共查询到20条相似文献,搜索用时 296 毫秒
1.
2.
用直接计算的方法对一类Hamilton系统的两个Abel积分比值的单调性进行讨论,指出该单词性条件可由两个判定函数直接确定. 相似文献
3.
用直接计算的方法对文献中给出的第三类函数的一种特殊形式给出其积分比值单调性的判别条件. 相似文献
4.
Monotonicity of the ratios of two Abelian integrals for Hamiltonian systems with parameters 下载免费PDF全文
We study the monotonicity of the ratios of two Abelian integrals $\oint_{\gamma_{i}(h)}ydx$ $\backslash$ $\oint_{\gamma_{0i}(h)}xydx$ over three period annuli $\{\gamma_i(h)\}$, for $i=1, 2, 3$, defined by a seventh-degree hyperelliptic Hamiltonian $H(x,y)=y^2+\Psi(x)$ with a parameter. The parameter makes the problem more challenging to analyze. To over the difficulty, we apply some criterion with the help of transformations, tools in computer algebra such as boundary polynomial theory to determine the monotonicity of the ratios. Our results establish the existence and uniqueness of limit cycle bifurcated from each period annulus. 相似文献
5.
6.
该文建立了Hersch-Pfluger偏差函数ψK(r)和第二类完全椭圆积分ε(r)之间的关系. 通过对完全椭圆积分及某些初等函数的组合的单调性和凹凸性的研究获得了完全椭圆积分的一些不等式, 并且藉此得到Hersch-Pfluger偏差函数ψK(r)的几个渐进精确的上界估计. 相似文献
7.
In this paper, the authors study monotonicity and convexity of the generalized elliptic integrals and certain combinations of these special functions, such as ma(r) and μa(r). Making use of these results, the authors obtain some sharp inequalities for the so-called Ramanujan's generalized modular functions. 相似文献
8.
We establish some monotonicity results and inequalities involving elliptic integrals of the first and the second kind.
Work sponsored by the Ministero dell’Università e della Ricerca Scientifica e Tecnologica of Italy. 相似文献
9.
FuzzyIntegralsofSet-valuedFunctionsZhangDeliandWangZixiao(Dept.ofMath.JilinProv,Inst.ofEducationChangchun,Jilin,130022,P.R.Ch... 相似文献
10.
第一积分中值函数 总被引:2,自引:2,他引:0
樊守芳 《数学的实践与认识》2007,37(15):189-193
通过上下确界,给出了"第一积分中值函数"的定义,对"第一积分中值函数"的分析性质进行了系统的讨论,证明了"第一积分中值函数"的单调性、可积性、连续性、可导性等分析性质. 相似文献
11.
In this paper, two identities involving a function defined by the complete elliptic integrals of the first and second kinds are proved. Some functional inequalities and elementary estimates for this function are also derived from the properties of monotonicity and convexity of this function. As applications, some functional inequalities and the growth of the exterior modulus of a rectangle are studied. 相似文献
12.
Modular equations occur in number theory, but it is less known that such equations also occur in the study of deformation
properties of quasiconformal mappings. The authors study two important plane quasiconformal distortion functions, obtaining
monotonicity and convexity properties, and finding sharp bounds for them. Applications are provided that relate to the quasiconformal
Schwarz Lemma and to Schottky’s Theorem. These results also yield new bounds for singular values of complete elliptic integrals.
相似文献
13.
Monotonicity of the ratio of two Abelian integrals for a class of symmetric hyperelliptic Hamiltonian systems 下载免费PDF全文
Rasool Kazemi 《Journal of Applied Analysis & Computation》2018,8(1):344-355
In this paper we study the monotonicity of the ratio of two hyperelliptic Abelian integrals $I_0(h)=\oint_{\Gamma_h}ydx$ and $I_1(h)=\oint_{\Gamma_h}xydx$ for which $\Gamma_h$ is a continuous family of periodic orbits of a Newtonian system with Hamiltonian function of the form $H(x,y)=\frac{1}{2}{y^2}\pm \Psi(x)$, where $\Psi$ is an arbitrary even function of degree six. 相似文献
14.
