• 호남수학학술지
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• 제33권2호
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• pp.187-206
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• 2011

The main object of this paper is to present generalization of extended beta function, extended hypergeometric and confluent hypergeometric function introduced by Chaudhry et al. and obtained various integral representations, properties of beta function, Mellin transform, beta distribution, differentiation formulas transform formulas, recurrence relations, summation formula for these new generalization.

• 호남수학학술지
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• 제46권2호
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• pp.313-334
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• 2024

In the current study, our aim is to define new generalized extended beta and hypergeometric types of functions. Next, we methodically determine several integral representations, Mellin transforms, summation formulas, and recurrence relations. Moreover, we provide log-convexity, Turán type inequality for the generalized extended beta function and differentiation formulas, transformation formulas, differential and difference relations for the generalized extended hypergeometric type functions. Also, we additionally suggest a generating function. Further, we provide the generalized extended beta distribution by making use of the generalized extended beta function as an application to statistics and obtaining variance, coefficient of variation, moment generating function, characteristic function, cumulative distribution function, and cumulative distribution function's complement.

• 대한수학회논문집
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• 제25권1호
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• pp.105-110
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• 2010

In this paper, we introduce the concept of $\beta$-preconvex sets on preconvexity spaces. We study some properties for $\beta$-preconvex sets by using the co-convexity hull and the convexity hull. Also we introduce and study the concepts of ${\beta}c$-convex function and $\beta^*c$-convex function.

• Kyungpook Mathematical Journal
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• 제61권4호
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• pp.765-779
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• 2021

The fundamental goal of this paper is to investigate some inequalities involving the special beta function in n variables. Our theoretical results obtained here are extensions and refinements for some inequalities already discussed in the literature.

• 호남수학학술지
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• 제36권2호
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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.

• 호남수학학술지
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• 제33권3호
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• pp.407-418
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• 2011

There are two kinds of closing method for a given braid ${\beta}{\in}B_{2n}$, a braid closure $\hat{\beta}$ and a plat closure $\bar{\beta}$. In the article, we find a relation between the Conway potential function ${\nabla}_{\hat{\beta}}$ of braid closure $\hat{\beta}$ and ${\nabla}_{\hat{\beta}}$ of plat closure $\bar{\beta}$.

• Journal of the Korean Statistical Society
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• 제26권1호
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• pp.1-22
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• 1997

In the linear regression model $y_{i}$ = .alpha. $x_{i}$ $^{T}$ .beta. + .epsilon.$_{i}$ , i = 1,2,...,n, the weighted pairwise absolute deviation (WPAD) estimator was defined by minimizing the dispersion function D (.beta.) = .sum..sum.$_{{i $w_{{ij}}$$\mid$ $r_{j}$ (.beta.) $r_{i}$ (.beta.)$\mid$, where $r_{i}$ (.beta.)'s are residuals and $w_{{ij}}$'s are weights. This estimator can achive bounded total influence with positive breakdown by choice of weights $w_{{ij}}$. In this paper, we consider a more general type of dispersion function than that of D(.beta.) and propose a pairwise GM-estimator based on the dispersion function. Under some regularity conditions, the proposed estimator has a bounded influence function, a high breakdown point, and asymptotically a normal distribution. Results of a small-sample Monte Carlo study are also presented. presented.

• IMMUNE NETWORK
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• 제9권1호
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• pp.27-33
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• 2009

Macrophages generated in vitro using macrophage-colony stimulating factor (M-CSF) and interleukin (IL)-6 from bone marrow cells (BM-Mp) are defective in antigen presenting cell (APC) function as shown by their ability to induce the proliferation of anti-CD3 mAb-primed syngeneic T cells. However, they do express major histocompatibility (MHC) class I and II molecules. accessory molecules and intracellular adhesion molecules. Here we demonstrate that the defective APC function of macrophages is mainly due to production of $TGF-{\beta}1$ by BM-Mp. Methods: Microarray analysis showed that $TGF-{\beta}1$ was highly expressed in BM-Mp, compared to a macrophage cell line, B6D. which exerted efficient APC function. Production of $TGF-{\beta}1$ by BM-Mp was confirmed by neutralization experiments of $TGF-{\beta}1$ as well as by real time-polymerase chain reaction (PCR). Results: Addition of $anti-TGF-{\beta}1$ monoclonal antibody to cultures of BM-Mp and anti-CD3 mAb-primed syngeneic T cells efficiently induced the proliferation of syngeneic T cells. Conversely, the APC function of B6D cells was almost completely suppressed by addition of $TGF-{\beta}1$. Quantitative real time-PCR analysis also confirmed the enhanced expression of $TGF-{\beta}1$ in BM-Mp. Conclusion: The defective APC function of macrophages generated in vitro with M-CSF and IL-6 was mainly due to the production of $TGF-{\beta}1$ by macrophages.

• Molecules and Cells
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• 제26권3호
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• pp.291-298
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• 2008

Human karyopherin ${\beta}3$, highly homologous to a yeast protein secretion enhancer (PSE1), has often been reported to be associated with a mediator of a nucleocytoplasmic transport pathway. Previously, we showed that karyopherin ${\beta}3$ complemented the PSE1 and KAP123 double mutant. Our research suggested that karyopherin beta has an evolutionary function similar to that of yeast PSE1 and/or KAP 123. In this study, we performed yeast two-hybrid screening to find a protein which would interact with karyopherin ${\beta}3$ and identified apolipoprotein A-I (apo A-I), a secretion protein with a primary function in cholesterol transport. By using in vitro binding assay, co-immunoprecipitation, and colocalization studies, we defined an interaction between karyopherin ${\beta}3$ and apo A-I. In addition, overexpression of karyopherin ${\beta}3$ significantly increased apo A-I secretion. These results suggest that karyopherin ${\beta}3$ plays a crucial role in apo A-I secretion. These findings may be relevant to the study of a novel function of karyopherin ${\beta}3$ and coronary artery diseases associated with apo A-I.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제4권1호
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• pp.71-76
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• 1997

A new proof of the well-known identity involved in the Beta function B(p, q) is given by using the theory of hypergeometric series and a brief history of Gamma function is also provided. The method here is shown to be able to apply to evaluate some definite integrals.