• Honam Mathematical Journal
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• v.36 no.2
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• pp.357-385
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• 2014

Recently several authors have extended the Gamma function, Beta function, the hypergeometric function, and the confluent hypergeometric function by using their integral representations and provided many interesting properties of their extended functions. Here we aim at giving further extensions of the abovementioned extended functions and investigating various formulas for the further extended functions in a systematic manner. Moreover, our extension of the Beta function is shown to be applied to Statistics and also our extensions find some connections with other special functions and polynomials such as Laguerre polynomials, Macdonald and Whittaker functions.

• Honam Mathematical Journal
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• v.36 no.2
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• pp.345-355
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• 2014

The main objective of this paper is to obtain a formula containing eleven interesting results for the reducibility of Kamp$\acute{e}$ de F$\acute{e}$riet function. The results are derived with the help of two general results for the series $_2F_1(2)$ very recently presented by Kim et al. Well known Kummer's second theorem and its contiguous results proved earlier by Rathie and Nagar, and Kim et al. follow special cases of our main findings.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.865-874
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• 2017

In the theory of hypergeometric and generalized hypergeometric series, classical summation theorems have been found interesting applications in obtaining various series identities for ${\Pi}$, ${\Pi}^2$ and ${\frac{1}{\Pi}}$. The aim of this research paper is to provide twelve general formulas for ${\frac{1}{\Pi}}$. On specializing the parameters, a large number of very interesting series identities for ${\frac{1}{\Pi}}$ not previously appeared in the literature have been obtained. Also, several other results for multiples of ${\Pi}$, ${\Pi}^2$, ${\frac{1}{{\Pi}^2}}$, ${\frac{1}{{\Pi}^3}}$ and ${\frac{1}{\sqrt{\Pi}}}$ have been obtained. The results are established with the help of the extensions of classical Gauss's summation theorem available in the literature.

• Asian-Australasian Journal of Animal Sciences
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• v.19 no.8
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• pp.1071-1078
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• 2006

Three buffalo populations viz. Bhadawari, Tarai and local buffaloes of Kerala were genotyped using 24 heterologous polymorphic microsatellite loci. A total of 140 alleles were observed with an average observed heterozygosity of 0.63. All the loci were neutral and 18 out of the 24 loci were in Hardy Weinberg Equilibrium. The $F_{IS}$ values (estimate of inbreeding) for 16 loci in all the three populations were negative. This indicated lack of population structure in the three populations. The effective number of immigrants was 5.88 per generation between the Tarai and Bhadawari populations which was quite high suggesting substantial gene flow. The genetic distances revealed closeness between the Tarai and Bhadawari populations which was expected from geographical contiguity. The FST values were not significantly different from zero showing no population differentiation. The Correspondence Analysis based on the allelic frequency data clustered the majority of the Tarai and Bhadawari individuals as an admixture.

• Journal of Plant Biotechnology
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• v.6 no.3
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• pp.189-192
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• 2004

Adventitious multiple shoots were developed from leaf, petiole and internode explants of Geophila reniformis D. Don. on MS medium supplemented with various concentrations of $N^6$-benzylaminopurine (BAP) or Kinetin (KIN) alone or in combination with indole-3-acetic acid (IAA). Leaf showed maximum organogenetic potential, followed by petiole and internode. Murashige and Skoog (MS) medium supplemented with 22.22 $\mu{M}$ BAP and 4.57 $\mu{M}$ IAA induced maximum shoot buds from leaf explants. Internodal segments showed low potential of direct organogenesis. The regenerated shoots rooted the best in presence of 10.75 - 13.44 $\mu{M}$ $\alpha$-naphthalene acetic acid (NAA) along with 2.22 $\mu{M}$ BAP, and were successfully established in the field with a survival rate of 89.11%.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.439-447
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• 2015

Very recently the authors have obtained a very interesting reduction formula for the Srivastava's triple hypergeometric series $F^{(3)}$(x, y, z) by applying the so-called Beta integral method to the Henrici's triple product formula for the hypergeometric series. In this sequel, we also present three more interesting reduction formulas for the function $F^{(3)}$(x, y, z) by using the well known identities due to Bailey and Ramanujan. The results established here are simple, easily derived and (potentially) useful.

• Honam Mathematical Journal
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• v.37 no.3
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• pp.339-352
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• 2015

We aim at giving explicit expressions of $${\sum_{m,n=0}^{{\infty}}}{\frac{{\Delta}_{m+n}(-1)^nx^{m+n}}{({\rho})_m({\rho}+i)_nm!n!}$$, where i = 0, ${\pm}1$, ${\ldots}$, ${\pm}9$ and $\{{\Delta}_n\}$ is a bounded sequence of complex numbers. The main result is derived with the help of the generalized Kummer's summation theorem for the series $_2F_1$ obtained earlier by Choi. Further some special cases of the main result considered here are shown to include the results obtained earlier by Kim and Rathie and the identity due to Bailey.

• ALGAE
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• v.29 no.2
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• pp.121-126
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• 2014

Cephaleuros parasiticus and C. virescens were collected from Kerala and Tamil Nadu, India. Macroscopic and microscopic features were observed and their comparative features were discussed. The lesions of C. parasiticus occur on the upper and lower leaf surfaces although zoosporangia form only on the lower surface. The thalli grow subepidermally and intramatrically, causing necrosis of whole leaf tissue. On the other hand C. virescens thalli develop on the upper surface and zoosporangia form on the upper surface, the thalli grow subcuticularly, and only the host epidermal and palisade cells are necrosed. Syzygium aromaticum and Polyalthia longifolia are new host plants of C. parasiticus and C. virescens, respectively.

• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.439-446
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• 2015

The main objective of this paper is to establish certain explicit expressions for the Humbert functions ${\Phi}_2$(a, a + i ; c ; x, -x) and ${\Psi}_2$(a ; c, c + i ; x, -x) for i = 0, ${\pm}1$, ${\pm}2$, ..., ${\pm}5$. Several new and known summation formulas for ${\Phi}_2$ and ${\Psi}_2$ are considered as special cases of our main identities.

• Coupled systems mechanics
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• v.8 no.4
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• pp.289-298
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• 2019

Reinforced concrete can be considered as a heterogeneous material consisting of coarse aggregate, mortar mix and reinforcing bars. This paper presents a two-dimensional mesoscopic analysis of reinforced concrete beams using a simple two-phase mesoscopic model for concrete. The two phases of concrete, coarse aggregate and mortar mix are bonded together with reinforcement bars so that inter force transfer will occur through the material surfaces. Monte Carlo's method is used to generate the random aggregate structure using the constitutive model at mesoscale. The generated models have meshed such that there is no material discontinuity within the elements. The proposed model simulates the load-deflection behavior, crack pattern and ultimate load of reinforced concrete beams reasonably well.