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带扩散扰动项的风险模型 被引量:1
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作者 张鸿雁 郭凯 刘立成 《经济数学》 2002年第2期44-48,共5页
引入一个新的概念—标准索赔额 ,在文 [3]的基础上建立一种新的风险过程并研究其破产概率。
关键词 风险过程 标准索赔额 扩散扰动 破产概率
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多孔介质中的一类双扩散扰动模型的解的连续依赖性 被引量:3
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作者 石金诚 肖胜中 《应用数学和力学》 CSCD 北大核心 2020年第10期1092-1102,共11页
研究了定义在有界区域上的多孔介质中一类双扩散扰动模型解的结构稳定性.假设模型在区域的边界上满足非齐次Robin边界条件,利用能量分析的方法和微分不等式技术,首先得到了解的先验估计;然后在此基础上推出了关于解的微分不等式;通过积... 研究了定义在有界区域上的多孔介质中一类双扩散扰动模型解的结构稳定性.假设模型在区域的边界上满足非齐次Robin边界条件,利用能量分析的方法和微分不等式技术,首先得到了解的先验估计;然后在此基础上推出了关于解的微分不等式;通过积分该微分不等式,最后建立了解对Lewis数Le的连续依赖性结果.该结果表明,双扩散扰动模型用来描述多孔介质中流体的流动情况是精确的. 展开更多
关键词 扩散扰动方程组 连续依赖性 Rayleigh数 Lewis数
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带扩散扰动的复合泊松模型上的按比例分红策略
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作者 李旸 张春生 《天津师范大学学报(自然科学版)》 CAS 北大核心 2009年第2期5-9,共5页
考虑带扩散扰动的复合泊松模型上的按比例分红策略,运用复合泊松过程逼近布朗运动,得到了直至破产前所有分红的期望折现值V(x;b)所满足的微分积分方程组,当索赔是指数分布时,给出了V(x;b)的确切表达式.
关键词 复合泊松模型 扩散扰动 按比例分红 布朗运动 期望折现值
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一类双扩散扰动模型的解对边界系数的连续依赖性研究
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作者 石金诚 肖胜中 《中央民族大学学报(自然科学版)》 2020年第4期22-30,34,共10页
本文研究了多孔介质中的一类双扩散扰动模型的解的结构稳定性。首先我们推导出若干有用的先验估计,然后借助这些先验界推出了解的差所满足的微分不等式,最后通过求解该不等式得到了解对边界系数的连续依赖性结果。
关键词 扩散扰动方程组 结构稳定性 连续依赖性 Rayleigh系数 Lewis系数
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关于马氏切换的双扰动中立型跳扩散过程的注记
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作者 毛伟 刘海洋 +1 位作者 杨卫东 岳安琪 《江苏第二师范学院学报》 2016年第12期9-10,共2页
Lju D和Yang Y在文献[1]中证明了带有马尔科夫调制和泊松跳的双扰动中立型扩散过程解的存在唯一性.然而发现[1]中主要结果,定理3.1的条件(H2)和证明都是错误的.我们主要改正并证明[1]中相关结果.
关键词 扰动中立型扩散过程 马尔科夫调制 泊松跳
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扰动扩散流动分析法测定土壤氮、磷技术研究 被引量:2
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作者 李灿 李振峰 +4 位作者 马刘正 张伟 李晓冬 VIJAYA Raghavan 胡建东 《农业环境科学学报》 CAS CSCD 北大核心 2022年第8期1846-1854,共9页
随着国家对农业面源氮、磷污染防治力度的加大,土壤氮、磷测定技术迫切需要改善。本研究在对常规的扩散对流(Dispersion convection)和强迫对流(Forced convection)流动分析方法基础上,提出了扰动扩散(Perturbation diffusion)流动分析... 随着国家对农业面源氮、磷污染防治力度的加大,土壤氮、磷测定技术迫切需要改善。本研究在对常规的扩散对流(Dispersion convection)和强迫对流(Forced convection)流动分析方法基础上,提出了扰动扩散(Perturbation diffusion)流动分析方法,以实现土壤氮、磷全自动化快速测定与分析。扰动扩散流动分析方法是将样品和试剂定量化后集中在化学反应腔中进行反应,然后程序控制蠕动泵对化学反应腔中反应物进行反复扰动,待化学反应完全稳定后流入光电探测单元完成土壤氮、磷含量测定。采用取自湖北潜江的土壤样品对扰动扩散流动分析方法进行了系统验证,实验结果表明,本研究提出的方法与常规紫外可见分光光度法对氮、磷测定相比,基于硫酸钠和碳酸氢钠联合浸提的土壤铵态氮测量值相关系数为0.9155,基于氯化钙浸提的土壤铵态氮、硝态氮和水溶性磷测量值相关系数分别为0.9985、0.9901和0.9911。铵态氮、硝态氮和水溶性磷的检出限分别为0.0554、0.0203 mg·L^(-1)和0.0084 mg·L^(-1),相对标准偏差(RSD,n=7)分别为1.8%、4.8%和1.0%。 展开更多
关键词 土壤速效氮 土壤速效磷 扰动扩散 化学反应腔 吸光光谱 可调光程
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扰动扩散方程初值问题的近似对称约化 被引量:2
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作者 李吉娜 朱晓宁 程利芳 《物理学报》 SCIE EI CAS CSCD 北大核心 2013年第2期20-24,共5页
本文利用近似广义条件对称方法研究一类带有源项的非线性扩散方程的初值问题.给出所研究方程的分类并将偏微分方程的初值问题约化为常微分方程的初值问题,通过求解约化后的常微分方程组可得相对应偏微分方程初值问题的近似解.
