Potential of a Spheroid with Generalized Exponential Density Distribution

2015 ◽  
Vol 24 (4) ◽  
Author(s):  
B. P. Kondratyev ◽  
E. N. Kireeva
Keyword(s):  
Density Distribution ◽  
Numerical Integration ◽  
Hypergeometric Function ◽  
Computing Time ◽  
Analytical Form ◽  
Gauss Hypergeometric Function ◽  
Exponential Density ◽  
Time Required ◽  
Internal Potential

AbstractThe internal potential of an inhomogeneous layered spheroid with a small ellipticity and general exponential density distribution is derived in an analytical form. The results are presented in the form of standard Gauss hypergeometric function and validated numerically. The computing time when using this formula is noticeably smaller than the time required by numerical integration.

scholarly journals Closed-Form Expressions for Numerical Evaluation of Self-Impedance Terms Involved on Wire Antenna Analysis by the Method of Moments

Electronics ◽  
2021 ◽  
Vol 10 (11) ◽  
pp. 1316
Author(s):  
Carlos-Ivan Paez-Rueda ◽  
Arturo Fajardo ◽  
Manuel Pérez ◽  
Gabriel Perilla
Keyword(s):  
Numerical Integration ◽  
Method Of Moments ◽  
Computing Time ◽  
Basis Functions ◽  
Wire Antenna ◽  
Complex Geometries ◽  
Point Matching ◽  
Piecewise Constant ◽  
Matching Procedure ◽  
Time Required

This paper proposes new closed expressions of self-impedance using the Method of Moments with the Point Matching Procedure and piecewise constant and linear basis functions in different configurations, which allow saving computing time for the solution of wire antennas with complex geometries. The new expressions have complexity O(1) with well-defined theoretical bound errors. They were compared with an adaptive numerical integration. We obtain an accuracy between 7 and 16 digits depending on the chosen basis function and segmentation used. Besides, the computing time involved in the calculation of the self-impedance terms was evaluated and compared with the time required by the adaptative quadrature integration solution of the same problem. Expressions have a run-time bounded between 50 and 200 times faster than an adaptive numerical integration assuming full computation of all constant of the expressions.

INTEGRAL TRANSFORM OF K4-FUNCTION

2021 ◽  
Vol 21 (2) ◽  
pp. 429-436
Author(s):  
SEEMA KABRA ◽  
HARISH NAGAR
Keyword(s):  
Laplace Transform ◽  
Hypergeometric Function ◽  
Integral Transform ◽  
Integral Transforms ◽  
Gauss Hypergeometric Function ◽  
Wright Function ◽  
Generalized Wright Function ◽  
Special Cases ◽  
Euler Transform

In this present work we derived integral transforms such as Euler transform, Laplace transform, and Whittaker transform of K4-function. The results are given in generalized Wright function. Some special cases of the main result are also presented here with new and interesting results. We further extended integral transforms derived here in terms of Gauss Hypergeometric function.

Analytic expressions for annuities based on Makeham–Beard mortality laws

2020 ◽  
pp. 1-13
Author(s):  
David C. Bowie
Keyword(s):  
Hypergeometric Function ◽  
Mortality Rates ◽  
Gauss Hypergeometric Function ◽  
Mortality Data ◽  
Exponential Increase ◽  
Analytic Expressions ◽  
Life Annuities ◽  
Appell Function

Abstract This note derives analytic expressions for annuities based on a class of parametric mortality “laws” (the so-called Makeham–Beard family) that includes a logistic form that models a decelerating increase in mortality rates at the higher ages. Such models have been shown to provide a better fit to pensioner and annuitant mortality data than those that include an exponential increase. The expressions derived for evaluating single life and joint life annuities for the Makeham–Beard family of mortality laws use the Gauss hypergeometric function and Appell function of the first kind, respectively.

