Most Down Articles

Published in last 1 year | In last 2 years| In last 3 years| All| Most Downloaded in Recent Month| Most Downloaded in Recent Year|

Most Downloaded in Recent Month

Please wait a minute...


For Selected: View Abstracts Download Citations EndNote Reference Manager ProCite BibTeX RefWorks Toggle Thumbnails

Select

Dual Hopf Algebras from a Quiver and Dual Quiver Quantum Groups Chen Lili; Li Fang Acta mathematica scientia,Series A    2009, 29 (2): 505-516.   Abstract （393）      PDF（pc） （363KB）（1159）       Save In [3] and [6], the Hopf algebra structures of path algebra and path coalgebra on a Hopf quiver and a covering quiver respect to a weight sequence respectively were introduced independently. The main aim of this paper is to show the dually one-to-one correspondent relations between their structures (see Theorems 2.1 and 2.4). As applications, firstly, the authors obtain some important results about the Hopf algebra structure on the quotient of path algebra on a cycle; then, they prove that the Sweedler's fourdimensional Hopf algebra H4 is not only quasi-triangular but also co-quasi-triangular. Lastly, they characterize the graded automorphism group of the Hopf algebras on the path algebra of a Schurian covering quiver, according to that on the path coalgebra of a Schurian Hopf quiver. Reference | Related Articles | Metrics

Select

Characterizations of the Weak Boundedness for Commutators of Hardy-Type Operators on Central Morrey Spaces Ji Lei, Wei Mingquan, Yan Dunyan Acta mathematica scientia,Series A    2025, 45 (4): 1013-1022.   Abstract （124）   HTML （4）    PDF（pc） （556KB）（145）       Save We provide some characterizations of the boundedness for commutators of $n$-dimensional Hardy-type operators $H_b$ and $H^*_b$ from the central Morrey space $\dot{M}^{p,\lambda}(\mathbb{R}^n)$ to the weak central Morrey space $W\dot{M}^{p,\lambda}(\mathbb{R}^n)$, which extends the corresponding results on Lebesgue spaces. Reference | Related Articles | Metrics

Select

Monotonicity of Solutions for Parabolic Equations Related to Fractional Order $p$-Laplace Operators on the Upper Half Space Ma Jingjing, Wei Na Acta mathematica scientia,Series A    2025, 45 (4): 1086-1099.   Abstract （25）   HTML （1）    PDF（pc） （595KB）（99）       Save In this paper, we consider the nonlinear parabolic equation associated with the fractional $p$-Laplace operator on the upper half space $\begin{cases} \frac{\partial u}{\partial t}(x,t)+(-\triangle)^s_pu(x,t)=f(u(x,t)), &\quad(x,t)\in\mathbb{R}^{n}_+\times(0,\infty),\\ u(x,t)>0, &\quad(x,t)\in\mathbb{R}^{n}_+\times(0,\infty),\\ u(x,t)=0, &\quad(x,t)\notin\mathbb{R}^{n}_+\times(0,\infty). \end{cases}$ First, the narrow region principle and the maximum principle for antisymmetric functions are proved in both bounded and unbounded domains. Then, the Hopf lemma for antisymmetric functions is established. Finally, using the method of moving planes, the monotonicity of solutions to the parabolic equation associated with the fractional $p$-Laplace operator on the upper half space is demonstrated. Reference | Related Articles | Metrics

Select

Iterative Algorithms of Common Elements for the Set of Solutions of Split Feasibility Problem and the Set of Common Fixed Points of a Finite Family of Quasi-Nonexpansive Operators Zhang Yuting, Gao Xinghui, Peng Jianying Acta mathematica scientia,Series A    2025, 45 (1): 256-268.   Abstract （205）   HTML （5）    PDF（pc） （619KB）（130）       Save In real Hilbert spaces, we construct a new algorithm to find a common solution of the split feasibility problem and the fixed points problem involving a finite family of quasi-nonexpansive mappings. Under appropriate conditions, it is proved that the iteration sequence by the algorithm strongly converges to a common solution of the split feasibility problem and the fixed points problem by using the demi-closed principle and properties of projection operators and conjugate operators. The effectiveness of the algorithm is verified by numerical experiments. The results of this paper improve and extend recent some relative results. Table and Figures | Reference | Related Articles | Metrics

