• Honam Mathematical Journal
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• v.39 no.2
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• pp.297-305
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• 2017

Let ${\alpha}$ > 0 be a real number and $(s_{\alpha}(n))_{n{\geq}1}$ be the lexicographically greatest Sturmian word of slope ${\alpha}$. We investigate Dirichlet series of the form ${\sum}^{\infty}_{n=1}s_{\alpha}(n)n^{-s}$. To do this, a generalization of Euler's totient function is required. For a real ${\alpha}$ > 0 and a positive integer n, an arithmetic function ${\varphi}{\alpha}(n)$ is defined to be the number of positive integers m for which gcd(m, n) = 1 and 0 < m/n < ${\alpha}$. Under a condition Re(s) > 1, this paper establishes an identity ${\sum}^{\infty}_{n=1}s_{\alpha}(n)n^{-S}=1+{\sum}^{\infty}_{n=1}{\varphi}_{\alpha}(n)({\zeta}(s)-{\zeta}(s,1+n^{-1}))n^{-s}$.

• The Pure and Applied Mathematics
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• v.20 no.1
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• pp.37-50
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• 2013

In the theory of hypergeometric functions of one or several variables, a remarkable amount of mathematicians's concern has been given to develop their transformation formulas and summation identities. Here we aim at presenting explicit expressions (in a single form) of the following weighted Appell's function $F_1$: $$(1+2x)^{-a}(1+2z)^{-b}F_1\;\(c,\;a,\;b;\;2c+j;\;\frac{4x}{1+2x},\;\frac{4z}{1+2z}\)\;(j=0,\;{\pm}1,\;{\ldots},\;{\pm}5)$$ in terms of Exton's triple hypergeometric $X_9$. The results are derived with the help of generalizations of Kummer's second theorem very recently provided by Kim et al. A large number of very interesting special cases including Exton's result are also given.

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.963-972
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• 2023

In this paper, geometrically convex and s-convex functions in third and fourth sense are merged to form (g, s)-convex function. Characterizations of (g, s)-convex function, algebraic and functional properties are presented. In addition, novel functions based on the integral of (g, s)-convex functions in the third sense are created, and inequality relations for these functions are explored and examined under particular conditions. Further, there are also some relationships between (g, s)-convex function and previously defined functions. The (g, s)-convex function and its derivatives will then be used to extend the well-known H-H and Fejer's type inequalities. In order to obtain the previously mentioned conclusions, several special cases from previous literature for extended H-H and Fejer's inequalities are also investigated. The relation between the average (mean) values and newly created H-H and Fejer's inequalities are also examined.

• Proceedings of the KIEE Conference
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• 1991.07a
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• pp.657-665
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• 1991

Although orthogonal function is introduced in control theory in early 1970's, it is not perfect. Since the concept of integral operator by Chen and Hsiao in mid 1970's, orthogonal function (for example Walsh, Block-pulse, Haar, Laguerre, Legendre, Chebychev etc) has been widely applied In system's analysis and identification, model reduction, state estimation, optimal control, signal processing, image processing, EEG, and ECG etc. The reason why Walsh Functions introduces in control theory is that as integral of Walsh function is also developed in Walsh orthogonal function, if we transfer give system into integral equation and introduce Walsh function. We can know that system's characteristic by algebraical expression. This approach is based on least square error and that result is expressed as computer calculation and partly continuous constant value which is easy to apply. Such a Walsh function has been actively studied in USA, TAIWAN, INDO, CHINA, EUROPE etc and in domestic, author has studied it for 10 years since it was is introduced in 1982. This paper is consider the that author has studied for 10 years and Walsh function's efficiency.

