• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제8권2호
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• pp.7-13
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• 2004

A Conjugate Gradient (CG) algorithm for unconstrained minimization is proposed which is invariant to a nonlinear scaling of a strictly convex quadratic function and which generates mutually conjugate directions for extended quadratic functions. It is derived for inexact line searches and is designed for the minimization of general nonlinear functions. It compares favorably in numerical tests with the original Dixon algorithm on which the new algorithm is based.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.173-190
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• 2011

In this paper, we construct a new approach of affine scaling interior algorithm using the affine scaling conjugate gradient and Lanczos methods for bound constrained nonlinear optimization. We get the iterative direction by solving quadratic model via affine scaling conjugate gradient and Lanczos methods. By using the line search backtracking technique, we will find an acceptable trial step length along this direction which makes the iterate point strictly feasible and the objective function nonmonotonically decreasing. Global convergence and local superlinear convergence rate of the proposed algorithm are established under some reasonable conditions. Finally, we present some numerical results to illustrate the effectiveness of the proposed algorithm.

• 한국의류학회지
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• 제1권1호
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• pp.25-29
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• 1977

The warmth retentivity of natural and syntheic waddings as bedding stuff, and further, the machanism of heat transmission through conduction, radiation and convection were analysed. The materials used were cotton, silk, and wool as natural waddings, and polyamide, polyester, regular acrylic, conjugate acrylic, regular polyprepylene and conjugate polypropylene as synthetic waddings. The results of this study are as follow: 1. The warmth retentivity is highest in silk. Following silk in descending order is cotton, conjugate acrylic, polyester, regular acrylic, wool, polyamide, conjugate polypropylene and regular polypropylene. There is not any significant relationship between warmth retentivity and the conductivity of the fibers. 2. Transmission by radiation through the fiber waddings is highest in conjugate polypropylene. Following conjugate polypropylene in descending order is regular polypropylene. polyester. polyamide, conjugate acrylic, regular acrylic, wool, cotton, and silk. This is seen to be in nearly reversed order to the abovementioned order of warmth retentivity. In this respect, warmth retentivity with loose fibreous material as in the case of bedding stuff is primarily affected by the interceptive function of the fibers in heat radiation. 3. Warmth retentivity becomes lower with increasing air content of the waddings. This is because heat transmission by radiation incrases as air content increases. The air content increase is due to the fact that the air is unable to intercept heat radiation. In addition, heat transmission accelates in proportion to the increase in convection as the air gap enlarges.

• 대한수학회논문집
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• 제12권4호
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• pp.895-904
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• 1997

Let B(z) be a power series with operator coefficients where multiplication by B(z), T, is a contractive and everywhere defined transforamtion in the square summable power series. Then there is a Julia operator U for T such that $$ U = (T D)(\tilde{D}^* L) \in B(H \oplus D, K \oplus \tilde{D}), $$ where D is the state space of a conjugate canonical linear system with transfer function B(z).

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제9권1호
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• pp.55-61
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• 2005

A Conjugate Gradient algorithm for unconstrained minimization is proposed which is invariant to a nonlinear scaling of a strictly convex quadratic function and which generates mutually conjugate directions for extended quadratic functions. It is derived for inexact line searches and for general functions. It compares favourably in numerical tests (over eight test functions and dimensionality up to 1000) with the Dixon (1975) algorithm on which this new algorithm is based.

• East Asian mathematical journal
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• 제17권2호
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• pp.375-383
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• 2001

In this paper we deal with the duality theory of optimality for an optimal control problem governed by a class of second order evolution equations. First we establish the dual control systems by using conjugate functions and then associate them to the original optimization problem.

• 한국전자파학회논문지
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• 제15권8호
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• pp.775-780
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• 2004

본 논문은, 각 채널이 여파기와 군지연 등화기로 구성되는, 위성용 다중채널 입력 멀티플렉서에서 사용되는 군지연-등화되는 여파기의, Simulated Annealing(SA) 기법과 Conjugate Gradient(CG) 기법의 새로운 결합형 설계 방식에 의한 구현을 기술한다. SA기법은 8차 타원적분형 여파기, CG기법은 2극 등화기 각각의 회로 설계변수들의 값을 찾아내는데 이용된다. 측정결과는 설계된 부품의 spec.에 대하여 성능이 만족함과 설계기법의 타당성을 나타낸다.

• Structural Engineering and Mechanics
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• 제12권1호
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• pp.85-100
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• 2001

In this paper, an analytical procedure for solving several static and dynamic problems of non-uniform beams is proposed. It is shown that the governing differential equations for several stability, free vibration and static problems of non-uniform beams can be written in the from of a unified self-conjugate differential equation of the second-order. There are two functions in the unified equation, unlike most previous researches dealing with this problem, one of the functions is selected as an arbitrary expression in this paper, while the other one is expressed as a functional relation with the arbitrary function. Using appropriate functional transformation, the self-conjugate equation is reduced to Bessel's equation or to other solvable ordinary differential equations for several cases that are important in engineering practice. Thus, classes of exact solutions of the self-conjugate equation for several static and dynamic problems are derived. Numerical examples demonstrate that the results calculated by the proposed method and solutions are in good agreement with the corresponding experimental data, and the proposed procedure is a simple, efficient and exact method.

• Steel and Composite Structures
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• 제28권2호
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• pp.195-207
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• 2018

First-order reliability method (FORM) is enhanced based on the search direction using relaxed conjugate reliability (RCR) approach for the embedded nanocomposite beam under buckling failure mode. The RCR method is formulated using discrete conjugate map with a limited scalar factor. A dynamical relaxed factor is proposed to control instability of proposed RCR, which is adjusted using sufficient descent condition. The characteristic of equivalent materials for nanocomposite beam are obtained by micro-electro-mechanical model. The probabilistic model of nanocomposite beam is simulated using the sinusoidal shear deformation theory (SSDT). The beam is subjected to external applied voltage in thickness direction and the surrounding elastic medium is modeled by Pasternak foundation. The governing equations are derived in terms of energy method and Hamilton's principal. Using exact solution, the implicit buckling limit state function of nanocomposite beam is proposed, which is involved various random variables including thickness of beam, length of beam, spring constant of foundation, shear constant of foundation, applied voltage, and volume fraction of ZnO nanoparticles in polymer. The robustness, accuracy and efficiency of proposed RCR method are evaluated for this engineering structural reliability problem. The results demonstrate that proposed RCR method is more accurate and robust than the excising reliability methods-based FORM. The volume fraction of ZnO nanoparticles and the applied voltage are the sensitive variables on the reliable levels of the nanocomposite beams.

• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.139-152
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• 2003

In this paper, we characterize a vector-valued convex set function by its epigraph. The concepts of a vector-valued set function and a vector-valued concave set function we given respectively. The definitions of the conjugate functions for a vector-valued convex set function and a vector-valued concave set function are introduced. Then a Fenchel duality theorem in multiobjective programming problem with set functions is derived.