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| There are 1488 papers published in subject: since this site started. | |||
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| 1. Stability and convergence of a consistent splitting GSAV scheme for the the time-dependent thermally coupledmagnetohydrodynamics equations | |||
| LU Chao,ZHANG Tong | |||
| Mathematics 29 March 2024 | |||
| Show/Hide Abstract | Cite this paper︱Full-text: PDF (0 B) | |||
| Abstract:The paper mainly considers and analyzes the first order, linear and fully-decoupled numerical schemefor the time-dependent incompressible thermally coupled magnetohydrodynamic equations.Firstly, an equivalent system of the original problem is formed by introducing the suitable generalizedscalar auxiliary variable, the consist splitting method is employed to construct the ideal numerical scheme.Then, a series of linear algebra equations with the constant coefficients at each time step.As a consequence, the computational size is reduces and the computational cost is saved.Secondly, the unconditional stability results of numerical solutions are established by the energy methodand the recursive analysis method. Finally, the convergence results of numerical approximations are presented by introducing the Stokes pressure and using the mathematical induction method | |||
| TO cite this article:LU Chao,ZHANG Tong. Stability and convergence of a consistent splitting GSAV scheme for the the time-dependent thermally coupledmagnetohydrodynamics equations[OL].[29 March 2024] http://en.paper.edu.cn/en_releasepaper/content/4762954 | |||
| 2. Defect-correction variational multiscale methods for the stationary incompressible magnetohydrodynamics flow | |||
| ZHANG Hui-Min,Zhang Tong | |||
| Mathematics 25 March 2024 | |||
| Show/Hide Abstract | Cite this paper︱Full-text: PDF (0 B) | |||
| Abstract:In this paper, the defect correction variational multiscale method (DCVMM) based on local Gauss integrations is developed for the stationary incompressible magnetohydrodynamics (MHD) problem. Firstly, we review the variational multiscale method (VMM) for solving the stationary incompressible magnetohydrodynamics problem, and give the stability and convergence of the numerical solutions. Sencondly, the DCVMM based on local Gauss integrations is developed for the stationary incompressible MHD problem, and the stability and optimal error results of the numerical solutions are established. Finally, some numerical examples are provided to indicate with the obtained theoretical findings and show the performances of the considered numerical schemes. | |||
| TO cite this article:ZHANG Hui-Min,Zhang Tong. Defect-correction variational multiscale methods for the stationary incompressible magnetohydrodynamics flow[OL].[25 March 2024] http://en.paper.edu.cn/en_releasepaper/content/4762956 | |||
| 3. Bright solitons for a (3+1)-dimensional hyperbolic nonlinear Schr\"{o}dinger equation | |||
| WANG Jing-Ying,JIANG Yan,TIAN Bo | |||
| Mathematics 21 March 2024 | |||
| Show/Hide Abstract | Cite this paper︱Full-text: PDF (0 B) | |||
| Abstract:In this paper, the (3+1)-dimensional hyperbolic nonlinear Schr\"{o}dinger equation is studied, which describes the propagation dynamics of optical solitons in mono-mode fibers. Based on the bilinear forms of the equation,the bright one- and two-solitons solutions of the equation are obtained by using the Hirota method. At the same time, the properties of soliton solutions are further analyzed by images. It can be observed that the amplitude and shape of the bright one soliton remain unchanged during propagation, and that the interaction between the bright two solitons is elastic. The influence of parameter change on soliton solutions is also explained. | |||
| TO cite this article:WANG Jing-Ying,JIANG Yan,TIAN Bo. Bright solitons for a (3+1)-dimensional hyperbolic nonlinear Schr\"{o}dinger equation[OL].[21 March 2024] http://en.paper.edu.cn/en_releasepaper/content/4762952 | |||
| 4. Second-order projection algorithm of Kelvin-Voigt model | |||
