• 대한수학회보
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• 제39권3호
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• pp.423-430
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• 2002

Given operators X and Y acting on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. An interpolating operator for n-operators satisfies the equation $AX_{}i$ = $Y_{i}$ for i/ = 1,2,…, n. In this article, we obtained the following : Let X ＝ ($x_{i\sigma(i)}$ and Y ＝ ($y_{ij}$ be operators in B(H) such that $X_{i\sigma(i)}\neq\;0$ for all i. Then the following statements are equivalent. (1) There exists an operator A in Alg L such that AX = Y, every E in L reduces A and A is a self-adjoint operator. (2) sup ${\frac{\parallel{\sum^n}_{i=1}E_iYf_i\parallel}{\parallel{\sum^n}_{i=1}E_iXf_i\parallel}n\;\epsilon\;N,E_i\;\epsilon\;L and f_i\;\epsilon\;H}$ < $\infty$ and $x_{i,\sigma(i)}y_{i,\sigma(i)}$ is real for all i = 1,2, ....

• 대한수학회지
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• 제55권3호
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• pp.593-604
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• 2018

Recently, a new version of expansiveness which is closely attached to some certain weak version of hyperbolicity was given for $C^1$ vector fields as following: a $C^1$ vector field X will be called rescaling expansive on a compact invariant set ${\Lambda}$ of X if for any ${\epsilon}$ > 0 there is ${\delta}$ > 0 such that, for any $x,\;y{\in}{\Lambda}$ and any time reparametrization ${\theta}:{\mathbb{R}}{\rightarrow}{\mathbb{R}}$, if $d({\varphi}_t(x),\,{\varphi}_{{\theta}(t)}(y)){\leq}{\delta}{\parallel}X({\varphi}_t(x)){\parallel}$ for all $t{\in}{\mathbb{R}}$, then ${\varphi}_{{\theta}(t)}(y){\in}{\varphi}_{(-{\epsilon},{\epsilon})}({\varphi}_t(x))$ for all $t{\in}{\mathbb{R}}$. In this paper, some equivalent definitions for rescaled expansiveness are given.

• 대한수학회보
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• 제38권3호
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• pp.487-493
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• 2001

$Let \Omega$ be a bounded convex domain in C^n$ with smooth boundary. Let M be a subvariety of $\Omega$ which intersects $\partial$$\Omega$ transversally. Suppose that $\Omega$ is totally convex at any point of $\partial$M in the complex tangential directions.For f $\epsilon$O(M)$\bigcap$/TEX>$C^{\infty}$($\overline{M}$/TEX>), there exists F $\epsilon$ o ($\Omega$))$\bigcap$/TEX>$C^{\infty}$($\overline{\Omega}$/TEX>) such that F(z) = f(z) for z $\epsilon$ M.

• 한국전기전자재료학회논문지
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• 제21권10호
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• pp.896-900
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• 2008

A measurement method of the dielectric constant of materials whose standard sample is not prepared easily is proposed. The unprepared sample of the material is placed in a cavity, and the resonant frequency is measured. A commercial software simulates the same sample and the cavity leading to find the correct dielectric constant. The measured samples include a ceramic, a forced glass, and a powdered enamel. The measured dielectric constant of a ceramic, a forced glass, and a powdered enamel are 11-j0.0033(${\epsilon}_{\gamma}=11,\;tan{\delta}=0.0003$), 4.15-j0.053(${\epsilon}_{\gamma}=4.15,\;tan{\delta}=0.0128$), and 3.9-j0.042(${\epsilon}_{\gamma}=3.9,\;tan{\delta}=0.0108$) respectively.

• 대한기계학회논문집B
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• 제21권6호
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• pp.735-746
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• 1997

A nonlinear low-Reynolds-number k-.epsilon. model of Park and Sung was extended to predict the flows over a step with inclined wall, where a boundary layer flow without separation and a separated and reattaching flow coexist. For a better prediction of the flows, a slight modification was made on the function of the wall damping( $f_{\mu}$) and the model constant ( $C_{{\epsilon}1}$) in the .epsilon.-equation. The model performance was validated by comparing the model predictions with the experiment. It was shown that the flows over a step with inclined wall are simulated successfully with the present model.ent model.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2003년도 춘계학술대회
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• pp.2083-2088
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• 2003

This study was performed to analyze the velocity and temperature distributions of the land aquaculture tank for fish breeding. In this study, we analyzed the velocity and temperature distributions in aquarium tank, and the finite volume method and standard ${\kappa}-{\epsilon}$ turbulence model with the SIMPLE computational algorithm are used to study the water flow in the aquarium. The main calculation parameters of the aquarium tank are the inlet flow rate with from 0.5 to 2.0L/M.

