• 대한수학회논문집
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• 제18권4호
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• pp.767-779
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• 2003

We consider a model of population dynamics whose mortality function is unbounded. We approximate the solution of the model using a discontinuous Galerkin finite element for the age variable and a backward Euler for the time variable. We present several numerical examples. It is experimentally shown that the scheme converges at the rate of $h^{3/2}$ in the case of piecewise linear polynomial space.

• 한국산학기술학회논문지
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• 제14권5호
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• pp.2140-2149
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• 2013

혁신에서 불확실성이나 불연속을 경영한다는 것은 대부분의 기업에게 어려운 과제이다. 기업의 지속 가능한 장기적인 생존을 위해 불연속 혁신이 내포하고 있는 문제 중 하나는 혁신가의 딜레마이다. 특히 불연속 혁신과 기존 사업자간의 동태적인 상황은 연구자들과 기업 경영자들에게 큰 관심사항이다. 본 논문은 불연속 혁신이라는 현상을 설명하는 이론적 배경으로 격변이론을 도입한다. 즉, 불연속 혁신에 대한 기업전략의 동태적인 현상을 격변이론의 틀에서 해석함으로써 혁신딜레마를 극복하는 제어인자를 도출한다. 이를 위해 본 논문은 불연속 혁신의 네 가지 유형으로 기술 불연속, 제품 불연속, 사업 불연속, 그리고 소비자 선호도 불연속을 정의하고, 각각의 유형별로 불연속 혁신 실사례를 격변이론의 관점에서 해석함으로써 불연속 혁신을 중심으로 한 기업간 경쟁의 동태적인 상황을 분석하였다. 이러한 분석 과정은 기업 간 경쟁 속에서 예측이 떨어지는 불연속적인 상황에 미리 대처할 수 있는 제어인자를 발굴할 수 있도록 해준다.

• Korean Journal of Mathematics
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• 제13권2호
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• pp.161-176
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• 2005

We consider a model of population dynamics whose mortality function is unbounded. We note that the regularity of the solution depends on the growth rate of the mortality near the maximum age. We propose Gauss-Legendre methods along the characteristics to approximate the solution when the solution is smooth enough. It is proven that the scheme is convergent at fourth-order rate in the maximum norm. We also propose discontinuous Galerkin finite element methods to approximate the solution which is not smooth enough. The stability of the method is discussed. Several numerical examples are presented.

• Structural Engineering and Mechanics
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• 제85권2호
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• pp.207-216
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• 2023

Three time-discontinuous Galerkin quadrature element methods (TDGQEMs) are developed for structural dynamic problems. The weak-form time-discontinuous Galerkin (TDG) statements, which are capable of capturing possible displacement and/or velocity discontinuities, are employed to formulate the three types of quadrature elements, i.e., single-field, single-field/least-squares and two-field. Gauss-Lobatto quadrature rule and the differential quadrature analog are used to turn the weak-form TDG statements into a system of algebraic equations. The stability, accuracy and numerical dissipation and dispersion properties of the formulated elements are examined. It is found that all the elements are unconditionally stable, the order of accuracy is equal to two times the element order minus one or two times the element order, and the high-order elements possess desired high numerical dissipation in the high-frequency domain and low numerical dissipation and dispersion in the low-frequency domain. Three fundamental numerical examples are investigated to demonstrate the effectiveness and high accuracy of the elements, as compared with the commonly used time integration schemes.

• 대한수학회논문집
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• 제22권4호
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• pp.623-640
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• 2007

The Lotka-McKendrick model which describes the evolution of a single population is developed from the well known Malthus model. In this paper, we introduce the Lotka-McKendrick model. We approximate the solution to the model using hp-discontinuous Galerkin finite element method. The numerical results show that the presented hp-discontinuous Galerkin method is very efficient in case that the solution has a sharp decay.

• 대한수학회논문집
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• 제18권3호
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• pp.569-580
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• 2003

The Lotka-McKendrick equation which describes the evolution of a single population under the phenomenological conditions is developed from the well-known Malthus’model. In this paper, we introduce the Lotka-McKendrick equation for the description of the dynamics of a population. We apply a discontinuous Galerkin finite element method in age-time domain to approximate the solution of the system. We provide some numerical results. It is experimentally shown that, when the mortality function is bounded, the scheme converges at the rate of $h^2$ in the case of piecewise linear polynomial space. It is also shown that the scheme converges at the rate of $h^{3/2}$ when the mortality function is unbounded.

• 전기의세계
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• 제28권6호
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• pp.47-51
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• 1979

An optimal problem in which the dynamics is nonlinear and the cost functional includes a discontinuous integrand is investigated. By using Neustadt's abstract maximum principle, a necessary conditions in the form of Pontryagin's maximum principle is derived and it is further shown that this necessary condition is also a sufficient condition for normal problems with linear-in-the-state systems.

• 대한수학회지
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• 제59권1호
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• pp.105-127
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• 2022

It is known that the maximal invariant set of a continuous iterative dynamical system in a compact Hausdorff space is equal to the intersection of its forward image sets, which we will call the first minimal image set. In this article, we investigate the corresponding relation for a class of discontinuous self maps that are on the verge of continuity, or topologically almost continuous endomorphisms. We prove that the iterative dynamics of a topologically almost continuous endomorphisms yields a chain of minimal image sets that attains a unique transfinite length, which we call the maximal invariance order, as it stabilizes itself at the maximal invariant set. We prove the converse, too. Given ordinal number ξ, there exists a topologically almost continuous endomorphism f on a compact Hausdorff space X with the maximal invariance order ξ. We also discuss some further results regarding the maximal invariance order as more layers of topological restrictions are added.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.113-126
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• 2005

The Cahn-Hilliard equation is modeled to describe the dynamics of phase separation in glass and polymer systems. A priori error estimates for the Cahn-Hilliard equation have been studied by the authors. In order to control accuracy of approximate solutions, a posteriori error estimation of the Cahn-Hilliard equation is obtained by discontinuous Galerkin method.

• 전력전자학회논문지
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• 제12권3호
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• pp.241-247
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• 2007

LLC 하프브리지 다중 출력용 컨버터의 보조 출력부와 같이, 펄스 전압을 입력으로 갖는 PWM 컨버터에서는 출력 정전압 제어를 위하여 스위치의 턴 온 제어 방식을 필요로 한다. 본 논문에서는 전류 불연속 모드로 동작하는 벅 컨버터의 새로운 도통시간 턴 온 제어방식에 대하여 논하였다. 제안된 LEM 제어 방식의 PWM 동작 원리를 설명하였으며, 임펄스 응답 이론을 근거로 인덕터 전류의 소신호 주파수 응답 특성을 고찰하였다. 또한 60인치 PDP 어드레스용 100W급 파워 모듈에 적용함으로서 제안된 제어 방식의 타당성을 검증하였다.