共查询到20条相似文献,搜索用时 31 毫秒
1.
《Journal of Nonlinear Mathematical Physics》2013,20(4):479-483
Abstract In this paper, we get an asymptotic expansion of the q-gamma function Γq(x). Also, we deduced q-analogues of Gauss’ multiplication formula and Legendre’s relation which give the known results when q tends to 1. 相似文献
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R. S. Mendes L. C. Malacarne C. Anteneodo 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,57(3):357-363
We investigate the dynamics of football matches.
Our goal is to characterize statistically the temporal sequence of ball movements in this collective sport game, searching
for traits of complex behavior. Data were collected over a variety of matches in South American, European and World championships
throughout 2005 and 2006. We show that the statistics of ball touches presents power-law tails and can be described by q-gamma
distributions. To explain such behavior we propose a model that provides information on the characteristics of football dynamics.
Furthermore, we discuss the statistics of duration of out-of-play intervals, not directly related to the previous scenario. 相似文献
4.
Yi Qin Paul Douriaguine 《Journal of Quantitative Spectroscopy & Radiative Transfer》2004,84(2):159-168
In an accompanying paper, we develop the computational expressions for the higher order perturbation of the radiative transfer equation, and present some numerical results for typical cases. In this article, we discuss a number of issues regarding the implementation of the HOP computation: obtaining the Green's function, its expansion as a double series of Legendre polynomials, and obtaining the adjoint radiance of more general sources such as those for the fluxes at arbitrary altitudes. Examples of Green's function and its expansion coefficients are presented. 相似文献
5.
T. A. Ishkhanyan Y. Pashayan-Leroy M. R. Gevorgyan C. Leroy A. M. Ishkhanyan 《Journal of Contemporary Physics (Armenian Academy of Sciences)》2016,51(3):229-236
Considering the equations for some functions involving the first or the second derivatives of the biconfluent Heun function, we construct two expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta functions. The first series applies single Beta functions as expansion functions, while the second one involves a combination of two Beta functions. The coefficients of expansions obey four- and five-term recurrence relations, respectively. It is shown that the proposed technique is potent to produce series solutions in terms of other special functions. Two examples of such expansions in terms of the incomplete Gamma functions are presented. 相似文献
6.
YAN Zhen-Ya 《理论物理通讯》2002,38(10)
Recently, we obtained thirteen families of Jacobian elliptic function solutions of mKdV equation by usingour extended Jacobian elliptic function expansion method. In this note, the mKdV equation is investigated and anotherthree families of new doubly periodic solutions (Jacobian elliptic function solutions) are fbund again by using a newtransformation, which and our extended Jacobian elliptic function expansion method form a new method still called theextended Jacobian elliptic function expansion method. The new method can be more powertul to be applied to othernonlinear differential equations. 相似文献
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利用高阶窗函数结合连分式展开等技术研究并建立一种水平层状各向异性介质中电磁场并矢Green函数的快速有效算法. 首先借助于高阶窗函数将构成并矢Green函数的Sommerfeld积分转化成广义快速下降路径上积分,并给出高阶窗函数Hankel变换的一种新的更高阶幂级数展开式以及严格的Lommel函数表达式,以满足在全空间上高精度计算并矢Green函数的要求. 在此基础上,用Bessel函数的零点将积分路径划分成一系列小区间并通过改进的自适应Gauss求积公式确定各个小区间上的积分值,然后引入连分式展开法对各个区间上的积分值求和,从而使整个积分的收敛效率得到大大提高. 最后通过数值结果验证本方法的有效性.
关键词:
高阶窗函数
连分式展开
并矢Green函数
层状各向异性介质 相似文献
8.
利用边界层型函数,研究了ENSO事件随机动力学的某一模型,给出了这一问题的n阶渐 近展开式,将相关结论应用于特殊的ENSO事件,并得到了零阶渐近解,为分析ENSO事件的变 化状态提供了依据.
关键词:
ENSO事件
边界层型函数
渐近展开式 相似文献
9.
YAN Zhen-Ya 《理论物理通讯》2002,38(4):400-402
Recently, we obtained thirteen families of Jacobian elliptic function solutions of mKdV equation by using our extended Jacobian elliptic function expansion method. In this note, the mKdV equation is investigated and another three families of new doubly periodic solutions (Jacobian elliptic function solutions) are found again
by using a new transformation, which and our extended Jacobian elliptic
function expansion method form a new method still called the
extended Jacobian elliptic function expansion method. The new method can
be more powerful to be applied to other nonlinear differential equations. 相似文献
10.
Exact solutions of the atmospheric (2+1)-dimensional nonlinear incompressible non-hydrostatic Boussinesq (INHB) equations are researched by Combining function expansion and symmetry method. By function expansion, several expansion coefficient equations are derived. Symmetries and similarity solutions are researched in order to obtain exact solutions of the INHB equations. Three types of symmetry reduction equations and similarity solutions for the expansion coefficient equations are proposed. Non-traveling wave solutions for the INHB equations are obtained by symmetries of the expansion coefficient equations. Making traveling wave transformations on expansion coefficient equations, we demonstrate some traveling wave solutions of the INHB equations. The evolutions on the wind velocities, temperature perturbation and pressure perturbation are demonstrated by figures, which demonstrate the periodic evolutions with time and space. 相似文献
11.
