• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.415-425
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• 2005

This paper outlines a reliable strategy for solving nonlinear Volterra-Fredholm integro-differential equations. The modified form of Adomian decomposition method is found to be fast and accurate. Numerical examples are presented to illustrate the accuracy of the method.

• 대한수학회보
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• 제44권4호
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• pp.807-816
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• 2007

For the stochastic differential inclusion on infinite dimensional space of the form $dX_t{\in}\sigma(X_t)dW_t+b(X_t)dt$, where ${\sigma}$, b are set-valued maps, W is an infinite dimensional Hilbert space valued Q-Wiener process, we prove the boundedness and continuity of solutions under the assumption that ${\sigma}$ and b are closed convex set-valued satisfying the Lipschitz property using approximation.

• 대한수학회보
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• 제40권1호
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• pp.159-165
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• 2003

We consider the stochastic differential inclusion of the form $dX_t\;\in\;\sigma(t,\;X_t)db_t+b(t,\;X_t)dt$, where $\sigma$, b are set-valued maps, B is a standard Brownian motion. We prove the boundedness of solutions under the assumption that $\sigma$ and b satisfy the local Lipschitz property and linear growth.

• 대한수학회보
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• 제43권4호
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• pp.791-804
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• 2006

This paper is concerned with a second-order iterated differential equation of the form $c_0x'(Z)+c_1x'(z)+c_2x(z)=x(az+bx(z))+h(z)$ with the distinctive feature that the argument of the unknown function depends on the state. By constructing a convergent power series solution of an auxiliary equation, analytic solutions of the original equation are obtained.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.261-272
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• 2005

In this paper, boundedness criteria are established for solutions of a class of impulsive functional differential equations with infinite delays of the form $x'(t) = F(t, x(\cdot)), t > t^{\ast} {\Delta}x(t_{k})= I(t_{k}, x(t_{k}^{-})), k = 1,2,...$ By using Lyapunov functions and Razumikhin technique, some new Razumikhin-type theorems on boundedness are obtained.

• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.581-588
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• 2007

We reconsider the classical orthogonal polynomials which are solutions to a second order differential equation of the form $$l_2(x)y'(x)+l_1(x)y'(x)={\lambda}_ny(x)$$. We investigate two characterization theorems of F. Marcellan et all and K.H.Kwon et al. which gave necessary and sufficient conditions on $l_1(x)\;and\;l_2(x)$ for the above differential equation to have orthogonal polynomial solutions. The purpose of this paper is to give a proof that each result in their papers respectively is equivalent.

• International Journal of CAD/CAM
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• 제6권1호
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• pp.157-166
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• 2006

In order to model blending surfaces with curvature continuity, in this paper we apply sixth order partial differential equations (PDEs), which are solved with a composite power series based method. The proposed composite power series based approach meets boundary conditions exactly, minimises the errors of the PDEs, and creates almost as accurate blending surfaces as those from the closed form solution that is the most accurate but achievable only for some simple blending problems. Since only a few unknown constants are involved, the proposed method is comparable with the closed form solution in terms of computational efficiency. Moreover, it can be used to construct 3- or 4-sided patches through the satisfaction of continuities along all edges of the patches. Therefore, the developed method is simpler and more efficient than numerical methods, more powerful than the analytical methods, and can be implemented into an effective tool for the generation and manipulation of complex free-form surfaces.

• 정보처리학회논문지D
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• 제16D권4호
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• pp.463-474
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• 2009

OLAP 이나 e-비즈니스 환경에서는 다차원 데이터의 효율적인 분석을 위하여, 데이터를 여러 형태로 표현하거나 저장한다. 이러한 다차원 구조의 데이터를 차원 애트리뷰트들의 값으로 표시되는 넓은 형태의 수평 뷰로 표현한다. 수평 뷰는 여러 소스로부터 수집한 요약 정보를 유지하도록 실체 뷰로서 저장되며, 복잡한 질의들을 효율적으로 처리하기 위해 사용된다. 그러나, 소스 데이터가 변경될 경우 수평 뷰들의 내용도 수정해야 하는 데, 소스 데이터들이 여러 사이트에 분산되어 있기 때문에 수평 뷰를 관리하는 것은 어렵다. 따라서, 본 연구에서는 점진적인 뷰 관리 방법 중의 하나로 차등 파일을 이용하여 수평 뷰를 관리하는 효율적인 방법을 제시한다. 이러한 방법은 상용 RDBMS에서 제공하는 PIVOT 연산을 이용하여 저장된 수직 형태의 소스 테이블을 수평 뷰로 변환하고, 수직 테이블의 변경 사항을 반영한 차등 파일을 이용하여 수평 뷰에서도 동일하게 적용하는 방법이다. 이를 위해, 우선 저장된 수직 테이블에서 수평 뷰로 변환하여 처리하는 전체적인 프레임워크를 제안한다. 제안한 프레임워크 하에서 수직 테이블을 수평 뷰로 변환하는 PIVOT 연산을 정의한다. 다음으로, 수직 테이블로부터 데이터가 변경될 경우, 데이터에 대한 변경 사항을 차등 파일로 저장한 후, 이를 이용하여 수평 뷰를 갱신하는 방법을 제안한다. 특히, 차등 파일의 구조는 수평 뷰의 구조와 다르기 때문에, 수평 뷰에 적합하도록 변경 사항을 변환해야 한다. 마지막으로 실험을 통하여 제안한 방법은 다른 방법에 비해서 평균 1.2$\sim$5.0배까지 성능을 향상시킴을 보인다.

• Kyungpook Mathematical Journal
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• 제56권4호
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• pp.1141-1160
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• 2016

In this paper, a symbolic algorithm for solving a regular initial value problem (IVP) for a system of linear differential-algebraic equations (DAEs) with constant coeffcients has been presented. Algebra of integro-differential operators is employed to express the given system of DAEs. We compute a canonical form of the given system which produces another simple equivalent system. Algorithm includes computing the matrix Green's operator and the vector Green's function of a given IVP. Implementation of the proposed algorithm in Maple is also presented with sample computations.

• ETRI Journal
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• 제35권5호
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• pp.827-837
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• 2013

In this paper, we present wideband common-mode (CM) noise suppression using a vertical stepped impedance electromagnetic bandgap (VSI-EBG) structure for high-speed differential signals in multilayer printed circuit boards. This technique is an original design that enables us to apply the VSI-EBG structure to differential signals without sacrificing the differential characteristics. In addition, the analytical dispersion equations for the bandgap prediction of the CM propagation in the VSIEBG structure are extracted, and the closed-form expressions for the bandgap cutoff frequencies are derived. Based on the dispersion equations, the effects of the impedance ratio, the EBG patch length, and via inductances on the bandgap of the VSI-EBG structure for differential signals are thoroughly examined. The proposed dispersion equations are verified through agreement with the full-wave simulation results. It is experimentally demonstrated that the proposed VSI-EBG structure for differential signaling suppresses the CM noise in the wideband frequency range without degrading the differential characteristics.