• 충청수학회지
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• 제13권2호
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• pp.71-79
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• 2001

We study only free actions of finite abelian groups G on the 3-dimensional nilmanifold, up to topological conjugacy. we shall deal with only one out of 15 distinct almost Bieberbach groups up to Seifert local invariant.

• Kyungpook Mathematical Journal
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• 제58권3호
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• pp.573-581
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• 2018

In this paper we consider all orientation-preserving ${\mathbb{Z}}_{p^2}$-actions on 3-dimensional handlebodies $V_g$ of genus g > 0 for p an odd prime. To do so, we examine particular graphs of groups (${\Gamma}(v)$, G(v)) in canonical form for some 5-tuple v = (r, s, t, m, n) with r + s + t + m > 0. These graphs of groups correspond to the handlebody orbifolds V (${\Gamma}(v)$, G(v)) that are homeomorphic to the quotient spaces $V_g/{\mathbb{Z}}_{p^2}$ of genus less than or equal to g. This algebraic characterization is used to enumerate the total number of ${\mathbb{Z}}_{p^2}$-actions on such handlebodies, up to equivalence.

• 충청수학회지
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• 제32권3호
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• pp.365-381
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• 2019

We study free actions of finite nonabelian groups on 3-dimensional nilmanifolds with the first homology ${\mathbb{Z}}^2{\oplus}{\mathbb{Z}}_2$, up to topological conjugacy. We show that there exist three kinds of nonabelian group actions in ${\pi}_1$, two in ${\pi}_2$ or ${\pi}_{5,i}$(i = 1, 2, 3), one in the other cases, and clarify what those groups are.

• 대한수학회지
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• 제54권5호
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• pp.1411-1440
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• 2017

We study free actions of finite groups on 3-dimensional nil-manifolds with the first homology ${\mathbb{Z}}^2{\oplus}{\mathbb{Z}}_p$. By the works of Bieberbach and Waldhausen, this classification problem is reduced to classifying all normal nilpotent subgroups of almost Bieberbach groups of finite index, up to affine conjugacy.

• 대한수학회지
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• 제40권3호
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• pp.563-575
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• 2003

We show that if a connected Stein manifold M of dimension n has the holomorphic automorphism group Aut(M) isomorphic to $Aut(C^k {\times}(C^*)^{n - k})$ as topological groups, then M itself is biholomorphically equivalent to C^k{\times}(C^*)^{n - k}$. Besides, a new approach to the study of U(n)-actions on complex manifolds of dimension n is given.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제23권4호
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• pp.219-233
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• 2020

Teachers' intervention in small groups is a research area that needs more research attention. Ehrenfeld and Horn (2020) identified teachers' group work monitoring routines that consist of four recurrent talk moves: 1) Initiation, 2) Entry, 3) Focus, and 4) Exit. To better understand prospective teachers' (PTs) intervention in small groups in mathematics classrooms, I investigated how PTs' intervention actions and purposes are related to the monitoring routines, particularly, in terms of Focus moves. I analyzed 26 PTs' responses to four written scenarios, each of which depicts interactions among students in a small group. I identified 1) types of PTs' math talk, 2) types of PTs' non-math talk, 3) types of intervention purposes, and 4) patterns of intervention actions and purposes by scenario. This study contributes to understanding PTs' intervention actions and purposes in mathematics instruction.

• 충청수학회지
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• 제14권2호
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• pp.27-35
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• 2001

We shall deal with ten cases out of 15 distinct almost Bieberbach groups up to Seifert local invariant. In those cases we will show that if G is a finite abelian group acting freely on the standard nilmanifold, then G is cyclic, up to topological conjugacy.

• 호남수학학술지
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• 제41권4호
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• pp.851-861
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• 2019

In this paper we consider proper semialgebraic actions of semialgebraic groups on semialgebraic sets. We prove the equivariant version of the semialgebraic local-triviality of semialgebraic maps.

• 대한가정학회지
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• 제38권12호
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• pp.29-45
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• 2000

The purposes of this study were to determine what factors influence risk perceptions of females and males for milk produced using food-related biotechnology, to test whether risk perceptions or other factors influence self-protection actions and to estimate milk demand response in light of self-protection actions and other economic and demographic factors. The expected utility model was applied to explain the way consumers would take self-protection actions regarding risk perceptions and to drive milk demand. Telephone interviews were conducted and the data were collected from households(females=1,029, males=437) nationwide in the U.S. And the data were analyzed by Heckman two-step method using the software package LIMDEP. Risk perceptions were found to be influenced not by demographic factors but by outrage factors as well as attitudinal factors in both females and males, although some factors were different. In addition, risk perceptions and labeling availability were found to significantly influence self-protection actions in both groups. Furthermore, as an important concern in this study, self-protection action was found to significantly influence milk demand in only male group, implying a consistent behavior of males. Also milk price and household size were found to significantly influence milk demand in both groups. In fact, the results did demonstrate that labeling availability significantly influenced self-protection actions. That is, in markets where labeled laternatives were present, concerned consumers were more likely to self protect by substituting to these products. A policy implication of this result is that labeling food products produced using biotechnology enhances consumer choice. Hence, consumer could express a more accurate demand response and reduce the perceived food safety risk. Furthermore, education for females might be necessary to have a consistent behavior because self-protection action did not significantly influence female's milk demand, though they have greater risk perceptions than males have.

• 대한수학회지
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• 제40권2호
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• pp.273-286
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• 2003

Let $F^{\alpha}$G be a twisted group algebra. A subalgebra of $F^{\alpha}$G generated by all class sums of partition P of G is called a projective class algebra in $F^{alpha}$G associated with partition P. In this paper we study various partitions of G determined by actions of certain operator groups on G and construct projective class algebras depending on the actions. With regard to projective class algebras, we investigate structures of associated skew group algebras and fixed group algebras.