• 대한기계학회:학술대회논문집
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• 대한기계학회 2001년도 춘계학술대회논문집C
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• pp.398-401
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• 2001

There are two methods to calculate design sensitivity such as direct differentiation method and adjoint method. A sort of direct differentiation method for design sensitivity analysis costs too much when number of design variables is much larger than the number of response functions whose design sensitivity analyses are required. Therefore, an adjoint method is suggested for the case that the dimension of design variables is lager than the number of response function. An adjoint method is required to compute adjoint variables from the simultaneous linear system equation, the so-called adjoint equation, requiring only the eigenvalue and its associated eigenvectors for mode being differentiated. This method has been extended to the repeated eigenvalue problem. In this paper, we propose an adjoint method for deign sensitivity analysis of damped vibratory systems with distinct eigenvalues.

• 대한수학회지
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• 제31권3호
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• pp.477-492
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• 1994

For the eigenvalue problem of $Au = \lambda u$ where A is considered as a semi-bounded self-adjoint operator on a Hilbert space, we are used to apply two complentary methods finding upper bounds and lower bounds to the eigenvalues. The most popular method for finding upper bounds may be the Rayleigh-Ritz method which was developed in the 19th century while a method for computing lower bounds may be the method of intermediate eigenvalue problems which has been developed since 1950's. In the method of intermediate eigenvalue problems (IEP), we consider the original operator eigenvalue problem as a perturbation of a simpler, resolvable, self-adjoint eigenvalue problem, called a base problem, that gives rough lower bounds.

• Nuclear Engineering and Technology
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• 제27권3호
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• pp.374-384
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• 1995

해석함수 전개 노달방법의 수학적 수한해를 AFEN코드에 약간의 수정을통하여 AFEN노달 방정식의 전치행 렬 방정식을 풀어서 계산하였다. 또한 이 수반해를 사용하여 섭동이론(정확한 섭동이론과 일차근사 섭동이론)을 이용한 계산이 반응도 변화를 예측하기 위해 두개의 잘 알려진 표준문제를 통하여 수행되었다. 본 연구에서 수반해의 계산방법은 물리적 수반해 및 정방정식의 고유치를 필요로 하지 않는다. 계산결과들은 본 논문에서 계산된 수반해가 AFEN방법의 정화한 수학적 수반해임을 보여준다.

• 전기학회논문지P
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• 제65권3호
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• pp.171-177
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• 2016

Noise problem that occurs in living environment is a big trouble in the economic, social and environmental aspects. In this paper, the filtered-X LMS algorithms, the adjoint LMS algorithms, and the robust adjoint LMS algorithms will be introduced for applications in active noise control(ANC). The filtered-X LMS algorithms is currently the most popular method for adapting a filter when the filter exits a transfer function in the error path. The adjoint LMS algorithms, that prefilter the error signals instead of divided reference signals in frequency band, is also used for adaptive filter algorithms to reduce the computational burden of multi-channel ANC systems such as the 3D space. To improve performance of the adjoint LMS ANC system, an off-line measured transfer function is connected parallel to the LMS filter. This parallel-fixed filter acts as a noise controller only when the LMS filter is abnormal condition. The superior performance of the proposed system was compared through simulation with the adjoint LMS ANC system when the adaptive filter is in normal and abnormal condition.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2008년도 추계학술대회A
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• pp.418-423
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• 2008

Among various sensitivity evaluation techniques, semi-analytical method is quite popular since this method is more advantageous than analytical method and global finite difference method. However, SAM reveals severe inaccuracy problem when relatively large rigid body motions are identified for individual elements. Such errors result from the numerical differentiation of the pseudo load vector calculated by the finite difference scheme. In the present study, the adjoint variable method combined with complex variable is proposed to obtain the shape and size sensitivity for structural optimization. The complex variable can present accurate results regardless of the perturbation size as well as easy to be implemented. Through a few numerical examples of the static problem for the structural sensitivity, the efficiency and reliability of the adjoint variable method combined with complex variable is demonstrated.

