• 호남수학학술지
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• 제29권4호
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• pp.577-588
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• 2007

Bearman's rotation theorem is not only very important in pure mathematics but also plays the key role for various research areas, related to Wiener measure. In 2002, the author and professor Im introduced the concept of analogue of Wiener measure, a kind of generalization of Wiener measure and they presented the several papers associated with it. In this article, we prove a formula on analogue of Wiener measure, similar to the formula in Bearman's rotation theorem.

• 호남수학학술지
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• 제30권4호
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• pp.723-732
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• 2008

In this note, we establish the uniqueness theorem of conditional expectation on analogue of Wiener measure space for given distributions and prove the simple formula of conditional expectation on analogue of Wiener measure which is essentially similar to Park and Skoug's formula on the concrete Wiener measure.

• 한국실내디자인학회논문집
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• 제20권2호
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• pp.64-71
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• 2011

There are a method to analyze reactions or psychological condition and a method to observe visitor's behavioral reaction as methods to measure and evaluate humans' recognition behavior reaction of humans. The measure of the eye movement as a method to living body's reaction and psychological condition has an advantage to measure the information acceptance reaction of view recognition of the stimulus of view composition factors which has been used since a long time ago in other research areas, but almost not studies have been made on the exhibition views in museums. Therefore, on the premise of such recognition, this study aimed at obtaining various types of information through vision angles of visitor in exhibition space of an museum and judging space information, at measuring the condition of information acceptance through attention experiments and observation investigation of and finding out the disposition and characteristics so as to verify the relationship between the exhibition space and exhibition Method.

• 대한수학회지
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• 제33권3호
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• pp.541-555
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• 1996

The Fourier transform plays a central role in the theory of distribution on Euclidean spaces. Although Lebesgue measure does not exist in infinite dimensional spaces, the Fourier transform can be introduced in the space $(S)^*$ of generalized white noise functionals. This has been done in the series of paper by H.-H. Kuo [1, 2, 3], [4] and [5]. The Fourier transform $F$ has many properties similar to the finite dimensional case; e.g., the Fourier transform carries coordinate differentiation into multiplication and vice versa. It plays an essential role in the theory of differential equations in infinite dimensional spaces.

• 대한수학회지
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• 제33권4호
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• pp.993-1008
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• 1996

The white noise analysis, initiated by Hida [3] in 1975, has been developed to an infinite dimensional distribution theory on Gaussian space $(E^*, \mu)$ as an infinite dimensional analogue of Schwartz distribution theory on Euclidean space with Legesgue measure. The mathematical framework of white noise analysis is the Gel'fand triple $(E) \subset (L^2) \subset (E)^*$ over $(E^*, \mu)$ where $\mu$ is the standard Gaussian measure associated with a Gel'fand triple $E \subset H \subset E^*$.

• 대한수학회논문집
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• 제17권1호
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• pp.71-80
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• 2002

We give a formulation of the large deviation property for rescalings of random measures on the d-dimensional Euclidean space R$^{d}$ . The approach is global in the sense that the objects are Radon measures on R$^{d}$ and the dual objects are the continuous functions with compact support. This is applied to the cluster random measures with Poisson centers, a large class of random measures that includes the Poisson processes.

• 대한수학회논문집
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• 제35권3호
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• pp.907-916
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• 2020

In this paper, we introduce the notion of p-distance in a complex uncertain sequence space. By using the concepts of p-distance, we give some theorems of convergence. Also, in a complex uncertain sequence space, we develope some properties on convergence in measure.

• 한국정보디스플레이학회:학술대회논문집
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• 한국정보디스플레이학회 2002년도 International Meeting on Information Display
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• pp.617-620
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• 2002

Quantitative analysis of dynamic false contours on PDP is essential to evaluate the performance of algorithms for false contour reduction. It also serves as an optimization criterion for selecting the subfield pattern. In this paper, a color difference in uniform color space is defined as a new measure for dynamic false contours. Unlike the measures in previous works, it accounts for the channel dependencies among the RGB color channels.

• 음성과학
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• 제3권
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• pp.148-155
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• 1998

As an application of dimensional analysis in the theory of chaos and fractals, we studied and estimated the information dimension for various phonemes. By constructing phase-space vectors from the time-series speech signals, we calculated the natural measure and the Shannon's information from the trajectories. The information dimension was finally obtained as the slope of the plot of the information versus space division order. The information dimension showed that it is so sensitive to the waveform and time delay. By averaging over frames for various phonemes, we found the information dimension ranges from 1.2 to 1.4.

• 대한수학회논문집
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• 제10권1호
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• pp.207-213
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• 1995

Let $(\Omega, F, P)$ be a probability space with F a $\sigma$-algebra of subsets of the measure space $\Omega$ and P a probability measure on $\Omega$. Suppose $a > 0$ and let $(F_t)_{t \in [0,a]}$ be an increasing family of sub-$\sigma$-algebras of F. If $r > 0$, let $J = [-r,0]$ and $C(J, R^n)$ the Banach space of all continuous paths $\gamma : J \to R^n$ with the sup-norm $\Vert \gamma \Vert = sup_{s \in J}$\mid$\gamma(s)$\mid$$ where $$\mid$\cdot$\mid$$ denotes the Euclidean norm on $R^n$. Let E,F be separable real Banach spaces and L(E,F) be the Banach space of all continuous linear maps $T : E \to F$.