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991.
林甲富 《数学的实践与认识》1999,(3)
本文用初等的方法研究sum from n=1 to(1/n~(2m))(m∈N)的求和问题。这个问题最先由Euler[8]解决。文献[1][6]给出了另两种求解方法。特别地,对于m=1的情形,即sum from n=1 to ∞(1/n~2)=((π~2)/6),已有许多不同的证明方法,可见文献[2][3][4][5]以及那里的参考文献。本文的想法,主要受文献[5][6]的启发而来的。 相似文献
992.
任意振幅单摆周期近似公式 总被引:1,自引:1,他引:0
文中提出一个精度较高的单摆周期近似公式,在任意振幅范围内,其计算结果可代替椭圆积分表. 相似文献
993.
The multi-linear variable separation approach is reviewed in this article. The method has been recently established and successfully
solved a large number of nonlinear systems. One of the most exciting findings is that the basic multi-linear variable separation
solution can be expressed by a universal formula including two (1+1)-dimensional functions, and at least one is arbitrary
for integrable systems. Furthermore, the method has been extended in two different ways so as to enroll more low dimensional
functions in the solution.
相似文献
994.
Reverse scans in square wave voltammetry (SWV) leading to the regeneration of the substance initially present in solution are studied. Widths and peak potentials of waves in SWV performed with both negative and positive potential scans allow us to determine easily the kinetic parameters of a slow electrochemical reaction. The theoretical treatment is verified using the U(V)–U(VI) system in a carbonate medium, which has already been studied by Krulic, Fatouros and Chevalet [J. Electronal. Chem. 251 (1988) 151]. 相似文献
995.
A. V. Astashenok A. A. Zaitsev 《Computational Mathematics and Mathematical Physics》2008,48(4):688-691
The influence of cubic nonlinearity on the dispersion relation for long waves on a water surface is analyzed. In the long wavelength limit, it is shown that the dispersion relation is not affected by the cubic terms. The results are compared with the dispersion relation for stationary solutions to the Korteweg—de Vries equation. 相似文献
996.
In this preliminary paper we introduce a mathematical model based on an autocatalytic reaction scheme with termination, and general reaction orders. Rigorous stability analysis and numerical solutions are presented which illustrate that the problem can for certain parameter values admit a stable stationary pattern in the concentration of the autocatalyst and reactant. This pattern forms at the rear of a permanent form travelling wave or pulse solution. 相似文献
997.
Beric Skews 《Experiments in fluids》2005,39(5):875-884
Previous detailed studies of the interaction of a shock wave with a perforated sheet considered the impact of a shock wave
on a plate with regularly spaced slits giving area blockages of 60 and 67%, at various angles of incidence, and resulting
in both regular and Mach reflection. The current work extends this study to a much wider variety of plate geometries. Blockage
ratios of 20, 25, 33, 50, and 67 and inclinations of 45, 60, 75, and 90° to the shock wave were tested. Four different thicknesses
of plate were tested at the same frontal blockage in order to assess the effects of gap guidance. Tests were conducted at
two shock Mach numbers of 1.36 and 1.51 (inverse pressure ratios of 0.4 and 0.5). It is found that secondary reflected and
transmitted waves appear due to the complex interactions within the grid gaps, and that the vortex pattern which is generated
under the plate is also complex due to these interactions. The angle of the reflected shock, measured relative to the plate,
decreases with plate blockage and the angle of inflow to the plate reduces with increasing blockage. By analysing the flow
on the underside of the plate the pseudo-steady flow assumption is found to be a reasonable approximation. Both the pressure
difference and the stagnation pressure loss across the plate are evaluated. It is found that over the range tested the plate
thickness has a minimal effect. 相似文献
998.
999.
J. Banasiak 《Acta Appl Math》1997,49(2):199-228
The fact that a solution of a wave equation with strong damping can be approximated by a solution of an appropriate diffusion equation has been common knowledge to physicists and mathematicians for a few decades. In numerous branches of science one can find attempts to prove this results by various ad hoc methods. However, it seems to be difficult to trace a rigorous and exhaustive treatment of the subject. By using a recently developed asymptotic procedure, first applied in kinetic theory, we present a systematic approach to a wide spectrum of singularly perturbed hyperbolic problems and we also hope that our method will provide new insight into the field. 相似文献
1000.
The Lévy-Khintchine formula or, more generally, Courrège's theorem characterizes the infinitesimal generator of a Lévy process or a Feller process on Rd. For more general Markov processes, the formula that comes closest to such a characterization is the Beurling-Deny formula for symmetric Dirichlet forms. In this paper, we extend these celebrated structure results to include a general right process on a metrizable Lusin space, which is supposed to be associated with a semi-Dirichlet form. We start with decomposing a regular semi-Dirichlet form into the diffusion, jumping and killing parts. Then, we develop a local compactification and an integral representation for quasi-regular semi-Dirichlet forms. Finally, we extend the formulae of Lévy-Khintchine and Beurling-Deny in semi-Dirichlet forms setting through introducing a quasi-compatible metric. 相似文献