• Journal of applied mathematics & informatics
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• 제9권2호
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• pp.845-850
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• 2002

Given vectors x and y in a filbert space H, an interpolating operator for vectors is a bounded operator T such that Tx = y. An interpolating operator for n vectors satisfies the equation $Tx_i=y_i$, for i = 1, 2 …, n. In this article, we investigate self-adjoint interpolation problems for vectors in tridiagonal algebra.

• 호남수학학술지
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• 제29권1호
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• pp.55-60
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• 2007

Given operators X and Y acting on a Hilbert space $\cal{H}$, an interpolating operator is a bounded operator A such that AX = Y. In this article, we showed the following : Let $\cal{L}$ be a subspace lattice acting on a Hilbert space $\cal{H}$ and let X and Y be operators in $\cal{B}(\cal{H})$. Let P be the projection onto $\bar{rangeX}$. If FE = EF for every $E\in\cal{L}$, then the following are equivalent: (1) $sup\{{{\parallel}E^{\perp}Yf\parallel\atop \parallel{E}^{\perp}Xf\parallel}\;:\;f{\in}\cal{H},\;E\in\cal{L}\}\$ < $\infty$, $\bar{range\;Y}\subset\bar{range\;X}$, and < Xf, Yg >=< Yf,Xg > for any f and g in $\cal{H}$. (2) There exists a self-adjoint operator A in Alg$\cal{L}$ such that AX = Y.

• Journal of Mechanical Science and Technology
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• 제16권5호
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• pp.710-719
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• 2002

This study investigates a nonlinear inverse convection problem for a laminar-forced convective flow between two parallel plates. The upper plate is exposed to unknown heat flux while the lower plate is insulated. The unknown heat flux is determined using temperature measured on the lower plate. The thermophysical properties of the fluid are temperature dependent, which renders the problem nonlinear. The sequential gradient method is applied to this nonlinear inverse problem in order to solve the problem efficiently. The function specification method is incorporated to stabilize the sequential estimation. The corresponding adjoint formalism is provided. Accuracy and stability have been examined for the proposed method with test cases. The tendency of deterministic error is investigated for several parameters. Stable solutions are achieved eve]1 with severely impaired measurement data.

• 호남수학학술지
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• 제30권4호
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• pp.685-691
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• 2008

Given operators $X_i$ and $Y_i$ (i = 1, 2, ${\cdots}$, n) acting on a Hilbert space $\mathcal{H}$, an interpolating operator is a bounded operator A acting on $\mathcal{H}$ such that $AX_i$ = $Y_i$ for i= 1, 2, ${\cdots}$, n. In this article, if the range of $X_k$ is dense in H for a certain k in {1, 2, ${\cdots}$, n), then the following are equivalent: (1) There exists a self-adjoint operator A in $\mathcal{B}(\mathcal{H})$ stich that $AX_i$ = $Y_i$ for I = 1, 2, ${\cdots}$, n. (2) $sup\{{\frac{{\parallel}{\sum}^n_{i=1}Y_if_i{\parallel}}{{\parallel}{\sum}^n_{i=1}X_if_i{\parallel}}:f_i{\in}H}\}$ < ${\infty}$ and < $X_kf,Y_kg$ >=< $Y_kf,X_kg$> for all f, g in $\mathcal{H}$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권4호
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• pp.407-414
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• 2008

In this paper, we study the self-adjoint second order boundary value problem with integral boundary conditions: (p(t)x'(t))'+f(t,x(t))=0, t $${\in}$$ (0,1), x'(0)=0, x(1) = $${\int}_0^1$$ x(s)g(s)ds. A new result on the existence of positive solutions is obtained. The interesting points are: the first, we employ a new tool-the recent Leggett-Williams norm-type theorem for coincidences; the second, the boundary value problem is involved in integral condition; the third, the solutions obtained are positive.