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26 December 2024, Volume 44 Issue 6 Previous Issue    Next Issue

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Some Properties of Quasi-Periodic Functions and Their Applications Hu Keqi, Zhang Qingcai Acta mathematica scientia,Series A. 2024, 44 (6):  1415-1425.  Abstract ( 189 )   RICH HTML PDF (560KB) ( 330 )   Save In this paper, we estimate relevant properties of quasi-periodic functions, and these properties are applied. Under the additional condition, the conjecture proposed by Yang is solved. References | Related Articles | Metrics

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The Adjoint Operator of Commutators Wang Xiaomin, Wu Deyu Acta mathematica scientia,Series A. 2024, 44 (6):  1426-1432.  Abstract ( 107 )   RICH HTML PDF (469KB) ( 158 )   Save In this paper, the adjoint operator problem of the commutators $[A, B] = AB-BA$ of two unbounded operators $A$ and $B$ is studied by the spectral theory and block operator matrix theory. The sufficient conditions for the relationship $[A,B]^*=(AB-BA)^*=B^*A^*-A^*B^*=-[A^*,B^*]$ hold are given. In the end, concrete examples is given to illustrate the effectiveness of criterions. References | Related Articles | Metrics

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Lyapunov-Type Inequalities for Dirichlet Problems of Multi-Term Caputo Fractional Differential Equations Zhang Wei, Chen Keyuan, Wu Yi, Ni Jinbo Acta mathematica scientia,Series A. 2024, 44 (6):  1433-1444.  Abstract ( 92 )   RICH HTML PDF (542KB) ( 93 )   Save This paper investigates the Lyapunov-type inequalities for a class of multi-term fractional differential equations with with a parameter, subject to Dirichlet boundary conditions. We first transform the fractional boundary value problem into an integral equation with Green's functions, then prove the relevant properties of the Green's functions, and finally obtain the corresponding Lyapunov-type inequalities using a priori estimation method. Multi-term fractional differential equations belong to the category of non-local equations, and their complexity exceeds that of single-term fractional differential equations. Studying the Lyapunov-type inequalities for multi-term fractional boundary value problems is of significant importance for the qualitative analysis of boundary value problems of multi-term fractional nonlinear differential equations. Figures and Tables | References | Related Articles | Metrics

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The Existence of Global Strong Solution to the Compressible Axisymmetric Navier-Stokes Equations with Density-Dependent Viscosities Gong Simeng, Zhang Xueyao, Guo Zhenhua Acta mathematica scientia,Series A. 2024, 44 (6):  1445-1475.  Abstract ( 149 )   RICH HTML PDF (704KB) ( 117 )   Save In this paper, we consider the compressible Navier-Stokes equations with viscous-dependent density in 3D space, and obtain a global axisymmetric strong solution with small energy and large initial oscillations in a periodic domain $\Omega=\{(r,z)\vert r=\sqrt{x^2+y^2},(x,y,z)\in\mathbb{R}^3,r\in I\subset(0,+\infty),z\in(-\infty,+\infty)\}$. When $z\rightarrow\pm\infty$, the initial density remains in a non-vacuum state. The results also show that as long as the initial density is far away from the vacuum, the solution will not develop the vacuum state in any time. And the exact decay rates of the solution is obtained. References | Related Articles | Metrics

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Existence of Positive Solutions for a Bending Elastic Beam Equation Huo Huixia, Li Yongxiang Acta mathematica scientia,Series A. 2024, 44 (6):  1476-1484.  Abstract ( 64 )   RICH HTML PDF (534KB) ( 136 )   Save This paper discusses the existence of the positive solution of the fourth-order boundary value problem$\left\{\begin{array}{ll} u^{(4)}(x)=f(x,u(x),u''(x)),\quad x\in [0,\,1],\\ u'(0)=u'''(0)=u(1)=u''(1)=0,\end{array}\right.$which models the deformations of a statically elastic beam, where $\,f:[0,\,1]\times\mathbb{R}^{+}\times\mathbb{R}^{-}\to\mathbb{R}^{+}$ is continuous. Under that the nonlinearity $f(x,\,u,\,v)$ satisfies some inequality conditions, the existence results of positive solutions of this problem are obtained by applying the fixed point index theory in cones. Figures and Tables | References | Related Articles | Metrics

