• East Asian mathematical journal
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• 제16권1호
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• pp.9-16
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• 2000

The authors aim at providing some identities involving the hypergeometric function via some known or presumably new formulas for the incomplete Beta and their associated functions. Some properties of the Beta and Gamma functions are also considered.

• 대한수학회지
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• 제53권2호
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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.

• 대한수학회논문집
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• 제33권4호
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• pp.1285-1301
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• 2018

This paper is devoted to the study of $Tur{\acute{a}}n$-type inequalities for some well-known special functions such as Gauss hypergeometric functions, generalized complete elliptic integrals and confluent hypergeometric functions which are derived by using a new form of the Cauchy-Bunyakovsky-Schwarz inequality. We also apply these inequalities for some sample of interest such as incomplete beta function, incomplete gamma function, elliptic integrals and modified Bessel functions to obtain their corresponding $Tur{\acute{a}}n$-type inequalities.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제5권2호
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• pp.123-132
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• 1998

Let F and G denote the distribution functions of the failure times and the censoring variables in a random censorship model. Susarla and Van Ryzin(1978) verified consistency of $F_{\alpha}$, he NPBE of F with respect to the Dirichlet process prior D($\alpha$), in which they assumed F and G are continuous. Assuming that A, the cumulative hazard function, is distributed according to a beta process with parameters c, $\alpha$, Hjort(1990) obtained the Bayes estimator $A_{c,\alpha}$ of A under a squared error loss function. By the theory of product-integral developed by Gill and Johansen(1990), the Bayes estimator $F_{c,\alpha}$ is recovered from $A_{c,\alpha}$. Continuity assumption on F and G is removed in our proof of the consistency of $A_{c,\alpha}$ and $F_{c,\alpha}$. Our result extends Susarla and Van Ryzin(1978) since a particular transform of a beta process is a Dirichlet process and the class of beta processes forms a much larger class than the class of Dirichlet processes.

• Molecules and Cells
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• 제42권8호
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• pp.589-596
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• 2019

${\beta}Pix$ is a guanine nucleotide exchange factor for the Rho family small GTPases, Rac1 and Cdc42. It is known to regulate focal adhesion dynamics and cell migration. However, the in vivo role of ${\beta}Pix$ is currently not well understood. Here, we report the production and characterization of ${\beta}Pix$-KO mice. Loss of ${\beta}Pix$ results in embryonic lethality accompanied by abnormal developmental features, such as incomplete neural tube closure, impaired axial rotation, and failure of allantois-chorion fusion. We also generated ${\beta}Pix$-KO mouse embryonic fibroblasts (MEFs) to examine ${\beta}Pix$ function in mouse fibroblasts. ${\beta}Pix$-KO MEFs exhibit decreased Rac1 activity, and defects in cell spreading and platelet-derived growth factor (PDGF)-induced ruffle formation and chemotaxis. The average size of focal adhesions is increased in ${\beta}Pix$-KO MEFs. Interestingly, ${\beta}Pix$-KO MEFs showed increased motility in random migration and rapid wound healing with elevated levels of MLC2 phosphorylation. Taken together, our data demonstrate that ${\beta}Pix$ plays essential roles in early embryonic development, cell spreading, and cell migration in fibroblasts.

• 대한수학회지
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• 제53권5호
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• pp.1183-1210
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• 2016

During the past four decades or so, due mainly to a wide range of applications from natural sciences to social sciences, the so-called fractional calculus has attracted an enormous attention of a large number of researchers. Many fractional calculus operators, especially, involving various special functions, have been extensively investigated and widely applied. Here, in this paper, in a systematic manner, we aim to establish certain image formulas of various fractional integral operators involving diverse types of generalized hypergeometric functions, which are mainly expressed in terms of Hadamard product. Some interesting special cases of our main results are also considered and relevant connections of some results presented here with those earlier ones are also pointed out.

