• 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.

• 대한수학회지
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• 제36권1호
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• pp.97-107
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• 1999

Given a C-dynamical system (A, G, $\alpha$) with a locally compact group G, two kinds of C-algebras are made from it, called the full C-crossed product and the reduced C-crossed product. In this paper, we extend the theory of the classical C-crossed product to the C-dynamical system (A, G, $\alpha$) with a left-cancellative semigroup M with unit. We construct a new C-algebra A $\alpha$rM, the reduced crossed product of A by the semigroup M under the action $\alpha$ and investigate some properties of A $\alpha$rM.

• 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.

• 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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• 제10권2호
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• pp.103-118
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• 2003

We estimate the stable rank of twisted crossed products of $C^{*}-algebras$ by topological Abelian groups. As an application we estimate the stable rank of twisted crossed products of $C^{*}-algebras$ by solvable Lie groups. In particular, we obtain the stable rank estimate of twisted group $C^{*}-algebras$ of solvable Lie groups by the (reduced) dimension and (generalized) rank of groups.

• 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.

• 대한수학회보
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• 제60권2호
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• pp.529-539
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• 2023

In this paper, we study nuclearity of semigroup crossed products for quasi-lattice ordered groups. We show the relationships among nuclearity of the semigroup crossed product, amenability of the quasi-lattice ordered group and nuclearity of the underlying C^*-algebra.

• 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.

• Childhood Kidney Diseases
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• 제12권2호
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• pp.262-266
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• 2008

교차성 신전위는 두 개의 신장이 정중선의 같은 편에 나란히 위치하는 선천성 신장병이다. 대개 기형은 오른쪽에 있고 융합되어 있는 경우가 융합되지 않는 경우의 8배에 달한다. 교차성 신전위는 흔한 질환은 아니지만, 영아에서 복부에 낭성 종물이 만져지고 반대편에 신장이 없는 경우에는 고려해 보아야 한다. 다낭 형성 이상을 동반한 융합된 교차성 신전위는 대부분 초음파로 진단되므로 진단을 위해 더 이상의 검사가 필요하지 않은 경우가 많다. 그러나 방사선 동위원소를 이용한 신주사로 교차성 신전위의 기능여부를 파악해야 하고, 배설성 방광요로조영술로 방광요관 역류나 신우요관이행부의 협착이 있는지 확인해야 한다. 다낭 형성 이상을 동반한 융합된 교차성 신전위에 대한 연구는 거의 없는 실정으로 저자들은 발열, 복통을 주소로 내원한 3세 남아에서 초음파를 시행하여 다낭 형성 이상을 동반한 융합된 교차성 신전위 1례를 경험하였기에 보고하는 바이다.

• 대한물리의학회지
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• 제14권3호
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• pp.13-20
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• 2019

PURPOSE: Sitting with crossed legs may have an effect on maintaining a healthy body posture and proper functioning of the respiratory system. Thus, this study's objective was to identify whether or not sitting with crossed legs affects the vertebral angle, chest wall mobility, the pulmonary function, and the activity of the respiratory muscles. METHODS: Thirty healthy subjects were recruited for this study (16 males and 14 females). The vertebral angle, chest wall mobility, pulmonary function, and the activity of the respiratory muscle were measured while the subjects sat in the correct posture and these factors were again measured with the subjects seated with their legs crossed. Three-dimensional motion analysis was used to determine the trunk and lumbar vertebral angles. Surface electromyography was employed to measure the sternocleidomastoid, the rectus abdominis, and the external and internal oblique abdominis muscles. A tapeline was utilized to evaluate the subjects' chest wall mobility. Spirometry was assessed to determine the forced vital capacity and forced expiratory volume in one second. Paired t-tests were then performed (p<.05). RESULTS: There were significant differences in the trunk and lumbar flexion angles, the chest wall mobility, the activity of the right external oblique muscle, and the left internal oblique abdominis muscle. However, the difference in pulmonary function did not reach statistical significance. CONCLUSION: A crossed leg posture caused slight thoracic extension and lumbar flexion, which may lead to a decrease of the chest wall mobility and also to an imbalance of the abdominal muscles. Therefore, sitting with a crossed leg posture should be avoided. Yet a crossed leg posture did not have any clinical effect on the pulmonary function of healthy people. It may be necessary to study the effects of sitting with crossed legs over an extended period of time for patients suffering with impaired respiratory function.