• Title, Summary, Keyword: function

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THE GREEN FUNCTION AND THE SZEGŐ KERNEL FUNCTION

  • Chung, Young-Bok
    • 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.

NEW CLASS OF INTEGRALS INVOLVING GENERALIZED HYPERGEOMETRIC FUNCTION AND THE LOGARITHMIC FUNCTION

  • Kim, Yongsup
    • Communications of the Korean Mathematical Society
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    • v.31 no.2
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    • pp.329-342
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    • 2016
  • Motivated essentially by Brychkov's work [1], we evaluate some new integrals involving hypergeometric function and the logarithmic function (including those obtained by Brychkov[1], Choi and Rathie [3]), which are expressed explicitly in terms of Gamma, Psi and Hurwitz zeta functions suitable for numerical computations.

INTEGRAL REPRESENTATIONS OF THE k-BESSEL'S FUNCTION

  • Gehlot, Kuldeep Singh;Purohit, Sunil Dutt
    • Honam Mathematical Journal
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    • v.38 no.1
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    • pp.17-23
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    • 2016
  • This paper deals with the study of newly defined special function known as k-Bessel's function due to Gehlot [2]. Certain integral representations of k-Bessel's function are investigated. Known integrals of classical Bessel's function are seen to follow as special cases of our main results.

A study on the function relation model of the individualization in mobile phone (휴대전화의 개인화 기능 관계 모델에 대한 연구)

  • Lee, Tae-Suk;Ban, Yeong-Hwan
    • 한국HCI학회:학술대회논문집
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    • pp.944-948
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    • 2009
  • The mobile phone is the most private device for mobile communication. The goal of this paper is to present function relation model of the individualization and to analyze the task in the model by function pattern and function relation model in mobile phone. Function, activity, activity flow, intent of the activity, function group and influence between function and function group are used to present the function relation model which illustrates the relationship of the function in product. And this model drew up the function relation model for mobile phone. The function relation model for mobile phone based on the function pattern by the newest 3 phone's over 320 functions and 21 function groups. Last, to rearrange the function relation model to center on the individualization, the internal/ external memory to save and use the information for individualization function is placed to middle of the model. The main tasks of the model are storing, inquiry and interlock. The important methods to reinforce the individualization function are to develop the tasks which are the relations between the functions.

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Analysis of the Tasks to Find Intersection Points of a Function and Its Inverse Function (역함수와의 교점을 구하는 과제에 대한 분석)

  • Heo, Nam Gu
    • The Mathematical Education
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    • v.55 no.3
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    • pp.335-355
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    • 2016
  • The purpose of this study is to analyze tasks to find intersection points of a function and its inverse function. To do this, we produced a task and 64 people solved the task. As a result, most people had a cognitive conflict related to inverse function. Because of over-generalization, most people regarded intersection points of a function and y=x as intersection points of a function and its inverse. To find why they used the method to find intersection points, we investigated 10 mathematics textbooks. As a result, 23 tasks were related a linear function, quadratic function, or irrational function. 21 tasks were solved by using an equation f(x)=x. 3 textbooks presented that a set of intersection points of a function and its inverse was not equal to a set of intersection points of a function and y=x. And there was no textbook to present that a set of intersection points of a function and its inverse was equal to a set of intersection points of $y=(f{\circ}f)(x)$ and y=x.

On the Radial Basis Function Networks with the Basis Function of q-Normal Distribution

  • Eccyuya, Kotaro;Tanaka, Masaru
    • Proceedings of the IEEK Conference
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    • pp.26-29
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    • 2002
  • Radial Basis Function (RBF) networks is known as efficient method in classification problems and function approximation. The basis function of RBF networks is usual adopted normal distribution like the Gaussian function. The output of the Gaussian function has the maximum at the center and decrease as increase the distance from the center. For learning of neural network, the method treating the limited area of input space is sometimes more useful than the method treating the whole of input space. The q-normal distribution is the set of probability density function include the Gaussian function. In this paper, we introduce the RBF networks with the basis function of q-normal distribution and actually approximate a function using the RBF networks.

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Does a cognitive-exercise combined dual-task training have better clinical outcomes for the elderly people with mild cognitive impairment than a single-task training?

  • Park, Jin-Hyuck
    • Therapeutic Science for Rehabilitation
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    • v.6 no.2
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    • pp.71-83
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    • 2017
  • Objective: This study was to develop and verify the effects of the exercise-cognitive combined dual-task training program on cognitive function and depression of the elderly with mild cognitive impairment(MCI). Methods: The subjects were randomly assigned to the exercise-cognitive combined dual-task training group(n=32) or single-task training group(n=31). To identify the effects on cognitive function, general cognitive function, frontal lobe function, and attention/working memory were measured. Depression was evaluated using Korean version of Geriatric Depression Scale. The outcome measurements were performed before and after the 8 weeks of intervention(2 days per week). Results: After 8 weeks, general cognitive function, frontal cognitive function, attention/working memory function, depression of the dual-task training group were significantly increased than those of the single-task training group(p<0.05). Conclusion: The results indicated that an exercise-cognitive combined dual-task training for MCI was effective in improving general cognitive function, frontal /executive function, attention/working memory function and reducing depression.

CERTAIN INTEGRAL FORMULAS ASSOCIATED WITH ALEPH (ℵ)-FUNCTION

  • Agarwal, Praveen;Jain, Shilpi;Karimov, Erkinjon T.;Prajapati, Jyotindra C.
    • Communications of the Korean Mathematical Society
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    • v.32 no.2
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    • pp.305-319
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    • 2017
  • Recently many authors have investigated so-called Aleph (${\aleph}$)-function and its various properties. Here, in this paper, we aim at establishing certain integral formulas involving the Aleph (${\aleph}$)-function. Precisely, integrals with product of Aleph (${\aleph}$)-function with Jacobi polynomials, Bessel Maitland function, general class of polynomials were under consideration. Some interesting special cases of our main result are also considered and shown to be connected with certain known ones.

EXTENSION OF EXTENDED BETA, HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTIONS

  • Choi, Junesang;Rathie, Arjun K.;Parmar, Rakesh K.
    • Honam Mathematical Journal
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    • v.36 no.2
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    • pp.357-385
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    • 2014
  • Recently several authors have extended the Gamma function, Beta function, the hypergeometric function, and the confluent hypergeometric function by using their integral representations and provided many interesting properties of their extended functions. Here we aim at giving further extensions of the abovementioned extended functions and investigating various formulas for the further extended functions in a systematic manner. Moreover, our extension of the Beta function is shown to be applied to Statistics and also our extensions find some connections with other special functions and polynomials such as Laguerre polynomials, Macdonald and Whittaker functions.