• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.827-844
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• 2016

Here, in this paper, we aim at establishing some new unified integral and differential formulas associated with the $\bar{H}$-function. Each of these formula involves a product of the $\bar{H}$-function and Srivastava polynomials with essentially arbitrary coefficients and the results are obtained in terms of two variables $\bar{H}$-function. By assigning suitably special values to these coefficients, the main results can be reduced to the corresponding integral formulas involving the classical orthogonal polynomials including, for example, Hermite, Jacobi, Legendre and Laguerre polynomials. Furthermore, the $\bar{H}$-function occurring in each of main results can be reduced, under various special cases.

• Kyungpook Mathematical Journal
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• v.46 no.3
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• pp.307-313
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• 2006

In this paper, we first establish an interesting new finite integral whose integrand involves the product of a general class of polynomials introduced by Srivastava [13] and the generalized H-function ([9], [10]) having general argument. Next, we present five special cases of our main integral which are also quite general in nature and of interest by themselves. The first three integrals involve the product of $\bar{H}$-function with Jacobi polynomial, the product of two Jacobi polynomials and the product of two general binomial factors respectively. The fourth integral involves product of Jacobi polynomial and well known Fox's H-function and the last integral involves product of a Jacobi polynomial and 'g' function connected with a certain class of Feynman integral which may have practical applications.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.4
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• pp.537-543
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• 2015

In [9], the authors determine an infinite class of non-unimodal Gorenstein sequence, which includes the example $$\bar{h}_1\text{ = (1, 125, 95, 77, 71, 77, 95, 125, 1)}$$. They raise a question whether there is a Gorenstein algebra with Hilbert function $$\bar{h}_2\text{= (1, 125, 95, 77, 70, 77, 95, 125, 1)}$$, which has remained an open question. In this paper, we prove that there is no Gorenstein algebra with Hilbert function $\bar{h}_2$.

• Kyungpook Mathematical Journal
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• v.48 no.2
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• pp.165-171
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• 2008

The aim of this paper is to evaluate four finite integrals involving the product of Srivastava's polynomials, a generalized hypergeometric function and $\bar{H}$-function proposed by Inayat Hussian which contains a certain class of Feynman integrals. At the end, we give an application of our main findings by connecting them with the Riemann-Liouville type of fractional integral operator. The results obtained by us are basic in nature and are likely to find useful applications in several fields notably electric networks, probability theory and statistical mechanics.

• Kyungpook Mathematical Journal
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• v.43 no.4
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• pp.489-494
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• 2003

In this paper, we first establish an interesting theorem involving the $\bar{H}$-function introduced by Inayat-Hussain ([7], [8]). The convergence and existence condition, basic properties of this function were given by Buschman and Srivastava ([2]). Next, we obtain certain new integrals and an expansion formula by the application of our theorem. On account of the most general nature of the functions involved herein, our main findings are capable of yielding a large number of new, interesting and useful integrals, expansion formulae involving simple special functions and polynomials as their special cases. A known special case of our main theorem in also given ([11]).

• Korean Journal of Soil Science and Fertilizer
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• v.48 no.6
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• pp.712-723
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• 2015

This study was conducted to develop the SWCC estimation equation using scaling technique, and to investigate relative sensitivity of the SWCC according to the soil water tension, for the four kinds of soil texture such as Sand [S], Sandy Loam [SL], Loam [L] and Clay Loam [CL]. The SWCC estimation equation of scale factor [${\Theta}sc$] (Eq. 1) was developed based on the log function (Eq. 2) and exponential function (Eq. 3). ${\Theta}sc=[({\Theta}-{\Theta}r)/({\Theta}s-{\Theta}r)]$ (Eq. 1) ${\Theta}sc=-0.196ln(H)+0.4888$ (Eq. 2) ${\Theta}sc=0.3804(H)^{(-0.448)}$ (Eq. 3) where, ${\Theta}$: water content (g/g %), ${\Theta}s$: water content at 0.1bar, ${\Theta}r$: water content at 15bar, H: soil water tension (matric potential) (bar) Relative sensitivity of soil water content was decreased as increase soil water tension, those according to soil water tension were 0.952~0.620 compared to 0.1bar case. Relative sensitivity of scale factor was also decreased as increase soil water tension, those according to soil water tension were 0.890~0.577 compared to 0.2bar case.

• Kyungpook Mathematical Journal
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• v.18 no.2
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• pp.311-319
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• 1978

This paper deals with the evaluation of two definite integrals involving spheroidal wave function, H-function of two variables, and the generalized hypergeometric function. Also, an expansion formula for the product of generalized hypergeometric function and the H-function of two variables has been obtained. Since the H-function of two variables, spheroidal wave functions, and the generalized hypergeometric function may be transformed into a number of higher transcendental functions and polynomials, the results obtained in this paper include some known results as their particular cases. As an application of such results, a problem of heat conduction in a non-homogenous bar has been solved by using the generalized Legendre transform [9].

• Bulletin of the Korean Mathematical Society
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• v.55 no.3
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• pp.819-835
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• 2018

Let $f=h+{\bar{g}}$ be a normalized harmonic mapping in the unit disk $\mathbb{D}$. In this paper, we obtain the sharp radius of univalence, fully starlikeness and fully convexity of the harmonic linear differential operators $D^{\epsilon}{_f}=zf_z-{\epsilon}{\bar{z}}f_{\bar{z}}({\mid}{\epsilon}{\mid}=1)$ and $F_{\lambda}(z)=(1-{\lambda)f+{\lambda}D^{\epsilon}{_f}(0{\leq}{\lambda}{\leq}1)$ when the coefficients of h and g satisfy harmonic Bieberbach coefficients conjecture conditions. Similar problems are also solved when the coefficients of h and g satisfy the corresponding necessary conditions of the harmonic convex function $f=h+{\bar{g}}$. All results are sharp. Some of the results are motivated by the work of Kalaj et al. [8].

• East Asian mathematical journal
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• v.25 no.2
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• pp.221-227
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• 2009

In this paper, we introduce the generalized H$\ddot{o}$lder space with a majorant function and prove the H$\ddot{o}$lder regularity for solutions of the Cauchy-Riemann equation in the generalized Holder spaces on a bounded convex domain in $\mathbb{C}^2$.

• Proceedings of the KIEE Conference
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• 1996.07b
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• pp.757-759
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• 1996

This paper proposes an application of artificial neural networks to the bus-bar separation in a substation for radial network operation. For the effective bus-bar operation, the insecurity index of transmission line load is introduced. For the radial network operation. the constraints of bus-bar switch is formulated in the performance function with the insecurity index. The determination of bus-bar switching is to find the states of 0 or 1 in the circuit breakers. In this paper, it is tested that the bus-bar separation of binary optimization problem can be solved by Hopfield networks with adequate manipulations.