• 대한수학회보
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• 제21권2호
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• pp.99-106
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• 1984

J. Yeh has recently introduced the concept of conditional Wiener integrals which are meant specifically the conditional expectation E$^{w}$ (Z vertical bar X) of a real or complex valued Wiener integrable functional Z conditioned by the Wiener measurable functional X on the Wiener measure space (A precise definition of the conditional Wiener integral and a brief discussion of the Wiener measure space are given in Section 2). In [3] and [4] he derived some inversion formulae for conditional Wiener integrals and evaluated some conditional Wiener integrals E$^{w}$ (Z vertical bar X) conditioned by X(x)=x(t) for a fixed t>0 and x in Wiener space. Thus E$^{w}$ (Z vertical bar X) is a real or complex valued function on R$^{1}$. In this paper we shall be concerned with the random vector X given by X(x) = (x(s$_{1}$),..,x(s$_{n}$ )) for every x in Wiener space where 0=s$_{0}$ $_{1}$<..$_{n}$ =t. In Section 3 we will evaluate some conditional Wiener integrals E$^{w}$ (Z vertical bar X) which are real or complex valued functions on the n-dimensional Euclidean space R$^{n}$ . Thus we extend Yeh's results [4] for the random variable X given by X(x)=x(t) to the random vector X given by X(x)=(x(s$_{1}$).., x(s$_{n}$ )).

• 대한수학회지
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• 제38권6호
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• pp.1191-1204
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• 2001

The paper is devoted to the study of fractional integration and differentiation on a finite interval [a, b] of the real axis in the frame of Hadamard setting. The constructions under consideration generalize the modified integration $\int_{a}^{x}(t/x)^{\mu}f(t)dt/t$ and the modified differentiation ${\delta}+{\mu}({\delta}=xD,D=d/dx)$ with real $\mu$, being taken n times. Conditions are given for such a Hadamard-type fractional integration operator to be bounded in the space $X^{p}_{c}$(a, b) of Lebesgue measurable functions f on $R_{+}=(0,{\infty})$ such that for c${\in}R=(-{\infty}{\infty})$, in particular in the space $L^{p}(0,{\infty})\;(1{\le}{\le}{\infty})$. The existence almost every where is established for the coorresponding Hadamard-type fractional derivative for a function g(x) such that $x^{p}$g(x) have $\delta$ derivatives up to order n-1 on [a, b] and ${\delta}^{n-1}[x^{\mu}$g(x)] is absolutely continuous on [a, b]. Semigroup and reciprocal properties for the above operators are proved.

• 대한수학회보
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• 제36권3호
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• pp.589-597
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• 1999

Let G be a closed subspace of a Banach space X and let (S,$\Omega$,$\mu$) be a $\sigma$-finite measure space. It was known that $L_1$(S,G) is proximinal in $L_1$(S,X) if and only if $L_p$(S,G) is proximinal in $L_p$(S,X) for 1$\infty$. In this article we show that this result remains true when "proximinal" is replaced by "Chebyshev". In addition, it is shown that if G is a proximinal subspace of X such that either G or the kernel of the metric projection $P_G$ is separable then, for 0 < p $\leq$ $\infty$. $L_p$(S,G) is proximinal in $L_p$(S,X)

• 대한수학회논문집
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• 제28권2호
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• pp.285-295
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• 2013

In this note we present sufficient conditions for the existence of Radon-Nikodym derivatives (RND) of operator valued measures with respect to scalar measures. The RND is characterized by the Bochner integral in the strong operator topology of a strongly measurable operator valued function with respect to a nonnegative finite measure. Using this result we also obtain a characterization of compact sets in the space of operator valued measures. An extension of this result is also given using the theory of Pettis integral. These results have interesting applications in the study of evolution equations on Banach spaces driven by operator valued measures as structural controls.

• 대한수학회논문집
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• 제10권1호
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• pp.93-107
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• 1995

In their paper [2,3], Cameron and Storvick introduced some classes $S"+m$ and of functionals on classical Wiener spaces $C_0[a,b]$. For such functionals, they showed that the analytic Feynman integral exists and they gave some formulas for this integral. Moreover they obtained that the functionals of the form $$ (1.1) F(x) = exp {\int^b_a{\theta(s,x(x))dx} $$ are in S" where they assumbed that the potential $\delta : [a,b] \times R \to C$ satisfies (i) for each $s \in [a,b], \theta(s,\cdot)$ is the Fourier-Stieltjes transform of $\sigma_s \in M(R)$, (ii) for each Borel subset E of $[a,b] \times R, \sigma_s (E^{(s)})$ is a Borel measurable function of s on [a,b], and (iii) the total variation $\Vert \sigma_s \Vert$ of $\sigma_s$ is bounded as a function of s.tion of s.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1997년도 추계학술대회 학술발표 논문집
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• pp.115-120
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• 1997