| GONG Xiao-Juan,CHEN Chuan-Jun | |||
| Mathematics 18 March 2024 | |||
| Show/Hide Abstract | Cite this paper︱Full-text: PDF (0 B) | |||
| Abstract:This paper considers a second-order projection scheme for solving the Kelvin-Voigt problem using the Crank-Nicolson scheme. The backward Euler scheme is employed for the time derivative term, while a semi-implicit scheme is used for the nonlinear term discretization. To enhance computational efficiency, a projection method is adopted to decouple velocity and pressure, thereby decomposing the considered model into two linear sub-problems, thereby simplifying the problem solution. The paper provides stability and convergence analysis of the numerical solution, demonstrating that the numerical scheme is unconditionally stable under certain conditions on the stabilization factor, and the errors of the velocity field in the L2 and H1 norms are second-order and first-order, respectively. Finally, the effectiveness of the numerical scheme is verified through numerical examples. | |||
| TO cite this article:GONG Xiao-Juan,CHEN Chuan-Jun. Second-order projection algorithm of Kelvin-Voigt model[OL].[18 March 2024] http://en.paper.edu.cn/en_releasepaper/content/4762481 | |||
| 5. Dynamics of a Predator-Prey Model with Fear Effect and Patch Structure | |||
| LAN Zi-Teng,ZHANG Yu-Wei,WEN Luo-Sheng,ZHANG Tian-Ran | |||
| Mathematics 16 March 2024 | |||
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| Abstract:Due to the fear to predation risk preys may decrease birth rate or flee high level of predators patch to prey-only patch at a cost of decreased resources. In this paper a predator-prey model with fear effect and patch structure is constructed to study how the fear and diffusion affect predator-prey dynamics. The stability of equilibria and existence of Hopf bifurcation are studied. The fear to predation risk can be modeled by two types of parameters: $k$, $a_{21}$ and $a_{12}$, where high level of fear leads to large $k$ and thus low level of prey's birth rate; high level of fear results in large prey's diffusive rate $a_{21}$ from predator-prey patch 1 to prey-only patch 2, and great hunger and bad ability of remembering fear in patch 1 cause large prey's diffusive rate $a_{12}$ from patch 2 to patch 1. Numerical simulations are as follows. (1) In some cases, large $k$ can stabilize the predator-prey system by excluding the existence of periodic solutions when $a_{21}$ is small. However, when $a_{21}$ is large the change of $k$ can not lead to periodic oscillations. In addition, when $a_{21}$ is larger, the predators will die out. Thus, the oscillation behavior or the persistence of predators may be overestimated if the diffusive behaviors $a_{21}$ is weakened or ignored. (2) Under some situations, the change of $a_{12}$ causes Hopf bifurcations twice. This implies that the oscillation behavior may be underestimated or overestimated if the diffusive behavior $a_{12}$ is weakened. %Numerical simulations show that high levels of fear (or low birth rate of preys) can stabilize the predator-prey system by excluding the existence of periodic solutions. However, high level of dispersal caused by fear from predator-prey patch to predator-free patch can stabilize the predator-prey system. On the contrary, high level of dispersal caused by starvation from predator-free patch to predator-prey patch can induce periodic oscillations. % These conclusions imply that the oscillation behavior may be underestimated or overestimated according to whether the fear effect to predation risk (or low birth rate of preys) or dispersal caused by starvation dominates if the dispersal is ignored. | |||
| TO cite this article:LAN Zi-Teng,ZHANG Yu-Wei,WEN Luo-Sheng, et al. Dynamics of a Predator-Prey Model with Fear Effect and Patch Structure[OL].[16 March 2024] http://en.paper.edu.cn/en_releasepaper/content/4762503 | |||
| 6. Dynamics and control of malaria transmission model with vaccination and patch structure | |||
| ZENG Si-Jia, ZHANG Tian-Ran, ZHANG Tian-Ran | |||