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Pseudo-Almost Automorphic Solutions to A Class of Differential Inclusions Ye Li, Liu Yongjian, Liu Aimin Acta mathematica scientia,Series A. 2024, 44 (6):  1485-1498.  Abstract ( 72 )   RICH HTML PDF (621KB) ( 109 )   Save This paper is dedicated to the study of the pseudo-almost automorphic $C^0$-solutions to a class of differential inclusion problems which have mixed nonlocal plus local initial conditions. Baseing on the fixed point theorem, theory of operator semigroups, and the properties of pseudo-almost automorphic functions, using $\varepsilon$-discretisation techniques the existence of $C^0$-solutions for differential inclusion is discussed directly in the space which is composed by all pseudo-almost automorphic functions. References | Related Articles | Metrics

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Uniformly Convergent NIPG Methods for a Singularly Perturbed Convection-Diffusion Problem with a Discontinuous Convection Coefficient Xu Lei, Liu Libin Acta mathematica scientia,Series A. 2024, 44 (6):  1499-1510.  Abstract ( 63 )   RICH HTML PDF (586KB) ( 127 )   Save In this paper, a higher order NIPG method on a Bakhvalov-type mesh for a singularly perturbed convection-diffusion problem with a discontinuous convection coefficient is studied. Based on Gauß Radau interpolation and Lagrange interpolation, the convergence of optimal order in an energy norm is derived. Numerical experiments are proposed to confirm our theoretical results. Figures and Tables | References | Related Articles | Metrics

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Breather and Rogue Wave on the Periodic/Double Periodic Background and Interaction Solutions of the Generalized Derivative Nonlinear Schr$\rm\ddot{o}$dinger Equation Lou Yu, Zhang Yi Acta mathematica scientia,Series A. 2024, 44 (6):  1511-1519.  Abstract ( 53 )   RICH HTML PDF (3267KB) ( 157 )   Save The nonlinear Schr$\rm\ddot{o}$dinger equation is a very important integrable system in the field of physics and applied mathematics. In this paper, the breather and rogue wave on the periodic/double periodic background and the collision solutions of breather and rogue wave for the generalized derivative nonlinear Schr$\rm\ddot{o}$dinger equation are studied by using the Darboux transformation. Firstly, the Darboux transformation of the generalized derivative nonlinear Schr$\rm\ddot{o}$dinger equation is constructed. Then, by using the Darboux transformation, the breather and rogue wave on the periodic/double periodic background and the collision solutions are derived. Finally, by means of the figures, the structures of interesting new solutions are analyzed in detail, which also provide a theoretical basis for studying the physical mechanism of the new solution. Figures and Tables | References | Related Articles | Metrics

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Degeneration Behaviors of Solutions and Hybrid Solutions for the New (3+1)-Dimensional KP Equation Guo Yanfeng, Cui Jingyi, Xiao Haijun, Zhang Jingjun Acta mathematica scientia,Series A. 2024, 44 (6):  1520-1536.  Abstract ( 56 )   RICH HTML PDF (6402KB) ( 151 )   Save We concentrate on the nonlinear wave solutions of the new (3+1)-dimensional KP equation, which was firstly proposed by Wazwaz in 2022. Based on the Hirota bilinear form, the $P$-breathing solutions are mainly obtained from the $N$-soliton solutions utilizing the module resonance technique. Then, using parameter limit approach, the Lump solutions are derived by degenerating behaviors of the homoclinic breathing solutions and $N$-soliton solutions on the basis of the special relations of parameters. In addition, from the partial degeneration of the $N$-soliton solutions, some hybrid solutions are investigated by the interaction solutions among the breathing, soliton and Lump solutions. Figures and Tables | References | Related Articles | Metrics

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Global Gevrey Regularity and Analyticity of a Weakly Dissipative Camassa-Holm Equation Meng Zhiying, Yin Zhaoyang Acta mathematica scientia,Series A. 2024, 44 (6):  1537-1549.  Abstract ( 51 )   RICH HTML PDF (4476KB) ( 81 )   Save This article mainly studies the well posedness of the Cauchy problem of a weakly dissipative Camassa-Holm equation in Sobolev-Gevrey spaces. Firstly, we demonstrate the local Gevrey regularity and analyticity of this equation. Then, we discuss the continuity of the data-to-solution map. Finally, we obtain the global Gevrey regularity of this system in Gevrey class $G_{\sigma}$ with $\sigma\geq 1$ in time. References | Related Articles | Metrics

