• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.11
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• pp.1612-1619
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• 2017

In this note, a complete proof of Utkin's theorem is presented for SI(single input) uncertain nonlinear systems. The invariance theorem with respect to the two nonlinear transformation methods so called the two diagonalization methods is proved clearly, comparatively, and completely for SI uncertain nonlinear systems. With respect to the sliding surface and control input transformations, the equation of the sliding mode i.e., the sliding surface is invariant, which is proved completely. Through an illustrative example and simulation study, the usefulness of the main results is verified. By means of the two nonlinear transformation methods, the same results can be obtained.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.4
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• pp.843-847
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• 2011

In this note, a proof of Utkin's theorem is presented for the SI(Single Input) uncertain integral linear case. The invariance theorem with respect to the two transformation methods so called the two diagonalization methods are proved clearly and comparatively for SI uncertain integral linear systems. With respect to the sliding surface transformation, the equation of the sliding mode, the sliding surface is invariant. Both the applied control inputs have the same gains. By means of the two transformation methods the same results can be obtained. Through an illustrative example and simulation study, the usefulness of the main results is verified.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.751-760
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• 2021

We study in this paper the right Rényi mean for a quantum divergence induced from the α - z Rényi relative entropy. Many properties including homogeneity, invariance under permutation, repetition and unitary congruence transformation, and determinantal inequality have been presented. Moreover, we give the identity of two right Rényi means with respect to tensor product.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.48 no.6
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• pp.8-14
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• 2011

In this note, a proof of Utkin's theorem is presented for SI(Single input) uncertain linear systems. The invariance theorem with respect to the two transformation methods so called the two diagonalization methods is proved clearly and comparatively for SI uncertain linear systems. With respect to the sliding surface transformation, the equation of the sliding mode i.e., the sliding surface is invariant. The control inputs by the two transformation methods both have the same gains. By means of the two transformation methods, the same results can be obtained. Through an illustrative example and simulation study, the usefulness of the main results is verified.

• Journal of the Korean Magnetics Society
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• v.14 no.6
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• pp.207-212
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• 2004

Eddy current (EC) testing methods are widely used in a variety of applications including the inspection of steam generator tubes in nuclear power plants, aircraft parts and airframes. A key factor that affects the EC signal is lift-off which means the physical distance between a sensor and a specimen in the testing. In practice, it is difficult to keep track of the actual value of the lift -off during a specific experiment, simulation or testing in the field, which is essential for accurate interpretation of the signal to be used in the following steps. Hence it is necessary to have a scheme to render the EC signal invariant to the effects of lift-off in spite of the changes in the real world. This paper describes a new method for compensating EC signals for variations in lift-off by acquiring an invariance feature using a homomorphic operator and neural network techniques. The signals from various lift-offs are transformed to obtain a zero lift-off equivalent signal that can be subsequently used for defect characterization in the next step.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.13 no.4
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• pp.179-191
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• 2013

The quincunx lattice is a non-separable sampling method in image processing. It treats the different directions more homogeneously and good frequency property than the separable two dimensional schemes. The high density discrete wavelet transformation is one that expands an N point signal to M transform coefficients with M > N. In two dimensions, this transform outperforms the standard discrete wavelet transformation in terms of shift-invariant. Although the transformation utilizes more wavelets, sampling rates are high costs. This paper proposed the high density discrete wavelet transform using quincunx sampling, which is a discrete wavelet transformation that combines the high density discrete transformation and non-separable processing method, each of which has its own characteristics and advantages. Proposed wavelet transformation can service good performance in image processing fields.

• Journal of Korea Society of Digital Industry and Information Management
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• v.8 no.1
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• pp.171-181
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• 2012

This paper introduces the double-density discrete wavelet transform(DWT) using quincunx sampling, which is a DWT that combines the double-density DWT and quincunx sampling method, each of which has its own characteristics and advantages. The double-density DWT is an improvement upon the critically sampled DWT with important additional properties: Firstly, It employs one scaling function and two distinct wavelets, which are designed to be offset from one another by one half. Secondly, the double-density DWT is overcomplete by a factor of two, and Finally, it is nearly shift-invariant. In two dimensions, this transform outperforms the standard DWT in terms of denoising; however, there is room for improvement because not all of the wavelets are directional. That is, although the double-density DWT utilizes more wavelets, some lack a dominant spatial orientation, which prevents them from being able to isolate those directions. A solution to this problem is a quincunx sampling method. The quincunx lattice is a sampling method in image processing. It treats the different directions more homogeneously than the separable two dimensional schemes. Proposed wavelet transformation can generate sub-images of multiple degrees rotated versions. Therefore, This method services good performance in image processing fields.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 1998.06b
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• pp.141-146
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• 1998

Currently virtual studio has used the cromakey method in which an image is captured, and the blue portion of that image is replaced by a graphic image or a real image. The replaced image must be changed according to the camera motion. This paper proposes a novel method to extract camera parameters using the recognition of pentagonal patterns which are painted on the blue screen. The corresponding parameters are position, direction and focal length of the camera in the virtual studio. At first, pentagonal patterns are found using invariant features of the pentagon. Then, the projective transformation of two projected images and the camera parameters are calculated using the matched points. Simulation results indicate that camera parameters are more easily calculated compared to the conventional methods.

• Journal of Educational Research in Mathematics
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• v.12 no.4
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• pp.509-521
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• 2002

The purpose of this paper is as follows: $^{\circleda}$ to disclose the essence of symmetry $^{\circledb}$ to propose the desirable strategy of problem-solving as to symmetry $^{\circledc}$ to clarify the relationship between symmetry and group $^{\circledd}$ to propose a way of introduction of 'group' in school mathematics according to its fundamental characteristic, symmetry. This study shows that the nature of symmetry is 'invariance under a transformation' and symmetry is the main idea of 'group'. In mathematics textbooks and mathematics education literature, we find out that the logic of symmetry is widespread. We illustrate two paradigmatic problem related to symmetrical logic and exemplify a desirable instruction of Pascal's triangle. This study also suggests a possibility of developing students' unformal and unconscious conception of group with sym metry idea from elementary to secondary school mathematics.

• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.405-413
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• 2001

The inverse boundary value problem for the steady state heat equation with convection term is considered in a simply connected bounded domain with smooth boundary. Taking the Dirichlet to Neumann map which maps the temperature on the boundary to the that flux on the boundary as an observation data, the global uniqueness for identifying the convection term from the Dirichlet to Neumann map is proved.