| Mathematics 15 March 2024 | |||
| Show/Hide Abstract | Cite this paper︱Full-text: PDF (0 B) | |||
| Abstract:Malaria is an infectious disease transmitted by mosquitoes, and this paper focuses on two different regions due to differences in prevention and control measures such as vaccination. When a movement of population and mosquitoes occurs between two patches, under what conditions will malaria eventually extinct or continue to spread. This article takes the basic regeneration number as the threshold parameter. When $\mathscr{R}_0< 1$ the disease will die out and when $\mathscr{R}_0> 1$ the disease will persist. In section 5, through numerical simulation, we found that rational distribution of vaccine number between two patches can minimize $\mathscr{R}_0$ and minimize the total number of infections when the number of vaccine is limited. The results show that the distribution of vaccine number is different from the conventional idea that the distribution is based on the patches population ratio. Due to the influence of population movement between patches, the optimal strategy for vaccine distribution needs to be based on the actual situation. | |||
| TO cite this article:ZENG Si-Jia, ZHANG Tian-Ran, ZHANG Tian-Ran. Dynamics and control of malaria transmission model with vaccination and patch structure[OL].[15 March 2024] http://en.paper.edu.cn/en_releasepaper/content/4762506 | |||
| 7. Normalized bound state solutions for mass supcritical fractional Schr\"{o}dinger equation with potential | |||
| BAO Xin,OU Zeng-Qi,LV Ying | |||
| Mathematics 06 March 2024 | |||
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| Abstract:In this paper, we study the following fractional Schr\"{o}dinger equation with prescribed mass\begin{equation*}\left\{\begin{aligned}&(-\Delta)^{s}u=\lambda u+a(x)|u|^{p-2}u,\quad\text{in $\mathbb{R}^{N}$},\\&\int_{\mathbb{R}^{N}}|u|^{2}dx=c^{2},\quad u\in H^{s}(\mathbb{R}^{N}),\end{aligned}\right.\end{equation*}where $0<s<1$, $N>2s$, $2+\frac{4s}{N}<p<2_{s}^{*}:=\frac{2N}{N-2s}$, $c>0$, $\lambda\in \mathbb{R}$ and $a(x)\in C^{1}(\mathbb{R}^{N},\mathbb{R}^{+})$ is a potential function. By using a minimax principle, we prove the existence of bounded state solution for the above problem under various conditions on $a(x)$. | |||
| TO cite this article:BAO Xin,OU Zeng-Qi,LV Ying. Normalized bound state solutions for mass supcritical fractional Schr\"{o}dinger equation with potential[OL].[ 6 March 2024] http://en.paper.edu.cn/en_releasepaper/content/4762069 | |||
| 8. Nonlinear Conjugate Gradient Methods for Scalar and Vector Optimization | |||
| ZHANG Bo-Ya,CHEN Chun-Rong | |||
| Mathematics 27 February 2024 | |||
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| Abstract:The nonlinear conjugate gradient methods utilize gradient information to search for the optimal solutions, and speed up the convergence rate by selecting conjugate search directions, which are characterized by fast convergence, low storage requirements, and wide applicability, as a result, it serves as an effective numerical method for solving nonlinear unconstrained optimization problems. In recent years, the nonlinear conjugate gradient methods have also been applied in the field of vector optimization. The focus of this paper is to introduce the research status and convergence results of some modified nonlinear conjugate gradient methods for scalar optimization, as well as the nonlinear conjugate gradient methods for vector optimization. | |||
| TO cite this article:ZHANG Bo-Ya,CHEN Chun-Rong. Nonlinear Conjugate Gradient Methods for Scalar and Vector Optimization[OL].[27 February 2024] http://en.paper.edu.cn/en_releasepaper/content/4762269 | |||
| 9. Multiple positive solutions for Kirchhoff type equation involving concave-convex nonlinearities | |||
| Qian-Li Chen,Zeng-Qi Ou | |||
| Mathematics 05 February 2024 | |||
