanish, we prove that the limit system admits a local classical solution. Moreover, we formally obtained an estimate on the difference between the parameterized Ericksen-Leslie's incompressible hyperbolic liquid crystal model and the corresponding limit system, which corresponds to a formal energy estimate of the difference of the classical solutions in $L^2$ space. References | Related Articles | Metrics

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Existence of Positive Radial Solution to a Class of Kirchhoff type Equation in ${\mathbb R}$$N$ Yihua Deng Acta mathematica scientia,Series A. 2021, 41 (1):  142-148.  Abstract ( 72 )   RICH HTML PDF (306KB) ( 86 )   Save In this paper, we discuss a class of Kirchhoff type equation whose energy function may not be of $C^1$ class. This equation is closely related to plasma physics and theories for propagation of laser beams. Using a change of variables, we get a new equivalent equation whose energy function is of $C^1$ class. Using a suitable Banach space and variational method, we prove that there is a positive radial solution to the given equation under proper conditions. References | Related Articles | Metrics

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Invariance Sets and Well-Posedness for the Weak Solution of Non-Autonomous Caputo Fractional Evolution Equation Xuanxuan Xi,Mimi Hou,Xianfeng Zhou Acta mathematica scientia,Series A. 2021, 41 (1):  149-165.  Abstract ( 71 )   RICH HTML PDF (394KB) ( 91 )   Save The purpose of this paper is to analyze the time-fractional non-autonomous evolution equation which is associated with a family of linear operators depending on the time parameter $t$. Using the representation theorem by Lions, we obtain the sufficient conditions for well-posedness of the weak solution. Based on an orthogonal projection, we establish the invariance criterion for the weak solution of the time-fractional evolution equation. The operators of investigated equations are time-dependent. References | Related Articles | Metrics

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Hopf Bifurcation and Stability for an Autocatalytic Reversible Biochemical Reaction Model Gaihui Guo,Xiaohui Liu Acta mathematica scientia,Series A. 2021, 41 (1):  166-177.  Abstract ( 58 )   RICH HTML PDF (776KB) ( 104 )   Save An autocatalytic reversible three-molecular biochemical reaction model subject to Neumann boundary conditions is considered. Firstly, the existence and stability of the Hopf bifurcation for the ordinary differential system are given. Secondly, the effect of diffusion coefficients on Turing instability is established and the existence of Hopf bifurcation is obtained for the partial differential system with diffusion. Then applying the normal form theory and center manifold theorem, the direction and stability of Hopf bifurcation are also given. Finally, some numerical simulations are carried out with the help of Matlab software to verify and supplement the theoretical results. Figures and Tables | References | Related Articles | Metrics

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Periodic Solutions of a Neutral Impulsive Predator-Prey Model with Holling-Type IV Functional Response Tingting Jiang,Zengji Du Acta mathematica scientia,Series A. 2021, 41 (1):  178-193.  Abstract ( 76 )   RICH HTML PDF (402KB) ( 88 )   Save This paper is concerned with a neutral impulsive predator-prey model with Holling-type IV functional response and delays. We obtain sufficient conditions on the existence of positive periodic solutions of this predator-prey model by using the Mawhin coincidence degree theory and analysis technique. References | Related Articles | Metrics

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Bootstrap Confidence Intervals for the Common Location Parameter of Several Skew-Normal Populations Rendao Ye,Zhongchi Wang,Kun Luo,Ya Lin Acta mathematica scientia,Series A. 2021, 41 (1):  194-216.  Abstract ( 68 )   RICH HTML PDF (496KB) ( 69 )   Save In this paper, we consider the interval estimation and hypothesis testing problems for the common location parameter of several skew-normal populations when the scale parameters and skewness parameters are unknown. Firstly, we estimate the unknown parameters using the methods of moment estimation and maximum likelihood estimation. Secondly, the Bootstrap confidence intervals and Bootstrap test statistics are constructed, which generalize the results given by Xu [1] under several normal populations. Thirdly, the Monte Carlo simulation results indicate that the Bootstrap confidence intervals based on the methods of moment estimation and maximum penalized likelihood estimation perform better than other four confidence intervals. Finally, the above approaches are applied to the real data examples of regional gross domestic product of China and bioavailability in order to verify the reasonableness and effectiveness of the proposed approaches. Figures and Tables | References | Related Articles | Metrics

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Dynamical Properties of Second-Order Dynamic Equations with a Nonpositive Neutral Coefficient on a Time Scale Ping Zhang,Jiashan Yang Acta mathematica scientia,Series A. 2021, 41 (1):  217-226.  Abstract ( 63 )   RICH HTML PDF (337KB) ( 72 )   Save This paper is concerned with dynamical behavior of second-order nonlinear non-autonomous delay dynamic equations with a nonpositive neutral coefficient on a time scale T. By using the time scales theory and combining with the classical inequality, we establish some new dynamical properties for the equations. The dynamical properties of dynamic equations are further generalized and perfected. References | Related Articles | Metrics

