• 대한수학회보
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• 제36권3호
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• pp.543-564
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• 1999

Consider a symmetric bilinear form defined on $\prod\times\prod$ by $_{\lambda\mu}$ = $<\sigma,fg>\;+\;\lambdaL[f](a)L[g](a)\;+\;\muM[f](b)m[g](b)$ ,where $\sigma$ is a quasi-definite moment functional, L and M are linear operators on $\prod$, the space of all real polynomials and a,b,$\lambda$ , and $\mu$ are real constants. We find a necessary and sufficient condition for the above bilinear form to be quasi-definite and study various properties of corresponding orthogonal polynomials. This unifies many previous works which treated cases when both L and M are differential or difference operators. finally, infinite order operator equations having such orthogonal polynomials as eigenfunctions are given when $\mu$=0.

• 대한수학회보
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• 제25권2호
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• pp.185-194
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• 1988

In [2], we have shown that the optimal boundary controls for hyperbolic systems in L$^{2}$-spaces can be attained in a feedback form via Riccati operators. A number of authors [1, 5, 7 and 10] have investigated approximations of Riccati operators arising in distributed parameter systems. They assumed bounded controls for parabolic systems. However, we in this paper study Galerkin approximations of Riccati operators and feedback controls for hyperbolic systems with unbounded control actions. Let us briefly introduce some results of [2]. Let .ohm. be an open bounded region in R$^{n}$ with smooth boundary .GAMMA. where n is a fixed positive integer. We consider a strictly hyperbolic differential operator H(x) of order 1 on .ohm. with noncharacteristic boundary on .GAMMA.

• 대한수학회지
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• 제57권6호
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• pp.1471-1484
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• 2020

It may very well be difficult to prove an eigenvalue inequality of Payne-Pólya-Weinberger type for the bi-drifting Laplacian on the bounded domain of the general complete metric measure spaces. Even though we suppose that the differential operator is bi-harmonic on the standard Euclidean sphere, this problem still remains open. However, under certain condition, a general inequality for the eigenvalues of bi-drifting Laplacian is established in this paper, which enables us to prove an eigenvalue inequality of Ashbaugh-Cheng-Ichikawa-Mametsuka type (which is also called an eigenvalue inequality of Payne-Pólya-Weinberger type) for the eigenvalues with lower order of bi-drifting Laplacian on the Gaussian shrinking soliton.

• Korean Journal of Mathematics
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• 제28권2호
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• pp.223-240
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• 2020

The paper is concerned with periodic linear evolution equations of the form x"(t) = A(t)x(t)+f(t), where A(t) is a family of (unbounded) linear operators in a Banach space X, strongly and periodically depending on t, f is an almost (or asymptotic) almost periodic function. We study conditions for this equation to have almost periodic solutions on ℝ as well as to have asymptotic almost periodic solutions on ℝ⁺. We convert the second order equation under consideration into a first order equation to use the spectral theory of functions as well as recent methods of study. We obtain new conditions that are stated in terms of the spectrum of the monodromy operator associated with the first order equation and the frequencies of the forcing term f.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1990년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 26-27 Oct. 1990
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• pp.1150-1155
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• 1990

This paper proposes an optimal redundancy resolution of a kinematically redundant manipulator while considering homotopy classes. The necessary condition derived by minimizing an integral cost criterion results in a second-order differential equation. Also boundary conditions as well as the necessary condition are required to uniquely specify the solution. In the case of a cyclic task, we reformulate the periodic boundary value problem as a two point boundary value problem to find an initial joint velocity as many dimensions as the degrees of redundancy for given initial configuration. Initial conditions which provide desirable solutions are obtained by using the basis of the null projection operator. Finally, we show that the method can be used as a topological lifting method of nonhomotopic extremal solutions and also show the optimal solution with considering the manipulator dynamics.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제18권1호
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• pp.61-74
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• 2014

This paper presents accurate and efficient numerical methods for calculating the sensitivities of two-asset European options, the Greeks. The Greeks are important financial instruments in management of economic value at risk due to changing market conditions. The option pricing model is based on the Black-Scholes partial differential equation. The model is discretized by using a finite difference method and resulting discrete equations are solved by means of an operator splitting method. For Delta, Gamma, and Theta, we investigate the effect of high-order discretizations. For Rho and Vega, we develop an accurate and robust automatic algorithm for finding an optimal value. A cash-or-nothing option is taken to demonstrate the performance of the proposed algorithm for calculating the Greeks. The results show that the new treatment gives automatic and robust calculations for the Greeks.

• 경영과학
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• 제25권3호
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• pp.87-99
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• 2008

Besieged by needs for upgrading the current Internet, social pressures, and regulatory concerns, a network operator may be left with few options to Improve his services. Yet he can still consider a transition prioritizing network services. In this paper, we describe a transition from a non-priority system to a prioritized one, using non-preemptive M/G/1 model. After reviewing the constraints and theoretical results from past research, we describe steps making the transition Pareto-improving, which boils down to a multi-goal search for a Pareto-improving state. We use a genetic algorithm that captures actual transition costs along with incentive-compatible and Pareto-Improving constraints. Simulation results demonstrate that the initial post-transition solutions are typically Pareto-improving. for non Pareto-improving solutions, the heuristic quickly generates Pareto-improving and incentive-compatible solutions.

• 대한수학회지
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• 제51권2호
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• pp.251-266
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• 2014

In this paper, we use Newton's method to approximate a locally unique solution of an equation in Banach spaces and introduce recurrent functions to provide a weaker semilocal convergence analysis for Newton's method than before [1]-[13], in some interesting cases, provided that the Fr$\acute{e}$chet-derivative of the operator involved is p-H$\ddot{o}$lder continuous (p${\in}$(0, 1]). Numerical examples involving two boundary value problems are also provided.

• 한국통신학회논문지
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• 제14권6호
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• pp.663-674
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• 1989

본 논문은 문서자동 처리시스템의 구현을 위하여 문서영상의 패턴 분절과 구분처리 방법에 대하여 기술하였다. 가우스 분포함수의 1차 미분 연산자에 의한 윤곽선 추출과 체인 코드법에 의한 영상 분절, 2차 적률과 2차원 Rf 거리 (변환 영역)등에 의한 패턴 구분을 행하였다. 제한된 영상에 대하여 적용한 결과 문자 영역이나 지문, 사진, 도장 등 도형정보 영역을 잘 구분할 수 있음을 알았으며 사용된 알고리즘의 유용성을 검증할 수 있었다.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1073-1088
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• 2010

In this article we want to formulate a disease transmission model, MSEIR model, for a population with individuals travelling between patches i and i + 1 and we derive an explicit formula for the basic reproductive number, $R_0$, employing the spectral radius of the next generation operator. Also, in this article we show that a system of ordinary differential equations for this model has a unique disease-free equilibrium and it is locally asymptotically stable if $R_0$ < 1 and unstable if $R_0$ > 1.