Select

Mountain-pass Solution and Ground State Solution for a Kirchhoff Type Elliptic Equation Wang Hanyi, Huang Shiyu, Xiang Jianlin Acta mathematica scientia,Series A    2025, 45 (4): 1041-1057.   Abstract （64）   HTML （0）    PDF（pc） （620KB）（76）       Save This paper mainly considers a kind of nonlinear elliptic equation with a Kirchhoff type nonlocal term $\begin{equation} -\left(a+b\int_{\mathbb{R}^3}\left| \nabla u\right|^2 \right)\Delta u+V(x)u=Q(x)\left| u\right|^{p-1}u, \quad x\in\mathbb{R}^3, \end{equation}$(0.1) where$ a,b>0 $are constants,$ p\in(1,5) $,$ V(x) $and$ Q(x) $are$ L^\infty(\mathbb{R}^3) $functions. It is known that if we apply the mountain pass lemma directly to obtain solution (i.e., mountain pass solution) to the equation (0.1), we must require$ 3\le p<5 $because of the appearance of nonlocal terms. When$ p\in(1,3) $, the fundamental difficulty in applying the mountain pass lemma is that we are unable to verify the boundedness of the (PS) sequence. To overcome this difficulty, when$ Q(x)\equiv 1 $, paper [Acta Math Sci, 2025, 45B(2): 385-400] introduced a new technique to demonstrate the equation (0.1) exists a mountain pass solution for all$ p\in(1,5) $, and discussed the relationship between the mountain pass solution and the ground state solution obtained. The purpose of this paper is to extend the results of [Acta Math Sci, 2025, 45B(2): 385-400] to the general case$ Q(x)\not\equiv 1 $. Reference | Related Articles | Metrics

Select

Global Smooth Solutions of the Damped Boussinesq Equations with a Class of Large Initial Data Zhu Weipeng, Li Jinlu, Wu Xing Acta mathematica scientia,Series A    2025, 45 (4): 1077-1085.   Abstract （39）   HTML （1）    PDF（pc） （555KB）（68）       Save The global regularity problem concerning the inviscid Boussinesq equations remains an open problem. In an attempt to understand this problem, we examine the damped Boussinesq equations and study how damping affects the regularity of solutions. In this paper, we consider the global existence to the damped Boussinesq equations with a class of large initial data, whose $L^\infty$ norm can be arbitrarily large. The idea is splitting the linear Boussinesq equations from the damped Boussinesq equations, the exponentially decaying solution of the former equations together with the structure of the Boussinesq equations help us to obtain the global smooth solutions. Reference | Related Articles | Metrics

Select

Fixed Points of Meromorphic Functions and Their Differences Zhaojun Wu Acta mathematica scientia,Series A    2019, 39 (6): 1476-1482.   Abstract （118）   HTML （1）    PDF（pc） （264KB）（198）       Save Let f be a transcendental meromorphic function in the complex plane C, k is a positive integer, Δf=f(z+1)-f(z), Δk+1 f=Δk f(z+1)-Δk f, k=1, 2, …. The author prove some results concerning the fixed points of the differences Δk f. The results obtained in this paper generalize some relative results. Reference | Related Articles | Metrics

Select

Optimality Conditions and Total Lagrange Dualities for Evenly Convex Optimization Problems Chen Hongye, Fang Donghui, Wu Kexing Acta mathematica scientia,Series A    2025, 45 (4): 1255-1267.   Abstract （28）   HTML （0）    PDF（pc） （550KB）（71）       Save In this paper, we study an evenly convex optimization problem with the objective function and constraint functions being proper evenly convex. By using the concept of c-subdifferential, we introduce some new notions of constraint qualifications. Under those new constraint qualifications, we provide necessary and sufficient conditions for the KKT rules to hold. Similarly, we provide characterizations for the evenly convex optimization problem to have total Lagrangian dualities and stable total Lagrangian dualities. Reference | Related Articles | Metrics

