• Kyungpook Mathematical Journal
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• v.47 no.1
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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.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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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.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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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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• v.54 no.2
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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.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.2
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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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• v.20 no.6
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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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• v.15 no.3
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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.

• Bulletin of the Korean Mathematical Society
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• v.48 no.6
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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].

• Journal of the Chungcheong Mathematical Society
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• v.27 no.4
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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 $L_{0,n}$.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.24 no.5
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• pp.541-548
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• 2013

This paper presents a vector network analysis system for 2-port scattering parameters of microwave devices using some basic microwave instruments/devices such as signal generators, vector voltmeter, directional couplers and frequency mixers. The analytical model and implementation method for scattering parameter measurements - which can replace the vector network analyzers - are presented. The performance of the implemented system is evaluated through 1- and 2-port scattering parameter measurements, respectively. The vector volt signals which determine the scattering parameters are detected in two distinct methods depending on the frequency band of interests; a direct-detection method with a single signal generator and vector voltmeter for relatively low band and a heterodyne method to frequency down-mix associated with an additional signal source as well as frequency mixers for high band are used, respectively. Using these two methods, scattering parameters of UHF and X bands are evaluated and their performances are verified through a comercial vector network analyzer.