• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.691-706
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• 2020

Necessary and sufficient conditions are provided under which the weighted Moore-Penrose inverse A^†_MN exists, where A is an adjointable operator between Hilbert C^⁎-modules, and the weights M and N are only self-adjoint and invertible. Relationship between weighted Moore-Penrose inverses A^†_MN is clarified when A is fixed, whereas M and N are variable. Perturbation analysis for the weighted Moore-Penrose inverse is also provided.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.101-112
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• 2007

In this paper, by using fractional power of operators and Sadovskii fixed point theorem, we study the controllability of abstract neutral functional integrodifferential systems with infinite delay. As application, an example is provided to illustrate the obtained results.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.5
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• pp.841-846
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• 2010

Reliability in electrical power system refers to normal operation for schedule time in some system that action consists. It means that if there is no contingency of electric power supply decrease or load curtailment, reliability of the system is high. In this paper, a method for evaluation of transmission capability is proposed considering reliability standards. Deterministic and probabilistic methods for evaluation of transmission capability has been studied. These researches considered uncertainty of system components or N-1 contingency only. However, the proposed method can inform customers and system operators more suitable transmission capability. Well-being method using state probabilities of system components proves to be a more effective method in this paper comparing with calculation of LOLE(Loss of Load Expectation). The length of calculation is shorter but it can give more practical information to the exact system operators. Well-being method is applied to IEEE-RTS 24bus system to evaluate reliability in case study. The result is compared with a existing way to evaluate reliability with LOLE and it shows that transmission capability connected with adjacent networks. This paper informs system operators and power suppliers of reliable information for operating power system.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.9-9
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• 2003

Let $\Omega$ be a bounded, open, and polygonal domain in $R^2$ with re-entrant corners. We consider the following Partial Differential Equations: $$(I-\nabla\nabla\cdot+\nabla^{\bot}\nabla\times)u\;=\;f\;in\;\Omega$$, $$n\cdotu\;0\;0\;on\;{\Gamma}_{N}$$, $${\nabla}{\times}u\;=\;0\;on\;{\Gamma}_{N}$$, $$\tau{\cdot}u\;=\;0\;on\;{\Gamma}_{D}$$, $$\nabla{\cdot}u\;=\;0\;on\;{\Gamma}_{D}$$ where the symbol $\nabla\cdot$ and $\nabla$ stand for the divergence and gradient operators, respectively; $f{\in}L^2(\Omega)^2$ is a given vector function, $\partial\Omega=\Gamma_{D}\cup\Gamma_{N}$ is the partition of the boundary of $\Omega$; nis the outward unit vector normal to the boundary and $\tau$represents the unit vector tangent to the boundary oriented counterclockwise. For simplicity, assume that both $\Gamma_{D}$ and $\Gamma_{N}$ are nonempty. Denote the curl operator in $R^2$ by $$\nabla\times\;=\;(-{\partial}_2,{\partial}_1$$ and its formal adjoint by $${\nabla}^{\bot}\;=\;({-{\partial}_1}^{{\partial}_2}$$ Consider a weak formulation(WF): Find $u\;\in\;V$ such that $$a(u,v):=(u,v)+(\nabla{\cdot}u,\nabla{\cdot}v)+(\nabla{\times}u,\nabla{\times}V)=(f,v),\;A\;v{\in}V$$. (2) We assume there is only one singular corner. There are many methods to deal with the domain singularities. We introduce them shortly and we suggest a new Finite Element Methods by using Singular representation for the solution.

• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.261-275
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• 2002

Let T be a local strongly accretive operator from a real uniformly smooth Banach space X into itself. It is proved that Ishikawa iterative schemes with errors converge strongly to a unique solution of the equations T$\_$x/ = f and x + T$\_$x/ = f, respectively, and are almost T$\_$b/-stable. The related results deal with the strong convergence and almost T$\_$b/-stability of Ishikawa iterative schemes with errors for local strongly pseudocontractive operators.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.12 no.5
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• pp.141-148
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• 2013

There are several problems in the conventional 2-D image processing and 3-D measurement systems. In the case of the 2-D image processing system, it is not possible to detect elevation data. In a 3-D measurement system, it requires a skillful operator and a lot of time for measuring data. Also, there exist data errors depending on operators. The limitation of detecting elevation data in the 2-D image processing system can be solved by laser diodes. In this study an algorithm that measures the accurate data in a subject face to be detected by combining laser diodes and a commercial CCD camera is developed. In the development process, a planar equation is developed using laser diodes and the equation is used to obtain a normal vector. Based on the results, an algorithm that transforms commercial CCD camera coordinates to 3-D coordinates is proposed. The completed measurement method will be applied to replace a manual measurement system for vehicle bodies and parts by an automated system.