• 대한수학회논문집
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• 제31권4호
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• pp.703-712
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• 2016

In this article, we derive a sharp estimates for the Taylor-Maclaurin coefficients of functions in some certain subclasses of spirallike functions which are defined by generalized Srivastava-Attiya operator. Several corollaries and consequences of the main result are also considered.

• 대한수학회보
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• 제59권2호
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• pp.431-452
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• 2022

For any positive integer 𝜇, we compute the mean value of the 𝜇-th derivative of quadratic Dirichlet L-functions over the rational function field 𝔽_q(t), where q is a power of 2.

• Korean Journal of Mathematics
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• 제32권1호
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• pp.173-182
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• 2024

In this paper, we derive the necessary and sufficient conditions for the Gaussian hypergeometric function to be in some subclasses of analytic functions.

• ETRI Journal
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• 제15권2호
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• pp.35-51
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• 1993

This paper presents function approximation based on nonparametric estimation. As an estimation model of function approximation, a three layered network composed of input, hidden and output layers is considered. The input and output layers have linear activation units while the hidden layer has nonlinear activation units or kernel functions which have the characteristics of bounds and locality. Using this type of network, a many-to-one function is synthesized over the domain of the input space by a number of kernel functions. In this network, we have to estimate the necessary number of kernel functions as well as the parameters associated with kernel functions. For this purpose, a new method of parameter estimation in which linear learning rule is applied between hidden and output layers while nonlinear (piecewise-linear) learning rule is applied between input and hidden layers, is considered. The linear learning rule updates the output weights between hidden and output layers based on the Linear Minimization of Mean Square Error (LMMSE) sense in the space of kernel functions while the nonlinear learning rule updates the parameters of kernel functions based on the gradient of the actual output of network with respect to the parameters (especially, the shape) of kernel functions. This approach of parameter adaptation provides near optimal values of the parameters associated with kernel functions in the sense of minimizing mean square error. As a result, the suggested nonparametric estimation provides an efficient way of function approximation from the view point of the number of kernel functions as well as learning speed.

• 한국환경복원기술학회지
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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.

• 수산경영론집
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• 제51권2호
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• pp.89-105
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• 2020

This study aimed to establish the public interest functions of fisheries and fishing villages, which is intended to help introduce and expand the public-purpose direct payment system in the fisheries sector. Firstly, this study looked at trends related to the public interest functions of domestic and foreign cases in similar fields in order to get implications for establishing public service functions in fisheries and fishing villages. Secondly, three criteria were defined for establishing the public interest functions of fisheries and fishing villages. Thirdly, the public interest functions of fisheries and fishing villages were defined through prior research, analysis of overseas cases, and consultation with experts in the fields of fisheries and fishing villages. As a result, the six public interest functions and the 14 detailed functions were defined. Finally, this study established a direction for preserving and improving the public interest functions of fisheries and fishing villages, and presented strategies for achieving them.

• 대한수학회논문집
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• 제31권1호
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• pp.65-94
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• 2016

In 1812, Gauss obtained fifteen contiguous functions relations. Later on, 1847, Henie gave their q-analogue. Recently, good progress has been done in finding more contiguous functions relations by employing results due to Gauss. In 1999, Cho et al. have obtained 24 new and interesting contiguous functions relations with the help of Gauss's 15 contiguous relations. In fact, such type of 72 relations exists and therefore the rest 48 contiguous functions relations have very recently been obtained by Rakha et al.. Thus, the paper is in continuation of the paper [16] published in Computer & Mathematics with Applications 61 (2011), 620.629. In this paper, first we obtained 15 q-contiguous functions relations due to Henie by following a different method and then with the help of these 15 q-contiguous functions relations, we obtain 72 new and interesting q-contiguous functions relations. These q-contiguous functions relations have wide applications.

• 충청수학회지
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• 제24권2호
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• pp.187-204
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• 2011

B. C. Carlson [Some extensions of Lardner's relations between $_0F_3$ and Bessel functions, SIAM J. Math. Anal. 1(2) (1970), 232-242] presented several useful relations between Bessel and generalized hypergeometric functions that generalize some earlier results. Here, by simply splitting Srivastava's hypergeometric function $H_B$ into eight parts, we show how some useful and generalized relations between Srivastava's hypergeometric functions $H_B$ and $F^{(3)}$ can be obtained. These main results are shown to be specialized to yield certain relations between functions $_0F_1$, $_1F_1$, $_0F_3$, ${\Psi}_2$, and their products including different combinations with different values of parameters and signs of variables. We also consider some other interesting relations between the Humbert ${\Psi}_2$ function and $Kamp\acute{e}$ de $F\acute{e}riet$ function, and between the product of exponential and Bessel functions with $Kamp\acute{e}$ de $F\acute{e}riet$ functions.

• 호남수학학술지
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• 제43권2호
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• pp.183-197
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• 2021

Recently several authors have extended the Beta function by using its integral representation. However, in many cases no expression of these extended functions in terms of classic special functions is known. In the present paper, we introduce a further extension by defining a family of functions G_r,s : ℝ^*₊ → ℂ, with r, s ∈ ℂ and ℜ(r) > 0. For given r, s, we prove that this function satisfies a second-order linear differential equation with rational coefficients. Solving this ODE, we express G_r,s as a combination of confluent hypergeometric functions. From this we deduce a new integral relation satisfied by Tricomi's function. We then investigate additional specific properties of G_r,1 which take the form of new non trivial integral relations involving exponential and error functions. We discuss the connection between G_r,1 and Stokes' first problem (or Rayleigh problem) in fluid mechanics which consists in determining the flow created by the movement of an infinitely long plate. For $r{\in}{\frac{1}{2}}{\mathbb{N}}^*$, we find additional relations between G_r,1 and Hermite polynomials. In view of these results, we believe the family of extended beta functions G_r,s will find further applications in two directions: (i) for improving our knowledge of confluent hypergeometric functions and Tricomi's function, (ii) and for engineering and physics problems.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제19권4호
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• pp.423-435
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• 2012

We give some properties of weak Bloch functions and also give some properties of ${\phi}$-uniform domains and ${\phi}$-John domains in terms of moduli of continuity of Bloch functions and weak Bloch functions.