• Journal of the Korean Mathematical Society
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• v.44 no.3
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• pp.499-509
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• 2007

Let m, n be positive integers or monic polynomials in $\mathbb{F}_q[T]$ with n|m. Let $K_m\;and\;K^+_m$ be the m-th cyclotomic field and its maximal real subfield, respectively. In this paper we define two matrices $D^+_{m,n}\;and\;D^-_{m,n}$ whose determinants give us the ratios $\frac{h(\mathcal{O}_{K^+_m})}{h(\mathcal{O}_{K^+_n})}$ and $\frac{h-(\mathcal{O}_K_m)}{h-(\mathcal{O}_K_n)}$ with some factors, respectively.

• Journal of the Korean Statistical Society
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• v.24 no.2
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• pp.337-347
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• 1995

In the problem of some sequential estimation, the stopping times may be written in the form $N(c) = inf{n \geq n_0; n \geq c^2 S^2_n/\delta^2 (\bar{X}_n)}$ where ${s^2_n}$ and ${\bar{X}_n}$ are the sequences of sample variance and sample mean of the independently and identically distributed (i.i.d.) random variables with distribution $F_{\theta}(x), \theta \in \Theta$, respectively, and $\delta$ is either constant or any given positive real valued function. We obtain some asymptotic normality and asymptotic expectation of the N(c) in various limiting situations. Specially, uniform asymptotic normality and uniform asymptotic expectation of the N(c) are given.

• 유공압시스템학회:학술대회논문집
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• 2010.06a
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• pp.81-85
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• 2010

This paper deals with the issue of motion control of a single rod cylinder-load system using simple adaptive control (SAC) method. Prior to controller design, the experiment of open-loop response has been performed. Based on it, design parameters of transfer function are obtained. The effect of parallel feedforward compensator has been investigated by computer simulation, suppressing the oscillatory motion. Through experiments it is conformed that the SAC method gives good tracking performance compared to the PD control method.

• Journal of KIEE
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• v.10 no.1
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• pp.7-15
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• 2000

Source separation is a statistical method, the goal of which is to separate the linear instantaneous mixtures of statistically independent sources without resorting to any prior knowledge. This paper addresses a source separation algorithm which is able to separate the mixtures of sub- and super-Gaussian sources. The nonlinear function in the proposed algorithm is derived from the generalized Gaussian distribution that is a set of distributions parameterized by a real positive number (Gaussian exponent). Based on the relationship between the kurtosis and the Gaussian exponent, we present a simple and efficient way of selecting proper nonlinear functions for source separation. Useful behavior of the proposed method is demonstrated by computer simulations.

• Journal of the Korean Institute of Landscape Architecture
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• v.25 no.1
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• pp.18-35
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• 1997

This research aims at exploring the relationship between urban greenery and urban landscape and thereby deriving proper planning indicators of urban landscape, For the purpose, this research used survey research method which asked urban residents to answer the research questionnaires about the urban landscape which was presented by slide projection. The analysis results are as follows: 1) urban residents have highly positive image about the greenery; 2) they highly evaluate urban beautification and amenity function of the greenery; 3) the supply of the greenery is very short regardless of the survey locations; 4) due to the small amount of the greenery, its role in landscape is little. Landscape assessment can be approached from various aspects. Urban residents cognitively regard greenery important, however, in real situation it is not necessarily true. There is a discrepancy of the residents'expectation for the role of the greenery in the reality. Therefore, it is difficult to apply residents'evaluation directly to landscape planning. It is recommended that both planners'judgement and the residents'expectation should be balanced in the planning process.

• Communications for Statistical Applications and Methods
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• v.26 no.3
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• pp.239-259
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• 2019

The transmuted generalized extreme value (TGEV) distribution was first introduced by Aryal and Tsokos (Nonlinear Analysis: Theory, Methods & Applications, 71, 401-407, 2009) and applied by Nascimento et al. (Hacettepe Journal of Mathematics and Statistics, 45, 1847-1864, 2016). However, they did not give explicit expressions for all the moments, tail behaviour, quantiles, survival and risk functions and order statistics. The TGEV distribution is a more flexible model than the simple GEV distribution to model extreme or rare events because the right tail of the TGEV is heavier than the GEV. In addition the TGEV distribution can adjusted various forms of asymmetry. In this article, explicit expressions for these measures of the TGEV are obtained. The tail behavior and the survival and risk functions were determined for positive gamma, the moments for nonzero gamma and the moment generating function for zero gamma. The performance of the maximum likelihood estimators (MLEs) of the TGEV parameters were tested through a series of Monte Carlo simulation experiments. In addition, the model was used to fit three real data sets related to financial returns.

• Journal of applied mathematics & informatics
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• v.41 no.6
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• pp.1181-1191
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• 2023

This paper investigates Young inequalities for matrices, a problem closely linked to operator theory, mathematical physics, and the arithmetic-geometric mean inequality. By obtaining new inequalities for unitarily invariant norms, we aim to derive a fresh Young inequality specifically designed for matrices.To lay the foundation for our study, we provide an overview of basic notation related to matrices. Additionally, we review previous advancements made by researchers in the field, focusing on Young improvements.Building upon this existing knowledge, we present several new enhancements of the classical Young inequality for nonnegative real numbers. Furthermore, we establish a matrix version of these improvements, tailored to the specific characteristics of matrices. Through our research, we contribute to a deeper understanding of Young inequalities in the context of matrices.