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Global Existence and Blow-Up for Semilinear Third Order Evolution Equation with Different Power Nonlinearities Shi Jincheng, Liu Yan Acta mathematica scientia,Series A. 2024, 44 (6):  1550-1562.  Abstract ( 52 )   RICH HTML PDF (4733KB) ( 165 )   Save This paper studies the Cauchy problem of a class of semilinear third-order evolution equations with different power-type nonlinear terms. Its linearized model is derived from the classical thermoelastic plate equations considering Fourier's law. Firstly, by using the appropriate $L^r\!-\!L^q$ estimation away from the asymptote and combining with the Banach fixed point theorem, the existence of the global solution under small initial conditions is obtained. Secondly, for the nonlinear terms that satisfy specific conditions, the explosion of the solution is proved by the test function method. Finally, based on these research results, some critical indicators of the semilinear third-order model are obtained. References | Related Articles | Metrics

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Invariant Measure of Impulsive Fractional Lattice System Zhang Yiran, Li Dingshi Acta mathematica scientia,Series A. 2024, 44 (6):  1563-1576.  Abstract ( 45 )   RICH HTML PDF (4449KB) ( 108 )   Save This paper first verifies the global validity of the solution of fractional lattice system. Then the paper establishes that the process generated by the solution operator is a continuous process, and it is verified that the process has pull-back asymptotic zero and pull-back attractor, and finally construct a set of Borel invariant probability measures of the process through the generalized Banach limit. References | Related Articles | Metrics

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Spatiotemporal Dynamics Induced by the Interaction Between Fear and Schooling Behavior in a Diffusive Model Xiao Jianglong, Song Yongli, Xia Yonghui Acta mathematica scientia,Series A. 2024, 44 (6):  1577-1594.  Abstract ( 68 )   RICH HTML PDF (6958KB) ( 162 )   Save In this paper, we study the spatiotemporal dynamics in a diffusive predator-prey model with the homogeneous Neumann boundary condition. Our study indicates that the interaction between fear and schooling behavior induces very rich and interesting spatiotemporal dynamics. The conditions for Turing instability and Turing-Hopf bifurcation emerging are explored at length. By utilizing the normal form method, the spatiotemporal dynamics of the spatial model near the Turing-Hopf bifurcation point are classified. And rich numerical simulations are used to confirm the theoretical analysis. Finally, we summarize the great influence of the fear effect and schooling behavior. We found that the schooling behavior of prey cannot counteract high-level fear, while it offsets the low-level fear. Moreover, the fear effect induces Turing instability of the system with the schooling behavior. However, the fear effect neither changes the stability of coexistence equilibrium, nor induces periodic solutions or Turing instability of the system without the schooling behavior. Figures and Tables | References | Related Articles | Metrics

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Weyl Mean Equicontinuity and Weyl Mean Sensitivity of A Random Dynamical System Lian Yuan, Liu Hongjun, Zhu Bin Acta mathematica scientia,Series A. 2024, 44 (6):  1595-1606.  Abstract ( 63 )   RICH HTML PDF (573KB) ( 83 )   Save In this article, we introduce the concepts of Weyl-mean equicontinuity and Weyl-mean sensitivity of a random dynamical system associated to an infinite countable discrete amenable group action. We obtain the dichotomy result to Weyl-mean equicontinuity and Weyl-mean sensitivity of a random dynamical system when the corresponding skew product transformation is minimal. References | Related Articles | Metrics

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Event-Triggered Control for a Class of Stochastic Time-Delay Nonlinear Systems Tang Jun, Wu Ailong Acta mathematica scientia,Series A. 2024, 44 (6):  1607-1616.  Abstract ( 60 )   RICH HTML PDF (746KB) ( 117 )   Save In this paper, the stability problem of stochastic time-varying delay differential nonlinear systems with external disturbances and uncertainties is discussed. In order to reduce the transmission frequency of the feedback control signal, the intermittent event triggering control strategy is adopted, and Zeno behavior is excluded. The practically input-to-state stability is used to describe the dynamic performance of control targets in event-triggered schemes. In addition, by means of linear matrix inequalities, theoretical criteria for stability of stochastic time-varying delay nonlinear systems with event-triggered feedback control are obtained. Finally, several examples and simulations are given to illustrate the validity of the results. Figures and Tables | References | Related Articles | Metrics