Select

Spreading Speeds for Partially Degenerate Models in Multi-Dimensional Time-Space Periodic Media Sun Zexin, Zhang Li, Bao Xiongxiong Acta mathematica scientia,Series A    2025, 45 (4): 1110-1127.   Abstract （37）   HTML （2）    PDF（pc） （660KB）（62）       Save The spreading speeds of partially degenerate reaction-diffusion systems with advection term and time-space periodic coefficients in multi-dimensional space has been studied in the current paper. In the direction of $\mathbf{e}\in S^{N-1}$, we use the the spreading properties of solution with front-like initial values to show that there is a finite spreading speed interval of such time-space periodic system in any direction and the interval admits a single spreading speed under certain special conditions. In the direction of $\mathbf{\eta}$, we introduce the concept of asymptotic spreading ray speed interval, and under the compact supported initial values, we show that such time-space periodic system exists an asymptotic spreading ray speed and an asymptotic spreading set. The results show that the Freidlin-G$\ddot{\rm a}$rtner's formula can be used to describe the asymptotic spreading ray speed for such partially degenerate systems. We also apply these results to some partially degenerate models in multi-dimensional time and space periodic media including the benthic-pelagic model, a dengue transmission model and man-environment-man epidemics model. Reference | Related Articles | Metrics

Select

BDF2-Type Finite Element Method for Time-Fractional Diffusion-Wave Equations on Nonuniform Grids Zhu Peng, Chen Yanping, Xu Xianyu Acta mathematica scientia,Series A    2025, 45 (4): 1268-1290.   Abstract （29）   HTML （2）    PDF（pc） （672KB）（64）       Save As is well known, the study of nonuniform grids can effectively solve the initial value singularity phenomenon of fractional Caputo -type derivatives. In the theoretical analysis of nonuniform grids, fractional discrete Grönwall inequality is often used for error analysis, but there is a lack of specific research on error structures. An error convolution structure (ECS) was designed on nonuniform grids for analyzing the time fractional diffusion wave equation. A quadratic interpolation approximation was applied Caputo -type derivatives, and the BDF2 -type finite element method on nonuniform grids was obtained by discretizing it using a reduction method and a discrete complementary convolution kernel. The discrete complementary convolution kernel is crucial in the convergence analysis of algorithms, as it simplify the process of finite element theory analysis and construct global consistency errors based on the properties of convolution kernels and interpolation estimates. The $L^2$-norm error and $H^1$-norm error of the BDF2 finite element scheme on nonuniform grids were estimated in detail, and verifies the consistency between the proposed finite element scheme and the theoretical convergence order through experiments. Table and Figures | Reference | Related Articles | Metrics

Select

The Study on Spectral Structure of Planar Self-Similar Measures with Four Element Digit Sets Lü Jun Acta mathematica scientia,Series A    2025, 45 (4): 1023-1040.   Abstract （43）   HTML （4）    PDF（pc） （621KB）（70）       Save Let $Q=\begin{pmatrix} b & 0\\ 0 & b \end{pmatrix}$ be an integer expanding matrix and let $\mathcal{D}=\left\{\begin{pmatrix} 0 \\ 0 \end{pmatrix},\begin{pmatrix} 1 \\ 0 \end{pmatrix},\begin{pmatrix} 0 \\ 1 \end{pmatrix},\begin{pmatrix} -1 \\ -1 \end{pmatrix} \right\}$ be a four element digit set. We considered the spectral structure of self-similar measure $\mu_{Q,\mathcal{D}}$ which generated by an integer expanding matrix $Q$ and a four element digits $\mathcal{D}$. It is well known that $\mu_{Q,\mathcal{D}}$ is a spectral measure if and only if $b=2q$ for some $q\in\mathbb{N}$. The spectrum for this spectral measure is the following set $\Lambda(Q,\mathcal{C}_q)=\left\{\sum_{k=0}^{n}Q^{k}\mathcal{C}_{q}:\,\,n\geq 1\right\}:=\mathcal{C}_{q}+Q\mathcal{C}_{q}+Q^{2}\mathcal{C}_{q}+\cdots,\,\,\text{all}\,\,\text{finite}\,\,\text{sums},$ where $\mathcal{C}_{q}=q\left\{\begin{pmatrix} 0 \\ 0 \end{pmatrix},\,\,\begin{pmatrix} 1 \\ 0 \end{pmatrix},\,\,\begin{pmatrix} 0 \\ 1 \end{pmatrix},\,\,\begin{pmatrix} 1 \\ 1 \end{pmatrix} \right\}$. In this paper, we investigate the structure of the maximum orthogonal set of $\mu_{Q,\mathcal{D}} $ through the maximum tree mapping and based on this, the relevant issues of its spectral eigenmatrix were discussed. Reference | Related Articles | Metrics

