• 전자공학회논문지SC
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• 제41권4호
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• pp.29-37
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• 2004

본 논문에서는 구동기 고장을 가지는 시간지연 특이시스템의 신뢰 H/sub ∞/ 상태궤환 제어기 설계방법을 제안한다. 미리 설정한 영역내에서의 구동기 고장이 발생함에도 불구하고 특이시스템의 점근적 안정성(asymptotic stability)과 H/sub ∞/ 성능지수를 만족하는 신뢰 H/sub ∞/ 제어기가 존재할 조건과 제어기 설계 기법을 선형행렬부등식, 특이값 분해(singular value decomposition), 슈어 여수정리(Schur complements), 변수 치환 등에 의하여 제시한다. 제안한 충분조건은 구하려는 모든 변수의 견지에서 하나의 선형행렬부등식으로 표현되기 때문에 모든 해를 동시에 구할 수 있다는 장점이 있다. 또한, 제안한 알고리듬을 이용하면 변수불확실성과 시간지연을 가지는 특이시스템에 대한 강인 신뢰(robust reliable) H/sub ∞/ 제어기 설계문제에도 쉽게 확장됨을 보인다. 마지막으로, 제안한 알고리듬의 타당성을 수치예제를 통하여 확인한다.

• 한국추진공학회:학술대회논문집
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• 한국추진공학회 1997년도 제8회 학술강연회논문집
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• pp.259-265
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• 1997

An analytical study has been peformed to investigate the unsteady ignition characteristics of pulse combustion. In many combustion applications, strain rate of the flow can significantly affect the combustion features; ignition, extinction, and reignition. In the pulse combustion, two jets (hot combustion gases and fresh mixtures) coming from the opposite side of the combustor will collide in the combustor forming a stagnation region where the chemical reaction is suppressed by the strain rate until this becomes below the critical value. In this research, the method of large activation energy asymptotic is adopted with one step irreversible kinetics to examine the ignition response to the periodic variation of the strain rate of flow. The results show the variation of the maximum value of strain rate can determine whether the ignition or extinction occur.

• 대한기계학회논문집B
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• 제22권8호
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• pp.1141-1151
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• 1998

An effective thermal conductivity measurement for suspensions of microparticles in oil mixture is conducted in order to evaluate the shear rate-dependence of the thermal conductivity of suspensions. Measurements are made for rotating Couette flows between two concentric cylinders. The rotating outer cylinder is immersed into a constant temperature water bath while the stationary inner cylinder is subject to a uniform heat fluff. Test fluids are made to be homogeneous suspensions, in which neutrally buoyant microparticles ($d=25{\sim}300{\mu}m$) are uniformly dispersed. The present measurements show strong shear-rate dependent thermal conductivities for the suspensions, which are higher than those at zero shear rate. The shear rate dependent thermal conductivity increases with the particle size and volume concentration.4 new model for shear rate-dependent thermal conductivity of microparticle suspensions is proposed; the correlation covers from zero shear rate value to asymptotic plateau value at moderately high shear rates.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.411-423
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• 2010

In this paper, a numerical method for singular perturbation problems arising in chemical reactor theory for general singularly perturbed two point boundary value problems with boundary layer at one end(left or right) of the underlying interval is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.

• 대한수학회보
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• 제48권4호
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• pp.713-724
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• 2011

We study the dynamics of transcendental entire functions with Siegel disks whose singular values are just two points. One of the two singular values is not only a superattracting fixed point with multiplicity more than two but also an asymptotic value. Another one is a critical value with free dynamics under iterations. We prove that if the multiplicity of the superattracting fixed point is large enough, then the restriction of the transcendental entire function near the Siegel point is a quadratic-like map. Therefore the Siegel disk and its boundary correspond to those of some quadratic polynomial at the level of quasiconformality. As its applications, the logarithmic lift of the above transcendental entire function has a wandering domain whose shape looks like a Siegel disk of a quadratic polynomial.

• 대한수학회보
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• 제54권4호
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• pp.1141-1158
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• 2017

In this paper, we study the value distribution of the derivative of a Dirichlet L-function $L^{\prime}(s,{\chi})$ at the a-points ${\rho}_{a,{\chi}}={\beta}_{a,{\chi}}+i{\gamma}_{a,{\chi}}$ of $L^{\prime}(s,{\chi})$. We give an asymptotic formula for the sum $${\sum_{{\rho}_{a,{\chi}};0<{\gamma}_{a,{\chi}}{\leq}T}\;L^{\prime}({\rho}_{a,{\chi}},{\chi})X^{{\rho}_{a,{\chi}}}\;as\;T{\rightarrow}{\infty}$$, where X is a fixed positive number and ${\chi}$ is a primitive character mod q. This work continues the investigations of Fujii [4-6], $Garunk{\check{s}}tis$ & Steuding [8] and the authors [12].

• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.1273-1287
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• 2008

In this paper, the numerical integration method for general singularly perturbed two point boundary value problems with mixed boundary conditions of both left and right end boundary layer is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.

• Journal of the Korean Statistical Society
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• 제26권3호
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• pp.289-297
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• 1997

It is well known that the spacings, the differences of two successive order statistics, in a random sample of size n from a distribution function F are independent and exponentially distributed if F is itself the exponential distribution. In this paper we obtain an asymptotically similar result on a fixed number of upper spacings as n .to. .infty. for a general F under the assumption that F is in the domain of attraction of some extreme value distribution. For a heavy or short tailed F, appropriate log transformations of the sample should be proceded to get the result. As a by-product, we also get that each upper spacing diverges in probability to .infty. and converges in probability to 0 as n .to. .infty. for a heavy and short tailed F, respectively, which is fully expected.

• Korean Journal of Mathematics
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• 제21권4호
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• pp.365-374
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• 2013

Let $k=\mathbb{F}_q(T)$ be a rational function field over the finite field $\mathbb{F}_q$, where q is a power of an odd prime number, and $\mathbb{A}=\mathbb{F}_q[T]$. Let ${\gamma}$ be a generator of $\mathbb{F}^*_q$. Let $\mathcal{H}_n$ be the subset of $\mathbb{A}$ consisting of monic square-free polynomials of degree n. In this paper we obtain an asymptotic formula for the mean value of $L(1,{\chi}_{\gamma}{\small{D}})$ and calculate the average value of the ideal class number $h_{\gamma}\small{D}$ when the average is taken over $D{\in}\mathcal{H}_{2g+2}$.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2000년도 춘계학술대회논문집B
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• pp.132-137
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• 2000

A complete theoretical treatment of the photothermal displacement technique has been performed for thermal diffusivity measurement in solid materials. The influence of parameters - radius and modulation frequency of pump beam and thickness of material - on the phase lag was studied. The phase decreases up to a certain position, then starts to increase and does have an asymptotic value. The position, where phase has the minimum value, is a function of thermal diffusion length thickness of sample, and radius of pump beam. A new method based on minimum phase lag is described to determine the thermal diffusivity of solid material.