• 대한수학회보
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• 제52권4호
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• pp.1077-1095
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• 2015

In this paper we study equivariant crossed modules in its link with strict graded categorical groups. The resulting Schreier theory for equivariant group extensions of the type of an equivariant crossed module generalizes both the theory of group extensions of the type of a crossed module and the one of equivariant group extensions.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권3호
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• pp.203-218
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• 2018

An old result of Whitehead says that the set of derivations of a group with values in a crossed G-module has a natural monoid structure. In this paper we introduce derivation of crossed polymodule and actor crossed polymodules by using Lue's and Norrie's constructions. We prove that the set of derivations of a crossed polygroup has a semihypergroup structure with identity. Then, we consider the polygroup of invertible and reversible elements of it and we obtain actor crossed polymodule.

• 대한수학회논문집
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• 제29권1호
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• pp.9-22
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• 2014

In this paper we state some applications of Gr-category theory to the classification problem of crossed modules and to that of group extensions of the type of a crossed module.

• Korean Journal of Mathematics
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• 제32권1호
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• pp.27-42
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• 2024

In this paper we define generalized double group-groupoids and crossed modules over generalized group-groupoids. Also we prove that these algebraic structures are categorically equivalent.

• Korean Journal of Mathematics
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• 제26권3호
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• pp.439-458
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• 2018

In this study, we interpret the notion of homotopy of morphisms in the category of crossed modules in a category C of groups with operations using the categorical equivalence between the categories of crossed modules and of internal categories in C. Further, we characterize the derivations of crossed modules in a category C and obtain new crossed modules using regular derivations of old one.

• Korean Journal of Mathematics
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• 제27권2호
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• pp.535-545
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• 2019

The main idea of this paper is to introduce the notion of $cat^1$-monoids and to prove that the category of crossed semimodules ${\mathcal{C}}=(A,B,{\partial})$ where A is a group is equivalent to the category of $cat^1$-monoids. This is a generalization of the well known equivalence between category of $cat^1$-groups and that of crossed modules over groups.

• Korean Journal of Mathematics
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• 제27권1호
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• pp.151-163
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• 2019

The aim of this paper is to consider the categorical equivalence between crossed modules within groupoids and 2-groupoids; and then relate normality and quotient in these two categories.

• Korean Journal of Mathematics
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• 제7권1호
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• pp.71-77
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• 1999

We show that if the stable rank of $B^{\alpha}$ is one, then the stable rank of B is less than or equal to the order of G for any action of a finite group G. Also we give a short proof to the known fact that if the action of a finite group on a $C^*$-algebra B is saturated then the canonical conditional expectation from B to $B^{\alpha}$ is of index-finite type and the crossed product $C^*$-algebra is isomorphic to the algebra of compact operators on the Hilbert $B^{\alpha}$-module B.

• 전기학회논문지
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• 제64권6호
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• pp.940-947
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• 2015

A Sitting posture is a very important issue for moderns who is mostly sedentary. Also, a wrong sitting posture causes back-pain and spinal disease. Many researchers have been proposed numerous approaches that classifying and monitoring for a sitting posture. In this paper, we proposed a real-time sitting posture monitoring system that was developed to measure pressure distribution in the human body. The proposed system consists of a pressure sensing module (six pressure sensors), data acquisition and processing module, a communication module and a display module for an individual sitting posture monitoring. The developed monitoring system can classify into five sitting postures, such as a correct sitting, sitting on forward inclination, leaning back sitting, sitting with a right leg crossed and a left leg crossed. In addition, when a user deviates from the correct posture, an alarm function is activated. We selected two kinds of chairs, one is rigid material and fixed form, the other one is a soft material and can adjust the height of a chair. In the experiments, we observed appearance changes for subjects in consequence of a comparison between before the correction of posture and after the correction of posture when using the proposed system. The data from twenty four subjects has been classified with a proposed classifier, achieving an average accuracy of 83.85%, 94.56% when the rigid chair and the soft chair, respectively.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1993년도 하계학술대회 논문집 A
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• pp.460-463
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• 1993

In this paper, The laser transmitter module is designed as the subsystem of the high repetitive laser rangefinder. The module consists of high voltage power supply, high voltage control circuits, high voltage discharger, electro-optic Q-switch driver, and laser resonator. The high voltage power supply is composed of 2-phase flyback converter. And it has 220W power level and 78% conversion efficiency. From the Q-switch driver of the crossed porro resonator, the phase retardation voltage is switched from 600V to -1500V with 200ns falling time. The module can be operated up to 15Hz. And it generates the laser pulse which has 20ns width and 80mJ.