• Research in Mathematical Education
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• v.3 no.1
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• pp.35-56
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• 1999

The evolution of the function concept was delineated in terms of the 17th and 18th Centuries' dependent nature of function, and the 19th and 20th Centuries' arbitrary and univalent nature of function. According to mathematics educators' beliefs about the value of the function concept in school mathematics, certain definitions of the concept tend to be emphasized. This study discusses three types - genetical (dependence), logical (settheoretical), analogical (machine/equations) - of definition of function and their values.

• Journal for History of Mathematics
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• v.23 no.3
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• pp.75-90
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• 2010

In this paper function concept is classified in the phenomenological aspect. According to the study, function concept is classified as causality, designation, operation, change, figure, morhism, variables, functional, and operator. This classifications are categorized as pre-level function, basic level function, and upper level function.

• Honam Mathematical Journal
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• v.36 no.3
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• pp.659-668
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• 2014

In this paper, we express the Green function in terms of the classical kernel functions in potential theory. In particular, we obtain a formula relating the Green function and the Szegő kernel function which consists of only the Szegő kernel function in a $C^{\infty}$ smoothly bounded finitely connected domain in the complex plane.

• East Asian mathematical journal
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• v.29 no.5
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• pp.545-550
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• 2013

A remarkably large number of integral formulas have been investigated and developed. Certain large number of integral formulas are expressed as derivatives of some known functions. Here we choose to recall such a formula to present explicit expressions in terms of Gamma function, Psi function and Polygamma functions. Some simple interesting special cases of our main formulas are also considered. It is also pointed out that the same argument can establish explicit integral formulas for other those expressed in terms of derivatives of some known functions.

• Proceedings of the Korea Institute of Convergence Signal Processing
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• 2000.08a
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• pp.1-4
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• 2000

In this paper, A useful nonlinear function for the RBF(Radial Basis Function) equalization is proposed. This proposed function need not calculate an exponential function that is generally used for conventional RBF equalizer and uses the only four rules of arithmetic. Therefore the computational requirement for the RBF equalizer with the proposed function is decreased. As a computer simulation result, the equalizer with the proposed function effectively reduce nonlinear intersymbol interference, caused by nonlinear communication channel.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.1167-1179
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• 2022

In this paper, we obtain some subsets of real numbers (ℝ) on which a fractional part function is defined as a real-valued continuous function. This gives rise to the analysis of the continuous properties of the fractional part function as a real-valued function. The analysis of fractional part function is helpful in the study of the dynamics of circle.

• 한국공간정보시스템학회:학술대회논문집
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• 2000.06a
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• pp.93-105
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• 2000

GIS is a powerful toolbox in managing spatial data associated with attribute data. However GIS is short of spatial analysis function and graphic user interface(GUI) function in dealing with dynamic planning problems. Decision Support Systems(DSS) make up for the shortage of GIS by providing GUI function, modeling function and database function. Spatial Decision Support Systems(SDSS), a new kind of DSS, incorporate display function, basic spatial analysis function and manipulation function of spatial data and attribute data of GIS and GUI function, modeling function and database function of DSS in dealing with spatial planning problems. Planning Support Systems(PSS) add more advanced spatial analysis function and intertemporal function to the functions of SDSS. This study focuses on the modeling of a PSS for capacity expansion of water-distribution network depending upon land use planning by using GIS, value engineering(VE) and life cycle costing(LCC). The PSS shows a guideline about the investment of water-distribution networks related to urban growth management through generating certain numbers of dynamic alternatives to supply the amount of water caused by land use planning.

• Journal of computational fluids engineering
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• v.14 no.4
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• pp.67-77
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• 2009

This paper is a continuation of a recent development on the Hermite-based divergence-free element method and deals with a non-isothermal fluid flow driven by the buoyancy force in a square cavity with temperature difference across the two sides. Two Hermite functions are considered for numerical computations in this paper. One is a cubic function and the other is a quartic function. The degrees-of-freedom of the cubic Hermite function are stream function and its first and second derivatives for the velocity field, and temperature and its first derivatives for the temperature field. The degrees-of-freedom of the quartic Hermite function include two second derivatives and one cross derivative of the stream function in addition to the degrees-of-freedom of the cubic stream function. This paper presents a brief review on the Hermite based divergence-free basis functions and its finite element formulations for the buoyancy driven flow. The present algorithm does not employ any upwinding or a stabilization term. However, numerical values and contour graphs for major flow variables showed good agreements with those by De Vahl Davis[6].

• Korean Journal of Childcare and Education
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• v.16 no.5
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• pp.47-67
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• 2020

Objective: The main purpose of this study was to investigate the direct effect of maternal parenting behavior and indirect effects through preschoolers'executive function on three types of social behavior, prosocial, aggressive and withdrawn behavior. Methods: A total of 299 mothers and their preschool-aged children were the subjects of this study. Mothers completed the questionnaire that included measures of their parenting behavior, preschoolers' executive function, and social behavior. Results: First, mothers' positive parenting behavior had a direct effect on preschoolers' prosocial behavior, and mothers' negative parenting behavior had direct effects on preschoolers' aggressive and withdrawn behavior. Second, mothers' positive parenting behavior had indirect effects on preschoolers' prosocial, aggressive and withdrawn behavior through preschoolers' executive function. In contrast, indirect paths from maternal negative parenting behavior to social behavior through preschoolers' execution function were not significant. Conclusion/Implications: These findings underscore the importance of executive function during early childhood and suggest the need for effective parenting programs to promote executive function.

• Honam Mathematical Journal
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• v.32 no.3
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• pp.389-397
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• 2010

Exton introduced 20 distinct triple hypergeometric functions whose names are Xi (i = 1,$\ldots$, 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_0F_1$, $_1F_1$, a Humbert function $\Psi_2$, a Humbert function $\Phi_2$. The object of this paper is to present 25 (presumably new) integral representations of Euler types for the Exton hypergeometric function $X_5$ among his twenty $X_i$ (i = 1,$\ldots$, 20), whose kernels include the Exton function X5 itself, the Exton function $X_6$, the Horn's functions $H_3$ and $H_4$, and the hypergeometric function F = $_2F_1$.