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101.
A version of Orlicz-Pettis Theorem is established for multiplier convergent series and quasi-homogeneous operator. Applications to spaces of quasi-homogeneous operators are given. 相似文献
102.
We investigate the asymptotic behavior of the eigenvalues and the eigenfunctions of q‐Sturm‐Liouville eigenvalue problems. For this aim we study the asymptotic behavior of q‐trigonometric functions as well as fundamental sets of solutions of the associated second order q‐difference equation. As in classical Sturm‐Liouville theory, the eigenvalues behave like zeros of q‐trigonometric functions and the eigenfunctions behave like q‐trigonometric functions. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 相似文献
103.
We analyze a discretization method for solving nonlinear integral equations that contain multiple integrals. These equations include integral equations with a Volterra series, instead of a single integral term, on one side of the equation. We prove existence and uniqueness of solutions, and convergence and estimates of the order of convergence for the numerical methods of solution. 相似文献
104.
This paper deals with large amplitude oscillation of a nonlinear pendulum attached to a rotating structure. By coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials, the governing differential equation with sinusoidal nonlinearity can be reduced to form a cubic-quintic Duffing equation. The resulting Duffing type temporal problem is solved by an analytic iteration approach. Two approximate formulas for the frequency (period) and the periodic solution are established for small as well as large amplitudes of motion. Illustrative examples are selected and compared to those analytical and exact solutions to substantiate the accuracy and correctness of the approximate analytical approach. 相似文献
105.
In a recent paper Lal and Yadov [4] obtained a theorem on the degree of approximation for a function belonging to the Lipschitz class Lipα using the product of the Cesàro and Euler means of order one of its Fourier series. In this paper we extend this result to any regular Hausdorff matrix for the same class of functions. 相似文献
106.
Ramesh B. Kudenatti Vishwanath B. AwatiN.M. Bujurke 《Applied mathematics and computation》2011,218(6):2952-2959
Third order nonlinear ordinary differential equations, subject to appropriate boundary conditions arising in fluid dynamics, are solved using three different methods viz., the Dirichlet series, method of stretching of variables, and asymptotic function method. Similarity transformations are used to convert the governing partial differential equations into nonlinear ordinary differential equations. The numerical results obtained from the above methods for various problems are given in terms of skin friction. Our study revealed that the results obtained from these methods agree well with those of direct numerical simulation of ordinary differential equations. Also, these methods have advantages over pure numerical methods in obtaining derived quantities such as velocity profile accurately for various values of the parameters at a stretch. 相似文献
107.
A new mathematical model of thermoelectric MHD theory has been constructed in the context of a new consideration of heat conduction with fractional orders. This model is applied to Stokes’ first problem for a conducting fluid with heat sources. Laplace transforms and state-space techniques [1] will be used to obtain the general solution for any set of boundary conditions. According to the numerical results and its graphs, conclusion about the new theory has been constructed. Some comparisons have been shown in figures to estimate the effects of the fractional order parameters on all the studied fields. 相似文献
108.
本文研究了全平面上零级和有限级Dirichlet级数及随机Dirichlet级数的下级增长性.利用型函数,得到了其系数和增长性之间的关系,以及当随机变量序列{X_n(ω)}满足一定条件时,零级和有限级随机Dirichlet级数在全平面上所确定的随机整函数在每条水平直线上的下级增长性几乎必然与相应的随机Dirichlet级数的下级增长性相同. 相似文献
109.
110.
Values of new series sum(((2n-1)!ζ(2n))/(2n + 2k)!)α2n from n=1 to ∞,sum(((2n-1)!ζ(2n))/(2n+2k +1)!)β2n from n=1 to ∞ are given concerning ζ(2k + 1),where k is a positive integer,α can be taken as 1,1/2,1/3,2/3,1/4,3/4,1/6,5/6 and β can be taken as 1,1/2.Some previous results are included as special cases in the present paper and new series converges more rapidly than those exsiting results for α = 1/3,or α = 1/4,or α = 1/6. 相似文献