共查询到20条相似文献,搜索用时 500 毫秒
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邹新堤 《数学物理学报(A辑)》1984,(1)
对解析特征函数的研究已有大量文献,从而显示了解析方法在概率统计中的意义和作用,但对解析分布函数的研究,长期以来所获结果并不多见,仅在近几年来才为一些数学工作者所重视,并获得了一些结果,本文利用解析的方法来讨论分布函数,得到了解析分布函数的条件和一些性质。 为了往后叙述的方便我们引进如下的定义。 相似文献
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本文分别针对一类扩散系数为非线性指数函数和幂函数的扩散方程,基于变分原理中的泛函极值理论分别提出了求解该方程Dirichlet边界和Neumann边界问题解析解的新方法,并证明了新方法是泛函问题极值解的充要性.以非饱和土壤水分运动问题为背景,给出了积水和恒通量条件下水平吸渗问题的解析解,并通过数值算例将解析解与数值解进行了比较分析,结果表明本文方法得到的解析解能够准确预测非饱和土壤水分水平吸渗问题的土壤含水量分布,是一种有效方法.因此本文方法为求解这一类非线性扩散方程提供了一种有效的新方法. 相似文献
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对泥沙反应扩散广义初边值问题,采用Laplace变换和复变函数中的Jordan引理,导出了一种解析解,它可作为Kwokming James Cheng的解析解形式的推广(对应于本文中r=0的解析解形式),并分析了利用解析解求解过程中的若干问题。 相似文献
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《数学的实践与认识》2016,(24)
定义和讨论了K-解析函数在典型域S~+={z:|z(k)|1}外的K-对称扩张函数,利用它把K-解析函数的Hilbert边值问题转化为Riemann边值问题,得到了K-解析函数类F(D(k))中Hilbert边值问题与Dirichlet边值问题的可解条件及其解的表达式.而解析函数和共轭解析函数都是K-解析函数的特例,所得结果,包含了解析函数和共轭解析函数中的相应结论. 相似文献
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Banach空间有界线性算子强连续双半群 总被引:3,自引:0,他引:3
许跟起 《纯粹数学与应用数学》1995,11(1):78-85
本文在Banach空间上研究单参数有界线性算子族-强连续双半群。 相似文献
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《Nonlinear Analysis: Real World Applications》2008,9(5):2302-2312
An epidemic model with standard incidence rate and treatment rate of infectious individuals is proposed to understand the effect of the capacity for treatment of infectives on the disease spread. It is assumed that treatment rate is proportional to the numbers of infectives below the capacity and is a constant when the number of infectives is greater than the capacity. It is proved that the existence and stability of equilibria for the model is not only related to the basic reproduction number but also the capacity for treatment of infectives. It is found that a backward bifurcation occurs if the capacity is small. It is also found that there exist bistable endemic equilibria if the capacity is low. 相似文献
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整环R称为ω-凝聚整环,是指R的每个有限型理想是有限表现型的.本文证明了ω-凝聚整环是v-凝聚整环,且若(RDTF,M)是Milnor方图,则在Ⅰ型情形,R是ω-凝聚整环当且仅当D和T都是ω-整环,且T_M是赋值环;对于Ⅱ-型情形,R是ω-凝聚整环当且仅当D是域,[F:D]<∞,M是R的有限型理想,T是ω-凝聚整环,且R_M是凝聚整环. 相似文献
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对于函数优化问题,传统蚁群算法存在着算法实现较难,求解速度慢,需要记忆功能,不容易与其他算法结合等问题,而已有二进制蚁群算法也存在着迭代次数过多,收敛速度慢等问题.借鉴二进制蚁群算法思想,将解空间直接二进制离散化求解,实验证明该算法在处理一元及多元函数优化方面均有较好的表现,通过对几个函数的测试(包括一元和多元),结果表明该改进算法具有较好的稳定性和收敛速度,算法性能良好. 相似文献
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A.M. Kovalev 《Journal of Applied Mathematics and Mechanics》2011,75(3):317-322
The stability of the zero solution of an autonomous non-linear system is considered. The problem of finding the variables in relation to which the solution is asymptotically stable if the Lyapunov function with a sign-definite derivative is known, is formulated and solved. The maximality of the set in relation to which the solution is asymptotically stable is established. The investigation is based on the method of auxiliary functions and clarifies the relation between the properties of invariance and the asymptotic stability of dynamical systems. The constructiveness of the results obtained is demonstrated by an example. 相似文献
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D.H Jacobson 《Journal of Mathematical Analysis and Applications》1974,47(1):153-161
It is known that the optimal controller for a linear dynamic system disturbed by additive, independently distributed in time, not necessarily Gaussian, noise is a linear function of the state variables if the performance criterion is the expected value of a quadratic form. This result is known to hold also when the noise is Gaussian and is multiplied by a linear function of the state and/or control variables.In this paper it is proved that the optimal controller for a discrete-time linear dynamic system with quadratic performance criterion is a linear function of the state variables when the additive random vector is a nonlinear function of the state and/or control variables and not necessarily Gaussian noise which is independently distributed in time, provided only that the mean value of the random vector is zero (there is no loss of generality in assuming this) and the covariance matrix of the random vector is a quadratic function of the state and/or control variables. The above-mentioned known results emerge as special cases and certain nonlinear other special cases are exhibited. 相似文献
