• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.769-783
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• 2021

Demirci ((1999) Vague groups. J. Math. Anal. Appl. 230, 142-156) introduced the concept of vague groups as one of uncertain reasoning structures where indistinguishable operators separate points. In this paper, we consider vague groups in which an indistinguishable operator does not need to separate points because it seems more appropriate to handle ambiguous situations. For our purposes we generalize or redefine some notions such as: vague closed subset, vague subgroup, vague kernel and vague injectiveness. Consequently we generalize most of the known results and obtain some new additional fundamental properties of vague groups, some of which are similar to ones of ordinary groups.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.609-614
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• 1995

Let (M, g) be a complete Riemannian manifold and G be a closed (connected) subgroup of the group of isometries of M. Then the union ${\MM}$ of all principal orbits is an open dense subset of M and the quotient map ${\MM} \longrightarrow {\BB} := {\MM}/G$ becomes a Riemannian submersion for the restriction of g to ${\MM}$ which gives the quotient metric on ${\BB}$. Namely, B is a singular (complete) Riemannian space such that $\partialB$ consists of non-principal orbits.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1077-1085
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• 1996

This paper provides examples which can not be approximate fibrations and shows that if $N^n$ is a closed aspherical manifold, $\pi_1(N)$ is hyperhophian, normally cohophian, and $\pi_1(N)$ has no nontrivial Abelian normal subgroup, then the product of $N^n$ and a sphre $S^m$ satisfies the property that all PL maps from an orientable manifold M to a polyhedron B for which each point preimage is homotopy equivalent to $N^n \times S^m$ necessarily are approximate fibrations.

• Bulletin of the Korean Mathematical Society
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• v.47 no.2
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• pp.307-317
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• 2010

In this paper we find necessary and sufficient conditions for weak amenability of the convolution Banach algebras A(K) and $L^2(K)$ for a compact hypergroup K, together with their applications to convolution Banach algebras $L^p(K)$ ($2\;{\leq}\;p\;<\;{\infty}$). It will further be shown that the convolution Banach algebra A(G) for a compact group G is weakly amenable if and only if G has a closed abelian subgroup of finite index.

• Proceedings of the Korea Inteligent Information System Society Conference
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• 2000.04a
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• pp.475-478
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• 2000

Recently encryption algorithms based on difficulties of factorization have been used with popularization. Prime number factorizations are progressed rapidly. In this paper, characteristics of elliptic curve are analyzed and generation of elliptic curves suitable for prime number factorization is discussed.

• Bulletin of the Korean Mathematical Society
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• v.49 no.5
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• pp.1101-1129
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• 2012

We study the geometry of the images of 1-dimensional homogeneous submersions for each of the model spaces X of the eight 3-dimensional geometries. In particular, We shall calculate the group of isometries and the curvatures of the base surfaces for each of the model spaces of 3-dimensional geometries, with respect to every closed subgroup of the isometries of X acting freely.

• Bulletin of the Korean Mathematical Society
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• v.54 no.4
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• pp.1229-1240
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• 2017

This paper presents a systematic study of the abstract harmonic analysis over spaces of complex measures on homogeneous spaces of compact groups. Let G be a compact group and H be a closed subgroup of G. Then we study abstract harmonic analysis of complex measures over the left coset space G/H.

• Journal of the Korean Mathematical Society
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• v.43 no.1
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• pp.29-43
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• 2006

The article deals with the problem of extending representations of a closed normal subgroup H to a topological group G. We show that the standard technique using group cohomology to solve the problem in the case of finite groups can be generalized in the category of topological groups if G/H is discrete.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.799-807
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• 2007

In this paper we study non-simply connected Riemannian manifolds of constant positive curvature which have an orbit of codimension one under the action of a connected closed Lie subgroup of isometries. When the action is reducible we characterize the orbits explicitly. We also prove that in some cases the manifold is homogeneous.

• Honam Mathematical Journal
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• v.40 no.4
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• pp.661-669
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• 2018

In this paper, we introduce and study the notion of a pseudonorm on a generalized group. Let G be a topological generalized group and let the family $\{G_x\}_{x{\in}e(G)}$ be locally finite. Then, we show that G is completely regular. Also, some well known results are generalized.