• Communications of the Korean Mathematical Society
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• v.25 no.4
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• pp.557-569
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• 2010

Suppose that n is a positive integer. For any real number $\alpha$($\beta$ resp.) with $\alpha$ < 1 ($\beta$ > 1 resp.), let $K^{(n)}(\alpha)$ ($K^{(n)}(\beta)$ resp.) be the class of analytic functions in the unit disk $\mathbb{D}$ with f(0) = f'(0) = $\cdots$ = $f^{(n-1)}(0)$ = $f^{(n)}(0)-1\;=\;0$, Re($\frac{zf^{n+1}(z)}{f^{(n)}(z)}+1$) > $\alpha$ (Re($\frac{zf^{n+1}(z)}{f^{(n)}(z)}+1$) < $\beta$ resp.) in $\mathbb{D}$, and for any ${\lambda}\;{\in}\;\bar{\mathbb{D}}$, let $K^{(n)}({\alpha},\;{\lambda})$ $K^{(n)}({\beta},\;{\lambda})$ resp.) denote a subclass of $K^{(n)}(\alpha)$ ($K^{(n)}(\beta)$ resp.) whose elements satisfy some condition about derivatives. For any fixed $z_0\;{\in}\;\mathbb{D}$, we shall determine the two regions of variability $V^{(n)}(z_0,\;{\alpha})$, ($V^{(n)}(z_0,\;{\beta})$ resp.) and $V^{(n)}(z_0,\;{\alpha},\;{\lambda})$ ($V^{(n)}(z_0,\;{\beta},\;{\lambda})$ resp.). Also we shall determine the extreme points of the families of analytic functions which satisfy $f(\mathbb{D})\;{\subset}\;V^{(n)}(z_0,\;{\alpha})$ ($f(\mathbb{D})\;{\subset}\;V^{(n)}(z_0,\;{\beta})$ resp.) when f ranges over the classes $K^{(n)}(\alpha)$ ($K^{(n)(\beta)$ resp.) and $K^{(n)}({\alpha},\;{\lambda})$ ($K^{(n)}({\beta},\;{\lambda})$ resp.), respectively.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.1085-1100
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• 2023

For any given function f, we focus on the so-called prescribed mean curvature problem for the measure e^-f(|x|2)dx provided thate^-f(|x|2) ∈ L¹(ℝⁿ⁺¹). More precisely, we prove that there exists a smooth hypersurface M whose metric is ds² = dρ² + ρ²d𝜉² and whose mean curvature function is ${\frac{1}{n}}(\frac{u^p}{{\rho}^{\beta}})e^{f({\rho}^2)}{\psi}(\xi)$ for any given real constants p, β and functions f and ψ where u and ρ are the support function and radial function of M, respectively. Equivalently, we get the existence of a smooth solution to the following quasilinear equation on the unit sphere 𝕊ⁿ, $${\sum_{i,j}}({{\delta}_{ij}-{\frac{{\rho}_i{\rho}_j}{{\rho}^2+|{\nabla}{\rho}|^2}})(-{\rho}ji+{\frac{2}{{\rho}}}{\rho}j{\rho}i+{\rho}{\delta}_{ji})={\psi}{\frac{{\rho}^{2p+2-n-{\beta}}e^{f({\rho}^2)}}{({\rho}^2+|{\nabla}{\rho}|^2)^{\frac{p}{2}}}}$$ under some conditions. Our proof is based on the powerful method of continuity. In particular, if we take $f(t)={\frac{t}{2}}$, this may be prescribed mean curvature problem in Gauss measure space and it can be seen as an embedded result in Gauss measure space which will be needed in our forthcoming papers on the differential geometric analysis in Gauss measure space, such as Gauss-Bonnet-Chern theorem and its application on positive mass theorem and the Steiner-Weyl type formula, the Plateau problem and so on.

• Tribology and Lubricants
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• v.39 no.6
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• pp.221-227
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• 2023

A rotordynamic system consists of components that undergo rotational motion. These components include shafts, impellers, thrust collars, and components that support rotation, such as bearings and seals. The motion of this type of rotating system can be modeled as two-dimensional motion and, accordingly, the equation of motion for the rotordynamic system can be represented using complex coordinates. The directional frequency response function (dFRF) can be derived from this complex coordinate system and used as an effective analytical tool for rotating machinery. However, the dFRF is not widely used in the field because most previous studies and commercial software are based on real coordinate systems. The objective of the current study is to introduce the dFRF and show that it can be an effective tool in rotordynamic analysis. In this study, the normal frequency response function (nFRF) and dFRF are compared under rotordynamic analysis for isotropic and unisotropic rotors. Results show that in the nFRF, the magnitude of the response is the same for both positive and negative frequencies, and the response is similar under all modes. Consequently, the severity of the mode cannot be identified. However, in the dFRF, the forward and backward modes are clearly distinguishable in the frequency domain of the isotropic rotor, and the severity of the mode can be identified for the unisotropic rotor.