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《Journal of Applied Mathematics and Mechanics》2003,67(1):67-72
The problem of internal waves excited by a point source in a two-layer atmosphere is investigated in a linear formulation. The lower layer is bounded by a horizontal surface and, the upper layer is unbounded. It is assumed that the vertical displacements and velocities of the particles vary continuously at the layer boundaries, and that the Brunt Väisälä frequency is constant in each layer but experiences discontinuities at the common boundary of the layers; the source is situated in the lower layer. The asymptotic behaviour of the perturbations in the lower layer at long times is investigated. The solution is found using integral transforms and is expressed in terms of double integrals of many-valued analytic functions. A transformation is proposed which enables the solution to be expressed as the sum of single integrals. The behaviour of these integrals at long times is found by the stationary-phase method. It is shown that a critical cone exists across which the asymptotic behaviour of the system undergoes a change. 相似文献
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An SIS epidemic model with a limited resource for treatment is introduced and analyzed. It is assumed that treatment rate is proportional to the number of infectives below the capacity and is a constant when the number of infectives is greater than the capacity. It is found that a backward bifurcation occurs if the capacity is small. It is also found that there exist bistable endemic equilibria if the capacity is low. 相似文献
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In this paper, a mathematical model describing the transmission dynamics of an infectious disease with an exposed (latent) period and waning vaccine-induced immunity is investigated. The basic reproduction number is found by applying the method of the next generation matrix. It is shown that the global dynamics of the model is completely determined by the basic reproduction number. By means of appropriate Lyapunov functionals and LaSalle’s invariance principle, it is proven that if the basic reproduction number is less than or equal to unity, the disease-free equilibrium is globally asymptotically stable and the disease fades out; and if the basic reproduction number is greater than unity, the endemic equilibrium is globally asymptotically stable and therefore the disease becomes endemic. 相似文献
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The purpose of the paper is to extend the principal eigenvalue and principal eigenfunction theory for time independent and periodic parabolic equations to random and general nonautonomous ones. In the random case, a notion of principal Lyapunov exponent serving as an analog of principal eigenvalue is introduced. It is shown that the principal Lyapunov exponent is deterministic and of simple multiplicity. It is also shown that there is a one-dimensional invariant random subbundle corresponding to the solutions that are globally defined and of the same sign, which serves as an analog of principal eigenfunction. In addition, monotonicity of the principal Lyapunov exponent with respect to the zero-order terms both in the equation and in the boundary condition is proved. When the second- and first-order terms are deterministic, it is proved that the principal Lyapunov exponent is greater than or equal to the principal eigenvalue of the associated time-averaged equation. In the general nonautonomous case, the concepts of principal spectrum, which serves as an analog of principal eigenvalue, and principal Lyapunov exponents are introduced. As is known, the principal spectrum is a compact interval. It is proved in the paper that the principal spectrum contains all the principal Lyapunov exponents. When the second and first-order terms are time independent, a lower estimate of the infimum of the principal spectrum is given in terms of an associated time-averaged equation. 相似文献