• 한국지능시스템학회:학술대회논문집
• /
• 한국지능시스템학회 2007년도 추계학술대회 학술발표 논문집
• /
• pp.195-198
• /
• 2007

In this paper, we consider Lebesgue-type theorems in non-additive measure theory and then investigate interval-valued Choquet integrals and interval-valued fuzzy integral with respect to a additive monotone set function. Furthermore, we discuss the equivalence among the Lebesgue's theorems, the monotone convergence theorems of interval-valued fuzzy integrals with respect to a monotone set function and find some sufficient condition that the monotone convergence theorem of interval-valued Choquet integrals with respect to a monotone set function holds.

• 한국지능시스템학회논문지
• /
• 제17권6호
• /
• pp.749-753
• /
• 2007

In this paper, we consider Lebesgue-type theorems in non-additive measure theory and then investigate interval valued Choquet integrals and interval-valued fuzzy integral with respect to a additive monotone set function. Furthermore, we discuss the equivalence among the Lebesgue's theorems, the monotone convergence theorems of interval-valued fuzzy integrals with respect to a monotone set function and find some sufficient condition that the monotone convergence theorem of interval-valued Choquet integrals with respect to a monotone set function holds.

• 한국전산응용수학회:학술대회논문집
• /
• 한국전산응용수학회 2003년도 KSCAM 학술발표회 프로그램 및 초록집
• /
• pp.7-7
• /
• 2003

We studied closed set-valued Choquet integrals in two papers(1997, 2000) and convergence theorems under some sufficient conditions in two papers(2003), for examples : (i) convergence theorems for monotone convergent sequences of Choquet integrably bounded closed set-valued functions, (ii) covergence theorems for the upper limit and the lower limit of a sequence of Choquet integrably bounded closed set-valued functions. In this presentation, we consider fuzzy number-valued functions and define Choquet integrals of fuzzy number-valued functions. But these concepts of fuzzy number-valued Choquet inetgrals are all based on the corresponding results of interval-valued Choquet integrals. We also discuss their properties which are positively homogeneous and monotonicity of fuzzy number-valued Choquet integrals. Furthermore, we will prove convergence theorems for fuzzy number-valued Choquet integrals. They will be used in the following applications : (1) Subjectively probability and expectation utility without additivity associated with fuzzy events as in Choquet integrable fuzzy number-valued functions, (2) Capacity measure which are presented by comonotonically additive fuzzy number-valued functionals, and (3) Ambiguity measure related with fuzzy number-valued fuzzy inference.

• 대한수학회지
• /
• 제41권2호
• /
• pp.319-344
• /
• 2004

In this paper, we define conditional integrals on abstract Wiener and Hilbert spaces and then obtain a formula for evaluating the integrals. We use this formula to establish the existence of conditional Feynman integrals for the classes $A^{q}$(B) and $A^{q}$(H) of functions on abstract Wiener and Hilbert spaces and then specialize this result to provide the fundamental solution to the Schrodinger equation with the forced harmonic oscillator.tor.

• 한국지능시스템학회논문지
• /
• 제18권2호
• /
• pp.183-186
• /
• 2008

우리는 퍼지 인벡스 집합, 퍼지 프리인벡스 함수, 퍼지 유사-프리인벡스 함수와 퍼지 로그 프리인벡스 함수를 생각한다. 무로푸시 등은 쇼케이적분과 그 응용에 관한 연구를 계속해오고 있다. 이 논문에서는 다음과 같은 쇼케이적분에서의 성질들을 조사한다: 퍼지 프리인벡스성, 퍼지 유사-프리인벡스성과 퍼지 로그 프리인벡스성, 즉, 쇼케이 적분에 의해 정의되는 범함수의 성질들임 더욱이 쇼케이적분의 제센 형태 부등식을 증명한다.

• Kyungpook Mathematical Journal
• /
• 제12권1호
• /
• pp.115-117
• /
• 1972

The purpose of the present paper is to evaluate certain integrals involving Laguerre, Jacobi and Hermite polynomials. These integrals are very useful in case of expansion of any polynomial in a series of Orthogonal polynomials [1, Theo. 56].

• Bulletin of the Korean Chemical Society
• /
• 제33권3호
• /
• pp.779-789
• /
• 2012

In the kinetic theory of dense fluids the many-particle collision bracket integral is given in terms of a classical collision operator defined in the phase space. To find an algorithm to compute the collision bracket integrals, we revisit the eigenvalue problem of the Liouville operator and re-examine the method previously reported [Chem. Phys. 1977, 20, 93]. Then we apply the notion and concept of the eigenfunctions of the Liouville operator and knowledge acquired in the study of the eigenfunctions to cast collision bracket integrals into more convenient and suitable forms for numerical simulations. One of the alternative forms is given in the form of time correlation function. This form, on a further manipulation, assumes a form reminiscent of the Chapman- Enskog collision bracket integrals, but for dense gases and liquids as well as solids. In the dilute gas limit it would give rise precisely to the Chapman-Enskog collision bracket integrals for two-particle collision. The alternative forms obtained are more readily amenable to numerical simulation methods than the collision bracket integrals expressed in terms of a classical collision operator, which requires solution of classical Lippmann-Schwinger integral equations. This way, the aforementioned kinetic theory of dense fluids is made fully accessible by numerical computation/simulation methods, and the transport coefficients thereof are made computationally as accessible as those in the linear response theory.

• Journal of the Korean Statistical Society
• /
• 제14권2호
• /
• pp.87-94
• /
• 1985

This paper extends the results of Ellis and Rosen (1982 a) to some more general integrals and applies our main theorem to compute the specific free energy of some models in statistical mechanics. The general integrals of this paper mean the integrals with respect to the probability measures induced by the sample mean of n i.i.d. random variables taking values in a separable Banach space.

• 대한수학회보
• /
• 제36권3호
• /
• pp.419-439
• /
• 1999

In this paper, we first develop a general formula for evaluating conditional abstract Wiener integrals of cylinder functions. we next use our formula to evaluate the conditional abstract wiener integral of various cylinder functions and then specialize our results to conditional Yeh-Wiener integrals to show that we can obtain the corresponding results by Park and Skoug. We finally obtain a Cameron-Martin translation theorem for conditional abstract Wiener integrals.

• 대한수학회지
• /
• 제43권2호
• /
• pp.425-443
• /
• 2006

The aim of this paper is to obtain several results in approximation by Jackson-type generalizations of complex Picard, Poisson-Cauchy and Gauss-Weierstrass singular integrals in terms of higher order moduli of smoothness. In addition, these generalized integrals preserve some sufficient conditions for starlikeness and univalence of analytic functions. Also approximation results for vector-valued functions defined on the unit disk are given.