• 충청수학회지
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• 제12권1호
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• pp.157-162
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• 1999

In this paper, we introduce approximate Perron-Stieltjes integral and approximate Roussel derivative and investigate the differentiability of indefinite approximate Perron-Stieltjes integral.

• 한국수학사학회지
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• 제18권3호
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• pp.107-117
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• 2005

본 논문에서는 선형 헨스톡 적분방정식과 조금 다른 선형 근사 헨스톡 적분방정식을 소개하고, 어떤 적분방정식이 헨스톡 적분의미에서는 해를 갖지 않지만 근사 헨스톡 적분의미에서는 해를 갖는 예를 보이고 더욱 더 우리는 선형 근사 헨스톡 적분방정식의 해의 존재성과 유일성에 대하여 연구하였다.

• 대한수학회보
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• 제41권2호
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• pp.257-267
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• 2004

In this paper, we introduce, for each approximate distribution $\~{T}$ of [a, b], the approximate Henstock-Stieltjes integral with value in Banach spaces. The Henstock integral is a special case of this where $\~{T}\;=\;\{(\tau,\;[a,\;b])\;:\;{\tau}\;{\in}\;[a,\;b]\}$. This new concept generalizes Henstock integral and abstract Perron-Stieltjes integral. We establish a uniform convergence theorem for approximate Henstock-Stieltjes integral, which is an improvement of the uniform convergence theorem for Perron-Stieltjes integral by Schwabik [3].

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.709-717
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• 2005

Integral equations occur naturally in many fields of mechanics and mathematical physics. We consider the Fredholm integral equation of the first kind.In this paper we are interested in integral equation of convolution type. We give approximate solution by Meyer wavelets

• 설비공학논문집
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• 제22권7호
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• pp.468-473
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• 2010

This paper deals with approximate integral solutions to the one-dimensional model describing the charging process of stratified thermal storage tanks. Temperature is assumed to be the form of Fermi-Dirac distribution function, which can be separated to two sets of cubic polynomials for each hot and cold side of thermal boundary layers. Proposed approximate integral solutions are compared to the previous works of the approximate analytic solutions and show reasonable agreement. The approach, however, has benefits in mathematical difficulties, complicated solution form and unstable convergence of series solution founded in the previous analytic solutions. Solutions for a semi-infinite region, which have simple closed form solutions, give close agreement to those for a finite region. Thermocline thickness is obtained in closed form and shows proportional behavior to the square root of time and inverse proportional behavior to the square root of flow rate.

• Journal of applied mathematics & informatics
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• 제33권5_6호
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• pp.699-721
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• 2015

This paper investigates the existence of mild solution for a fractional integro-differential equations with a deviating argument and nonlocal initial condition in an arbitrary separable Hilbert space H via technique of approximations. We obtain an associated integral equation and then consider a sequence of approximate integral equations obtained by the projection of considered associated nonlocal fractional integral equation onto finite dimensional space. The existence and uniqueness of solutions to each approximate integral equation is obtained by virtue of the analytic semigroup theory via Banach fixed point theorem. Next we demonstrate the convergence of the solutions of the approximate integral equations to the solution of the associated integral equation. We consider the Faedo-Galerkin approximation of the solution and demonstrate some convergenceresults. An example is also given to illustrate the abstract theory.

• Nonlinear Functional Analysis and Applications
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• 제26권1호
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• pp.83-92
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• 2021

This paper studies approximate solutions for a class of nonlinear diffusion population models. Our methods are to use the fundamental solution of heat equations to construct integral forms of the models and the well-known Banach compression map theorem to prove the existence of positive solutions of integral equations. Non-steady-state local approximate solutions for suitable harvest functions are obtained by utilizing the approximation theorem of multivariate continuous functions.

• 한국콘텐츠학회논문지
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• 제14권10호
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• pp.1-9
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• 2014

무안경식 3D 디스플레이를 위해 사용되는 집적영상은 일반적으로 평면 렌즈어레이로부터 생성되고 있으나, 좁은 시야각으로 인해 관찰자에게 넓은 시야영역을 제공하지 못한다. 이러한 단점을 보완하기 위해 곡면 렌즈어레이가 제안되었으며, 기술적, 비용적 한계로 인해 이상적인 곡면 렌즈어레이보다는 여러 개의 평면렌즈들을 곡면 유형으로 만든 근사곡면(Approximate Surface) 렌즈어레이가 사용된다. 본 논문에서는 반경 100mm의 구에 $20{\times}8$개의 사각형 평면 렌즈들을 배치하여 근사곡면 렌즈어레이를 구성하였으며, 그 결과 약 2배의 시야각을 넓힐 수 있었다. 특히, 기존연구에서는 집적영상을 수작업으로 만들어내고 있었으나, 본 논문에서는 집적영상을 실시간으로 생성하는 OpenCL GPU 병렬 처리 알고리즘을 제안한다. 그 결과, 다양한 3D 볼륨데이터에 대하여 $15{\times}15$ 크기의 근사곡면 렌즈어레이로부터 집적영상을 12-20 frame/sec 속도로 생성할 수 있었다.

• 대한수학회보
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• 제42권3호
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• pp.535-541
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• 2005

In this paper, we define the ap-Denjoy integral and investigate some properties of the ap-Denjoy integral.

• 충청수학회지
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• 제21권1호
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• pp.79-89
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• 2008

In this paper, we define the ap-Henstock integral and the ap-Denjoy integral of Banach-valued functions, and we investigate some properties of these two integrals. In particular, we show that the ap-Henstock integral is equivalent to the ap-Denjoy integral.