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A Quantum Dynamics of Heisenberg Model of the Neutron Associated with Beta Decay 预览
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作者 Vu B. Ho 《现代物理(英文)》 2019年第9期1065-1082,共18页
In this work we re-examine a model of the nucleons that involve the weak interaction which was once considered by Heisenberg;that is a neutron may have the structure of a dwarf hydrogen-like atom. We formulate a quant... In this work we re-examine a model of the nucleons that involve the weak interaction which was once considered by Heisenberg;that is a neutron may have the structure of a dwarf hydrogen-like atom. We formulate a quantum dynamics for the Heisenberg model of the neutron associated with interaction that involves the beta decay in terms of a mixed Coulomb-Yukawa potential and the More General Exponential Screened Coulomb Potential (MGESCP), which has been studied and applied to various fields of physics. We show that all the components that form the MGESCP potential can be derived from a general system of linear first order partial differential equations similar to Dirac relativistic equation in quantum mechanics. There are many interesting features that emerge from the MGESCP potential, such as the MGESCP potential can be reduced to the potential that has been proposed to describe the interaction between the quarks for strong force in particle physics, and the energy spectrum of the bound states of the dwarf hydrogen-like atom is continuous with respect to distance. This result leads to an unexpected implication that a proton and an electron may also interact strongly at short distances. We also show that the Yukawa potential when restrained can generate and determine the mathematical structures of fundamental particles associated with the strong and weak fields. 展开更多
关键词 Quantum Dynamics Beta Decay Weak and Strong Interactions DIRAC EQUATIONS COULOMB POTENTIAL YUKAWA POTENTIAL MGESCP POTENTIAL Differential EQUATIONS
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Stability for Functional Differential Equations with Delay in Banach Spaces 预览
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作者 Anna Kisiolek Ireneusz Kubiaczyk Aneta Sikorska-Nowak 《理论数学进展(英文)》 2019年第4期337-346,共10页
In this paper, using Sadovskii’s fixed point theorem and properties of the measure of noncompactness, we obtain asymptotic stability results for solutions of nonlinear differential equation with variable delay. Resul... In this paper, using Sadovskii’s fixed point theorem and properties of the measure of noncompactness, we obtain asymptotic stability results for solutions of nonlinear differential equation with variable delay. Results presented in this paper extend some previous results due to Burton?[1], Becker and Burton?[2], Ardjouni and Djoudi [3], and Jin and Luo?[4]. 展开更多
关键词 Fixed Point Differential EQUATIONS BANACH Space STABILITY MEASURE of Noncompactness
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STUDY OF THE STABILITY BEHAVIOUR AND THE BOUNDEDNESS OF SOLUTIONS TO A CERTAIN THIRD-ORDER DIFFERENTIAL EQUATION WITH A RETARDED ARGUMENT
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作者 A.M.Mahmoud D.A.M.Bakhit 《应用数学年刊:英文版》 2019年第1期99-110,共12页
Lyapunov direct method is employed to investigate the asymptotic behaviour and the boundedness of solutions to a certain third-order differential equation with delay and some new results are obtained. Our results impr... Lyapunov direct method is employed to investigate the asymptotic behaviour and the boundedness of solutions to a certain third-order differential equation with delay and some new results are obtained. Our results improve and complement some earlier results. Two examples are given to illustrate the importance of the topic and the main results obtained. 展开更多
关键词 delay DIFFERENTIAL EQUATIONS asymptotic BEHAVIOUR stability THIRD-ORDER DIFFERENTIAL EQUATIONS Lyapunov functional
一类带有逐段常变量的二阶微分方程的概周期解 预览
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作者 姚慧丽 张悦娇 侯盛楠 《哈尔滨理工大学学报》 CAS 北大核心 2019年第3期143-148,共6页
基于微分方程的概周期解比周期解更具有一般性,本文将对一类带有逐段常变量的二阶微分方程的概周期解进行研究。根据这类方程的解在整数点的连续性,构造了一类非齐次差分方程。利用对应的齐次差分方程的特征根,并借助于相应的差分方程... 基于微分方程的概周期解比周期解更具有一般性,本文将对一类带有逐段常变量的二阶微分方程的概周期解进行研究。根据这类方程的解在整数点的连续性,构造了一类非齐次差分方程。利用对应的齐次差分方程的特征根,并借助于相应的差分方程的概周期序列解和概周期函数以及概周期序列的一些性质,探讨了这类方程的概周期解的存在性以及该类解的唯一性。 展开更多
关键词 概周期解 概周期序列解 微分方程 差分方程 逐段常变量
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Damped and Divergence Exact Solutions for the Duffing Equation Using Leaf Functions and Hyperbolic Leaf Functions 预览
