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31.
Francisco M. Fernández 《Applied mathematics and computation》2011,217(13):6433-6436
We show that a simple and straightforward rational approximation to the Thomas-Fermi equation provides the slope at origin with unprecedented accuracy and that Padé approximants of relatively low order are far more accurate than more elaborate approaches proposed recently by other authors. We consider both the Thomas-Fermi equation for isolated atoms and for atoms in strong magnetic fields. 相似文献
32.
A. Tagliani 《Applied mathematics and computation》2011,218(8):4423-4432
The purpose of this paper is the recovering of a probability density function with support [0, 1] from the knowledge of its sequence of moments, i.e. the classical Hausdorff moment problem. To avoid the well-known ill-conditioning, firstly the moment curve is calculated from the assigned sequence of moments; next the unknown density is approximated by Maximum Entropy (MaxEnt) technique selecting some proper points on the moment curve. Exploiting convergence in entropy, a simplified quick procedure is suggested to recover the approximate density. An application to Laplace Transform inversion is illustrated. 相似文献
33.
Ebrahim Asadi Ahmad R. Farrahi Shahriar J. Fariborz 《Theoretical and Applied Fracture Mechanics》2011,56(2):112-121
The solutions of axisymmetric Volterra type climb and glide edge dislocations are obtained in a layer by means of the Hankel transforms. Utilizing the same procedure, Green’s function solution is obtained for a layer under self-equilibration normal ring traction. The distributed dislocation technique is used to construct integral equations for a system of co-axial annular cracks where the layer is under axisymmetric normal loads. These equations are solved numerically to obtain dislocation density on the cracks surfaces. The results are employed to determine stress intensity factors for annular and penny-shaped cracks and the interaction between two co-axial penny-shaped cracks is studied. Moreover, the stress intensity factors of the interacting cracks are determined such that they can be further used in conjunction with strain energy density (SED) failure criterion to obtain the possible direction of crack initiation that may not be apparent under mixed mode conditions. 相似文献
34.
The velocity field and the adequate shear stress corresponding to the longitudinal flow of a fractional second grade fluid, between two infinite coaxial circular cylinders, are determined by applying the Laplace and finite Hankel transforms. Initially the fluid is at rest, and at time t = 0+, the inner cylinder suddenly begins to translate along the common axis with constant acceleration. The solutions that have been obtained are presented in terms of generalized G functions. Moreover, these solutions satisfy both the governing differential equations and all imposed initial and boundary conditions. The corresponding solutions for ordinary second grade and Newtonian fluids are obtained as limiting cases of the general solutions. Finally, some characteristics of the motion, as well as the influences of the material and fractional parameters on the fluid motion and a comparison between models, are underlined by graphical illustrations. 相似文献
35.
This paper studies the Hankel determinants generated by a discontinuous Gaussian weight with one and two jumps. It is an extension in a previous study, in which they studied the discontinuous Gaussian weight with a single jump. By using the ladder operator approach, we obtain a series of difference and differential equations to describe the Hankel determinant for the single jump case. These equations include the Chazy II equation, continuous and discrete Painlevé IV. In addition, we consider the large n behavior of the corresponding orthogonal polynomials and prove that they satisfy the biconfluent Heun equation. We also consider the jump at the edge under a double scaling, from which a Painlevé XXXIV appeared. Furthermore, we study the Gaussian weight with two jumps and show that a quantity related to the Hankel determinant satisfies a two variables' generalization of the Jimbo‐Miwa‐Okamoto σ‐form of the Painlevé IV. 相似文献
36.
Based on the three dimensional elastic theory, the state equation of the axisymmetric free vibration of transversely isotropic
circular plates is established. Taking the advantage of finite Hankel transform, two exact solutions are derived for two boundary
conditions, i. e. the rigid-slipping boundary and elastic simply supported boundary. Finally, numerical results are presented
and compared with those of FEM.
The project is supported by the National Natural Science Foundation of China and the Zhejiang Provincial Natural Science Foundation. 相似文献
37.
Jakob Jonsson 《Journal of Combinatorial Theory, Series A》2005,112(1):117-142
For n?3, let Ωn be the set of line segments between vertices in a convex n-gon. For j?1, a j-crossing is a set of j distinct and mutually intersecting line segments from Ωn such that all 2j endpoints are distinct. For k?1, let Δn,k be the simplicial complex of subsets of Ωn not containing any (k+1)-crossing. For example, Δn,1 has one maximal set for each triangulation of the n-gon. Dress, Koolen, and Moulton were able to prove that all maximal sets in Δn,k have the same number k(2n-2k-1) of line segments. We demonstrate that the number of such maximal sets is counted by a k×k determinant of Catalan numbers. By the work of Desainte-Catherine and Viennot, this determinant is known to count quite a few other objects including fans of non-crossing Dyck paths. We generalize our result to a larger class of simplicial complexes including some of the complexes appearing in the work of Herzog and Trung on determinantal ideals. 相似文献
38.
We investigate a generalized form of a partial differential equation governing the diffusion of heavy pollutants into the atmosphere. In earlier treatments of the equation, the vertical component of turbulent exchange coefficient was assumed to be linear. Our generalization takes into account the nonlinear case of this component. Furthermore, two general identities involving the confluent hypergeometric function of the second kind are derived in the course of solving the given PDE. 相似文献
39.
The Lanczos method and its variants can be used to solve efficiently the rational interpolation problem. In this paper we
present a suitable fast modification of a general look-ahead version of the Lanczos process in order to deal with polynomials
expressed in the Chebyshev orthogonal basis. The proposed approach is particularly suited for approximating analytic functions
by means of rational interpolation at certain nodes located on the boundary of an elliptical region of the complex plane.
In fact, in this case it overcomes some of the numerical difficulties which limited the applicability of the look-ahead Lanczos
process for determining the coefficients both of the numerators and of the denominators with respect to the standard power
basis.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
40.
A. Bultheel 《Journal of Computational and Applied Mathematics》1984,10(3):301-328
A set of formulas is given for the relations that exist between the first and last block now or column of the inverse of a block Hankel or Toeplitz matrix. This is related to making arbitrary steps in a matrix Padé table. 相似文献