• Honam Mathematical Journal
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• v.34 no.1
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• pp.113-124
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• 2012

While investigating the Lauricella's list of 14 complete second-order hypergeometric series in three variables, Srivastava noticed the existence of three additional complete triple hypergeometric series of the second order, which were denoted by $H_A$, $H_B$ and $H_C$. Each of these three triple hypergeometric functions $H_A$, $H_B$ and $H_C$ has been investigated extensively in many different ways including, for example, in the problem of finding their integral representations of one kind or the other. Here, in this paper, we aim at presenting further integral representations for the Srivatava's triple hypergeometric function $H_A$.

• Journal of the Korean Statistical Society
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• v.13 no.1
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• pp.48-56
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• 1984

This paper considers one-sample and two-sample test for the logistic function by means of Kolmororov-Smirnov type statistics. The standard tables used for the Kolmogorov-Smirnov test are valid only when the function is completely specified; but they are not valid if the parameters of function are estimated from the sample. This note presents modified tables for the Kolmogorov-Sminov type staistic. These tables can be used to test the hypothesis that a sample comes from a logistic function when shape parameter $(\alpha)$ and location parameter $(\beta)$ must be estimated from the sample by the method of maximum likelihood. Monte Carlo method is employed to calculate the criticla values of the test. The tables of the critical values are provided.

• Communications for Statistical Applications and Methods
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• v.11 no.1
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• pp.161-168
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• 2004

A single-index model is useful in fields which employ multidimensional regression models. Many methods have been developed in parametric and nonparametric approaches. In this paper, posterior inference is considered and a wavelet series is thought of as a function approximated to a true function in the single-index model. The posterior inference needs a prior distribution for each parameter estimated. A prior distribution of each coefficient of the wavelet series is proposed as a hierarchical distribution. A direction $\beta$ is assumed with a unit vector and affects estimate of the true function. Because of the constraint of the direction, a transformation, a spherical polar coordinate $\theta$, of the direction is required. Since the posterior distribution of the direction is unknown, we apply a Metropolis-Hastings algorithm to generate random samples of the direction. Through a Monte Carlo simulation we investigate estimates of the true function and the direction.

• The Pure and Applied Mathematics
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• v.19 no.2
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• pp.137-145
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• 2012

While investigating the Lauricella's list of 14 complete second-order hypergeometric series in three variables, Srivastava noticed the existence of three additional complete triple hypergeometric series of the second order, which were denoted by $H_A$, $H_B$ and $H_C$. Each of these three triple hypergeometric functions $H_A$, $H_B$ and $H_C$ has been investigated extensively in many different ways including, for example, in the problem of finding their integral representations of one kind or the other. Here, in this paper, we aim at presenting further integral representations for the Srivatava's triple hypergeometric function $H_B$.

• Communications for Statistical Applications and Methods
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• v.3 no.1
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• pp.243-255
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• 1996

The number of neutron signals from a neutral particle beam(NPB) at the detector, without any errors, obeys Poisson distribution, Under two assumptions that NPB scattering distribution and aiming errors have a circular Gaussian distribution respectively, an exact probability distribution of signals becomes a Poisson-power function distribution. In this paper, we show that the error rate in simple hypothesis testing for the limiting Poisson-power function distribution is not zero. That is, the limit of ${\alpha}+{\beta}$ is zero when Poisson parameter$\kappa\rightarro\infty$, but this limit is not zero (i.e., $\rho\ell$>0)for the Poisson-power function distribution. We also give optimal decision algorithms for a specified error rate.

• 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 Applied and Pure Mathematics
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• v.5 no.1_2
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• pp.95-108
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• 2023

The Hadamard type inequalities for fractional integral operators of convex functions are studied at very large scale. This paper provides the Hadamard type inequalities for refined (α,h-m)-convex functions by utilizing Liouville-Caputo fractional (L-CF) derivatives. These inequalities give refinements of already existing (L-CF) inequalities of Hadamard type for many well known classes of functions provided the function h is bounded above by ${\frac{1}{\sqrt{2}}}$.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.205-213
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• 2022

In this paper we give a simple and direct proof of an Euler integral representation for a special class of _q+1F_q,k k-hypergeometric functions for q ≥ 2. The values of certain ₃F_2,k and ₄F_3,k functions at $x=\frac{1}{k}$, some of which can be derived using other methods. We may conclude that for k = 1 the results are reduced to [3].

• Journal of Ginseng Research
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• v.40 no.4
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• pp.334-343
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• 2016

Background: Progressed tissue culture techniques have allowed us to easily obtain mass products of tissue-cultured mountain ginseng over 100 yr old (TCMG-100). We investigated the effects of TCMG-100 extract on erectile function using in vitro and in vivo studies. Methods: To examine the relaxation effects and mechanisms of action of TCMG-100 on rabbit cavernosal strips evaluated in an organ bath. To investigate the long-term treatment effect of TCMG-100, 8-wk administration was performed. After administration of TCMG-100, intracavernosal pressure, cyclic guanosine monophosphate and nitric oxide (NO) levels of cavernosal tissue, serum testosterone level, histological observation of collagen fiber, endothelium, smooth muscle cell, and transforming growth factor-${\beta}1$ were investigated. Results: TCMG-100 extract displayed dose-dependent relaxation effects on precontracted rabbit corporal smooth muscle. The TCMG-100-induced relaxation was significantly reduced by removing the endothelium, and treatment with an NO synthase inhibitor or NO scavenger. Eight weeks of TCMG-100 administration increased intracavernosal pressure in a rat model. The levels of cyclic guanosine monophosphate and NO in the corpus callosum and serum testosterone level were also increased by TCMG-100 treatment. Furthermore, histological evaluation of collagen, smooth muscle, and endothelium showed increases in endothelium and smooth muscle, and a decrease in transforming growth factor-${\beta}1$ expression. Conclusion: These relaxation effects on corporal smooth muscle and increased erectile function suggest that TCMG-100 might be used as an alternative herbal medicine to improve erectile function.

• Food Science and Biotechnology
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• v.18 no.3
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• pp.630-635
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• 2009

This study was performed to analyze various antioxidants, to evaluate the antioxidative activities, and to measure the protective effect for gap junction intercellular communication (GJIC) to assess the functional potency of the cherry tomato. The ascorbic acid, lycopene, and ${\beta}-carotene$ were measured at $503.4{\pm}9.6$, $39.7{\pm}1.5$, and $7.4{\pm}0.3$ mg/100 g d.w., and ${\alpha}-$, ${\beta}+{\gamma}-$, ${\delta}-tocopherol$ contents were measured at $8.3{\pm}0.1$, $1.7{\pm}0.0$, and $0.1{\pm}0.0$ mg/100 g d.w., respectively. Cherry tomato extract using hexane/acetone/EtOH (2:1:1, CTE) exhibited a ABTS radical scavenging activity with an $IC_{50}$ value of $48.83{\pm}0.30\;{\mu}g/mL$. The cherry tomato protected against the inhibition of GJIC induced by $H_2O_2$ in WB-F344 rat liver epithelial cells, and the reduction in phosphorylated Cx43 was most clearly correlated with the concentration of CTE. These results demonstrated that the cherry tomato harbors a wealth of potent antioxidants and might be protect human body against the inhibition of the GJIC by toxic components.