• Korean Journal of Adult Nursing
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• v.17 no.2
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• pp.239-247
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• 2005

Purpose: The purpose of this study is to examine the relationship among body image, depression and sexual function in Korean postmenopausal women. Methods: Subjects were 96 postmenopausal women who have lived in Korea. Data was collected using Semantic Differential scale, CES-D, and FSFI. Results: The level of body image was positive, depression was mild, and sexual function was moderate. There were no significant correlation between depression and sexual function. The subjects who had more positive body image experienced higher sexual function and less depressed mood. Conclusion: These findings showed the need for a knowledge development program for nurses regarding women's sexual function. Also, nurses must do counseling with sexual partner's and consider patients' body image when counseling those who complain of sexual dysfunction.

• Korean Journal of Mathematics
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• v.9 no.1
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• pp.67-73
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• 2001

For some equation related with exponential function, we seek roots and find the properties of the roots. By using the relation of the roots and attractors, we find a region in the basin of attraction of the attractor at infinity for Newton's method for solving given equation.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09a
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• pp.90-93
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• 2003

The function, which represents the closed curve, is found from the sampling data by S-System in this study. Two methods are proposed. One is the extension of S-System. The data x and y are regarded as input data, and the data z=0 as output data. To avoid the trap into the invalid function, the judgment points (x$\_$j/, y/sug j/) are introduced. They are arranged in the inside and the outside of the closed curve. By introducing this concept, the functions representing closed curve are found by S-System. This method is simple because of a little extension of S-System. It is, however, difficult for the method to find the complex function like a hand-written curve. Then another method is also proposed. It uses the system incorporating the argument function. The closed curve can be expressed by the argument function. The relatively complex function, which represents the closed curve like a hand-written curve, is found by utilizing argument function.

• Proceedings of the IEEK Conference
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• 2003.07e
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• pp.2403-2406
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• 2003

When viewing images, the relative luminance of the surround has a profound impact on the apparent contrast of the image. The dark surround causes the image elements to appear lighter than those viewed in an illuminated surround. For this reason, it is worthwhile to briefly review the general results of brightness sealing under a various viewing condition. Two of the most often cited parers on the topic of brightness scaling are Stevens-stevens and Bartleson-Breneman's function. There are, however, significant differences between the perceptual functions for simple-field and complex-field viewing. In this paper, we research the relationship between Steven's power law and Bartleson-Breneman's function. We present an appropriate brightness perception function due to TV system viewing conditions. Highlight luminance peak and absolute brightness threshold value in various adaptation levels are obtained from the proposed brightness function . Also, the luminance value of black level to produce the same contrast ratio with variety of display highlight luminance peak is obtained from the proposed brightness function.

• Korean Journal of Child Studies
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• v.23 no.6
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• pp.65-79
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• 2002

The present study surveyed both the parents of 130 children with psychopathology and the parents of 240 normal children. children were between 2 and 12 years of age. No differences were found between parents in self-differentiation or in family function by type of disorder. Parents of children with psychopathology were lower than parents of normal children in self-differentiation; this was particularly evident in cognitive function-emotional function, and emotional cut-off. Patents of children with psychopathology were lower than parents of normal children in terms of family function. Multiple regression analyses indicated that parent's self-differentiation, children's psychopathology, and parent's education level had a significant influence on family function. The regression model explained 52% of the variance.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1055-1072
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• 2022

Our aim is to establish certain image formulas of the (p, 𝜈)-extended Gauss' hypergeometric function F_p,𝜈(a, b; c; z) by using Saigo's hypergeometric fractional calculus (integral and differential) operators. Corresponding assertions for the classical Riemann-Liouville(R-L) and Erdélyi-Kober(E-K) fractional integral and differential operators are deduced. All the results are represented in terms of the Hadamard product of the (p, 𝜈)-extended Gauss's hypergeometric function F_p,𝜈(a, b; c; z) and Fox-Wright function _rΨ_s(z). We also established Jacobi and its particular assertions for the Gegenbauer and Legendre transforms of the (p, 𝜈)-extended Gauss' hypergeometric function F_p,𝜈(a, b; c; z).