• Nuclear Engineering and Technology
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• v.49 no.1
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• pp.17-28
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• 2017

The modified power method has been studied by many researchers to calculate the higher eigenmodes and accelerate the convergence of the fundamental mode. Its application to multidimensional problems may be unstable due to degenerated or near-degenerated eigenmodes. Complex eigenmode solutions are occasionally encountered in such cases, and the shapes of the corresponding eigenvectors may change during the simulation. These issues must be addressed for the successful implementation of the modified power method. Complex components are examined and an approximation method to eliminate the usage of the complex numbers is provided. A technique to fix the eigenvector shapes is also provided. The performance of the methods for dealing with those aforementioned problems is demonstrated with two dimensional one group and three dimensional one group homogeneous diffusion problems.

• The Pure and Applied Mathematics
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• v.18 no.3
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• pp.185-199
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• 2011

In this paper, we present a new extended Jacobi method for computing eigenvalues and eigenvectors of Hermitian matrices which does not use any complex arithmetics. This method can be readily applied to skew-Hermitian and real skew-symmetric matrices as well. An example illustrating its computational efficiency is given.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.1
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• pp.66-76
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• 2003

The arbitrary V-notched crack problem is considered. The general expressions for the stress components on this problem are obtained as explicit series forms composed of independent unknown coefficients which are denoted by coefficients of eigenvector. For this results eigenvalue equation is performed first through introducing complex stress functions and applying the traction free boundary conditions. Next solving this equation, eigenvalues and corresponding eigenvectors are obtained respectively, and finally inserting these results into stress components, the general equations are obtained. These results are also shown to be applicable to the symmetric V-notched crack or straight crack. It can be shown that this solutions are composed of the linear combination of Mode I and Mode II solutions which are obtained from different characteristic equations, respectively. Through performing asymptotic analysis for stresses, the stress intensity factor is given as a closed form equipped with the unknown coefficients of eigenvector. In order to calculate the unknown coefficients. based on these general explicit equations, numerical programming using the overdetermined boundary collocation method which is algorithmed originally by Carpenter is also worked out. As this programming requires the input data, the commercial FE analysis for stresses is performed. From this study, for some V-notched problems, unknown coefficients can be calculated numerically and also fracture parameters are determined.

• Industrial Engineering and Management Systems
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• v.11 no.1
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• pp.54-69
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• 2012

Chan and Qi (SCM 8/3 (2003) 209) developed an innovative measurement method that aggregates performance measures in a supply chain into an overall performance index. The method is useful and makes a significant contribution to supply chain management. Nevertheless, it can be cumbersome in computation due to its highly complex algorithmic fuzzy model. In aggregating the performance information, weights used by Chan and Qi-which aim to address the imprecision of human judgments-are incompatible with weights in additive models. Furthermore, the default assumption of linearity of its scoring procedure could lead to an inaccurate assessment of the overall performance. This paper addresses these limitations by developing an alternative measurement that takes care of the above. This research integrates three different approaches to multiple criteria decision analysis (MCDA)-the multiattribute value theory (MAVT), the swing weighting method and the eigenvector procedure-to develop a comprehensive assessment of supply chain performance. One case study is presented to demonstrate the measurement of the proposed method. The performance model used in the case study relies on the Supply Chain Operations Reference (SCOR) model level 1. With this measurement method, supply chain managers can easily benchmark the performance of the whole system, and then analyze the effectiveness and efficiency of the supply chain.