Select

The Levenberg-Marquardt Algorithm for Solving the Generalized Complementarity Problems Yu Dongmei, Liu Dayi Acta mathematica scientia,Series A    2025, 45 (4): 1311-1326.   Abstract （20）   HTML （0）    PDF（pc） （1733KB）（60）       Save In this paper, the Levenberg-Marquardt type method is proposed for solving the generalized complementarity problems. Firstly, by integrating a class of complementary functions, the generalized complementarity problem is equivalently reformulated as a system of nonlinear equations. An adaptive modified Levenberg-Marquardt algorithm with line search is then introduced to address this reformulated problem. Furthermore, the convergence of the proposed algorithm is analyzed under appropriate conditions. Finally, numerical experiments are conducted to verify the feasibility and effectiveness of the proposed algorithm. Table and Figures | Reference | Related Articles | Metrics

Select

Affine Semigroup Dynamical Systems on $\mathbb{Z}_p$ Lu Xufei,Jiao Changhua,Yang Jinghua Acta mathematica scientia,Series A    2025, 45 (2): 305-320.   Abstract （266）   HTML （5）    PDF（pc） （707KB）（351）       Save Let $p\geqslant 2$ be a prime and $\mathbb{Z}_p$ be the ring of $p$-adic integers. For any $\alpha,\beta,z\in \mathbb{Z}_p$, define $f_{\alpha,\beta}(z)=\alpha z+\beta$. The first part of this paper studies all minimal subsystems of semigroup dynamical systems $(\mathbb{Z}_p,G)$ when $f_{\alpha_1,\beta_1}$ and $f_{\alpha_2,\beta_2}$ are commutative, where the semigroup $G=\{f_{\alpha_1,\beta_1}^n \circ f_{\alpha_2,\beta_2}^m: m,n \in \mathbb{N}\}$. In particular, we find the semigroup dynamical system $(\mathbb{Z}_p,G)\ (p\geqslant 3)$ is minimal if and only if $(\mathbb{Z}_p,f_{\alpha_1,\beta_1})$ or $(\mathbb{Z}_p,f_{\alpha_2,\beta_2})$ is minimal and we determine all the cases that $(\mathbb{Z}_2,G)$ is minimal. In the second part, we study weakly essentially minimal affine semigroup dynamical systems on $\mathbb{Z}_p$, which is a kind of minimal semigroup systems without any minimal single action. It is shown that such semigroup is non-commutative when $p\geqslant 3$. Moreover, for a fixed prime $p$, we find the least number of generators of a weakly essentially minimal affine semigroup on $\mathbb{Z}_p$. We show that such number is $2$ for $p=2$ and $3$ for $p=3$. Also, we show that such number is not greater than $p$. Reference | Related Articles | Metrics

Select

The Poincaré Bifurcation of a Class of Pendulum Equations Xu Junwen, Wu Hongxing, Sun Yangjian Acta mathematica scientia,Series A    2025, 45 (3): 843-849.   Abstract （37）   HTML （1）    PDF（pc） （532KB）（119）       Save In this paper, we mainly study the number of limit cycles bifurcate form the periodic orbits of pendulum equations under the perturbations for trigonometric polynomials of degree two. By improving the criterion function of determining the lowest upper bound of the number of zeros of Abelian Integrals, we show that the period annulus (around the origin) can be bifurcate at most two limit cycle (counting multiplicities). Table and Figures | Reference | Related Articles | Metrics

Select

Pullback Attractors and Invariant Measures for Retarded Lattice Reaction-Diffusion Equations Ni Siyan, Zou Tianfang, Zhao Caidi Acta mathematica scientia,Series A    2025, 45 (4): 1128-1143.   Abstract （19）   HTML （1）    PDF（pc） （616KB）（76）       Save In this article, the authors study the pullback attractor and invariant measures for retarded lattice reaction-diffusion equations. They first prove the global well-posedness of the addressed problem, and then show that the solution mappings generates a continuous process possessing a pullback attractor. Afterwards, they construct a family of invariant Borel probability measures for the process via the pullback attractor and the notion of generalized Banach limit. Reference | Related Articles | Metrics