关键词 扰动扩散方程 初值问题 近似广义条件对称
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扰动反应扩散型方程的近似对称约化
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作者 李吉娜 左苏丽 +1 位作者 石翠丽 郭得锋 《数学的实践与认识》 CSCD 北大核心 2012年第24期264-269,共6页
利用近似的广义条件对称方法研究扰动的反应扩散型方程的近似对称约化问题,得到所研究方程完全的分类并借助于近似广义条件对称将扰动的偏微分方程约化为扰动的常微分方程组.
关键词 扰动反应扩散型方程 近似对称约化 近似广义条件对称
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对国内破产理论研究中所用模型的一种分类
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作者 高合理 《滨州学院学报》 2011年第3期54-59,共6页
按照对经典风险模型修正的侧重点,把国内破产理论研究中使用的模型进行了分类,讨论了新模型构建的方向.
关键词 破产理论 利率 分红策略 扩散扰动 绝对破产
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A Parameter-Uniform Finite Difference Method for a Coupled System of Convection-Diffusion Two-Point Boundary Value Problems 被引量:3
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作者 Eugene O'Riordan Jeanne Stynes Martin Stynes 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2008年第2期176-197,共22页
A system of m (≥2) linear convection-diffusion two-point boundary value problems is examined,where the diffusion term in each equation is multiplied by a small parameterεand the equations are coupled through their c... A system of m (≥2) linear convection-diffusion two-point boundary value problems is examined,where the diffusion term in each equation is multiplied by a small parameterεand the equations are coupled through their convective and reactive terms via matrices B and A respectively.This system is in general singularly perturbed. Unlike the case of a single equation,it does not satisfy a conventional maximum princi- ple.Certain hypotheses are placed on the coupling matrices B and A that ensure exis- tence and uniqueness of a solution to the system and also permit boundary layers in the components of this solution at only one endpoint of the domain;these hypotheses can be regarded as a strong form of diagonal dominance of B.This solution is decomposed into a sum of regular and layer components.Bounds are established on these compo- nents and their derivatives to show explicitly their dependence on the small parameterε.Finally,numerical methods consisting of upwinding on piecewise-uniform Shishkin meshes are proved to yield numerical solutions that are essentially first-order conver- gent,uniformly inε,to the true solution in the discrete maximum norm.Numerical results on Shishkin meshes are presented to support these theoretical bounds. 展开更多
关键词 Singularly perturbed CONVECTION-DIFFUSION coupled system piecewise-uniform mesh
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A Finite Difference Scheme on a Priori Adapted Meshes for a Singularly Perturbed Parabolic Convection-Diffusion Equation 被引量:4
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作者 Grigory I.Shishkin 《Numerical Mathematics(Theory,Methods and Applications)》 SCIE 2008年第2期214-234,共21页
A boundary value problem is considered for a singularly perturbed parabolic convection-diffusion equation; we construct a finite difference scheme on α priori (sequentially) adapted meshes and study its convergence... A boundary value problem is considered for a singularly perturbed parabolic convection-diffusion equation; we construct a finite difference scheme on α priori (sequentially) adapted meshes and study its convergence. The scheme on α priori adapted meshes is constructed using a majorant function for the singular component of the discrete solution, which allows us to find α priori a subdomain where the computed solution requires a further improvement. This subdomain is defined by the perturbation parameter ε, the step-size of a uniform mesh in χ, and also by the required accuracy of the discrete solution and the prescribed number of refinement iterations K for improving the solution. To solve the discrete problems aimed at the improvement of the solution, we use uniform meshes on the subdomains. The error of the numerical solution depends weakly on the parameter ε. The scheme converges almost ε-uniformly, precisely, under the condition N^-1 = o (ε^v), where N denotes the number of nodes in the spatial mesh, and the value v = v(K) can be chosen arbitrarily small for suitable K. 展开更多
关键词 Singular perturbations convection-diffusion problem piecewise-uniform mesh α priori adapted mesh almost ε-uniform convergence
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PARAMETER-UNIFORM FINITE DIFFERENCE SCHEME FOR A SYSTEM OF COUPLED SINGULARLY PERTURBED CONVECTION-DIFFUSION EQUATIONS 被引量:5
