• 대한수학회지
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• 제48권1호
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• pp.133-146
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• 2011

We employ a hyperbolic tangent function to construct nonlinear transformations which are useful in numerical evaluation of weakly singular integrals and Cauchy principal value integrals. Results of numerical implementation based on the standard Gauss quadrature rule show that the present transformations are available for the singular integrals and, in some cases, give much better approximations compared with those of existing non-linear transformation methods.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2004년도 추계학술대회 학술발표 논문집 제14권 제2호
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• pp.331-334
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• 2004

본 논문에서, 우리는 부호가 있는 구간치 쇼케이적분을 정의하고 부호가 있는 수간치 쇼케이 적분이 이산과 단조성이 없는 경우를 모델화할 수 있는가를 보인다. 더욱이 일시적인 선택, 재화 가격과 복지평가 등의 응용에 관해서도 언급하고자한다.

• Journal of the Korean Statistical Society
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• 제36권3호
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• pp.411-421
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• 2007

The recent work by the authors (see, Withers, 1999; Withers and McGavin, 2006; Withers and Nadarajah, 2006) provided new expressions for repeated upper tail integrals of the univariate normal density and so also for the general Hermite function. Here we derive new expressions for repeated lower tail integrals of the same. The calculations involve the use of Moran's L-function and the Airy function. In particular, the Hermite functions are expressed in terms of Moran's L-function and vice versa.

• 대한수학회지
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• 제45권2호
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• pp.587-596
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• 2008

For convex bodies, chord power integrals were introduced and studied in several papers (see [3], [6], [14], [15], etc.). The aim of this article is to study them further, that is, we establish the Brunn-Minkowski-type inequalities and get the upper bound for chord power integrals of convex bodies. Finally, we get the famous Zhang projection inequality as a corollary. Here, it is deserved to mention that we make use of a completely distinct method, that is using the theory of inclusion measure, to establish the inequality.

• 대한수학회보
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• 제29권2호
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• pp.301-314
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• 1992

In this paper, motivated by [1] and [7] we give a sequential definition of conditional Wiener integral and then use this definition to evaluate conditional Wiener integral of several functions on C [0, T]. The sequential definition is defined as the limit of a sequence of finite dimensional Lebesgue integrals. Thus the evaluation of conditional Wiener integrals involves no integrals in function space [cf, 5].

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.489-503
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• 2007

In this paper, we define signed interval-valued Choquet integrals which have numerous applications in mathematical economics, informatiom theory, expected utility theory, and risk analysis on interval-valued random variables, for examples: interval-valued random payments and interval-valued random profiles, etc. And we discuss axiomatic characterizations of them. Furthermore, we fine some condition that comonotonic additivity of symmetric Choquet integrals on interval-valued random payments is satisfied and give two examples related the main theorem.

• 호남수학학술지
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• 제35권2호
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• pp.137-146
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• 2013

Motivated essentially by their potential for applications in a wide range of mathematical and physical problems, the log-sine and log-cosine integrals have been evaluated, in the existing literature on the subject, in many different ways. The main object of this paper is to present explicit evaluations of some families of log-sine and log-cosine integrals by making use of the familiar Beta function.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2005년도 춘계학술대회 학술발표 논문집 제15권 제1호
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• pp.170-173
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• 2005

We note that Jang et at. studied closed set-valued Choquet integrals with respect to fuzzy measures. In this paper, we consider Choquet integrals of compact set-valued functions, and prove some properties of them. In particular, using compact set-valued functions, instead of interval valued we investigate characterization of compact set-valued Choquet integrals.

• 호남수학학술지
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• 제43권1호
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• pp.26-34
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• 2021

In this paper two interesting double integrals involving product of two generalized hypergeometric functions have been evaluated in terms of gamma function. The results are derived with the help of known integrals involving hypergeometric functions recorded in the paper of Rathie et al. [6]. We also give several very interesting special cases.

• 호남수학학술지
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• 제42권4호
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• pp.653-665
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• 2020

In this paper, we establish new integral inequalities via Riemann-Liouville fractional integrals and Katugampola fractional integrals for the class of functions whose derivatives in absolute value are exponentially convex functions and exponentially s-convex functions in the second sense.