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作者 Kazunori Shinohara 《工程与科学中的计算机建模(英文)》 2019年第3期599-647,共49页
According to the wave power rule,the second derivative of a functionχ(t)with respect to the variable t is equal to negative n times the functionχ(t)raised to the power of 2n−1.Solving the ordinary differential equat... According to the wave power rule,the second derivative of a functionχ(t)with respect to the variable t is equal to negative n times the functionχ(t)raised to the power of 2n−1.Solving the ordinary differential equations numerically results in waves appearing in the figures.The ordinary differential equation is very simple;however,waves,including the regular amplitude and period,are drawn in the figure.In this study,the function for obtaining the wave is called the leaf function.Based on the leaf function,the exact solutions for the undamped and unforced Duffing equations are presented.In the ordinary differential equation,in the positive region of the variableχ(t),the second derivative d^2χ(t)/dt^2 becomes negative.Therefore,in the case that the curves vary with the time under the conditionχ(t)>0,the gradient dχ(t)/d constantly decreases as time increases.That is,the tangential vector on the curve of the graph(with the abscissa and the ordinate χ(t)changes from the upper right direction to the lower right direction as time increases.On the other hand,in the negative region of the variableχ(t),the second derivative d^2χ(t)/dt^2 becomes positive.The gradient d χ(t)/d constantly increases as time decreases.That is,the tangent vector on the curve changes from the lower right direction to the upper right direction as time increases.Since the behavior occurring in the positive region of the variable χ(t)and the behavior occurring in the negative region of the variableχ(t)alternately occur in regular intervals,waves appear by these interactions.In this paper,I present seven types of damped and divergence exact solutions by combining trigonometric functions,hyperbolic functions,hyperbolic leaf functions,leaf functions,and exponential functions.In each type,I show the derivation method and numerical examples,as well as describe the features of the waveform. 展开更多
关键词 Leaf functions hyperbolic leaf functions lemniscate functions jacobi elliptic functions ordinary differential equations duffing equation nonlinear equations
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A Review on Stochastic Multi-symplectic Methods for Stochastic Maxwell Equations 预览
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作者 Liying Zhang Chuchu Chen +1 位作者 Jialin Hong Lihai Ji 《应用数学与计算数学学报(英文)》 2019年第3期467-501,共35页
Stochastic multi-symplectic methods are a class of numerical methods preserving the discrete stochastic multi-symplectic conservation law. These methods have the remarkable superiority to conventional numerical method... Stochastic multi-symplectic methods are a class of numerical methods preserving the discrete stochastic multi-symplectic conservation law. These methods have the remarkable superiority to conventional numerical methods when applied to stochastic Hamiltonian partial differential equations (PDEs), such as long-time behavior, geometric structure preserving, and physical properties preserving. Stochastic Maxwell equations driven by either additive noise or multiplicative noise are a system of stochastic Hamiltonian PDEs intrinsically, which play an important role in fields such as stochastic electromagnetism and statistical radiophysics. Thereby, the construction and the analysis of various numerical methods for stochastic Maxwell equations which inherit the stochastic multi-symplecticity, the evolution laws of energy and divergence of the original system are an important and promising subject. The first stochastic multi-symplectic method is designed and analyzed to stochastic Maxwell equations by Hong et al.(A stochastic multi-symplectic scheme for stochastic Maxwell equations with additive noise. J. Comput. Phys. 268:255-268, 2014). Subsequently, there have been developed various stochastic multi-symplectic methods to solve stochastic Maxwell equations. In this paper, we make a review on these stochastic multi-symplectic methods for solving stochastic Maxwell equations driven by a stochastic process. Meanwhile, the theoretical results of well-posedness and conservation laws of the stochastic Maxwell equations are included. 展开更多