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作者 CEN Zhongdi 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2005年第4期498-510,共13页
A coupled system of singularly perturbed convection-diffusion equations is considered. The leading term of each equation is multiplied by a small positive parameter, but these parameters may have different magnitudes.... A coupled system of singularly perturbed convection-diffusion equations is considered. The leading term of each equation is multiplied by a small positive parameter, but these parameters may have different magnitudes. The solutions to the system have boundary layers that overlap and interact. The structure of these layers is analyzed, and this leads to the construction of a piecewise-uniform mesh that is a variant of the usual Shishkin mesh. On this mesh an upwind difference scheme is proved to be almost first- order accurate, uniformly in both small parameters. We present the results of numerical experiments to confirm our theoretical results. 展开更多
关键词 CONVECTION-DIFFUSION singular perturbation solution decomposition Shishkinmesh upwind finite difference scheme.
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Stability of planar waves in reaction-diffusion system 被引量:1
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作者 LU GuangYing WANG MingXin 《Science China Mathematics》 SCIE 2011年第7期1403-1419,共17页
This paper is concerned with the asymptotic stability of planar waves in reaction-diffusion system on Rn, where n 2. Under initial perturbation that decays at space infinity, the perturbed solution converges to planar... This paper is concerned with the asymptotic stability of planar waves in reaction-diffusion system on Rn, where n 2. Under initial perturbation that decays at space infinity, the perturbed solution converges to planar waves as t →∞. The convergence is uniform in Rn. Moreover, the stability of planar waves in reaction-diffusion equations with nonlocal delays is also established by transforming the delayed equations into a non-delayed reaction-diffusion system. 展开更多
关键词 traveling wave fronts STABILITY sup-sub solution reaction-diffusion system
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Stability of the rarefaction wave for a two-fluid plasma model with diffusion 被引量:2
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作者 DUAN RenJun LIU ShuangQian +1 位作者 YIN HaiYan ZHU ChangJiang 《Science China Mathematics》 SCIE CSCD 2016年第1期67-84,共18页
We study the large-time asymptotics of solutions toward the weak rarefaction wave of the quasineutral Euler system for a two-fluid plasma model in the presence of diffusions of velocity and temperature under small per... We study the large-time asymptotics of solutions toward the weak rarefaction wave of the quasineutral Euler system for a two-fluid plasma model in the presence of diffusions of velocity and temperature under small perturbations of initial data and also under an extra assumption θ_i,+/θ_e,+=θ_i,-/θ_e,-≥m_i/2m_e,namely, the ratio of the thermal speeds of ions and electrons at both far fields is not less than one half. Meanwhile,we obtain the global existence of solutions based on energy method. 展开更多
关键词 two-fluid plasma model rarefaction wave STABILITY
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Approximate Derivative-Dependent Functional Variable Separation for the Generalized Diffusion Equations with Perturbation 被引量:1
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作者 张顺利 吉飞宇 屈长征 《Communications in Theoretical Physics》 SCIE CAS CSCD 2012年第8期175-181,共7页
As an extension to the derivative-dependent functional variable separation approach, the approximate derivative-dependent functional variable separation approach is proposed, and it is applied to study the generalized... As an extension to the derivative-dependent functional variable separation approach, the approximate derivative-dependent functional variable separation approach is proposed, and it is applied to study the generalized diffusion equations with perturbation. Complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is obtained. As a result, the corresponding approximate derivative-dependent functional separable solutions to some resulting perturbed equations are derived by way of examples. 展开更多
关键词 generalized diffusion equation approximate derivative-dependent functional separable solution approximate generalized conditional symmetry
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