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31.
Christophe Arène Michael Naehrig Christophe Ritzenthaler 《Journal of Number Theory》2011,131(5):842-857
Text
This paper proposes new explicit formulas for the doubling and addition steps in Miller's algorithm to compute the Tate pairing on elliptic curves in Weierstrass and in Edwards form. For Edwards curves the formulas come from a new way of seeing the arithmetic. We state the first geometric interpretation of the group law on Edwards curves by presenting the functions which arise in addition and doubling. The Tate pairing on Edwards curves can be computed by using these functions in Miller's algorithm. Computing the sum of two points or the double of a point and the coefficients of the corresponding functions is faster with our formulas than with all previously proposed formulas for pairings on Edwards curves. They are even competitive with all published formulas for pairing computation on Weierstrass curves. We also improve the formulas for Tate pairing computation on Weierstrass curves in Jacobian coordinates. Finally, we present several examples of pairing-friendly Edwards curves.Video
For a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=nideQo-K9ME/. 相似文献32.
Korteweg-de Vries (KdV)-type equations can describe some physical phenomena in fluids, nonlinear optics, quantum mechanics, plasmas, etc. In this paper, with the aid of symbolic computation, the integrable sixth-order KdV equation is investigated. Darboux transformation (DT) with an arbitrary parameter is presented. Explicit solutions are derived with the DT. Relevant properties are graphically illustrated, which might be helpful to understand some physical processes in fluids, plasmas, optics and quantum mechanics. 相似文献
33.
Wei LiuQimin Zhang 《Applied mathematics and computation》2011,218(8):3973-3980
In general, most of stochastic age-structured system of three species do not have explicit solutions, thus numerical approximation schemes are invaluable tools for exploring their properties. The aim of this paper is to investigate the convergence of numerical approximation solution to the true solution for stochastic age-structured system of three species. 相似文献
34.
A procedure for the construction of high-order explicit parallel Runge-Kutta-Nyström (RKN) methods for solving second-order nonstiff initial value problems (IVPs) is analyzed. The analysis reveals that starting the procedure with a reference symmetric RKN method it is possible to construct high-order RKN schemes which can be implemented in parallel on a small number of processors. These schemes are defined by means of a convex combination of k disjoint si-stage explicit RKN methods which are constructed by connecting si steps of a reference explicit symmetric method. Based on the reference second-order Störmer-Verlet methods we derive a family of high-order explicit parallel schemes which can be implemented in variable-step codes without additional cost. The numerical experiments carried out show that the new parallel schemes are more efficient than some sequential and parallel codes proposed in the scientific literature for solving second-order nonstiff IVPs. 相似文献
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36.
The use of finite element and finite difference methods of spatial and temporal discretization for solving structural dynamics problems gives rise to purely numerical errors. Among the many numerical methods used to damp out the spurious oscillations occurring in the high frequency domain, it is proposed here to analyse and compare the well-known Bulk Viscosity method, which modifies the stresses calculations and a method recently presented by Tchamwa and Wielgosz, which is based on a modification of an explicit time integration algorithm. The efficiency of both methods is evaluated in a 2-D axisymmetric compressive test. 相似文献
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38.
《Wave Motion》2018
In this paper, the propagation of Rayleigh waves in orthotropic non-viscous fluid-saturated porous half-spaces with sealed surface-pores and with impervious surface is investigated. The main aim of the investigation is to derive explicit secular equations and based on them to examine the effect of the material parameters and the boundary conditions on the propagation of Rayleigh waves. By employing the method of polarization vector the explicit secular equations have been derived. These equations recover the ones corresponding to Rayleigh waves propagating in purely elastic half-spaces. It is shown from numerical examples that the Rayleigh wave velocity depends strongly on the porosity, the elastic constants, the anisotropy, the boundary conditions and it differs considerably from the one corresponding to purely elastic half-spaces. Remarkably, in the fluid saturated porous half-spaces, Rayleigh waves may travel with a larger velocity than that of the shear wave, a fact that is impossible for the purely elastic half-spaces. 相似文献
39.
Kenneth S. Berenhaut John D. Foley 《Journal of Mathematical Analysis and Applications》2006,322(2):1159-1167
This note employs path counting techniques to extend recent results on bounds for odd order linear recurrences to higher dimensions. The results imply optimal zero-free polydisks for multivariable power series with 0, 1 coefficients. Among the applications is a result that states that the optimal zero-free polydisk has radius approximately 1/(v+1), for large dimensions v. 相似文献
40.
考察一类具有磁场效应的非线性Schrodinger方程组的周期初值问题,构造了全离散的Fourier拟谱格式,利用有界延拓法,证明了其格式的收敛性与稳定性,并给出了误差估计及其算法分析,为对此模型的数值分析提供了理论基础和一个有效的算法.最后,通过数值例子,检验了理论结果的可信性. 相似文献