• 충청수학회지
• /
• 제7권1호
• /
• pp.141-152
• /
• 1994

We consider a numerical scheme for solving a nonlinear boundary integral equation (BIE) obtained by reformulation the nonlinear boundary value problem (BVP). We give a simple alternative to the standard collocation method for the nonlinear BIE. This method consists of one conventional linear system and another coupled linear system resulting from an auxiliary BIE which is obtained by differentiating both side of the nonlinear interior integral equations. We obtain an analogue BIE through the perturbation of the fundamental solution of Laplace's equation. We procure the super-convergence of approximate solutions.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제14권4호
• /
• pp.283-287
• /
• 2007

An extension of the contraction mapping theorem is provided in a Banach space setting to approximate fixed points of operator equations. Our approach is justified by numerical examples where our results apply whereas the classical contraction mapping principle cannot.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 2001년도 ICCAS
• /
• pp.41.5-41
• /
• 2001

A novel method is introduced for determining the weights of a regularization network which approximates one-to-many mapping. A conventional neural network will converges to the average value when outputs are multiple for one input. The capability of proposed network is demonstrated by an example of learning inverse mapping.

• 한국정밀공학회지
• /
• 제32권9호
• /
• pp.815-824
• /
• 2015

In this study, we conducted the approximate multi-objective optimization of gap sizes of pressurized-water reactor (PWR) annular fuels. To determine the contacting tendency of the inner-outer gaps between the annular fuel pellets and cladding, thermoelastic-plastic-creep (TEPC)analysis of PWR annular fuels was performed, using in-house FE code. For the efficient heat transfer at certain levels of stress, we investigated the tensile, compressive hoop stress and temperature, and optimized the gap sizes using the non-dominant sorting genetic algorithm (NSGA-II). For this, response surface models of objective and constraint functions were generated, using central composite (CCD) and D-optimal design. The accuracy of approximate models was evaluated through $R^2$ value. The obtained optimal solutions by NSGA-II were verified through the TEPC analysis, and we compared the obtained optimum solutions and generated errors from the CCD and D-optimal design. We observed that optimum solutions differ, according to design of experiments (DOE) method.

• Steel and Composite Structures
• /
• 제45권4호
• /
• pp.547-554
• /
• 2022

This paper studies the static stability of an axially graded column with the power-law gradient varying along the axial direction. For a nonhomogeneous column with one end linked to a rotational spring and loaded by a compressive force, respectively, an Euler problem is analyzed by solving a boundary value problem of an ordinary differential equation with varying coefficients. Buckling loads through the characteristic equation with the aid of the Bessel functions are exactly given. An alternative way to approximately determine buckling loads through the integral equation method is also presented. By comparing approximate buckling loads with the exact ones, the approximate solution is simple in form and enough accurate for varying power-law gradients. The influences of the gradient index and the rotational spring stiffness on the critical forces are elucidated. The critical force and mode shapes at buckling are presented in graph. The critical force given here may be used as a benchmark to check the accuracy and effectiveness of numerical solutions. The approximate solution provides a feasible approach to calculating the buckling loads and to assessing the loss of stability of columns in engineering.

• Journal of applied mathematics & informatics
• /
• 제28권3_4호
• /
• pp.813-821
• /
• 2010

In this paper, the tenth-order linear boundary value problems are solved using reproducing kernel method. The algorithm developed approximates the solutions, and their higher-order derivatives, of differential equations and it avoids the complexity provided by other numerical approaches. First a new reproducing kernel space is constructed to solve this class of tenth-order linear boundary value problems; then the approximate solutions of such problems are given in the form of series using the present method. Three examples compared with those considered by Siddiqi, Twizell and Akram [S.S. Siddiqi, E.H. Twizell, Spline solutions of linear tenth order boundary value problems, Int. J. Comput. Math. 68 (1998) 345-362; S.S.Siddiqi, G.Akram, Solutions of tenth-order boundary value problems using eleventh degree spline, Applied Mathematics and Computation 185 (1)(2007) 115-127] show that the method developed in this paper is more efficient.

• 한국통신학회논문지
• /
• 제22권8호
• /
• pp.1833-1841
• /
• 1997

집적광학에서 가장 기본적이고 필수적인 소자인 구형 유전체 도파로는 근사적인 해석방법에서부터 수치계산방법까지 여러가지 방법으로 연구되어왔다. 본 논문에서는 구형 유전체도파로의 해석을 위해 연속적인 섭동궤환방법을 이용하여 최적 등가도파로모델을 선택하고, 시뮬레이션을 통한 비교, 분석 결과, 섭동궤환방법을 이용해서 구한 전파상수가 다른 방법에 의해 얻어진 결과보다 더욱 정확한 값에 일치함으로써 최적의 근사치를 얻을 수 있음을 확인하였고, 또한 여기서 구한 전파 상수를 이용하여 여러 가지 집적광학 소자의 설계에 유용한 필드 특성을 표현하였다.

• 경영과학
• /
• 제28권2호
• /
• pp.1-16
• /
• 2011

In this study we suggested two optimization models to answer a question from an investor standpoint : how many convertible bonds should one convert, and how many keep? One model minimizes certain risk to the minimum required expected return, the other maximizes the expected return subject to the maximum acceptable risk. In comparison with Markowitz portfolio models, which use the variance of return, our models used Conditional Value-at-Risk(CVaR) for risk measurement. As a coherent measurement, CVaR overcomes the shortcomings of Value-at-Risk(VaR). But there are still difficulties in solving CVaR including optimization models. For this reason, we adopted Rockafellar and Uryasev's[18, 19] approach. Then we could approximate the models as linear programming problems with scenarios. We also suggested to extend the models with credit risk, and applied examples of our models to Hynix 207CB, a convertible bond issued by the global semiconductor company Hynix.

• Journal of information and communication convergence engineering
• /
• 제16권1호
• /
• pp.38-42
• /
• 2018

In this paper, we consider measurement allocation problem in a spatially correlated sensor field. Our goal is to determine the probability of each sensor's being measured based on its contribution to the estimation reliability; it is desirable that a sensor improving the estimation reliability is measured more frequently. We consider a spatial correlation model of a sensor field reflecting transmission power limit, noise in measurement and transmission channel, and channel attenuation. Then the estimation reliability is defined distortion error between event source and its estimation at sink. Motivated by the correlation nature, we model the measurement allocation problem into a cooperative game, and then quantify each sensor's contribution using Shapley value. Against the intractability in the computation of exact Shapley value, we deploy a randomized method that enables to compute the approximate Shapley value within a reasonable time. Besides, we envisage a measurement scheduling achieving the balance between network lifetime and estimation reliability.

• Journal of the Korean Data and Information Science Society
• /
• 제13권2호
• /
• pp.77-85
• /
• 2002

The statistical testing methods have been widely recognized to determine the plain and cipher texts. In fact, the randomness for a sequence from an encryption algorithm is necessary to guarantee security and reliance of cipher algorithm. Thus, the statistical randomness tests are used to discover cipher text. In this paper, we would provide the critical value for an approximate entropy test by estimating the nonlinear regression equation when the number of sequence and the level of significance are given. Thus, we can discern plan and cipher text for real problem with given number of sequence and the level of significance. Also, we confirm the fitness of the estimated critical values from the rate of success for plain or cipher text.