scholarly journals On Fractional Integral Inequalities Involving Hypergeometric Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
D. Baleanu ◽  
S. D. Purohit ◽  
Praveen Agarwal
Keyword(s):  
Hypergeometric Function ◽  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Gauss Hypergeometric Function ◽  
Liouville Type ◽  
Fractional Integral Operators ◽  
Special Cases ◽  
Chebyshev Functional

Here we aim at establishing certain new fractional integral inequalities involving the Gauss hypergeometric function for synchronous functions which are related to the Chebyshev functional. Several special cases as fractional integral inequalities involving Saigo, Erdélyi-Kober, and Riemann-Liouville type fractional integral operators are presented in the concluding section. Further, we also consider their relevance with other related known results.

scholarly journals On weighted inequalities for certain fractional integral operators

2006 ◽  
Vol 2006 ◽  
pp. 1-7
Author(s):  
R. K. Raina
Keyword(s):  
Hypergeometric Function ◽  
Fractional Integral ◽  
Integral Operators ◽  
Gauss Hypergeometric Function ◽  
Weighted Inequalities ◽  
Fractional Integral Operators

This paper considers the modified fractional integral operators involving the Gauss hypergeometric function and obtains weighted inequalities for these operators. Multidimensional fractional integral operators involving the H-function are also introduced.

SnBversion 2.2: an example of crystallographic multiprocessing

2002 ◽  
Vol 35 (3) ◽  
pp. 374-376 ◽  
Author(s):  
Jason Rappleye ◽  
Martins Innus ◽  
Charles M. Weeks ◽  
Russ Miller
Keyword(s):  
Shared Memory ◽  
Distributed Memory ◽  
Computing Time ◽  
Direct Methods ◽  
Fixed Number ◽  
Linear Speedup ◽  
Beowulf Clusters ◽  
Shared Memory Multiprocessor ◽  
Computing Platforms ◽  
Time Required

The computer programSnBimplements a direct-methods algorithm, known asShake-and-Bake, which optimizes trial structures consisting of randomly positioned atoms. Although largeShake-and-Bakeapplications require significant amounts of computing time, the algorithm can be easily implemented in parallel in order to decrease the real time required to achieve a solution. By using a master–worker model,SnBversion 2.2 is amenable to all of the prevalent modern parallel-computing platforms, including (i) shared-memory multiprocessor machines, such as the SGI Origin2000, (ii) distributed-memory multiprocessor machines, such as the IBM SP, and (iii) collections of workstations, including Beowulf clusters. A linear speedup in the processing of a fixed number of trial structures can be obtained on each of these platforms.

scholarly journals FRACS: modelling of the dust disc of the B[e] CPD-57° 2874 from VLTI/MIDI data

2010 ◽  
Vol 6 (S272) ◽  
pp. 382-383
Author(s):  
Philippe Bendjoya ◽  
Armando Domiciano de Souza ◽  
Gilles Niccolini
Keyword(s):  
Computing Time ◽  
Mid Infrared ◽  
Fitting Procedure ◽  
Dust Temperature ◽  
Tracing Algorithm ◽  
Short Computing Time ◽  
Time Required ◽  
Best Fit ◽  
Physical Quantities ◽  
Automatic Fitting

AbstractThe physical interpretation of spectro-interferometric data is strongly model dependent. On one hand, models involving elaborate radiative transfer solvers are in general too time consuming to perform an automatic fitting procedure and derive astrophysical quantities and their related errors. On the other hand, using simple geometrical models does not give sufficient insights into the physics of the object. We developed a numerical tool optimised for mid-infrared (mid-IR) interferometry, the Fast Ray-tracing Algorithm for Circumstellar Structures (FRACS). Thanks to the short computing time required by FRACS, best-fit parameters and uncertainties for several physical quantities were obtained, such as inner dust radius, relative flux contribution of the central source and of the dusty CSE, dust temperature profile, disc inclination.

Sign in / Sign up

Export Citation Format

Share Document