• Bulletin of the Korean Mathematical Society
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• 제55권6호
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• pp.1703-1711
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• 2018

The main aim of this paper is to study the fourth Hankel determinant for the class of functions with bounded turning. We also investigate for 2-fold symmetric and 3-fold symmetric functions.

• Kyungpook Mathematical Journal
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• 제59권2호
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• pp.325-333
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• 2019

Motivated by the results on generating functions investigated by H. Exton and many other authors, we derive certain (presumably) new generating functions for generalized Mittag-Leffler-type functions. Specifically, we introduce a new class of generating relations (which are partly bilateral and partly unilateral) involving the generalized Mittag-Leffler function. Also we present some special cases of our main result.

• Kyungpook Mathematical Journal
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• 제55권3호
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• pp.625-639
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• 2015

Differential subordinations and superordinations results are obtained for certain meromorphic functions in the punctured unit disk which are associated with an integral operator. These results are obtained by investigating appropriate classes of a dmissible functions. Sandwich-type results are also obtained.

• Journal of the Korean Society of Environmental Restoration Technology
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• 제4권3호
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• pp.38-48
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• 2001

A wetland is an ecosystem which is the most useful and highly-energetic transition area. This study has been carried out to develop the wetland function assessment methods and apply on the natural wetlands (Mul-young-ari wetland in Jeju-island and Bangdong wetland in Taejon Metropolitan city) using RAM (Rapid Assessment Method). The RAM is useful method for assessing the wetland functions in terms of general functions acquired by once or twice onsite surveying. Eight functions of 2-12 variables each are analyzed for assessing the wetland functions. The results are as follows : 1) The conservation values of two wetlands are "High". 2) In Mul-young-ari wetland, such functions as groundwater discharge, floral diversity and wildlife habitat, shoreline/stream bank protection are relatively high, but some functions such as flood/storm water storage, aesthetics and recreation are "Moderate" - "High". 3) In Bangdong wetland, such functions as floral diversity and wildlife habitat, groundwater discharge, flood/storm water storage, aesthetics and recreation are high, and another functions are "Moderate" - "High". The taxonomy of this study stems from assessing functions of inland wetlands using indices of RAM. So It is needed that consequent studies are to be performed with verifying the variables and indices.

• Kyungpook Mathematical Journal
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• 제58권2호
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• pp.231-242
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• 2018

We derive sharp upper bound on the initial coefficients and Hankel determinants for normalized analytic functions belonging to a class, introduced by Silverman, defined in terms of ratio of analytic representations of convex and starlike functions. A conjecture related to the coefficients for functions in this class is posed and verified for the first five coefficients.

• 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.

• Nonlinear Functional Analysis and Applications
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• 제27권1호
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• pp.169-187
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• 2022

There have been provided a surprisingly large number of summation formulae for generalized hypergeometric functions and series incorporating a variety of elementary and special functions in their various combinations. In this paper, we aim to consider certain generalized hypergeometric function ₃F₂ with particular arguments, through which a number of summation formulas for _p+1F_p(1) are provided. We then establish a power series whose coefficients are involved in generalized hypergeometric functions with unit argument. Also, we demonstrate that the generalized hypergeometric functions with unit argument mentioned before may be expressed in terms of Bell polynomials. Further, we explore several special instances of our primary identities, among numerous others, and raise a problem that naturally emerges throughout the course of this investigation.

• Proceedings of the Korea Water Resources Association Conference
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• 한국수자원학회 2021년도 학술발표회
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• pp.127-127
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• 2021

In order to estimate parameter uncertainty of hydrological models, the consideration of the likelihood functions which provide reliable parameters of model is necessary. In this study, the Bayesian Markov Chain Monte Carlo (MCMC) method with informal likelihood functions is used to analyze the uncertainty of parameters of the SURR model for estimating the hourly streamflow of Gunnam station of Imjin basin, Korea. Three events were used to calibrate and one event was used to validate the posterior distributions of parameters. Moreover, the performance of four informal likelihood functions (Nash-Sutcliffe efficiency, Normalized absolute error, Index of agreement, and Chiew-McMahon efficiency) on uncertainty of parameter is assessed. The indicators used to assess the uncertainty of the streamflow simulation were P-factor (percentage of observed streamflow included in the uncertainty interval) and R-factor (the average width of the uncertainty interval). The results showed that the sensitivities of parameters strongly depend on the likelihood functions and vary for different likelihood functions. The uncertainty bounds illustrated the slight differences from various likelihood functions. This study confirms the importance of the likelihood function selection in the application of Bayesian MCMC to the uncertainty assessment of the SURR model.

• Bulletin of the Korean Mathematical Society
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• 제36권4호
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• pp.809-822
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• 1999

In this paper, we introduce conditional Yeh-Wiener in-tegrals for generalized conditioning functions including vector-valued functions. And also we establish various evaluation formulas of conditional Yeh-Wiener integrals for generalized conditioning functions.

• Communications of the Korean Mathematical Society
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• 제30권4호
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• pp.403-414
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• 2015

Extensions of some classical special functions, for example, Beta function B(x, y) and generalized hypergeometric functions $_pF_q$ have been actively investigated and found diverse applications. In recent years, several extensions for B(x, y) and $_pF_q$ have been established by many authors in various ways. Here, we aim to generalize Appell's hypergeometric functions of two variables and Lauricella's hypergeometric function of three variables by using the extended generalized beta type function $B_p^{({\alpha},{\beta};m)}$ (x, y). Then some properties of the extended generalized Appell's hypergeometric functions and Lauricella's hypergeometric functions are investigated.