关键词 STOCHASTIC MULTI-SYMPLECTIC METHODS STOCHASTIC HAMILTONIAN partial differential EQUATIONS STOCHASTIC Maxwell EQUATIONS Structure-preserving METHODS
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REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATION WITH JUMPS AND VISCOSITY SOLUTION OF SECOND ORDER INTEGRO-DIFFERENTIAL EQUATION WITHOUT MONOTONICITY CONDITION: CASE WITH THE MEASURE OF LEVY INFINITE 预览
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作者 Lamine SYLLA 《数学物理学报:B辑英文版》 SCIE CSCD 2019年第3期819-844,共26页
We consider the problem of viscosity solution of integro-partial differential equation( IPDE in short) with one obstacle via the solution of reflected backward stochastic dif ferential equations(RBSDE in short) with j... We consider the problem of viscosity solution of integro-partial differential equation( IPDE in short) with one obstacle via the solution of reflected backward stochastic dif ferential equations(RBSDE in short) with jumps. We show the existence and uniqueness of a continuous viscosity solution of equation with non local terms, if the generator is not monotonous and Levy's measure is infinite. 展开更多
关键词 Integro-partial DIFFERENTIAL equation reflected stochastic DIFFERENTIAL equations with JUMPS viscosity solution NON-LOCAL operator
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Reconstructed Elzaki Transform Method for Delay Differential Equations with Mamadu-Njoseh Polynomials 预览
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作者 E. J. Mamadu H. I. Ojarikre 《数学和系统科学:英文版》 2019年第2期41-45,共5页
One of the solution techniques used for ordinary differential equations, partial and integral equations is the Elzaki Transform. This paper is an extension of Mamadu and Njoseh [1] numerical procedure (Elzaki transfor... One of the solution techniques used for ordinary differential equations, partial and integral equations is the Elzaki Transform. This paper is an extension of Mamadu and Njoseh [1] numerical procedure (Elzaki transform method (ETM)) for computing delay differential equations (DDEs). Here, a reconstructed Elzaki transform method (RETM) is proposed for the solution of DDEs where Mamadu-Njoseh polynomials are applied as basis functions in the approximation of the analytic solution. Using this strategy, a numerical illustration as in Ref.[1] is provided to the RETM as a basis for comparison to guarantee accuracy and consistency of the method. All numerical computations were performed with MAPLE 18 software. 展开更多
关键词 Elzaki TRANSFORM method Mamadu-Njoseh POLYNOMIALS DELAY DIFFERENTIAL EQUATIONS
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带阻尼项的奇异二阶微分方程正周期解的存在性 预览
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作者 苗亮英 《兰州文理学院学报:自然科学版》 2019年第1期6-9,14共5页
研究了一类带阻尼项的二阶线性算子的性质,获得了齐次线性方程格林函数的正性,最后运用Schauder不动点定理得到了奇异二阶微分方程正周期解的存在性.
关键词 正周期解 微分方程 阻尼 存在性
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A New Spectral Method Using Nonstandard Singular Basis Functions for Time-Fractional Differential Equations 预览
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作者 Wenjie Liu Li-Lian Wang Shuhuang Xiang 《应用数学与计算数学学报(英文)》 2019年第2期207-230,共24页
In this paper,we introduce new non-polynomial basis functions for spectral approximation of time-fractional partial differential equations (PDEs). Different from many other approaches,the nonstandard singular basis fu... In this paper,we introduce new non-polynomial basis functions for spectral approximation of time-fractional partial differential equations (PDEs). Different from many other approaches,the nonstandard singular basis functions are defined from some generalised Birkhoff interpolation problems through explicit inversion of some prototypical fractional initial value problem (FIVP) with a smooth source term. As such,the singularity of the new basis can be tailored to that of the singular solutions to a class of time-fractional PDEs,leading to spectrally accurate approximation. It also provides the acceptable solution to more general singular problems. 展开更多
关键词 Fractional differential equations Generalised BIRKHOFF INTERPOLATION NONSTANDARD SINGULAR basis function
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微分方程和李群表示
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作者 黎景辉 《数学进展》 CSCD 北大核心 2019年第3期257-301,共45页
本文介绍微分方程和李群表示的关系,特别是p进理论的近期进展.我们以柏原正树的五角图形为实表示理论的参考架,然后用Berthelot的算术D模理论和Schneider-Stuhler的楼的层理论介绍关于此图的P进类比所引起由Emerton,Kisin,Patel,Huyghe,... 本文介绍微分方程和李群表示的关系,特别是p进理论的近期进展.我们以柏原正树的五角图形为实表示理论的参考架,然后用Berthelot的算术D模理论和Schneider-Stuhler的楼的层理论介绍关于此图的P进类比所引起由Emerton,Kisin,Patel,Huyghe,Schmidt,Strauch所做的一些工作. 展开更多