• International Journal of Contents
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• 제3권1호
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• pp.1-8
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• 2007

The distributions of the minimum correlated F-variable arises in many applied statistical problems including simultaneous analysis of variance (SANOVA), equality of variance, selection and ranking populations, and reliability analysis. In this paper, negative binomial sampling technique is employed to derive the distributions of the minimum of chi-square variables and hence the distributions of the minimum correlated F-variables. The work presented in this paper is divided in two parts. The first part is devoted to develop some combinatorial identities arised from the negative binomial sampling. These identities are constructed and justified to serve important purpose, when we deal with these distributions or their characteristics. Other important results including cumulants and moments of these distributions are also given in somewhat simple forms. Second, the distributions of minimum, chisquare variable and hence the distribution of the minimum correlated F-variables are then derived within the negative binomial sampling framework. Although, multinomial theory applied to order statistics and standard transformation techniques can be used to derive these distributions, the negative binomial sampling approach provides more information regarding the nature of the relationship between the sampling vehicle and the probability distributions of these functions of chi-square variables. We also provide an algorithm to compute the percentage points of the distributions. The computation methods we adopted are exact and no interpolations are involved.

• Kyungpook Mathematical Journal
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• 제57권1호
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• pp.109-124
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• 2017

In this article the Srivastava-Owa-Ruscheweyh fractional derivative operator $\mathcal{L}^{\alpha}_{a,{\lambda}}$ is applied for defining and studying some new subclasses of analytic functions in the unit disk E. Inclusion results, radius problem and other results related to Bernardi integral operator are also discussed. Some applications related to conic domains are given.

• Communications for Statistical Applications and Methods
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• 제30권2호
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• pp.191-213
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• 2023

Unit distributions are frequently used in probability theory and statistics to depict meaningful variables having values between zero and one. Using convenient transformation, the unit inverse exponentiated weibull (UIEW) distribution, which is equally useful for modelling data on the unit interval, is proposed in this study. Quantile function, moments, incomplete moments, uncertainty measures, stochastic ordering, and stress-strength reliability are among the statistical properties provided for this distribution. To estimate the parameters associated to the recommended distribution, well-known estimation techniques including maximum likelihood, maximum product of spacings, least squares, weighted least squares, Cramer von Mises, Anderson-Darling, and Bayesian are utilised. Using simulated data, we compare how well the various estimators perform. According to the simulated outputs, the maximum product of spacing estimates has lower values of accuracy measures than alternative estimates in majority of situations. For two real datasets, the proposed model outperforms the beta, Kumaraswamy, unit Gompartz, unit Lomax and complementary unit weibull distributions based on various comparative indicators.

• 천문학회보
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• 제41권1호
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• pp.36.2-37
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• 2016

We study the long-term radio variability of 43 radio bright AGNs by exploiting the data base of the University of Michigan Radio Astronomy Observatory (UMRAO) monitoring program. The UMRAO database provides high quality lightcurves spanning 25 - 32 years in time at three observing frequencies, 4.8, 8, and 14.5 GHz. We model the periodograms (temporal power spectra) of the observed lightcurves as simple power-law noise (red noise, spectral power $P(f){\propto}f^{-{\beta}}$ using Monte Carlo simulations, taking into account windowing effects (red-noise leak, aliasing). The power spectra of 39 (out of 43) sources are in good agreement with the models, yielding a range in power spectral index (${\beta}$) from ${\approx}1$ to ${\approx}3$. We find a strong anti-correlation between ${\beta}$ and the fractal dimension of the lightcurves, which provides an independent check of the quality of our modelling of power spectra. We fit a Gaussian function to each flare in a given lightcurve to obtain the flare duration. We discover a correlation between ${\beta}$ and the median duration of the flares. We use the derivative of a lightcurve to obtain a characteristic variability timescale which does not depend on the assumed functional form of the flares, incomplete fitting, and so on. We find that, once the effects of relativistic Doppler boosting on the observed timescales are corrected, the variability timescales of our sources are proportional to the black hole mass to the power of ${\alpha}=1.70{\pm}0.49$. We see an indication for AGNs in different regimes of accretion rate, flat spectrum radio quasars and BL Lac objects, having different scaling relations with ${\alpha}{\approx}1$ and ${\approx}2$, respectively. We find that modelling the periodograms of four of our sources requires the assumption of broken powerlaw spectra. From simulating lightcurves as superpositions of exponential flares we conclude that strong overlap of flares leads to featureless simple power-law periodograms of AGNs at radio wavelengths in most cases (The paper is about to be submitted to ApJ).