• Honam Mathematical Journal
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• v.23 no.1
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• pp.91-111
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• 2001

In this paper we prove the following : Let M be a semi-invariant submanifold with almost contact metric structure (${\phi}$, ${\xi}$, g) of codimension 3 in a complex hyperbolic space $H_{n+1}{\mathbb{C}}$. Suppose that the third fundamental form n satisfies $dn=2{\theta}{\omega}$ for a certain scalar ${\theta}({\leq}{\frac{c}{2}})$, where ${\omega}(X,\;Y)=g(X,\;{\phi}Y)$ for any vectors X and Y on M. Then M has constant eigenvalues correponding the shape operator A in the direction of the distinguished normal and the structure vector ${\xi}$ is an eigenvector of A if and only if M is locally congruent to one of the type $A_0$, $A_1$, $A_2$ or B in $H_n{\mathbb{C}}$.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.7 s.250
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• pp.750-756
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• 2006

This study predicts the modified eigenvectors and eigenvalues of the non-proportional damped structure due to the change in the mass, damping and stiffness of structure by iterative method of the sensitivity coefficient using the original dynamic characteristic. The method is applied to the non-proportional damped 3 degree of freedom system by modifying the mass, damping and stiffness. The predicted dynamic characteristics are showed a good agreement with these from the structural reanalysis using the modified mass, damping and stiffness.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.14 no.4
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• pp.7-12
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• 2005

This study predicts the modified eigenvectors and eigenvalues of the damped structure due to the change in the mass, damping and stiffness of structure by calculation of the sensitivity coefficient using the original dynamic characteristic. The method is applied to examples of the damped 3 degree of freedom system by modifing the mass, damping and stiffness. The predicted dynamic characteristics are in good agreement with these from the structural reanalysis using the modified mass, damping and stiffness.

• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.649-668
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• 2000

In this paper we prove the following : Let M be a real (2n-1)-dimensional compact minimal semi-invariant submanifold in a complex projective space P(sub)n+1C. If the scalar curvature $\geq$2(n-1)(2n+1), then m is a homogeneous type $A_1$ or $A_2$. Next suppose that the third fundamental form n satisfies dn = 2$\theta\omega$ for a certain scalar $\theta$$\neq$c/2 and $\theta$$\neq$c/4 (4n-1)/(2n-1), where $\omega$(X,Y) = g(X,øY) for any vectors X and Y on a semi-invariant submanifold of codimension 3 in a complex space form M(sub)n+1 (c). Then we prove that M has constant principal curvatures corresponding the shape operator in the direction of the distingusihed normal and the structure vector ξ is an eigenvector of A if and only if M is locally congruent to a homogeneous minimal real hypersurface of M(sub)n (c).

• Structural Engineering and Mechanics
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• v.37 no.5
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• pp.561-573
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• 2011

For efficient calculation of natural modes of structures, a numerical scheme which accelerates convergence of the subspace iteration method by employing accelerated starting Lanczos vectors was proposed in 2005. This paper is an extension of the study. The previous study simply showed feasibility of the proposed method by analyzing structures with smaller degrees of freedom. While, the present study verifies efficiency of the proposed method more rigorously by comparing closeness of conventional and accelerated starting vectors to genuine eigenvectors. This study also analyzes an example structure with larger degrees of freedom and more complex constraints in order to investigate applicability of the proposed method.

• Journal of Information Processing Systems
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• v.18 no.3
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• pp.293-301
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• 2022

Direction of arrival (DOA) estimation of space signals is a basic problem in array signal processing. DOA estimation based on the multiple signal classification (MUSIC) algorithm can theoretically overcome the Rayleigh limit and achieve super resolution. However, owing to its inadequate real-time performance and accuracy in practical engineering applications, its applications are limited. To address this problem, in this study, a DOA estimation algorithm with high parallelism and precision based on an analysis of the characteristics of complex matrix eigenvalue decomposition and the coordinate rotation digital computer (CORDIC) algorithm is proposed. For parallel and single precision, floating-point numbers are used to construct an orthogonal identity matrix. Thus, the efficiency and accuracy of the algorithm are guaranteed. Furthermore, the accuracy and computation of the fixed-point algorithm, double-precision floating-point algorithm, and proposed algorithm are compared. Without increasing complexity, the proposed algorithm can achieve remarkably higher accuracy and efficiency than the fixed-point algorithm and double-precision floating-point calculations, respectively.