• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1281-1290
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• 2007

We introduce three spectral regularization methods for solving a backward heat conduction problem (BHCP). For the three spectral regularization methods, we give the stability error estimates with optimal order under an a-priori and an a-posteriori regularization parameter choice rule. Numerical results show that our theoretical results are effective.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.4
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• pp.631-642
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• 2016

This article deals with one-dimension backward heat conduction problem (BHCP). A new approach based on least squares support vector machines (LS-SVM) is proposed for obtaining their approximate solutions. The approximate solution is presented in closed form by means of LS-SVM, whose parameters are adjusted to minimize an appropriate error function. The approximate solution consists of two parts. The first part is a known function that satisfies initial and boundary conditions. The other is a product of two terms. One term is known function which has zero boundary and initial conditions, another term is unknown which is related to kernel functions. This method has been successfully tested on practical examples and has yielded higher accuracy and stable solutions.

• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.385-397
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• 2001

Consider an inverse problem of determining of the 2-D temperature distribution from known temperature given at some time T>0. Our aim is to find the temperature for 0

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.04b
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• pp.171-177
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• 1995

In this paper, the deformation method for inner and outer races of rollr-bearing bymeans of the warm precision forging is investigated. We adapted the process designsuch as following that, toincrease Die life, reduce heat transfer through conduction and the eccentricity of preform in warm forging of bearing gace, the bottom portion of billet is formed during upsetting process. Then it is backward extruded, and thus obtained ring preform is formed by combined extrusion. Also, we compared it with the froming method in China and Japan, and we have known it is more excellent method. Basides, this forming method is simulated by UBST which is based on the merits of UBET nd FEM. The results show that it is easy to know the exact location of neutral surface through the inspection of streamline during combined extrusion, and the velocity vector distribution along the surface of velocity discontinuity is investigationed. Also the effectiveness of this method is proved by te experiment using model material that is Plasticine.