Select

Single Population Dynamics Model of Fish with Seasonal Switching and Impulsive Perturbations Zeng Xiaping, Lu Wenwen, Pang Guoping, Liang Zhiqing Acta mathematica scientia,Series A    2025, 45 (4): 1206-1216.   Abstract （31）   HTML （1）    PDF（pc） （765KB）（60）       Save This paper considers a class of single population dynamics models for fish that incorporates seasonal switching and impulsive perturbations. It investigates the effects of these factors on fish population dynamics. By employing the discrete dynamical system theory and stroboscopic mapping, we derive the sufficient conditions for the permanence and extinction of the fish population system. Using rational difference equations and fixed point theory, we demonstrate the existence of a unique globally attractive positive periodic solution. Finally, numerical simulations are provided to validate the theoretical results. Table and Figures | Reference | Related Articles | Metrics

Select

A Toeplitz-Type Operator on Hardy Space $H^1(\mathbb{B}_{n})$ Wen Xinqi, Yuan Cheng Acta mathematica scientia,Series A    2025, 45 (4): 1161-1170.   Abstract （31）   HTML （0）    PDF（pc） （560KB）（54）       Save This paper investigates the boundedness of a Toeplitz operator $Q_\mu$ acting on the Hardy space $H^1(\mathbb{B}_{n})$. Let $\mu$ be a positive Borel measure on $\mathbb{B}_{n}$ and $0. The main results are following 1. If $\mu$ is a $(1,1)$-logarithmic Carleson measure, then $Q_\mu: H^1(\mathbb{B}_{n})\to H^1(\mathbb{B}_{n})$ is bounded; 2. If $Q_\mu: H^1(\mathbb{B}_{n})\to H^1(\mathbb{B}_{n})$ is bounded, then $\mu$ is a Carleson measure; 3. $Q_\mu: H^p(\mathbb{B}_{n})\to H^q(\mathbb{B}_{n})$ is bounded if and only if $\mu$ is a $(1+\frac1p-\frac1q)$-Carleson measure. Reference | Related Articles | Metrics

Select

Combined Denoising Methods for Complex Signals Wang Jiaxing, Yang Shuangquan, Dong Yichao Acta mathematica scientia,Series A    2025, 45 (4): 1229-1244.   Abstract （27）   HTML （0）    PDF（pc） （3726KB）（68）       Save Noise reduction in complex environments is of paramount importance for the accurate extraction and analysis of signals. Prevailing research predominantly centers on the application of single or combined methods in specific scenarios, but encounters challenges in effectively addressing the nonlinearity and non-stationarity of complex signals. Based on the measurement of non-stationarity, this study proposes a two-stage noise reduction strategy using CEEMDAN. The NS index is used to quantify the non-stationarity of modal components, achieving precise separation of high-frequency noise from low-frequency signals. A novel logarithmic threshold function is adopted to remove high-frequency noise, and the SG filtering method is combined to smooth low-frequency signals, significantly improving the noise reduction effect and signal reconstruction accuracy. The results indicate that the new method demonstrates outstanding modal discrimination and noise reduction performance under different signal-to-noise ratios and noise types. Table and Figures | Reference | Related Articles | Metrics

Select

The Existence of Two Non-Negative Solutions for the Generalized Choquard-Pekar Equation Li Jinju, Zhang Zhengjie Acta mathematica scientia,Series A    2017, 37 (3): 491-498.   Abstract （105）      PDF（pc） （293KB）（212）       Save In the paper, we used variational method to study the generalized Choquard-Pekar equation on RN. We get that there exists two non-negative solutions for our problem, one solution is a local minimum and the other is of the mountain pass type. Reference | Related Articles | Metrics

Select

Acta mathematica scientia,Series A    1997, 17 (4): 361-363.   Abstract （79）      PDF（pc） （221KB）（708）       Save Related Articles | Metrics