关键词 微分方程 李群 表示论 算术D模 旗簇
Interior gradient and Hessian estimates for the Dirichlet problem of semi-linear degenerate elliptic systems: A probabilistic approach
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作者 Jun Dai Shanjian Tang Bingjie Wu 《中国科学:数学英文版》 SCIE CSCD 2019年第10期1851-1886,共36页
In this paper, we give interior gradient and Hessian estimates for systems of semi-linear degenerate elliptic partial differential equations on bounded domains, using both tools of backward stochastic differential equ... In this paper, we give interior gradient and Hessian estimates for systems of semi-linear degenerate elliptic partial differential equations on bounded domains, using both tools of backward stochastic differential equations and quasi-derivatives. 展开更多
关键词 SEMI-LINEAR DEGENERATE ELLIPTIC systems quasi-derivatives BACKWARD stochastic differential equations DIRICHLET problems
Basic theory and stability analysis for neutral stochastic functional differential equations with pure jumps
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作者 Mengling LI Feiqi DENG Xuerong MAO 《中国科学:信息科学(英文版)》 SCIE EI CSCD 2019年第1期116-130,共15页
This paper investigates the existence and uniqueness of solutions to neutral stochastic functional differential equations with pure jumps(NSFDEwPJs).The boundedness and almost sure exponential stability are also consi... This paper investigates the existence and uniqueness of solutions to neutral stochastic functional differential equations with pure jumps(NSFDEwPJs).The boundedness and almost sure exponential stability are also considered.In general,the classical existence and uniqueness theorem of solutions can be obtained under a local Lipschitz condition and linear growth condition.However,there are many equations that do not obey the linear growth condition.Therefore,our first aim is to establish new theorems where the linear growth condition is no longer required whereas the upper bound for the diffusion operator will play a leading role.Moreover,the pth moment boundedness and almost sure exponential stability are also obtained under some loose conditions.Finally,we present two examples to illustrate the effectiveness of our results. 展开更多
关键词 NEUTRAL TERM stochastic functional differential equations PURE JUMPS existence and UNIQUENESS theorem stability analysis
HOLDER CONTINUITY FOR THE PARABOLIC ANDERSON MODEL WITH SPACE-TIME HOMOGENEOUS GAUSSIAN NOISE 预览
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作者 Raluca M BALAN Lluis Q UER-SARDANYONS 宋健 《数学物理学报:B辑英文版》 SCIE CSCD 2019年第3期717-730,共14页
In this article,we consider the Parabolic Anderson Model with constant initial condition,driven by a space-time homogeneous Gaussian noise,with general covariance function in time and spatial spectral measure satisfyi... In this article,we consider the Parabolic Anderson Model with constant initial condition,driven by a space-time homogeneous Gaussian noise,with general covariance function in time and spatial spectral measure satisfying Dalang's condition.First,we prove that the solution (in the Skorohod sense) exists and is continuous in Lp(Ω).Then,we show that the solution has a modification whose sample paths are H(o)lder continuous in space and time,under the minimal condition on the spatial spectral measure of the noise (which is the same as the condition encountered in the case of the white noise in time).This improves similar results which were obtained in [6,10] under more restrictive conditions,and with sub-optimal exponents for H(o)lder continuity. 展开更多
关键词 GAUSSIAN noise STOCHASTIC partial differential equations Malliavin CALCULUS
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THE APPROXIMATION SOLUTIONS FOR HIGHER DIMENSIONAL INTEGRO-DIFFERENTIAL EQUATIONS 预览
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作者 陈吕萍 《数学物理学报:B辑英文版》 SCIE CSCD 2019年第5期1309-1318,共10页
This work deals with approximation solutions to a type of integro-differential equations in several complex variables. It concerns the Cauchy formula on higher dimensional domains. In our study, we make use of multipl... This work deals with approximation solutions to a type of integro-differential equations in several complex variables. It concerns the Cauchy formula on higher dimensional domains. In our study, we make use of multiple power series expansions and an iterative computation method to solve a kind of integro-differential equation. We introduce a symmetrized topology product area which is called a bicylinder. We expand functions and derivatives of them to power series. Moreover we obtain unknown functions by comparing coefficients of the series on both sides of equations. We express the approximation solutions by a regular product of matrixes. 展开更多
