共查询到20条相似文献,搜索用时 860 毫秒
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2007年.作者翻译T.Needham所写的《可视的复分析》(Visual Complex Analysis.Oxford Univ.Press.2006)一书.以为这是一本很好的教本.值得许多同志花一点时间读一下.译后有一些感想.因此写了一篇较长的译后记.主要思想即认为数学基础课是通向数学主流的门户.译本将由人民邮电出版社出版.现在征得出版社的同意,将这篇译后记发表于此.在发表时又作了一点补充.补写的文字放在方括号内. 相似文献
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到复Grassmann流形的多重调和映照的构造 总被引:1,自引:0,他引:1
本文给出了一些到复Grassmann流形的多重调和映照的构造定理,从而推广了莫小欢,Burstall F. E.,Wood J. C.和 Udagawa S.的结果. 相似文献
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带球形空腔的广义热弹性无限大材料的弹性模量和传热系数与材料参考温度的相关性 总被引:2,自引:1,他引:1
利用具某一松弛时间的广义热弹性方程求解了带球形空腔的无限大材料问题.该材料的弹性模量和传热系数是可变的.空腔的内表面没有力作用,但有热冲击作用.利用Laplace变换求得直接逼近解.数值求解了Laplace逆变换.给出了温度、位移和应力的分布图. 相似文献
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非线性摄动电报方程解的渐近理论及应用 总被引:12,自引:1,他引:11
赖绍永 《数学物理学报(A辑)》1998,18(2):149-153
该文研究一类具初值问题的半线性电报方程解的渐近理论,在Sobolev空间中回答了VanHorssenW.T.与VanBurghA.H.P.[1]提出的问题. 相似文献
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The linearized stability analyses of two-dimension Burnett equations were studied in present paper for the first time. The characteristic stability equation of two-dimension original Burnett equation was first derived and the characteristic curve was achieved. The material derivatives in original Burnett equations are then replaced with the Euler and Navier-Stokes equations. The stabilities of these two alternative Burnett equations are then analyzed. The linearized stability analyses show that the two-dimension original Burnett and Euler-based Burnett equations are not stable while the Navier-Stokes-based Burnett equations are stable. The critical Knudsen number for the original Burnett and Euler-based Burnett equations are 0.074 and 0.353, respectively. These critical Knudsen number are smaller than those of corresponding one-dimension equations. The two-dimension Burnett equations are more unstable than one-dimension equations. 相似文献
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D. P. Babii S. K. Godunov V. T. Zhukov O. B. Feodoritova 《Computational Mathematics and Mathematical Physics》2007,47(3):427-441
Issues concerning difference approximations of overdetermined systems of hyperbolic equations are examined. The formulations of extended overdetermined systems are given for hydrodynamics equations, magnetohydrodynamics equations, Maxwell equations, and elasticity equations. Some approaches to the construction of difference schemes are discussed for these systems. 相似文献
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层状二维流动的基本方程式 总被引:1,自引:0,他引:1
在很多海洋、大气等二维流动问题中所用的动力学方程往往沿用推广后的河流水力学方程或"纳维-斯托克斯方程"其中把湍流阻力项写成这样的方程式和湍流阻力项用到实际问题上去,无疑是存在着极大的局限性,而将导致矛盾百出.本文则从雷诺方程出发,把所有的物理量沿深度加以平均,求出平均以后的物理量所满足的运动方程,连续方程和扩散方程. 相似文献
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This paper examines the properties of the homentropic Euler equations when the characteristics of the equations have been spatially averaged. The new equations are referred to as the characteristically averaged homentropic Euler (CAHE) equations. An existence and uniqueness proof for the modified equations is given. The speed of shocks for the CAHE equations are determined. The Riemann problem is examined and a general form of the solutions is presented. Finally, numerically simulations on the homentropic Euler and CAHE equations are conducted and the behaviors of the two sets of equations are compared. 相似文献
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S. Yu. Slavyanov 《Theoretical and Mathematical Physics》1999,119(1):393-406
A block diagram is suggested for classifying differential equations whose solutions are special functions of mathematical
physics. Three classes of these equations are identified: the hypergeometric, Heun, and Painlevé classes. The constituent
types of equations are listed for each class. The confluence processes that transform one type into another are described.
The interrelations between the equations belonging to different classes are indicated. For example, the Painlevé-class equations
are equations of classical motion for Hamiltonians corresponding to Heun-class equations, and linearizing the Painlevé-class
equations leads to hypergeometric-class equations. The “confluence principle” is stated, and an example of its application
is given.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 119, No. 1, pp. 3–19, April, 1999. 相似文献
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N. M. Borodachev 《Journal of Applied Mathematics and Mechanics》2001,65(6):1021-1024
Nine equations of compatibility of deformations are obtained in which, unlike the classical Saint-Venant compatibility equations, only first derivatives with respect to the coordinates occur. It is proved that, of these nine equations, only six are independent. It is shown that the classical compatibility equations can be obtained from these equations. 相似文献
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V.V. Rumyantsev 《Journal of Applied Mathematics and Mechanics》1996,60(6):899-909
It is shown that the generalized Poincaré and Chetayev equations, which represent the equations of motion of mechanical systems using a certain closed system of infinitesimal linear operators, are related to the fundamental equations of analytical dynamics. Equations are derived in quasi-coordinates for the case of redundant variables; it is shown that when an energy integral exists the operator X0 = ∂/∂t satisfies the Chetayev cyclic-displacement conditions. Using the energy integral the order of the system of equations of motion is reduced, and generalized Jacobi-Whittaker equations are derived from the Chetayev equations. It is shown that the Poincaré-Chetayev equations are equivalent to a number of equations of motion of non-holonomic systems, in particular, the Maggi, Volterra, Kane, and so on, equations. On the basis of these, and also of other previously obtained results, the Poincaré and Chetayev equations in redundant variables, applicable both to holonomic and non-holonomic systems, can be regarded as general equations of classical dynamics, equivalent to the well-known fundamental forms of the equations of motion, a number of which follow as special cases from the Poincaré and Chetayev equations. 相似文献
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D. S. Kats 《Differential Equations》2015,51(12):1589-1594
We study linear differential equations with holomorphic coefficients. We establish the reducibility of such equations to equations with degeneration in the principal symbol. For the case of cuspidal degeneration, we show that the solutions of such equations are resurgent whenever so are their right-hand sides. We also refine earlier-obtained asymptotics of solutions for some equations of this type. 相似文献
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A. V. Schmidt 《Computational Mathematics and Mathematical Physics》2007,47(2):249-261
Exact solutions to two-component systems of reaction-diffusion equations are sought by the method of linear determining equations (LDEs) generalizing the methods of the classical group analysis of differential equations. LDEs are constructed for a system of two second-order evolutionary equations. The results of solving the LDEs are presented for two-component systems of reaction-diffusion equations with polynomial nonlinearities in the diffusion coefficients. Examples of constructing noninvariant solutions are presented for the reaction-diffusion systems that possess invariant manifolds. 相似文献
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当具有n个自由度的系统加有P个冲击性的约束时,要求解系统的运动,一般都需要解含n+P个方程的方程组.本文提出以待定乘子法为基础,分别就取广义坐标和伪坐标的二种情况,从n个碰撞方程中消去未知的待定乘子,将碰撞方程简化为n-P个,它和P个冲击性约束方程一起组成了含n个方程的方程组,就能求解具有冲击性约束的碰撞问题,这比一般方法更为简便. 相似文献