• Kyungpook Mathematical Journal
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• 제60권4호
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• pp.781-795
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• 2020

In this paper, we obtain an analytical solution for an unsolved definite integral RC (m, n) from a 1915 paper of Srinivasa Ramanujan. We obtain our solution using the hypergeometric approach and an infinite series decomposition identity. Also, we give some generalizations of Ramanujan's integral RC (m, n) defined in terms of the ordinary hypergeometric function 2F3 with suitable convergence conditions. Moreover as applications of our result we obtain nine new infinite summation formulas associated with the hypergeometric functions 0F1, 1F2 and 2F3.

• East Asian mathematical journal
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• 제18권1호
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• pp.111-125
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• 2002

Many different families of infinite series were recently observed to be summable in closed forms by means of certain operators of fractional calculus(that is, calculus of integrals and derivatives of any arbitrary real or complex order). In this sequel to some of these recent investigations, the authors present yet another instance of applications of certain fractional calculus operators. Alternative derivations without using these fractional calculus operators are shown to lead naturally a family of analogous infinite sums involving hypergeometric functions.

• Wind and Structures
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• 제14권4호
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• pp.337-357
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• 2011

The collection of wind speed time series by means of digital data loggers occurs in many domains, including civil engineering, environmental sciences and wind turbine technology. Since averaging intervals are often significantly larger than typical system time scales, the information lost has to be recovered in order to reconstruct the true dynamics of the system. In the present work we present a simple algorithm capable of generating a real-time wind speed time series from data logger records containing the average, maximum, and minimum values of the wind speed in a fixed interval, as well as the standard deviation. The signal is generated from a generalized random Fourier series. The spectrum can be matched to any desired theoretical or measured frequency distribution. Extreme values are specified through a postprocessing step based on the concept of constrained simulation. Applications of the algorithm to 10-min wind speed records logged at a test site at 60 m height above the ground show that the recorded 10-min values can be reproduced by the simulated time series to a high degree of accuracy.

• 대한수학회논문집
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• 제36권1호
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• pp.63-101
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• 2021

In this research paper, an attempt has been made to provide an interesting extension of the well-known and useful Kummer's second theorem. Several applications have also been given.

• 대한수학회지
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• 제48권5호
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• pp.913-926
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• 2011

The family of q-Laguerre polynomials $\{L_n^{(\alpha)}({\cdot};q)\}_{n=0}^{\infty}$ is usually defined for 0 < q < 1 and ${\alpha}$ > -1. We extend this family to a new one in which arbitrary complex values of the parameter ${\alpha}$ are allowed. These so-called generalized q-Laguerre polynomials fulfil the same three term recurrence relation as the original ones, but when the parameter ${\alpha}$ is a negative integer, no orthogonality property can be deduced from Favard's theorem. In this work we introduce non-standard inner products involving q-derivatives with respect to which the generalized q-Laguerre polynomials $\{L_n^{(-N)}({\cdot};q)\}_{n=0}^{\infty}$, for positive integers N, become orthogonal.

• Nonlinear Functional Analysis and Applications
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• 제26권2호
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• pp.381-392
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• 2021

During the last several decades, a great variety of fractional kinetic equations involving diverse special functions have been broadly and usefully employed in describing and solving several important problems of physics and astrophysics. In this paper, we aim to find solutions of a type of fractional kinetic equations associated with the (p, q)-extended 𝜏 -hypergeometric function and the (p, q)-extended 𝜏 -confluent hypergeometric function, by mainly using the Laplace transform. It is noted that the main employed techniques for this chosen type of fractional kinetic equations are Laplace transform, Sumudu transform, Laplace and Sumudu transforms, Laplace and Fourier transforms, P_𝛘-transform, and an alternative method.

• 한국지능시스템학회:학술대회논문집
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• 한국지능시스템학회 2008년도 춘계학술대회 학술발표회 논문집
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• pp.299-305
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• 2008

In a series of research papers, the authors have studied some of the most important models of a contemporary universities, such as: the research university, the entrepreneurial university and the digital university and construct their Generalized Net (GN) models. This paper is based on the case-studies of Sofia University, the Technical University of Munich and the University of Edinburgh. The main focus is to put the analysis of the processes of the functioning of a university which effectively integrates Information and Communication Technologies (ICT) in all university activities. A concrete example based on the process of course administration at University of Edinburgh is considered. This university is in a process of developing an integrated information system covering most of the university activities. The opportunity of using GNs as a tool for modeling such processes is analyzed as well.

• 대한수학회논문집
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• 제15권1호
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• pp.51-57
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• 2000

The aim of this research is to provide twenty five integrals involving hypergeometric function in the form of a single integral. Fifty two interesting integrals follow as special cases of our main findings. These results are obtained with the help of generalized Watson's theorem on the sum of a $_3$F$_2$ recently obtained by Lavoie, Grondin and Rathie. The integrals given in this paper are simple, interesting and easily established, and they may be useful.

• Structural Engineering and Mechanics
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• 제3권4호
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• pp.341-358
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• 1995

The results of a series of ten W-shaped test specimens subjected to monotonic, quasi-static cyclic loading and fatigue type of loading in the form of constant amplitude tests are presented. The objectives were to assess and compare the rotation capacity and energy absorption of monotonically and cyclically loaded beams, and for the latter specimens to document the deterioration in the form of low cycle fatigue due to local buckling. In addition, strength and energy dissipation deterioration and damage models have been developed for the steel beam section under consideration. Finally, a generalized model which uses plate slenderness values and lateral slenderness is proposed for predicting rate in strength deterioration per reversal and cumulated damage after a given number of reversals.

• Structural Engineering and Mechanics
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• 제87권5호
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• pp.475-485
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• 2023

The present study deals with wave propagation in a modified couple-stress generalized thermoelastic solid under the effect of gravity and magnetic field. The problem is solved by a refined microtemperatures multi-phase-lags thermoelastic theory. The Fourier series and Laplace transforms will be used to obtain the general solution for any set of boundary conditions. Some comparisons have been shown in figures to estimate the effects of the gravity field, the magnetic field, and different theories of thermoelasticity in the presence of the hall current effect on all the physical quantities. Some particular cases of special interest have been deduced from the present investigation.