• 대한수학회보
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• 제58권2호
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• pp.419-431
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• 2021

In this paper we discuss the classical problem of finding conditions on the entire coefficients A(z) and B(z) guaranteeing that all nontrivial solutions of f" + A(z)f' + B(z)f = 0 are of infinite order. We assume A(z) is an entire function of completely regular growth and B(z) satisfies three different conditions, then we obtain three results respectively. The three conditions are (1) B(z) has a dynamical property with a multiply connected Fatou component, (2) B(z) satisfies T(r, B) ~ log M(r, B) outside a set of finite logarithmic measure, (3) B(z) is extremal for Denjoy's conjecture.

• 대한토목학회논문집
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• 제11권3호
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• pp.47-58
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• 1991

본 논문에서는 무한요소를 이용한 지반-구조물 상호작용 해석에 대하여 연구하였다. 적층지반(Layered Soil)과 같이 여러 가지 응력파가 동시에 전파되는 탄성지반의 외부영역을 효과적으로 모형화할 수 있는 동적무한요소를 개발하였으며, 요소행렬 구성시 수반되는 무한대 방향으로의 적분을 효과적으로 수행하기 위하여 Gauss-Laguerre 적분방법을 기초로 하여 새로이 고안된 적분방법을 제시하였다. 이 방법의 타당성은 반무한 탄성지반과 적층된 반무한 탄성지반 위에 놓여 있는 원형강판의 임피던스(Impedance) 함수를 구하여 해석적으로 구한 값들과 비교함으로써 검토하였다.

• Communications for Statistical Applications and Methods
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• 제3권1호
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• pp.257-265
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• 1996

We consider nonstationary autoregressive autoregressive process with infinite variance of error. In the case of infinite cariance, the limiting distribution of the estimated coefficient is different from that under the finite cariance assumption. In this paper we show that the bootstrap method can be used to approximate the distribution of ordinary least squares estimator of the coefficient in the first order random walk process with infinite variance through some empirical studies and we suggest a test procedure based on bootstrap method for the unit root test.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2002년도 ICCAS
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• pp.46.3-46
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• 2002

Most of the process control algorithms in practice are based on the finite dimensional control theory. However, many chemical processes are described by partial differential equations (PDE's) and are infinite dimensional in nature due to spatial variation. Especially when the convection is dominant and thus diffusion can be ignored, chemical processes that are described by a system of first order hyperbolic PDE's. Such processes include tubular reactors, fixed bed reactors and pressure swinging adsorption. Conventionally such infinite dimensional systems described by PDE's are controlled by finite dimensional controllers that are designed through finite dimensional reduction of the process m...

• 대한수학회논문집
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• 제36권2호
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• pp.277-298
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• 2021

In this paper, we propose an extension of the classical Bessel function by means of our ℓ-hypergeometric function [2]. As the main results, the infinite order differential equation, the generating function relation, and contour integral representations including Schläfli's integral analogue are derived. With the aid of these, other results including some inequalities are also obtained. At the end, the graphs of these functions are plotted using the Maple software.

• 한국해안해양공학회지
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• 제1권1호
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• pp.71-80
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• 1989

본 연구에서는 무한요소의 개념을 선형파의 회절 및 방사문제에 적용하는 방법에 대해서 연구하였다. 유체의 동압에 의한 하중은 관성력이 중요하다고 가정하여, 점성효과는 무시하였다. 물체 주변의 내부영역은 통상적인 유한요소를 사용하여 모형화하였으며, 외부영역은 특수한 형상함수를 갖는 무한요소로 모형화하였다. 본 연구에서 개발된 무한요소의 형상함수는, 외부영역의 속도포텐셜을 보다 잘 나타내기 위하여, 외부영역의 해를 해석적 고유함수로 표시하였을 때 나타나는 진행파항과 첫번째 산란파항의 점근적인 형태를 사용하여 결정하였으며, 수치해석상의 효율성을 증가시키기 위하여, 무한요소의 시스템행렬 구성시 나타나게 되는 무한방향으로의 적분을 해석적으로 수행하였다. 본 무한요소의 효율성 및 타당성을 입증하기 위하여, 실제 많이 응용되고 있는 연직 축대칭 구조물을 대상으로 수치해석을 수행하였다. 수치해석결과, 아주 적은 수의 요소로 유체영역을 분할했음에도 불구하고, 적분방정식을 이용한 기존의 여러결과들과 아주 잘 일치함을 알 수 있었다. 또한, 해석의 효율성과 해의 정확도에 직접적으로 영향을 주는 무한요소의 위치와 유한요소의 크기에 대한 기준설정을 위한 수치실험도 수행하였다.

• 대한수학회보
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• 제48권4호
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• pp.813-838
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• 2011

In this paper, we prove sufficient conditions for controllability of second order semi-linear neutral impulsive differential inclusions on unbounded domain with infinite delay in Banach spaces using the theory of strongly continuous Cosine families. We shall rely on a fixed point theorem due to Ma for multi-valued maps. The controllability results in infinite dimensional space has been proved without compactness on the family of Cosine operators.

• 한국지진공학회:학술대회논문집
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• 한국지진공학회 2000년도 춘계 학술발표회 논문집 Proceedings of EESK Conference-Spring
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• pp.451-457
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• 2000

In many dynamic problems such as foundation vibrations ultrasonic nondestructive evaluation and blasting analysts are confronted with the problem of wave propagation in an infinite or semi-infinite media. In order to simulate this situation by a finite analytical model provisions must be made to absorb the stress waves arriving at the boundary. Absorbing boundaries are mathematical artifacts used to prevent wave reflections at the boundaries of discrete models for infinite media under dynamic loads. An analytical study is carried out to examine the effectiveness of Lysmer-Kuhlemeyer model one of the most widely used absorbing boundaries. Validity of the absorbing boundary conditions suggested by Lymer-Kuhlemeyer is examined by adopting the solution of Ewing et al. to the problem of plane waves from a harmonic normal force on the surface of an elastic half-space. The Ewing's problem is than numerically simulated using the finite element method on a semi-circular mesh with and without absorbing boundaries which are represented by viscous dashpots. The absorption ratios are calculated by comparing the displacements at the absorbing boundaries to those at the free field without absorbing boudaries.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1991년도 봄 학술발표회 논문집
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• pp.8-14
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• 1991

The finite element technique incorporating infinite elements is applied to analyzing the general three dimensional wave-structure interaction problems within the limits of linear wave theory. The hydrodynamic farces are assumed to be inertially dominated, and viscous effects are neglected. In order to analyze the corresponding boundary value problems efficiently, two types of elements are developed. One is the infinite element for modeling the radiation condition at infinity, and the other is the fictitious bottom boundary element for the case of deep water. To validate those elements, numerical analyses are performed for several floating structures. Comparisons with the results from culler available solution methods show that the present method incorporating tile infinite and the fictitious bottom boundary elements gives good results.

• East Asian mathematical journal
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• 제18권1호
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• pp.111-125
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• 2002

Many different families of infinite series were recently observed to be summable in closed forms by means of certain operators of fractional calculus(that is, calculus of integrals and derivatives of any arbitrary real or complex order). In this sequel to some of these recent investigations, the authors present yet another instance of applications of certain fractional calculus operators. Alternative derivations without using these fractional calculus operators are shown to lead naturally a family of analogous infinite sums involving hypergeometric functions.