• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.575-591
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• 2023

Motivated by several generalizations of the Pochhammer symbol and their associated families of hypergeometric functions and hypergeometric polynomials, by choosing to use a very generalized Pochhammer symbol, we aim to introduce certain extensions of the generalized Lauricella function F⁽ⁿ⁾_A and the Humbert's confluent hypergeometric function Ψ⁽ⁿ⁾ of n variables with, as their respective particular cases, the second Appell hypergeometric function F₂ and the generalized Humbert's confluent hypergeometric functions Ψ₂ and investigate their several properties including, for example, various integral representations, finite summation formulas with an s-fold sum and integral representations involving the Laguerre polynomials, the incomplete gamma functions, and the Bessel and modified Bessel functions. Also, pertinent links between the major identities discussed in this article and different (existing or novel) findings are revealed.

• Journal of Microbiology and Biotechnology
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• v.4 no.4
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• pp.360-363
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• 1994

A colorimetric assay for $\gamma$-glutamyl transpeptidase ($\gamma$-CTP; E.C 2.3.2.2) employing 2, 4, 6-trinitrobenzene sulfonate (TNBS) to detect the amount of disappeared acceptor via transpeptidation, has been developed. Under the experimental conditions using L-$\gamma$-glutamyl ethyl ester and L-phenylalanine as $\gamma$-glutamyl donor and acceptor, respectively, it was found that the decreased absorbance of yellow color at 420 nm was strictly related to the amount of L-$\gamma$-glutamyl-L-phenylalanine (L-$\gamma$-Glu-L-Phe) formed, which was determined by DEAE-cellu-lose column chromatography. Concentrations of the enzyme and $\gamma$-glutamyl products were able to be determinedin the nanogram and nanomoles per milliliter range, respectively, with high precision and reliability. This novel assay system may therefore be a useful means for understanding of catalytic function of the $\gamma$-CTP spectrophotometrically without any usage of sophisticated instruments.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.287-304
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• 2017

Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [Integral Transforms Spec. Funct. 23 (2012), 659-683] by means of the incomplete Pochhammer symbols $({\lambda};{\kappa})_{\nu}$ and $[{\lambda};{\kappa}]_{\nu}$, we first introduce incomplete Fox-Wright function. We then define the families of incomplete extended Hurwitz-Lerch Zeta function. We then systematically investigate several interesting properties of these incomplete extended Hurwitz-Lerch Zeta function which include various integral representations, summation formula, fractional derivative formula. We also consider an application to probability distributions and some special cases of our main results.

• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.691-700
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• 1998

Simulation algorithms for one-sided and two-sided trun-cated gamma distributions are proposed. These algorithms suggest the optimal choice of derived functions. Some results of simulation are given. Finally an application with real data is presented.

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.365-374
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• 2013

Let $k=\mathbb{F}_q(T)$ be a rational function field over the finite field $\mathbb{F}_q$, where q is a power of an odd prime number, and $\mathbb{A}=\mathbb{F}_q[T]$. Let ${\gamma}$ be a generator of $\mathbb{F}^*_q$. Let $\mathcal{H}_n$ be the subset of $\mathbb{A}$ consisting of monic square-free polynomials of degree n. In this paper we obtain an asymptotic formula for the mean value of $L(1,{\chi}_{\gamma}{\small{D}})$ and calculate the average value of the ideal class number $h_{\gamma}\small{D}$ when the average is taken over $D{\in}\mathcal{H}_{2g+2}$.

• Proceedings of the KSMRM Conference
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• 2002.11a
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• pp.128-128
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• 2002

목적： Gamma-Variate Function을 이용하여 뇌 관류에 관련하는 새로운 재구성 영상 (CBV, CBF, MTT, TTP, BAT)을 산출할 수 있는 프로그램을 개발 및 평가 대상 및 방법： 뇌 관류와 관련한 정량적인 재구성 영상(CBV, CBF, MTT, TTP, BAT)을 얻기 위하여 Gamma-Variate Function을 이용한 Post-processing 프로그램을 개발하였다. 자기공명영상은 1.5T ＆ 3.0T Magnum (Medinus Co., Ltd.)을 사용하였으면, 개발된 프로그램 평가를 위해 스핀에코 -EPI 펄스시퀀스(TR 2000 ms, TE 80 ms, FOV 260 mm, matrix 92$\times$128)를 사용하여 관류강조영상을 획득하였다.

• Proceedings of the Ginseng society Conference
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• 2006.05a
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• pp.83-88
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• 2006

In this study we examined the potential for the synergistic augmentation of the activity of inflammatory mouse peritoneal macrophages by stimulation with RGAP combined with IFN-$\gamma$. The moderate augmentative effect induced by preincubation with RGAP was observed in the production of IL-1, IL-6 and NO but not TNF-$\alpha$. In addition, IFN-$\gamma$ had a low activating effect. Following preincubation with both RGAP A and IFN-$\gamma$, a marked enhancement of secretory activity and tumoricidal activity was noted in mouse peritoneal macrophages. Treatment of peritoneal macrophage with combination increased the generation of IL-1, IL-6, TNF-$\alpha$ and NO, whereas the production of reactive oxygen species were not altered. These results demonstrate the synergistic effects on macrophage function of RGAP in combination with IFN-$\gamma$ and suggest that the ability of IFN-$\gamma$ to prime macrophages to produce secretory molecules in response to RGAP may have implications for immunotherapy with this combination.

• JSTS:Journal of Semiconductor Technology and Science
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• v.10 no.4
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• pp.251-259
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• 2010

We proposed a tail function parameter extraction procedure for the establishment of a robust ion implantation database. We showed that, for the expression of ion implantation profiles, there are many local minimum values set for the third and fourth moment parameters of $\gamma$ and $\beta$ for the Pearson function that comprises the standard dual Pearson and tail functions. We proposed the use of a joined tail function as a mediate function to extract $\gamma$ and $\beta$, and demonstrated that this enables us to extract the parameters uniquely. Other parameters associated with channeling phenomena can also be simply and uniquely extracted by our procedure.

• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.19-35
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• 2018

Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [30] and the second Appell function [6], we introduce here the incomplete Lauricella functions ${\gamma}^{(n)}_A$ and ${\Gamma}^{(n)}_A$ of n variables. We then systematically investigate several properties of each of these incomplete Lauricella functions including, for example, their various integral representations, finite summation formulas, transformation and derivative formulas, and so on. We provide relevant connections of some of the special cases of the main results presented here with known identities. Several potential areas of application of the incomplete hypergeometric functions in one and more variables are also pointed out.

• International Journal of Reliability and Applications
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• v.16 no.2
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• pp.81-98
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• 2015

The Exponentiated Gamma (EG) distribution is one of the important families of distributions in lifetime tests. In this paper, a new generalized version of this distribution which is called kumaraswamy Exponentiated Gamma (KEG) distribution is introduced. A new distribution is more flexible and has some interesting properties. A comprehensive mathematical treatment of the KEG distribution is provided. We derive the $r^{th}$ moment and moment generating function of this distribution. Moreover, we discuss the maximum likelihood estimation of the distribution parameters. Finally, an application to real data sets is illustrated.