• 한국지능시스템학회:학술대회논문집
• /
• 한국지능시스템학회 2007년도 추계학술대회 학술발표 논문집
• /
• pp.362-365
• /
• 2007

• 대한수학회지
• /
• 제57권2호
• /
• pp.451-470
• /
• 2020

Let C[0, T] denote an analogue of Wiener space, the space of real-valued continuous functions on the interval [0, T]. For a partition 0 = t₀ < t₁ < ⋯ < t_n < t_n+1 = T of [0, T], define X_n : C[0, T] → ℝⁿ⁺¹ by X_n(x) = (x(t₀), x(t₁), …, x(t_n)). In this paper we derive a simple evaluation formula for Radon-Nikodym derivatives similar to the conditional expectations of functions on C[0, T] with the conditioning function X_n which has a drift and does not contain the present position of paths. As applications of the formula with X_n, we evaluate the Radon-Nikodym derivatives of the functions ∫₀^T[x(t)]^mdλ(t)(m∈ℕ) and [∫₀^Tx(t)dλ(t)]² on C[0, T], where λ is a complex-valued Borel measure on [0, T]. Finally we derive two translation theorems for the Radon-Nikodym derivatives of the functions on C[0, T].

• 정보보호학회논문지
• /
• 제12권4호
• /
• pp.3-14
• /
• 2002

본 논문에서는 대학교를 대상으로 하여 발생 가능한 위협을 분류하여 그에 따른 손실의 크기를 수치화 하는 방법론을 제시하고자 한다. 이러한 손실의 수치화는 경제학적 예측모델을 수립함으로서, 향후 동일한 피해 사례에 대한 예측을 용이하게 하여 손실비용을 최소화하는데 있어서 하나의 방법론이 될 수가 있다. 손실을 수치화 시키는 방법은 다음과 같은 단계로 나눌 수가 있다. 첫째로는 자산을 평가한다. 둘째로는 자산에 영향을 미치는 위협요소를 분류한다. 셋째로는 자산이 가지고 있는 취약성을 분석한다. 넷째로는 어떠한 위협요소가 자산에 손실을 발생시켰을 경우에 손실의 크기를 수치화 시킨다. 그러면 이렇게 수치화 시키는 방법을 예제를 통해서 설명하려고 한다.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제1권1호
• /
• pp.25-27
• /
• 1994

Suppose that X is a Banach space with continuous dual $X^{**}$, ($\Omega$, $\Sigma$, ${\mu}$) is a finite measure space. f : $\Omega\;{\longrightarrow}$ $X^{*}$ is a weakly measurable function such that $\chi$$^{**}$ f $\in$ $L_1$(${\mu}$) for each $\chi$$^{**}$ $\in$ $X^{**}$ and $T_{f}$ : $X^{**}$ \longrightarrow $L_1$(${\mu}$) is the operator defined by $T_{f}$($\chi$$^{**}$) = $\chi$$^{**}$f. In this paper we study the properties of bounded $X^{*}$ - valued weakly measurable functions and bounded $X^{*}$ - valued weak＊ measurable functions.(omitted)

• Journal of applied mathematics & informatics
• /
• 제11권1_2호
• /
• pp.391-399
• /
• 2003

Let (X,S,$\mu$) be a measure space and M be the vector space of all real valued S-measurable functions defined on (X,S,$\mu$). For $E\;{\in}\;S$ with $\mu(E)\;<\;{\infty}$, $d_E$ is a pseudometric on M. With the notion of D = {$d_E$\mid$E\;{\in}\;S,\mu(E)\;<\;{\infty}$}, in this paper we investigate some topological structure T of M. Indeed, we shall show that it is possible to define a complete invariant metric on M which is compatible with the topology T on M.

• 전기학회논문지
• /
• 제67권2호
• /
• pp.277-284
• /
• 2018

In this paper, a new numerical method of finding the roots of a nonlinear system is proposed, which extends the conventional fixed point iterative method by relaxing the constraints on it. The proposed method determines the real valued roots and expands the convergence region by relaxing the constraints on the conventional fixed point iterative method, which transforms the diverging root searching iterations into the converging iterations by employing the metric induced by the geometrical characteristics of a polynomial. A metric is set to measure the distance between a point of a real-valued function and its corresponding image point of its inverse function. The proposed scheme provides the convenience in finding not only the real roots of polynomials but also the roots of the nonlinear systems in the various application areas of science and engineering.

• 대한수학회지
• /
• 제54권1호
• /
• pp.319-357
• /
• 2017

There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions in a way such that uniformly bounded sequences of functions that converge pointwise in the weak (or norm) topology of E are sent to sequences that converge in the weak, norm or weak* topology of the target space. As an application, a new description of uniform closures of convex subsets of C(X, E) is given. Also new and strong results on integral representations of continuous linear operators defined on C(X, E) are presented. A new classes of vector measures are introduced and various bounded convergence theorems for them are proved.

• 한국지능시스템학회논문지
• /
• 제14권3호
• /
• pp.262-266
• /
• 2004

일반적으로 Lebesgue 적분에서 성립하지만 퍼지적분에서 성립되지 않는 성질이 몇 가지 있다. 그 중 하나가 선형성이다. 본 논문에서는 선형성 표현식에서 덧셈을 supremum 으로 곱셈을 infimum으로 대신한 퍼지선형성의 정의를 소개하고 구간값을 갖는 함수의 준노름 퍼지적분이 퍼지가법성을 갖는 퍼지 측도와 연속인 준 노름이 saturated 조건을 만족할 때, [Max] 조건을 만족하는 가측함수에 대해 퍼지선형성이 성립함을 보였다.

• Journal of the Korean Data and Information Science Society
• /
• 제14권1호
• /
• pp.131-141
• /
• 2003

In this paper, we prove that multi-variate fuzzy polynomials are universal approximators for multi-variate fuzzy functions which are the extension principle of continuous real-valued function under $T_W-based$ fuzzy arithmetic operations for a distance measure that Buckley et al.(1999) used. We also consider a class of fuzzy polynomial regression model. A mixed non-linear programming approach is used to derive the satisfying solution.

• 대한수학회보
• /
• 제52권5호
• /
• pp.1579-1586
• /
• 2015

In this paper we investigate the barrellednes of some spaces of X-valued measures, X being a barrelled normed space, and provide examples of non barrelled spaces of bounded linear operators from a Banach space X into a barrelled normed space Y, equipped with the uniform convergence topology.