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$\alpha$-Robust Optimal Investment Strategy Under Inflation Chen Yating, Liu Haiyan, Chen Mi Acta mathematica scientia,Series A. 2024, 44 (6):  1617-1629.  Abstract ( 47 )   RICH HTML PDF (659KB) ( 81 )   Save This paper focuses on the optimal investment problem with model uncertainty under inflation. It is assumed that there are risk-free assets, risky assets and inflation-indexed bonds used to hedge inflation risk in the financial market, in which the price of risky assets obeys the CEV model, and then the price index level is used to discount the price of each type of asset to present its true price, and the investment model is built by applying the $\alpha$-maxmin mean-variance utility function and the equilibrium investment strategy and value function are obtained by solving the HJB equation. Finally, the trend of optimal investment strategies under parameter variations is analyzed by numerical simulation. Figures and Tables | References | Related Articles | Metrics

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Two-Step Inertial Bregman Proximal Alternating Linearized Minimization Algorithm for Nonconvex and Nonsmooth Problems Jing Zhao, Chenzheng Guo Acta mathematica scientia,Series A. 2024, 44 (6):  1630-1651.  Abstract ( 63 )   RICH HTML PDF (9184KB) ( 160 )   Save In this paper, for solving a class of nonconvex and nonsmooth nonseparable optimization problems, based on proximal alternating linearized minimization method we propose a new iterative algorithm which combines two-step inertial extrapolation and Bregman distance. By constructing appropriate benefit function, with the help of Kurdyka-Łojasiewicz property we establish the convergence of the whole sequence generated by proposed algorithm. We apply the proposed algorithm to solve sparse nonnegative matrix factorization, signal recovery and quadratic fractional programming problems, and show the effectiveness of proposed algorithm. Figures and Tables | References | Related Articles | Metrics

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The Tensor Scheme BCGSTAB Algorithm for Solving Stein Tensor Equations Ma Changfeng, Xie Yajun, Bu Fan Acta mathematica scientia,Series A. 2024, 44 (6):  1652-1664.  Abstract ( 62 )   RICH HTML PDF (638KB) ( 171 )   Save The biconjugate gradient stabilized (BCGSTAB) method is a fast and smoothly converging variant of biconjugate gradient (BiCG) method. In this paper, we generalize BCGSTAB method to solve the Stein tensor equation. We raise the algorithm of tensor format and specific proof process of existence of a solution. And we present the convergence theorem of this algorithm. Numerical experiments demonstrate this algorithm is effective and feasible for solving the Stein tensor equation. Figures and Tables | References | Related Articles | Metrics

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Multi-Scale Approach for Diffeomorphic Image Registration with Fractional-Order Regularization Based on Quasiconformal Theory Wang Huinan, Han Huan Acta mathematica scientia,Series A. 2024, 44 (6):  1665-1688.  Abstract ( 57 )   RICH HTML PDF (2521KB) ( 106 )   Save Two significant challenges relating to image registration include the issue of mesh folding and the unresolved problem of greedy registration. To tackle these challenges, a multi-scale approach for diffeomorphic image registration model with fractional-order regularization based on quasiconformal theory is proposed in this paper. It employs fractional-order differential to achieve a smooth energy functional minima without mesh folding and a priori regular terms. Furthermore, the existence of solution for the proposed model and the convergence of the multi-scale approach are proved. And numerical tests are performed to demonstrate that the proposed algorithm effectively eliminates mesh folding and generates superior registration results. Figures and Tables | References | Related Articles | Metrics

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Stability of Solutions for Controlled Systems of Generalized Multiobjective Multi-Leader-Follower Games Under Bounded Rationality Zhang Yongxue, Jia Wensheng Acta mathematica scientia,Series A. 2024, 44 (6):  1689-1702.  Abstract ( 82 )   RICH HTML PDF (601KB) ( 175 )   Save In this paper, the stability of solutions for controlled systems of generalized multiobjective multi-leader-follower games is studied under the framework of bounded rationality. We construct an appropriate rational function by the nonlinear scalarization method, and prove that the model is structurally stable and robust to $\varepsilon$-equilibrium. This means that most of the problems for controlled systems of generalized multiobjective multi-leader-follower games are stable on the meaning of Baire category, and also shows that, under certain conditions, the problem model can be approximated to complete rationality by bounded rationality. References | Related Articles | Metrics