System identification is the task of inferring a mathematical description of a dynamic system from a series of measurements of the system. There are several motives for establishing mathematical descriptions of dynamic systems. Typical applications encompass simulation, prediction, fault diagnostics, and control system design. The paper demonstrates that neural networks can be used effective for the identification of nonlinear dynamical systems. The content of this paper concerns dynamic neural network models, where not all inputs to and outputs from the networks are measurable. Only one model type is treated, the well-known Innovation State Space model(Kalman Predictor). The identification is based only on input/output measurements, so in fact a non-linear Extended Kalman Filter problem is solved. Even for linear models this is a non-linear problem without any assurance of convergence, and in spite of this fact an attempt is made to apply the principles from linear models, an extend them to non-linear models. Computer simulation results reveal that the identification scheme suggested are practically feasible.

• Journal of Mechanical Science and Technology
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• 제19권2호
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• pp.618-624
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• 2005

We present a new state-space approach to construct a dynamic output feedback controller which stabilizes a class of linear time invariant systems. All the states of the given system are not measurable and only the output is used to design the stabilizing control law. In the design scheme, however, we first assume that the given system can be stabilized by a feedback law composed of the output and its derivatives of a certain order. Beginning with this assumption, we systematically construct a dynamic system which removes the need of the derivatives. The main advantage of the proposed controller is regarding the controller order, which may be smaller than that of conventional output feedback controller. Using a simple numerical example, it is shown that the order of the proposed controller is indeed smaller than that of reduced-order observer based output feedback controller.

• Kyungpook Mathematical Journal
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• 제55권2호
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• pp.345-353
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• 2015

Subnormality of bounded weighted composition operators on $L^2({\Sigma})$ of the form $Wf=uf{\circ}T$, where T is a nonsingular measurable transformation on the underlying space X of a ${\sigma}$-finite measure space (X, ${\Sigma}$, ${\mu}$) and u is a weight function on X; is studied. The standard moment sequence characterizations of subnormality of weighted composition operators are given. It is shown that weighted composition operators are subnormal if and only if $\{J_n(x)\}^{+{\infty}}_{n=0}$ is a moment sequence for almost every $x{{\in}}X$, where $J_n=h_nE_n({\mid}u{\mid}^2){\circ}T^{-n}$, $h_n=d{\mu}{\circ}T^{-n}/d{\mu}$ and $E_n$ is the conditional expectation operator with respect to $T^{-n}{\Sigma}$.

• 천문학회보
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• 제40권1호
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• pp.77.3-78
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• 2015

It is known that the galaxy evolution by direct interaction between galaxies is most active in a galaxy group. As a result, the satellite galaxies are closely related to their central galaxy in properties such as morphology, color and star formation rate (so-called 'galactic conformity'). However, it is not clear yet whether such conformity between galaxies is found in a galaxy cluster. Recently, Lee et al. (2014) have found a measurable correlation between the colors of bright galaxies and the mean colors of their faint companions in a cluster WHL J085910.0+294957 at z = 0.3, using the photometrically-selected cluster members. They suggest that such correlation may be the vestige of infallen groups in the cluster as one possibility. In order to confirm the small-scale conformity in galaxy clusters with higher reliability, we study the Virgo cluster using the Extended Virgo Cluster Catalog (EVCC). The cluster members are selected spectroscopically unlike in WHL J085910.0+294957. We examine the galactic conformity in two distinct areas of the Virgo cluster: the inner X-ray emission region and its outer region. We find a marginal conformity in color (> $2{\sigma}$ significance to bootstrap uncertainty) in the outer region, while no meaningful signal of small-scale conformity is detected in the X-ray emission region. We discuss the implication of this result, focusing on cluster mass assembly and cluster environmental effects on galaxy evolution.

• 천문학회보
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• 제38권2호
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• pp.55.1-55.1
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• 2013

The properties of bright galaxies are closely related to those neighbors and satellite galaxies. However, the effects of nearby companion are known to be very weak in a galaxy cluster, when the companions are bright galaxies. On the other hand, until now, it has not been clear whether the properties of bright galaxies are affected by their faint satellites in a galaxy cluster. Recently, J. H. Lee et al. (in preparation) have found that the colors of bright galaxies in WHL J085910.0+294957, a galaxy cluster at z = 0.3, show a measurable correlation with the mean colors of faint galaxies around them. To confirm that result and to investigate the host-satellite relationship depending on cluster properties, we carry out follow-up studies of a few galaxy clusters, beginning with Abell 3659 (z ~ 0.0907) imaged in the g' and r' bands using IMACS on the Magellan (Baade) 6.5m telescope. Cluster members are selected based on the distributions of color, size and concentration along magnitude and spatial distribution. In this poster, we present some preliminary results: marginal correlations in color between bright galaxies and their faint companions are found at the central region of Abell 3659. The implication of these results is discussed.