一个推广的二变量时滞积分不等式及其应用 总被引:1,自引:1,他引:0
建立了一类二变量的时滞积分不等式,不等式包含一个一重积分和两个二重积分,二重积分内包含两个不同的没有假设单调性的未知函数的复合函数.使用单调化技术,给出积分不等式中未知函数的估计.结果能对相关文献中考虑的积分不等式中未知函数进行估计.进一步,结果给出了一类积分-微分方程解的估计. 相似文献
15.
B.J. Stoyanov R.A. Farrell J.F. Bird 《Journal of Computational and Applied Mathematics》1994,50(1-3):533-543
Asymptotic expansions of certain finite and infinite integrals involving products of two Bessel functions of the first kind are obtained by using the generalized hypergeometric and Meijer functions. The Bessel functions involved are of arbitrary (generally different) orders, but of the same argument containing a parameter which tends to infinity. These types of integrals arise in various contexts, including wave scattering and crystallography, and are of general mathematical interest being related to the Riemann—Liouville and Hankel integrals. The results complete the asymptotic expansions derived previously by two different methods — a straightforward approach and the Mellin-transform technique. These asymptotic expansions supply practical algorithms for computing the integrals. The leading terms explicitly provide valuable analytical insight into the high-frequency behavior of the solutions to the wave-scattering problems. 相似文献
16.
Martin E. Muldoon 《Journal of Mathematical Analysis and Applications》2008,343(1):436-445
We reexamine and continue the work of J. Vosmansky [J. Vosmanský, Zeros of solutions of linear differential equations as continuous functions of the parameter k, in: J. Wiener, J.K. Hale (Eds.), Partial Differential Equations, Proceedings of Conference, Edinburg, TX, 1991, in: Pitman Res. Notes Math. Ser., vol. 273, 1992, pp. 253-257] on the concept of continuous ranking of zeros of certain special functions from the point of view of the transformation theory of second-order linear differential equations. This leads to results on higher monotonicity of such zeros with respect to the rank and to the evaluation of some definite integrals. The applications are to Airy, Bessel and Hermite functions. 相似文献
17.
Nikolaos Bournaveas 《偏微分方程通讯》2013,38(7-8):1167-1193
Abstract We show a method to eliminate a type of mixed asymptotics in certain free boundary problems, and give two examples of its application. It appears that these problems cannot be handled by the monotonicity formula of Alt et al. [Alt, H. W., Caffarelli, L. A., Friedman, A. (1984). Variational problems with two phases and their free boundaries. Trans. Am. Math. Soc. 282(2):431–461] or by the more recent monotonicity formula of Caffarelli et al. [Caffarelli, L. A., Jerison, D., Kenig, C. E. (2002). Some new monotonicity theorems with applications to free boundary problems. Ann. Math. (2) 155(2):369–404]. 相似文献
18.
G. D. Anderson T. Sugawa M. K. Vamanamurthy M. Vuorinen 《Mathematische Zeitschrift》2010,266(1):181-191
We describe, in terms of generalized elliptic integrals, the hyperbolic metric of the twice-punctured sphere with one conical
singularity of prescribed order. We also give several monotonicity properties of the metric and a couple of applications. 相似文献
19.
王晓瑾 《纯粹数学与应用数学》2016,32(3):318-323
通过对参数λ,μ的讨论,主要利用函数的单调性理论,已有对数完全单调函数的性质以及幂函数的积分表达式研究了函数Gλ,μ(x)及函数[Gλ,μ(x)]-1的对数完全单调性,并在此基础上得到了一定条件下函数Gλ,μ(x)及[Gλ,μ(x)]-1对数完全单调的充要条件. 相似文献
20.
Fanghua LIN 《数学年刊B辑(英文版)》2009,30(5):645-652
The author presents a simple approach to both regularity and singularity theorems for free boundaries in classical obstacle problems. This approach is based on the monotonicity of several variational integrals, the Federer-Almgren dimension reduction and stratification theorems, and some simple PDE arguments. 相似文献