• Proceedings of the KSME Conference
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• 2001.11b
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• pp.377-382
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• 2001

A suboptimal control law in turbulent pipe flow is derived and tested. Two sensing variables ${\partial}p/{\partial}{\theta}\;|_w\;and\;{\partial}{\upsilon}_{\theta}/{\partial}r\;|_w$ are applied with two actuations ${\phi}_{\theta}$ and ${\phi}_r$. To test the suboptimal control law, direct numerical simulations of turbulent pipe flow at $Re_r=150$ are performed. When the control law is applied, a $13{\sim}23%$ drag reduction is achieved. The most effective drag reduction is made at the pair of ${\partial}{\upsilon}_{\theta}/{\partial}r\;|_w$ and ${\theta}_r$. An impenetrable virtual wall concept is useful for analyzing the near-wall suction and blowing. The virtual wall concept is useful for analyzing the near-wall behavior of the controlled flow. Comparison of the present suboptimal control with that of turbulent channel flow reveals that the curvature effect is insignificant.

• Honam Mathematical Journal
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• v.25 no.1
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• pp.95-115
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• 2003

Consider the problem of estimating a $p{\times}1$ mean vector ${\theta}(p{\geq}4)$ under the quadratic loss, based on a sample $X_1,\;{\cdots}X_n$. We find an optimal decision rule within the class of Lindley type decision rules which shrink the usual one toward the mean of observations when the underlying distribution is that of a variance mixture of normals and when the norm $||{\theta}-{\bar{\theta}}1||$ is known, where ${\bar{\theta}}=(1/p)\sum_{i=1}^p{\theta}_i$ and 1 is the column vector of ones. When the norm is restricted to a known interval, typically no optimal Lindley type rule exists but we characterize a minimal complete class within the class of Lindley type decision rules. We also characterize the subclass of Lindley type decision rules that dominate the sample mean.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1027-1039
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• 2005

Consider the problem of estimating a $p{\times}1$ mean vector $\theta(p\geq4)$ under the quadratic loss, based on a sample $X_1$, $X_2$, $\cdots$, $X_n$. We find a Lindley type decision rule which shrinks the usual one toward the mean of observations when the underlying distribution is that of a variance mixture of normals and when the norm $\parallel\;{\theta}-\bar{{\theta}}1\;{\parallel}$ is restricted to a known interval, where $bar{{\theta}}=\frac{1}{p}\;\sum\limits_{i=1}^{p}{\theta}_i$ and 1 is the column vector of ones. In this case, we characterize a minimal complete class within the class of Lindley type decision rules. We also characterize the subclass of Lindley type decision rules that dominate the sample mean.

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.875-886
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• 2000

Let G denote either of the groups $GL_2(q)$ or $SL_2(q)$. Then ${\theta}$:G -> G given by ${\theta}(A)$ = ${(A^t)}^{-l}$, where $A^t$ denotes the transpose of the matrix A, is an automorphism of G. Therefore we may form the group G.$<{\theta}>$ which is the split extension of the group G by the cyclic group $<{\theta}>$ of order 2. Our aim in this paper is to find the complex irreducible character table of G.$<{\theta}>$.

• Journal of the Korean Mathematical Society
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• v.50 no.4
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• pp.727-753
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• 2013

In this paper, we introduce three new broad classes of second-order generalized convex functions, namely, ($\mathcal{F}$, $b$, ${\phi}$, ${\rho}$, ${\theta}$)-sounivex functions, ($\mathcal{F}$, $b$, ${\phi}$, ${\rho}$, ${\theta}$)-pseudosounivex functions, and ($\mathcal{F}$, $b$, ${\phi}$, ${\rho}$, ${\theta}$)-quasisounivex functions; formulate eight general second-order duality models; and prove appropriate duality theorems under various generalized ($\mathcal{F}$, $b$, ${\phi}$, ${\rho}$, ${\theta}$)-sounivexity assumptions for a multiobjective programming problem containing arbitrary norms.

• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1879-1903
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• 2017

In this paper we study the closure property and probability tail asymptotics for randomly weighted sums $S^{\Theta}_n={\Theta}_1X_1+{\cdots}+{\Theta}_nX_n$ for long-tailed random variables $X_1,{\ldots},X_n$ and positive bounded random weights ${\Theta}_1,{\ldots},{\Theta}_n$ under similar dependence structure as in [26]. In particular, we study the case where the distribution of random vector ($X_1,{\ldots},X_n$) is generated by an absolutely continuous copula.

• Korean Journal of Materials Research
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• v.6 no.9
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• pp.925-930
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• 1996

Zr이 0.03wt%함유된 Mg-8.14Li-3.93AI 합금의 시효거동을 미소경도와 미세조직의 변화, 열분석 등으로 조사하였다. Zr의 첨가로 인하여 3원계 Mg-8.23Li-4.02A에 비하여 조직이 미세화되었으며 모든 시효조건에서 경도값이 높게 나타났다. 열분석결과 발열피크는 준안정 석출상인 MgLi2AI($\theta$)의 석출과 $\theta$상에서 안정상인 AILi으로의 변화와 관련된 것이고, 흡열피크는 $\theta$와 AILi상의 재용해에 대응되는 것으로 판단되었다. 피크 경도값(103Hv)은 $\theta$의 석출이 완료되는 393K에서 0.5시간 시효시 나타났으며 피크 경도조건에서의 미세조건은 $\beta$기지에 $\theta$와 AILi상이 공존하고 있음을 투과식 전자현미경으로 확인하였다.

• Journal of the Korean Society for Precision Engineering
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• v.18 no.2
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• pp.90-95
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• 2001

f-$\theta$len is one of the important parts in Laser Scanning Unit because it affects on the optical performance of Laser Scanning Unit dominantly. It is necessary to find out the relationship between the surface profile error of f-$\theta$lens and the beam profile focusing on the Organic Photo Conductive drum in order to analysis the beam profile problems such as appearance of side lobe and expansion of center lobe. In this research, a simulation process which relates the surface profile characteristics to the beam profile has been developed by CODE V. The simulated beam profile also have been compared with the measurement results.

• Journal of the Korean Statistical Society
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• v.24 no.2
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• pp.303-312
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• 1995

We consider the following type of general semi-parametric non-linear regression model : $y_i = f_i(\theta) + \epsilon_i, i=1, \cdots, n$ where ${f_i(\cdot)}$ represents the set of non-linear functions of the unknown parameter vector $\theta' = (\theta_1, \cdots, \theta_p)$ and ${\epsilon_i}$ represents the set of measurement errors with unknown distribution. Under suitable finite-sample, small-dispersion asymptotic framework, we derive a general lower bound for the asymptotic mean squared error (AMSE) matrix of the Gauss-consistent estimator of $\theta$. We then prove the fundamental result that the general non-linear least squares estimator (NLSE) is an optimal estimator within the class of all regular Gauss-consistent estimators irrespective of the type of the distribution of the measurement errors.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.2
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• pp.269-278
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• 2008

Let ${\partial}D$ be the boundary of the open unit disk D in the complex plane and $L^p({\partial}D)$ the class of all complex, Lebesgue measurable function f for which $\{\frac{1}{2\pi}{\int}_{-\pi}^{\pi}{\mid}f(\theta){\mid}^pd\theta\}^{1/p}<{\infty}$. Let P be the orthogonal projection from $L^p({\partial}D)$ onto ${\cap}_{n<0}$ ker $a_n$. For $f{\in}L^1({\partial}D)$, ${\hat{f}}(z)=\frac{1}{2\pi}{\int}_{-\pi}^{\pi}P_r(t-\theta)f(\theta)d{\theta}$ is the harmonic extension of f. Let ${\hat{P}}$ be the composition of P with the harmonic extension. In this paper, we will show that if $1, then ${\hat{P}}:L^p({\partial}D){\rightarrow}H^p(D)$ is bounded. In particular, we will show that ${\hat{P}}$ is unbounded on $L^{\infty}({\partial}D)$.