• 대한기계학회논문집
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• 제19권8호
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• pp.2039-2050
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• 1995

The nonlinear low-Reynolds-number k..epsilon. model of park and Sung is extended to predict the turbulent heat transports in separated and reattaching flows. The equations of the temperature variance( $k_{\theta}$ and its dissipation rate(.epsilon.$_{\theta}$ are solved, in concert with the equations of the turbulent kinetic energy(k) and its dissiation rate(.epsilon). In the present model, the near-wall effect and the non-equilibrium effect are fully taken into consideration. The validation of the model is then applied to the turbulent flow behind a backward-facing step and the flow over a blunt body. The predicted results of the present model are compared and evaluated with the relevant experiments.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1995년도 Proceedings of the Korea Automation Control Conference, 10th (KACC); Seoul, Korea; 23-25 Oct. 1995
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• pp.10-13
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• 1995

This paper considers the linear-quadratic optimal regulator problem for nonstandard singularly perturbed systems making use of the recursive technique. We first derive a generalized Riccati differential equation by the Hamilton-Jacobi equation. In order to obtain the feedback gain, we must solve the generalized algebraic Riccati equation. Using the recursive technique, we show that the solution of the generalized algebraic Riccati equation converges with the rate of convergence of O(.epsilon.). The existence of a bounded solution of error term can be proved by the implicit function theorem. It is enough to show that the corresponding Jacobian matrix is nonsingular at .epsilon. = 0. As a result, the solution of optimal regulator problem for nonstandard singularly perturbed systems can be obtained with an accuracy of O(.epsilon.$^{k}$ ). The proposed technique represents a significant improvement since the existing method for the standard singularly perturbed systems can not be applied to the nonstandard singularly perturbed systems.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제17권4호
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• pp.267-278
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• 2013

We consider zero range processes with density dependent jump rates g given by $g=g(n,k)=g_1(n)g_2(k/n)$ with $g_1(x)=x^{-\alpha}$ and $$g_2(x)=\{^{x^{-\alpha}\;if\;a&lt;x}_{Mx^{-\alpha}\;if\;x{\leq}a}$$. (0.1) In this case, with 1/2 < a < 1 and ${\alpha}$ > 0, we show that non-complete condensation occurs with maximum cluster size an. More precisely, for any ${\epsilon}$ > 0, there exists $M^*$ > 0 such that, for any 0 < M ${\leq}M^*$, the maximum cluster size is between (a - ${\epsilon}$)n and (a + ${\epsilon}$)n for large n. This provides a simple example of non-complete condensation under perturbation of rates which are deep in the range of perfect condensation (e.g. ${\alpha}$ >> 1) and supports the instability of the condensation transition.

• 한국소성가공학회:학술대회논문집
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• 한국소성가공학회 1999년도 춘계학술대회논문집
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• pp.135-139
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• 1999

The static softening behavior of AISI 4140 could be characterized by the hot torsion test in the temperature ranges of 10$0^{\circ}C$~120$0^{\circ}C$ and strain rate ranges of 0.05/sec~5/sec. Deformation efficiency which was based on dynamic materials model was calculated from flow stress curves obtained continuous deformation. Interrupted deformation was performed with 2 pass deformation in the pass strain ranges of 0.25{{{{ epsilon _p}}}} ~3{{{{ epsilon _p}}}} and interrupted time ranges of 0.5~100sec. The dependences of process variables pass strain ({{{{ epsilon _i}}}}) stain rate ({{{{ {. } atop {$\varepsilon$ } }}}}) temperature (T) and interpass time ({{{{ {t }_{i } }}}}) on static recrystallization (SRX) and metadynamic recrystallization .(MDRX) could be indicidually predicted from the modified Avrami's equations. Comparison of the softening kinetics between MDRX and SRX showed that the rate of MDRX was more rapid than that of SRX for the same deformation variables. Controlled multipass deformations were performed using deformation efficiency static and metadynamic recrystallization of AISI 4140.