关键词 integro-differential equations POLYNOMIAL approach CAUCHY FORMULA bicylinder
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EULER SCHEME FOR FRACTIONAL DELAY STOCHASTIC DIFFERENTIAL EQUATIONS BY ROUGH PATHS TECHNIQUES 预览
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作者 Johanna GARZON Samy TINDEL Soledad TORRES 《数学物理学报:B辑英文版》 SCIE CSCD 2019年第3期747-763,共17页
In this note, we study a discrete time approximation for the solution of a class of delayed stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H ∈(1/2,1). In order to prove ... In this note, we study a discrete time approximation for the solution of a class of delayed stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H ∈(1/2,1). In order to prove convergence, we use rough paths techniques. Theoretical bounds are established and numerical simulations are displayed. 展开更多
关键词 FRACTIONAL BROWNIAN motion stochastic differential equations ROUGH paths discrete time APPROXIMATION
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微分方程解次数的界 预览
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作者 李爱平 《宁夏师范学院学报》 2019年第1期12-17,共6页
针对微分方程解次数界的求解问题,提出了一种用于计算二维非退化多项式微分方程代数解的算法.算法首先基于Moulin Ollagnier证明,将指数写成具有非负整数系统的奇异叶面特征比的线性组合,获得度数为1和2的丢番图方程组,从而确定多项式1... 针对微分方程解次数界的求解问题,提出了一种用于计算二维非退化多项式微分方程代数解的算法.算法首先基于Moulin Ollagnier证明,将指数写成具有非负整数系统的奇异叶面特征比的线性组合,获得度数为1和2的丢番图方程组,从而确定多项式1形式的界.然后对算法基于的定理进行证明,最后利用实例进行验证,说明所提算法的有效性和可行性. 展开更多
关键词 微分方程 次数 有界
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常系数非齐次线性微分方程的特解探究 预览
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作者 吴亚敏 《黄冈师范学院学报》 2019年第3期25-31,共7页
本文针对求常系数非齐次线性微分方程的特解进行了探究,根据右端函数f(x)的三种不同的pm(x),e^λxpm(x),e^αx[pm1(x)cosβx+pm2(x)]类型,给出其伴随方程概念,都统一到第一种类型pm(x)上来,两种通过对m+1元线性方程组的求解,得到常系数... 本文针对求常系数非齐次线性微分方程的特解进行了探究,根据右端函数f(x)的三种不同的pm(x),e^λxpm(x),e^αx[pm1(x)cosβx+pm2(x)]类型,给出其伴随方程概念,都统一到第一种类型pm(x)上来,两种通过对m+1元线性方程组的求解,得到常系数非齐次线性微分方程的特解,关键思路是求伴随方程的解。还可以用来求某些不定积分,简化积分计算过程。 展开更多
关键词 微分方程 特征方程 伴随方程 线性方程组
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Backward Euler-Maruyama method applied to nonlinear hybrid stochastic differential equations with time-variable delay
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作者 Chengjian Zhang Ying Xie 《中国科学:数学英文版》 SCIE CSCD 2019年第3期597-616,共20页
In this paper, we consider strong convergence and almost sure exponential stability of the backward Euler-Maruyama method for nonlinear hybrid stochastic differential equations with time-variable delay. Under the loca... In this paper, we consider strong convergence and almost sure exponential stability of the backward Euler-Maruyama method for nonlinear hybrid stochastic differential equations with time-variable delay. Under the local Lipschitz condition and polynomial growth condition, it is proved that the backward Euler-Maruyama method is strongly convergent. Additionally, the moment estimates and almost sure exponential stability for the analytical solution are proved. Also, under the appropriate condition, we show that the numerical solutions for the backward Euler-Maruyama methods are almost surely exponentially stable. A numerical experiment is given to illustrate the computational effectiveness and the theoretical results of the method. 展开更多
关键词 NONLINEAR HYBRID stochastic differential equations time-variable delay BACKWARD Euler-Maruyama method strong convergence ALMOST surely exponential stability
Partial Differential Equations and Continuum Mechanics:a Collection of Papers Dedicated to Professor Philippe G. Ciarlet on the Occasion of His 80th Birthday
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作者 Cristinel MARDARE Tong YANG 《应用数学学报:英文版》 SCIE CSCD 2019年第1期1-2,共2页
Preface This Special Issue in'Acta Mathematicae Applicatae Sinica(English Series)'gathers peer reviewed papers dedicated to Professor Philippe G.Ciarlet on the occasion of his eightieth birthday.Written by fri... Preface This Special Issue in'Acta Mathematicae Applicatae Sinica(English Series)'gathers peer reviewed papers dedicated to Professor Philippe G.Ciarlet on the occasion of his eightieth birthday.Written by friends and colleagues from France and Hong Kong/China,they stand as a testimony of their admiration for an exceptional human being and mathematician. 展开更多
关键词 Partial Differential Equations CONTINUUM Mechanics
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