• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.669-690
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• 1998

In this paper we develop a new theory of adjoint and symmetric method in the class of general implicit one-step fixed-stepsize methods. These methods arise from simple and natral def-initions of the concepts of symmetry and adjointness that provide a fruitful basis for analysis. We prove a number of theorems for meth-ods having these properties and show in particular that only the symmetric methods possess a quadratic asymptotic expansion of the global error. In addition we give a very simple test to identify the symmetric methods in practice.

• East Asian mathematical journal
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• v.30 no.2
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• pp.93-121
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• 2014

In this paper we study generating and proving methods of symmetric inequalities. We analyze various literatures related with proofs of symmetric inequalities. As a result, we can describe generating method of symmetric inequalities, and suggest some symmetric inequalities that are generated by using parameterization to elementary symmetric polynomials. And we are able to classify some proving methods, and show proofs of symmetric inequalities.

• Communications of the Korean Mathematical Society
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• v.19 no.2
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• pp.375-388
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• 2004

For solving symmetric systems of linear equations, it is shown that a new Krylov subspace method can be obtained. The new approach is one of the projection methods, and we call it the projection method for convenience in this paper. The projection method maintains the residual vector like simpler GMRES, symmetric QMR, SYMMLQ, and MINRES. By studying the quasiminimal residual method, we show that an extended projection method and the scaled symmetric QMR method are equivalent.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1167-1178
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• 2011

In this paper, we further investigate the local Hermitian and skew-Hermitian splitting (LHSS) iteration method and the modified LHSS (MLHSS) iteration method for solving generalized nonsymmetric saddle point problems with nonzero (2,2) blocks. When A is non-symmetric positive definite, the convergence conditions are obtained, which generalize some results of Jiang and Cao [M.-Q. Jiang and Y. Cao, On local Hermitian and Skew-Hermitian splitting iteration methods for generalized saddle point problems, J. Comput. Appl. Math., 2009(231): 973-982] for the generalized saddle point problems to generalized nonsymmetric saddle point problems with nonzero (2,2) blocks. Numerical experiments show the effectiveness of the iterative methods.

• Structural Monitoring and Maintenance
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• v.6 no.4
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• pp.291-315
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• 2019

Fatigue cracks are inevitable in circumstances in which the cyclic loading exists. Therefore, many of mechanical components are in a risk of being in exposure to fatigue cracks. On the other hand, renewing the facilities or infrastructures is not always possible. Therefore, retrofitting the structures by means of the available methods, such as crack arrest methods is logical and in some cases inevitable. In this regard, this paper considers three popular crack arrest methods (e.g., drilling stop-hole, steel welded patch, and carbon fiber reinforced (CFRP) patch), which have been compared by using extended finite element method (XFEM). In addition, effects in terms of the width and thickness of patches and the configuration of drilling stop holes have been evaluated. Test results indicated that among the considered methods, CFRP patches were the most effective means for arresting cracks. Besides, in the case of arresting by means of drilling stop holes, drilling two holes next to the crack-tip was more effective than blunting the crack-tip by drilling one hole. In other words, the results indicated that the use of symmetric welded metal patches could lead to a 21% increase in fatigue life, as compared to symmetric stop holes. Symmetric CFRP patches enhanced the fatigue life of cracked specimen up to 77%, as compared to drilling symmetric stop holes. In addition, in all cases, symmetric configurations were far better than asymmetric ones.

• Communications for Statistical Applications and Methods
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• v.15 no.4
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• pp.483-496
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• 2008

This paper proposes a class of perturbed symmetric distributions associated with the bivariate elliptically symmetric(or simply bivariate elliptical) distributions. The class is obtained from the nontruncated marginals of the truncated bivariate elliptical distributions. This family of distributions strictly includes some univariate symmetric distributions, but with extra parameters to regulate the perturbation of the symmetry. The moment generating function of a random variable with the distribution is obtained and some properties of the distribution are also studied. These developments are followed by practical examples.

• Communications of the Korean Mathematical Society
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• v.9 no.2
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• pp.439-448
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• 1994

It is known that the steepest descent(SD) method and the conjugate gradient(CG) method [1, 2, 5, 6] converge when these methods are applied to solve linear systems of the form Ax = b, where A is symmetric and positive definite. For some finite difference discretizations of elliptic problems, one gets positive definite matrices that are almost symmetric. Practically, the SD method and the CG method work for these matrices. However, the convergence of these methods is not guaranteed theoretically. The SD method is also called Orthores(1) in iterative method papers. Elman [4] states that the convergence proof for Orthores($\kappa$), with $\kappa$ a positive integer, is not heard. In this paper, we prove that the SD method and the CG method converge when the $\iota$$^2$ matrix norm of the non-symmetric part of a positive definite matrix is less than some value related to the smallest and the largest eigenvalues of the symmetric part of the given matrix.(omitted)

• International Journal of CAD/CAM
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• v.9 no.1
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• pp.103-109
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• 2010

Recently, various conformal geometric methods have been presented for non-rigid surface matching and registration. This work proposes to improve the robustness of conformal geometric methods to the boundaries by incorporating the symmetric information of the input surface. We presented two symmetric conformal mapping methods, which are based on solving Riemann-Cauchy equation and curvature flow respectively. Experimental results on geometric data acquired from real life demonstrate that the symmetric conformal mapping is insensitive to the boundary occlusions. The method outperforms all the others in terms of robustness. The method has the potential to be generalized to high genus surfaces using hyperbolic curvature flow.

• Korean Management Science Review
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• v.21 no.2
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• pp.43-60
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• 2004

Every iteration of interior-point methods of large scale optimization requires computing at least one orthogonal projection. In the practice, symmetric variants of the Gaussian elimination such as Cholesky factorization are accepted as the most efficient and sufficiently stable method. In this paper several specific implementation issues of the symmetric factorization that can be applied for solving such equations are discussed. The code called McSML being the result of this work is shown to produce comparably sparse factors as another implementations in the $MATLAB^{***}$ environment. It has been used for computing projections in an efficient implementation of self-regular based interior-point methods, McIPM. Although primary aim of developing McSML was to embed it into an interior-point methods optimizer, the code may equally well be used to solve general large sparse systems arising in different applications.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.23 no.11
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• pp.94-101
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• 2009

This paper poses tracking control and torque control methods to reduce torque ripple for bilateral symmetric trainers. As opposed to the conventional method, the torque control method for active joint movement is proposed. Using a step motor (PK296-03b, step angle: $1.8^{\circ}$), a simulator for a bilateral symmetric trainer is created, and the effectiveness of the proposed control method is verified through experiment results.