In this paper, we have successfully extended the Jacobian elliptic
function expansion approach to nonlinear differential-difference
equations. The Hybrid lattice equation is chosen to illustrate this approach. As a consequence, twelve families of Jacobian elliptic function solutions with different parameters of the Hybrid lattice equation are obtained. When the modulus m→1 or 0, doubly-periodic solutions degenerate to solitonic solutions and trigonometric function solutions, respectively. 相似文献
12.
E. Tala-Tebue Z.I. Djoufack A. Djimeli-Tsajio A. Kenfack-Jiotsa 《Chinese Journal of Physics (Taipei)》2018,56(3):1232-1246
In order to investigate the nonlinear fractional Zoomeron equation, we propose three methods, namely the Jacobi elliptic function rational expansion method, the exponential rational function method and the new Jacobi elliptic function expansion method. Many kinds of solutions are obtained and the existence of these solutions is determined. For some parameters, these solutions can degenerate to the envelope shock wave solutions and the envelope solitary wave solutions. A comparison of our new results with the well-known results is made. The methods used here can also be applicable to other nonlinear partial differential equations. The fractional derivatives in this work are described in the modified Riemann–Liouville sense. 相似文献
13.
Wolfram Koepf Predrag M. Rajković Sladjana D. Marinković 《Journal of Nonlinear Mathematical Physics》2016,23(3):343-350
In this short communication, we want to pay attention to a few wrong formulas which are unfortunately cited and used in a dozen papers afterwards. We prove that the provided relations and asymptotic expansion about the q-gamma function are not correct. This is illustrated by numerous concrete counterexamples. The error came from the wrong assumption about the existence of a parameter which does not depend on anything. Here, we apply a similar procedure and derive a correct formula for the q-gamma function. 相似文献
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YAN Zhen-Ya 《理论物理通讯》2002,38(2):143-146
An extended Jacobian elliptic function
expansion method presented recently by us is applied to the mKdV equation such
that thirteen families of Jacobian elliptic function solutions including both new solutions and Fu's all results are obtained. When the modulus
m→1 or 0, we can find the corresponding six solitary wave solutions and six trigonometric function solutions. This shows that our method is more powerful to construct more exact Jacobian elliptic function solutions and can be applied to
other nonlinear differential
equations. 相似文献
16.
固体热胀冷缩实验一般都采用"金属环+金属球"进行演示.本文对该演示实验相关物理原理进行了深入研究,并利用固体热胀冷缩特性作为"激光电路系统的通断控制"开关,利用"光路的微小放大作用"显现固体热胀冷缩的效果,研制出一种新型固体热胀冷缩综合演示仪. 相似文献
17.
In this paper, an extended Jacobi elliptic function rational expansion method is proposed for constructing new forms of exact Jacobi elliptic function solutions to nonlinear partial differential equations by means of making a more general transformation. For illustration, we apply the method to the (2 1)-dimensional dispersive long wave equation and successfully obtain many new doubly periodic solutions, which degenerate as soliton solutions when the modulus m approximates 1. The method can also be applied to other nonlinear partial differential equations. 相似文献
18.
H. Flores-Llamas 《辐射效应与固体损伤》2013,168(1):48-60
The shape of the peaks in thermoluminescence (TL) dosimetry can be represented by the so-called temperature integral. In this article, we present a very efficient method, based on a continued fraction approach to the incomplete gamma function, intended to calculate the overall temperature integral which includes the frequency factor ∝ T a . The single glow-peak algorithm for linear and exponential heating rates is derived. In the first case, the method provides a good approximation with a maximum relative error of 1.1×10?5 within the 0.1≤E/kT≤90 range in the case of a=0. It is shown that, in general, the method is efficient, converges quickly and can be adopted in the numerical fitting of glow lines in order to obtain the parameters relevant to thermoluminescence (TL). The utility of this approach is exemplified by adjusting the standard LiF: Mg, Ti (TLD-100) using five and six TL peaks, determining that peak 6 is present and observable in the analysed spectrum. Finally, methods such as asymptotic expansion of the temperature integral by asymptotic series, convergent series, Lagrange continued fractions and a new obtained continued fraction approximations are compared to the method proposed here, in case of linear heating. 相似文献
19.
ZHU Jia-Min MA Zheng-Yi 《理论物理通讯》2006,46(3):393-396
In this paper, using the variable coefficient generalized projected Rieatti equation expansion method, we present explicit solutions of the (2+1)-dimensional variable coefficients Broer-Kaup (VCBK) equations. These solutions include Weierstrass function solution, solitary wave solutions, soliton-like solutions and trigonometric function solutions. Among these solutions, some are found for the first time. Because of the three or four arbitrary functions, rich localized excitations can be found. 相似文献
20.
ZHENG Ying ZHANG Yuan-Yuan ZHANG Hong-Qing 《理论物理通讯》2006,46(1):5-9
In this paper, an extended Jacobi elliptic function rational expansion method is proposed for constructing new forms of exact Jacobi elliptic function solutions to nonlinear partial differential equations by means of making a more general transformation. For illustration, we apply the method to the (2+1)-dimensional dispersive long wave equation and successfully obtain many new doubly periodic solutions, which degenerate as soliton solutions when the modulus m approximates 1. The method can also be applied to other nonlinear partial differential equations. 相似文献