• Kyungpook Mathematical Journal
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• 제47권1호
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• pp.91-103
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• 2007

In this paper we prove the Hyers-Ulam-Rassias stability by considering the cases that the approximate remainder ${\varphi}$ is defined by $f(x{\ast}y)+f(x{\ast}y^{-1})-2g(x)-2g(y)={\varphi}(x,y)$, $f(x{\ast}y)+g(x{\ast}y^{-1})-2h(x)-2k(y)={\varphi}(x,y)$, where (G, *) is a group, X is a real or complex Hausdorff topological vector space and f, g, h, k are functions from G into X.

• 대한수학회보
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• 제33권3호
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• pp.377-383
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• 1996

We consider in this paper the following nonlinear regression model $$ (1.1) y_t = f(x_t, \theta_o) + \in_t, t = 1, \ldots, n, $$ where $y_t$ is the tth response, $x_t$ is m-vector imput variable, $\theta_o$ is a p-vector of unknown parameter belong to a parameter space $\Theta, f:R^m \times \Theta \ to R^1$ is a nonlinear known function, and $\in_t$ are independent unobservable random errors with finite second moment.

• 대한수학회보
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• 제50권6호
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• pp.1915-1922
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• 2013

We prove the admissibility of the space $L_0(\mathcal{A},X)$ of vector-valued measurable functions determined by real-valued finitely additive set functions defined on algebras of sets.

• Kyungpook Mathematical Journal
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• 제54권2호
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• pp.189-195
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• 2014

Let X be a compact metric space, B be a unital commutative Banach algebra and ${\alpha}{\in}(0,1]$. In this paper, we first define the vector-valued (B-valued) ${\alpha}$-Lipschitz operator algebra $Lip_{\alpha}$ (X, B) and then study its structure and characterize of its maximal ideal space.

• 충청수학회지
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• 제28권2호
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• pp.207-215
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• 2015

The main goal in the present paper is to obtain a particular solution $g_{{\lambda}{\mu}}$, ${\Gamma}^{\nu}_{{\lambda}{\mu}}$ and an algebraic solution $\bar{g}_{{\lambda}{\mu}}$, $\bar{\Gamma}^{\nu}_{{\lambda}{\mu}}$ by means of $g_{{\lambda}{\mu}}$, ${\Gamma}^{\nu}_{{\lambda}{\mu}}$ in UFT $X_4$.

• Communications for Statistical Applications and Methods
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• 제20권6호
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• pp.491-498
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• 2013

We consider support vector machines(SVM) to predict Y with p numerical variables $X_1$, ${\ldots}$, $X_p$. This paper aims to build a biplot of p explanatory variables, in which the first dimension indicates the direction of SVM classification and/or regression fits. We use the geometric scheme of kernel principal component analysis adapted to map n observations on the two-dimensional projection plane of which one axis is determined by a SVM model a priori.

• Communications for Statistical Applications and Methods
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• 제15권3호
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• pp.343-351
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• 2008

By supervised learning with p predictors, we frequently obtain a prediction function of the form $y\;=\;f(x_1,...,x_p)$. When $p\;{\geq}\;3$, it is not easy to understand the inner structure of f, except for the case the function is formulated as additive. In this study, we propose to use p simple graphs for visual understanding of complex prediction functions produced by several supervised learning engines such as LOESS, neural networks, support vector machines and random forests.

• 대한수학회보
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• 제48권6호
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• pp.1225-1233
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• 2011

In this paper, without assumption of monotonicity, we study the compactness and the connectedness of the weakly efficient solutions set to vector equilibrium problems by using scalarization method in locally convex spaces. Our results improve the corresponding results in [X. H. Gong, Connectedness of the solution sets and scalarization for vector equilibrium problems, J. Optim. Theory Appl. 133 (2007), 151-161].

• 충청수학회지
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• 제27권4호
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• pp.571-579
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• 2014

In this paper, we present new vector generators of a matrix subalgebra $L_{0,n}$, which is isomorphic to the Clifford algebra $C{\ell}_{0,n}$, and we obtain the matrix form of inverse of a vector in $L_{0,n}$. Moreover, we consider the solution of a linear equation $xg_2=g_2x$, where $g_2$ is a vector generator of $L_{0,n}$.

• 한국전자파학회논문지
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• 제24권5호
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• pp.541-548
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• 2013

본 논문에서는 상용 벡터 회로망 분석기를 사용하지 않고도, 신호 발생기, 벡터 전압 수신기, 방향성 결합기, 주파수 혼합기 등의 기본적인 초고주파 장비/소자를 활용하여 평가하고자 하는 초고주자 소자의 2-포트 산란 계수를 측정할 수 있는 시스템을 제안한다. 벡터 회로망 분석기를 대용할 수 있는 산란 계수 측정 시스템의 해석적 모델과 제작방법을 제시하고, 이를 1-포트와 2-포트 소자에 대하여 각각 적용한 산란 계수를 측정하여 구현된 시스템을 평가하였다. 평가 주파수 대역에 따라 비교적 낮은 대역에서는 단일 신호 발생기와 벡터 전압 수신기를 사용한 직접 수신법을, 높은 대역에서는 추가의 신호원과 주파수 혼합기를 사용하여 신호를 하향 복조하는 헤테로다인 방식을 사용하여 산란 계수를 결정짓는 벡터 전압을 수신하였다. 이들 각각의 수신 방법으로 UHF와 X 대역 초고주파 소자의 2-포트 산란 계수를 평가하였고, 그 유효성을 상용 벡터 회로망 분석기로 검증하였다.