• 대한수학회지
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• 제54권1호
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• pp.319-357
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• 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.

• 대한수학회보
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• 제48권4호
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• pp.779-789
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• 2011

In this paper we study the Banach space $L^1$(G) of real valued measurable functions which are integrable with respect to a vector measure G in the sense of D. R. Lewis. First, we investigate conditions for a scalarly integrable function f which guarantee $f{\in}L^1$(G). Next, we give a sufficient condition for a sequence to converge in $L^1$(G). Moreover, for two vector measures F and G with values in the same Banach space, when F can be written as the integral of a function $f{\in}L^1$(G), we show that certain properties of G are inherited to F; for instance, relative compactness or convexity of the range of vector measure. Finally, we give some examples of $L^1$(G) related to the approximation property.

• 천문학회보
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• 제46권1호
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• pp.43.4-44
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• 2021

99942 Apophis is an Sq-type Aten group Near-Earth Asteroid (NEA) with an estimated size of 370 m. It will approach the Earth to come within the geostationary orbit during the upcoming encounter on April 13, 2029 to offer a unique chance to study its 1) global properties, 2) surface arrangements, and 3) their detectable changes expected to happen, in sub-meter scale. What measurable scientific goals for the asteroid in this "once a millennium" event could transform our knowledge of planetary science and defense? The Apophis rendezvous mission aims to understand the characteristics of the small solar system body's nature. It also prepares for potential threats from natural objects by measuring in-situ surface, shape, rotation, and orbit changes expected to occur when the target asteroid passes close to the Earth in 2029. We will present an overview of the mission scheduled to be launched from late 2026 to early 2027 and introduce scientific objectives.

• 충청수학회지
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• 제22권4호
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• pp.743-748
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• 2009

In 1970, Fernique proved that there is a positive real number $\alpha$ such that $\int_{\mathbb{B}}\exp\{\alpha{\parallel}x{\parallel}^{2}\}dP(x)$ is finite where ($\mathbb{B},\;P$) is an abstract Wiener measure space and ${\parallel}\;{\cdot}\;{\parallel}$ is a measurable norm on ($\mathbb{B},\;P$) in [2, 3]. In this article, we investigate the existence of the integral $\int_{c}\exp\{\alpha(sup_t{\mid}x(t){\mid})^p\}dm_{\varphi}(x)$ where ($\mathcal{C}$, $m_{\varphi}$) is the analogue of Wiener measure space and p and $\alpha$ are both positive real numbers.

• 대한수학회논문집
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• 제38권3호
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• pp.787-805
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• 2023

Let (Ω, µ) be a measure space and {τ_α}_α∈Ω be a normalized continuous Bessel family for a finite dimensional Hilbert space 𝓗 of dimension d. If the diagonal ∆ := {(α, α) : α ∈ Ω} is measurable in the measure space Ω × Ω, then we show that $$\sup\limits_{{\alpha},{\beta}{\in}{\Omega},{\alpha}{\neq}{\beta}}\,{\mid}{\langle}{\tau}_{\alpha},\,{\tau}_{\beta}{\rangle}{\mid}^{2m}\,{\geq}\,{\frac{1}{({\mu}{\times}{\mu})(({\Omega}{\times}{\Omega}{\backslash}{\Delta})}\;\[\frac{{\mu}({\Omega})^2}{\({d+m-1 \atop m}\)}-({\mu}{\times}{\mu})({\Delta})\],\;{\forall}m{\in}{\mathbb{N}}.$$ This improves 48 years old celebrated result of Welch [41]. We introduce the notions of continuous cross correlation and frame potential of Bessel family and give applications of continuous Welch bounds to these concepts. We also introduce the notion of continuous Grassmannian frames.

• Journal of applied mathematics & informatics
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• 제30권3_4호
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• pp.647-653
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• 2012

In this paper, we consider fuzzy random sets as (measurable) mappings from a probability space into the set of fuzzy sets and prove a uniform strong law of large numbers for sequences of independent and identically distributed fuzzy random sets. Our results generalize those of Bass and Pyke(1984)and Jang and Kwon(1998).

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제13권1호
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• pp.83-90
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• 2013

Intervals can be used in the representation of uncertainty. In this regard, we consider monotone interval-valued set functions and the Choquet integral. This paper investigates characterizations of monotone interval-valued set functions and provides applications of the Choquet integral with respect to monotone interval-valued set functions, on the space of measurable functions with the Hausdorff metric.

• 대한수학회논문집
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• 제22권1호
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• pp.111-119
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• 2007

We consider the growth norm of a measurable function f defined by defined by $${\parallel}f{\parallel}-\sigma=ess\;sup\{\delta_D(z)^\sigma{\mid}f(z)\mid:z{\in}D\}$$, where $\delta_D(z)$ denote the distance from z to ${\partial}D$. We prove some kind of optimal growth norm estimates for a on convex domains.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2001년도 ICCAS
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• pp.151.2-151
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• 2001

In this paper, the design of a two-degree-of-freedom(TDF) controller is proposed to track the reference model, as well as to reject an influence of measurable disturbance for descrpitor system. The TDF controllers based on the Youla parametrization reveals that the design of the feedforward controller and the regulator can be done independently. First, to solve this problem, we will change descriptor system into regular state space system using a state feedback. And then, the feedforward controller is determined by solving a full information approach for augmented system with a nominal control constraint, and the regulator is designed by means of the loop-Shaping method.

• 대한수학회보
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• 제33권1호
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• pp.57-64
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• 1996

Let $(X, B, \mu)$ be a probability space. Then we say $\tau : X \to X$ is a measure-preserving transformation if $\mu(\tau^{-1} E) = \mu(E)$. and we call it an ergodic transformation if $\mu(\tau^{-1}E\DeltaE) = 0$ for a measurable subset E implies $\mu(E) = 0$. An equivalent definition is that constant functions are the only $\tau$-invariant functions.