• Journal of applied mathematics & informatics
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• v.36 no.1_2
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• pp.15-28
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• 2018

In this paper, we introduce a Stancu type generalization of genuine LupaŞ-Beta operators of integral type. We establish some moment estimates and the direct results in terms of classical modulus of continuity, Voronovskaja-type asymptotic theorem, weighted approximation, rate of convergence and pointwise estimates using the Lipschitz type maximal function. Lastly, we propose a king type modification of these operators to obtain better estimates.

• Kyungpook Mathematical Journal
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• v.53 no.3
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• pp.467-478
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• 2013

The purpose of the present paper is to establish some interesting results involving coefficient conditions, extreme points, distortion bounds and covering theorems for the classes $V_H({\beta})$ and $U_H({\beta})$. Further, various inclusion relations are also obtained for these classes. We also discuss a class preserving integral operator and show that these classes are closed under convolution and convex combinations.

• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.705-714
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• 2021

The Whittaker function and its diverse extensions have been actively investigated. Here we aim to introduce an extension of the Whittaker function by using the known extended confluent hypergeometric function 𝚽_p,v and investigate some of its formulas such as integral representations, a transformation formula, Mellin transform, and a differential formula. Some special cases of our results are also considered.

• Honam Mathematical Journal
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• v.26 no.1
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• pp.133-136
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• 2004

By elementry manipulation of series together with summations of Gauss and $Saalsch\ddot{u}tz$, Exton deduced a new two term relation for the hypergeometric function $_3F_2(1)$. The aim of this paper is to derive Exton's result from Thomae's formula, together with two known integral formulas and the Euler's transformation for $_2F_1$.

• Kyungpook Mathematical Journal
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• v.59 no.1
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• pp.125-134
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• 2019

Since the Mittag-Leffler function was introduced in 1903, a variety of extensions and generalizations with diverse applications have been presented and investigated. In this paper, we aim to introduce some presumably new and remarkably different extensions of the Mittag-Leffler function, and use these to present the pathway fractional integral formulas. We point out relevant connections of some particular cases of our main results with known results.

• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.929-967
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• 2016

Let p(t, x) be the fundamental solution to the problem $${\partial}^{\alpha}_tu=-(-{\Delta})^{\beta}u,\;{\alpha}{\in}(0,2),\;{\beta}{\in}(0,{\infty})$$. If ${\alpha},{\beta}{\in}(0,1)$, then the kernel p(t, x) becomes the transition density of a Levy process delayed by an inverse subordinator. In this paper we provide the asymptotic behaviors and sharp upper bounds of p(t, x) and its space and time fractional derivatives $$D^n_x(-{\Delta}_x)^{\gamma}D^{\sigma}_tI^{\delta}_tp(t,x),\;{\forall}n{\in}{\mathbb{Z}}_+,\;{\gamma}{\in}[0,{\beta}],\;{\sigma},{\delta}{\in}[0,{\infty})$$, where $D^n_x$ x is a partial derivative of order n with respect to x, $(-{\Delta}_x)^{\gamma}$ is a fractional Laplace operator and $D^{\sigma}_t$ and $I^{\delta}_t$ are Riemann-Liouville fractional derivative and integral respectively.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.385-393
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• 2003

Let Y(t) be a stochastic integral process represented by Brownian motion. We show that YHt (t) is continuous in t with probability one for Molder function Ht of exponent ${\beta}$ and finally we derive asymptotic self-similar process YM (t) which converges to Yw (t).

• Mycobiology
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• v.42 no.2
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• pp.167-173
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• 2014

A ${\beta}$-glucan synthase gene was isolated from the genomic DNA of polypore mushroom Sparassis crispa, which reportedly produces unusually high amount of soluble ${\beta}$-1,3-glucan (${\beta}$-glucan). Sequencing and subsequent open reading frame analysis of the isolated gene revealed that the gene (5,502 bp) consisted of 10 exons separated by nine introns. The predicted mRNA encoded a ${\beta}$-glucan synthase protein, consisting of 1,576 amino acid residues. Comparison of the predicted protein sequence with multiple fungal ${\beta}$-glucan synthases estimated that the isolated gene contained a complete N-terminus but was lacking approximately 70 amino acid residues in the C-terminus. Fungal ${\beta}$-glucan synthases are integral membrane proteins, containing the two catalytic and two transmembrane domains. The lacking C-terminal part of S. crispa ${\beta}$-glucan synthase was estimated to include catalytically insignificant transmembrane ${\alpha}$-helices and loops. Sequence analysis of 101 fungal ${\beta}$-glucan synthases, obtained from public databases, revealed that the ${\beta}$-glucan synthases with various fungal origins were categorized into corresponding fungal groups in the classification system. Interestingly, mushrooms belonging to the class Agaricomycetes were found to contain two distinct types (Type I and II) of ${\beta}$-glucan synthases with the type-specific sequence signatures in the loop regions. S. crispa ${\beta}$-glucan synthase in this study belonged to Type II family, meaning Type I ${\beta}$-glucan synthase is expected to be discovered in S. crispa. The high productivity of soluble ${\beta}$-glucan was not explained but detailed biochemical studies on the catalytic loop domain in the S. crispa ${\beta}$-glucan synthase will provide better explanations.

• Journal of the Korean Mathematical Society
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• v.53 no.2
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• pp.363-379
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• 2016

Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [Integral Transforms Spec. Funct. 23 (2012), 659-683] and the second Appell function [Appl. Math. Comput. 219 (2013), 8332-8337] by means of the incomplete Pochhammer symbols $({\lambda};{\kappa})_{\nu}$ and $[{\lambda};{\kappa}]_{\nu}$, we introduce here the family of the incomplete generalized ${\tau}$-hypergeometric functions $2{\gamma}_1^{\tau}(z)$ and $2{\Gamma}_1^{\tau}(z)$. The main object of this paper is to study these extensions and investigate their several properties including, for example, their integral representations, derivative formulas, Euler-Beta transform and associated with certain fractional calculus operators. Further, we introduce and investigate the family of incomplete second ${\tau}$-Appell hypergeometric functions ${\Gamma}_2^{{\tau}_1,{\tau}_2}$ and ${\gamma}_2^{{\tau}_1,{\tau}_2}$ of two variables. Relevant connections of certain special cases of the main results presented here with some known identities are also pointed out.

• Proceeding of EDISON Challenge
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• 2014.03a
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• pp.103-113
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• 2014

Hydrophobicity is the key concept to understand the role of water in protein folding, protein self-assembly, and protein-ligand interaction. Conventionally, hydrophobicity of amino acids in a protein has been argued based on hydrophobicity scales determined for individual free amino acids, assuming that those scales are unaltered when amino acids are embedded in a protein. Here, we investigate how the hydrophobicity of constituent amino acids depends on the protein context, in particular, on the total charge and secondary structures of a protein. To this end, we compute and analyze the hydration free energy - free energy change upon hydration quantifying the hydrophobicity - of three short proteins based on the integral-equation theory of liquids. We find that the hydration free energy of charged amino acids is significantly affected by the protein total charge and exhibits contrasting behavior depending on the protein net charge being positive or negative. We also observe that amino acids in the central ${\beta}$-strand sandwiched by ${\beta}$-sheets display more enhanced hydrophobicity than free amino acids, whereas those in the ${\alpha}$-helix do not clearly show such a tendency. Our results provide novel insights into the hydrophobicity of amino acids, and will be valuable for rationalizing and predicting the strength of water-mediated interaction involved in the biological activity of proteins.