• Journal of the Korean Mathematical Society
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• v.31 no.3
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• pp.375-391
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• 1994

In 1968k Cameron and Storvick introduced the analytic and the sequential operator-valued function space integral [2]. Since then, the theo교 of the analytic operator-valued function space integral has been investigated by many mathematicians - Cameron, Storvick, Johnson, Skoug, Lapidus, Chang and author etc. But there are not that many papers related to the theory of the sequential operator-valued function space integral. In this paper, we establish the existence of the sequential operator-valued function space integral as an operator from $L_p$ to $L_p'(1 and investigated the integral equation related to this integral.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.1
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• pp.57-63
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• 2020

We investigate the boundedness of the spectrum of a convex base function for a new function space. The result guarantees the continuity of the Calderón-Zygmund operators on the new space.

• Journal of the Korean Society of Environmental Restoration Technology
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• v.15 no.5
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• pp.31-48
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• 2012

The purpose of this study is to select indicators by a methodical approach and to establish a functional assessment system as a basic study for planning and constructing green space of forest. The types of green space were divided into 6 classes based on theoretical reviews of literature and the functions of green space were restricted to 'nature-ecological function', 'environment-control function' and 'usage function'. As a result of the selection of indicators, 35 indicators were initially selected by theoretical review and these indicators were reduced to 29 through brainstorming. Also, these indicators were classified into three functions such as 12 indicators (nature-ecological function), 8 indicators (environment-control function), 6 indicators (usage function) by analysis of suitability. According to the result of selection of the optimum indicators using MCB (Multiple Comparisons with the Best treatment) analysis, the optimum indicators of 7, 5, and 4 respectively by each function were selected for forest green space. The results of AHP (Analytic Hierarchy Process) for the establishment of the assessment system in forest, the weight of nature-ecological function was evaluated highest at 0.558, while the weight of environment-control and usage function were calculated at each 0.277, 0.165. 'Naturality (0.189)', 'Carbon sink (0.235)', and 'Accessibility (0.354)' among indicators showed highest by each function. The weight of indicator and assessment system may be used as a valuable guideline in case of assessing synthetically green space within urban planning.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.471-481
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• 2008

We develop a new function space $L_{\alpha}(X)$ that generalizes the classical Lebesgue space $L^p(X)$. The generalization is focused on a better explanation of the flux terms arising from many dynamics.

• Journal of the Korean Mathematical Society
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• v.56 no.5
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• pp.1387-1401
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• 2019

Consider a finite measure space (${\Omega}$, ${\Sigma}$, ${\mu}$) and a Banach space $X({\mu})$ consisting of (equivalence classes of) real measurable functions defined on ${\Omega}$ such that $f{\chi}_A{\in}X({\mu})$ and ${\parallel}f{\chi}_A{\parallel}{\leq}{\parallel}f{\parallel}$, ${\forall}f{\in}({\mu})$, $A{\in}{\Sigma}$. We prove that if it satisfies the subsequence property, then it is an ideal of measurable functions and has an equivalent norm under which it is a Banach function space. As an application we characterize norms that are equivalent to a Banach function space norm.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.339-350
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• 2005

A space-time fractional advection-dispersion equation (ADE) is a generalization of the classical ADE in which the first-order time derivative is replaced with Caputo derivative of order $\alpha{\in}(0,1]$, and the second-order space derivative is replaced with a Riesz-Feller derivative of order $\beta{\in}0,2]$. We derive the solution of its Cauchy problem in terms of the Green functions and the representations of the Green function by applying its Fourier-Laplace transforms. The Green function also can be interpreted as a spatial probability density function (pdf) evolving in time. We do the same on another kind of space-time fractional advection-dispersion equation whose space and time derivatives both replacing with Caputo derivatives.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.179-190
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• 2005

We deal with the Cauchy problem for the space-time fractional diffusion equation, which is obtained from standard diffusion equation by replacing the second-order space derivative with a Caputo (or Riemann-Liouville) derivative of order ${\beta}{\in}$ (0, 2] and the first-order time derivative with Caputo derivative of order ${\beta}{\in}$ (0, 1]. The fundamental solution (Green function) for the Cauchy problem is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. We derive explicit expression of the Green function. The Green function also can be interpreted as a spatial probability density function evolving in time. We further explain the similarity property by discussing the scale-invariance of the space-time fractional diffusion equation.

• Journal of the Korean Mathematical Society
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• v.46 no.2
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• pp.327-345
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• 2009

In this paper, we define generalized Fourier-Hermite functionals on a function space $C_{a,b}[0,\;T]$ to obtain a complete orthonormal set in $L_2(C_{a,b}[0,\;T])$ where $C_{a,b}[0,\;T]$ is a very general function space. We then proceed to give a necessary and sufficient condition that a functional F in $L_2(C_{a,b}[0,\;T])$ has a generalized Fourier-Wiener function space transform ${\cal{F}}_{\sqrt{2},i}(F)$ also belonging to $L_2(C_{a,b}[0,\;T])$.

• Journal of the Korean Institute of Rural Architecture
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• v.5 no.3
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• pp.34-43
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• 2003

This study attempts to understanding of outer space elements in a rural house through an analysis nouns for function definition phase in design value engineering. To choose main check objects, this study examines requests by rural dwellers and analyze function definition in design value engineering. The rural dwellers prefers that barrier free design, outdoor working space and security of calamity. Each selected elements are classified the nouns into a main noun by analysis function definition nouns at design VE phase. The nouns are reclassified into the main nouns as a distance, a space, and a form.

• The Pure and Applied Mathematics
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• v.4 no.1
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• pp.47-60
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• 1997

In the theory of the conditional Wiener integral, the integrand is a functional of the standard Wiener process. In this paper we consider a conditional function space integral for functionals of more general stochastic process and the generalized Kac-Feynman integral equation. We first show that the existence of a partial differential equation. We then show that the generalized Kac-Feynman integral equation is equivalent to the partial differential equation.