• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권1호
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• pp.1-17
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• 2008

Here, we consider the existence and uniqueness solution of nonlinear integral equation of the second kind of type Volterra-Hammerstein. Also, the normality and continuity of the integral operator are discussed. A numerical method is used to obtain a system of nonlinear integral equations in position. The solution is obtained, and many applications in one, two and three dimensionals are considered.

• 충청수학회지
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• 제15권2호
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• pp.41-46
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• 2003

In this paper, we investigate the $SP_{\alpha}$-integral and the $M_{\alpha}$-integral defined on an interval of the n-dimensional Euclidean space $\mathbb{R}^n$. In particular, we show that these two integrals are equivalent.

• 대한수학회지
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• 제46권5호
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• pp.1087-1103
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• 2009

Given a system of s independent 1-forms on a smooth manifold M of dimension m, we study the existence of integral manifolds by means of various generalized versions of the Frobenius theorem. In particular, we present necessary and sufficient conditions for there to exist s'-parameter (s' < s) family of integral manifolds of dimension p := m-s, and a necessary and sufficient condition for there to exist integral manifolds of dimension p', p' $\leq$ p. We also present examples and applications to complex analysis in several variables.

• 충청수학회지
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• 제24권3호
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• pp.469-480
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• 2011

Park, Ryu, and Lee recently defined a Henstock-type integral, which lies entirely between the McShane and the Henstock integrals. This paper presents two characterizing convergence conditions for this integral, and derives other known convergence theorems as corollaries.

• 한국경영과학회지
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• 제21권2호
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• pp.49-58
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• 1996

The generalized Erlang loss function, extensively studied in the literature, is revisited. We study the steady state loss probability in M/M/s/s + c queueing system and prove that it satisfies the first and second order properties in integral number of servers as well as integral queue capacities. Also we study the problem of allocating integral number of servers and queue capacities, and develop an algorithm to obtian an optimal allocation of them individually and jointly with the small number of computations.

• 충청수학회지
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• 제27권4호
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• pp.661-674
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• 2014

In this paper, we define the $M_{\alpha}$-delta integral and investigate the relation between the $M_{\alpha}$ and $M_{\alpha}$-delta integrals on time scales.

• 대한수학회논문집
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• 제37권2호
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• pp.415-421
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• 2022

This paper presents a fundamental theorem of calculus, an integration by parts formula and a version of equiintegrability convergence theorem for the M_α-integral using the M_α-strong Lusin condition. In the convergence theorem, to be able to relax the condition of being point-wise convergent everywhere to point-wise convergent almost everywhere, the uniform M_α-strong Lusin condition was imposed.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2002년도 춘계 학술발표회 논문집
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• pp.55-60
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• 2002

We present an extension of the Wong-Zakai type approximation theorem for a multiple stochastic integral. Using a piecewise linear approximation $W^{(n)}$ of a Wiener process W, we prove that the multiple integral processes {${\int}_{0}^{t}{\cdots}{\int}_{0}^{t}f(t_{1},{\cdots},t_{m})W^{(n)}(t_{1}){\cdots}W^{(n)}(t_{m}),t{\in}[0,T]$} where f is a given symmetric function in the space $C([0,T]^{m})$, converge to the multiple Stratonovich integral of f in the uniform $L^{2}$-sense.

• 대한수학회지
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• 제33권4호
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• pp.763-775
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• 1996

For $Q = [0,S] \times [0,T]$ let C(Q) denote Yeh-Wiener space, i.e., the space of all real-valued continuous functions x(s,t) on Q such that x(0,t) = x(s,0) = 0 for every (s,t) in Q. Yeh [10] defined a Gaussian measure $m_y$ on C(Q) (later modified in [13]) such that as a stochastic process ${x(s,t), (s,t) \epsilon Q}$ has mean $E[x(s,t)] = \smallint_{C(Q)} x(s,t)m_y(dx) = 0$ and covariance $E[x(s,t)x(u,\upsilon)] = min{s,u} min{t,\upsilon}$. Let $C_\omega \equiv C[0,T]$ denote the standard Wiener space on [0,T] with Wiener measure $m_\omega$. Yeh [12] introduced the concept of the conditional Wiener integral of F given X, E(F$\mid$X), and for case X(x) = x(T) obtained some very useful results including a Kac-Feynman integral equation.

• 대한수학회논문집
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• 제29권2호
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• pp.227-237
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• 2014

For an $m{\times}n$ nonnegative integral matrix A, a generalized inverse of A is an $n{\times}m$ nonnegative integral matrix G satisfying AGA = A. In this paper, we characterize nonnegative integral matrices having generalized inverses using the structure of nonnegative integral idempotent matrices. We also define a space decomposition of a nonnegative integral matrix, and prove that a nonnegative integral matrix has a generalized inverse if and only if it has a space decomposition. Using this decomposition, we characterize nonnegative integral matrices having reflexive generalized inverses. And we obtain conditions to have various types of generalized inverses.