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Transportation Inequalities for Mixed Stochastic Differential Equations Liping Xu,Zhi Li Acta mathematica scientia,Series A. 2021, 41 (1):  227-236.  Abstract ( 58 )   RICH HTML PDF (342KB) ( 77 )   Save In this paper, we discuss a class of stochastic differential equations containing both Wiener process and fractional Brownian motion with Hurst parameter $1/2<H<1$. By using some transformation technique and approximation argument, we establish the quadratic transportation inequalities for the law of the solution of the equations under investigation under the $d_2$ metric and the uniform metric $d_{\infty}$. References | Related Articles | Metrics

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A Double Projection Algorithm for Solving Variational Inequalities Shenglian Wan Acta mathematica scientia,Series A. 2021, 41 (1):  237-244.  Abstract ( 59 )   RICH HTML PDF (315KB) ( 74 )   Save In this paper, a new double projection algorithm for solving variational inequalities is proposed. By constructing a new class of hyperplanes that strictly separate the current iteration and variational inequality solution sets and improving proof of existing results, We prove that the infinite sequence generated by the algorithm is globally convergent, and establish the convergence rate analysis under local error and Lipschitz conditions. Figures and Tables | References | Related Articles | Metrics

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Differential Evolution Algorithms for Boundary Layer Problems on Bakhvalov-Shishkin Mesh Qin Zhou,Lizheng Cheng Acta mathematica scientia,Series A. 2021, 41 (1):  245-253.  Abstract ( 55 )   RICH HTML PDF (511KB) ( 97 )   Save In this paper, the convection-diffusion equation with left boundary layer or right boundary layer is solved on Bakhvalov-Shishkin mesh. The parameter in Bakhvalov-Shishkin mesh is optimized by differential evolution algorithm, and we obtain numerical solution with optimal accuracy on Bakhvalov-Shishkin mesh. Three numerical examples are simulated, and the numerical results show that the differential evolution algorithm is accurate and convergence. Especially, the numerical solution accuracy of the boundary layer is obviously better than that of fixed mesh parameters. Figures and Tables | References | Related Articles | Metrics

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Analysis of the Fluid Model Driven by M/M/c Queue with Single Working Vacation Zikun Li,Xiuli Xu,Dequan Yue Acta mathematica scientia,Series A. 2021, 41 (1):  254-268.  Abstract ( 59 )   RICH HTML PDF (786KB) ( 80 )   Save In this paper, introducing working vacation strategy into an M/M/c queue, the fluid model driven by a multi-server queue with single working vacation is studied. Using quasi birth-and-death process and matrix-geometric method, the steady-state distribution of the queue length is obtained.The net input rate structure is constructed, and the matrix differential equations satisfied by the joint stationary distribution of the fluid model are derived. Furthermore, by using Laplace-Stieltjes Transform (LST) method, the probability of the empty buffer content and the mean of the buffer content in the stable case are obtained. Finally, the application of the model in multi-channel wireless Mesh network is presented, and the influence of parameter on system performance index is demonstrated in numerical examples. Figures and Tables | References | Related Articles | Metrics

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Analysis of $M$/$G$/1 Queueing System for Single Server Vacation Without Interruption Under the Control of $D$-Policy Qionglin Liu,Yinghui Tang Acta mathematica scientia,Series A. 2021, 41 (1):  269-288.  Abstract ( 63 )   RICH HTML PDF (692KB) ( 76 )   Save This paper studies the $M/G/1$ queueing system for single server vacation without interruption under the control of $D$-policy, in which when the server is transferred on vacation, the server starts service immediately if the total service times of waiting customers is no less than a given positive threshold $D$. Applying the total probability decomposition technique, renewal theory and the Laplace transform tool, the transient queue length distribution from any initial state is discussed. Both the expressions of the Laplace transformation of the transient queue length distribution and the recursive expressions of the steady-state queue length distribution are derived. Meanwhile, the stochastic decomposition structure of the steady-state queue length and the explicit expression of the additional queue distribution are displayed. Furthermore, by employing the steady-state queue length distribution $\left\{ {{p}_{j}}, j=0, 1, 2, \cdots \right\}$, we discuss the optimization design of the system capacity and illustrate the important effect of the steady-state queue length distribution. Finally, the explicit expression of the long-run expected cost rate is derived under a given cost structure. And by numerical calculation, we determine the optimal control policy ${{D}^{*}}$ for minimizing the long-run expected cost per unit time as well as the combined control strategy $({{T}^{*}}, {{D}^{*}})$ when the vacation time is fixed duration $T(>0)$. Figures and Tables | References | Related Articles | Metrics