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| Abstract:In this paper, we study the existence of multiple positive solution for the following equation: \begin{equation} \label{eq0} \left\{ \begin{aligned} &-\left(a+b\int_{\mathbb{R}^{3}}|\nabla u|^{2}dx\right)\Delta u+V_{\lambda}(x)u=f(x)|u|^{q-2}u+g(x)|u|^{p-2}u ,&x\in \mathbb{R}^{3},\\ &u>0,u\in H^{1}(\mathbb{R}^{3}), \end{aligned} \right. \end{equation} where $a,b>0$ are constants, $1<q<2$, $4<p<6$ and $V_{\lambda}(x)=\lambda V^{+} (x)-V^{-}(x)$, $V^{\pm}=\max\{\pm V,0\}\ne 0$, $\lambda>0$. Assume that the functions $V, f, g$ satisfy the following conditions: $(V_{1})$\ $V^{+}\in C(\mathbb{R}^{3})$, $V^{-}\in L^{\frac{3}{2}}(\mathbb{R}^{3})$ with $\|V^{-} \|_{L^{\frac{3}{2}}}<aS$, where $S$ is the best Sobolev imbedding constant of $D^{1,2}(\mathbb{R}^{3})$ into $L^{6}(\mathbb{R}^{3})$; $(V_{2})$\ there exists $k>0$ such that $\{V^{+}<k\}=\{x\in \mathbb{R}^{3}: V^{+}(x)<k\}$ is nonempty and has finite measure; $(V_{3})$\ $\Omega:=$int$((V^{+} )^{-1}(0)$ is nonempty and has a smooth boundary with $\bar{\Omega} :=(V^{+})^{-1}(0)$, where $(V^{+})^{-1}(0):=\{x\in \mathbb{R}^{3}: V^{+}(x)=0\}$; $(f)$\ $f\in L^{\frac{6}{6-q}}(\mathbb{R}^{3})$ with the set $\{x\in \mathbb{R}^{3}: f(x)>0\}$ of positive measure; $(g_{1})$\ $g\in L^{\frac{6}{6-p}}(\mathbb{R}^3)$ with the set $\{x\in\mathbb{R}^{3}: g(x)>0\}$ of positive measure; $(g_{2})$ there exists a nonempty open set $\Omega_{g}\subset \Omega$ such that $g>0$ a.e. on $\Omega_{g}$. $(fg)$\ there is $\mu _{0}>1$ such that $$ \|f^{+}\|_{L^{\frac{6}{6-q}}}^{p-2}\|g^{+}\|_{L^{\frac{6}{6-p}}}^{2-q}< \left(\frac{\mu _{0}-1}{2d_6^{2}\mu_{0}(p-q)}\right)^{p-q}(2-q)^{2-q}(p-2)^{p-2}, $$ where $d_6$ is a embedding constant given in $\eqref{eq5}$ and $\|\cdot\|_{L^{s}}$ denotes the norm of Lebesgue space $L^{s}({\mathbb{R}^{3}})$. | |||
| TO cite this article:Qian-Li Chen,Zeng-Qi Ou. Multiple positive solutions for Kirchhoff type equation involving concave-convex nonlinearities[OL].[ 5 February 2024] http://en.paper.edu.cn/en_releasepaper/content/4762075 | |||
| 10. Poisson process Models of extreme volatility of Bitcoin prices | |||
| ZHANG Han,ZHANG Aidi,GAO Meng | |||
Mathematics 11 July 2023
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| Abstract:In recent years, digital currencies based on blockchain technology have received widespread attention from global investors and financial regulatory agencies, and the dramatic fluctuations of their price are the major conerns. Previous studies on asset price fluctuations mainly focused on traditional capital markets such as stocks and bonds, while there are less research on price fluctuations in the emerging digital currency market i.e. the Bitcoin. Bitcoin is a currency with intrinsic value that is difficult to quantify, produced entirely by computer computing power, and has no endorsement from any national government or financial institution as a financial asset. Therefore, as a financial asset, the Bitcoin prices often experience violent fluctuations due to numerous complex factors. In this study, two Poission process models, non-homogeneous Poisson process (NHPP) model and the fractional Poisson process (FPP) model, are used to fit the violent Bitcoin price volatility sequence. The NHPP model generalizes the intensity λ of the Poisson process to a function λ(t), reflecting the non-stationarity of violent Bitcoin price fluctuation events. The fractional Poisson process is also a generalization of the homogeneous Poisson process model, where the time interval distribution is extended from the exponential distribution to the Mittag-Leffler distribution. The fractional Poisson process reflects long-term memory effects. In this study, two Poisson point process models are applied to the event sequence of sharp fluctuations in the price of Bitcoin through estimating model parameters and graphical evaluation model fitting, and the ocurruing of the next is aslo predicted and analyzed. | |||
| TO cite this article:ZHANG Han,ZHANG Aidi,GAO Meng. Poisson process Models of extreme volatility of Bitcoin prices[OL].[11 July 2023] http://en.paper.edu.cn/en_releasepaper/content/4761142 | |||
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