• Korean Journal of Mathematics
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• v.5 no.1
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• pp.49-54
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• 1997

In this paper we study the generalized Reidemeister number $R({\varphi},{\psi})$ for a self-map $({\varphi},{\psi}):(X,G){\rightarrow}(X,G)$ of a transformation group (X, G), as an extension of the Reidemeister number $R(f)$ for a self-map $f:X{\rightarrow}X$ of a topological space X.

• The Pure and Applied Mathematics
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• v.14 no.4
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• pp.289-306
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• 2007

We define and study a concept of $H^f-space$ for a map, which is a generalized concept of an H-space, in terms of the Gottlieb set for a map. For a principal fibration $E_{\kappa}{\rightarrow}X$ induced by ${\kappa}:X{\rightarrow}X'\;from\;{\epsilon}:\;PX'{\rightarrow}X'$, we can obtain a sufficient condition to having an $H^{\bar{f}}-structure\;on\;E_{\kappa}$, which is a generalization of Stasheff's result [17]. Also, we define and study a concept of $co-H^g-space$ for a map, which is a dual concept of $H^f-space$ for a map. Also, we get a dual result which is a generalization of Hilton, Mislin and Roitberg's result [6].

• Journal of the Korean Mathematical Society
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• v.39 no.3
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• pp.387-395
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• 2002

In [11] Kim obtained fixed point theorems for maps defined on some “locally G-convex”subsets of a generalized convex space. Theorem 2 in Kim's article determines us to introduce, in this paper, the notion of K-G-convex space. In this framework we obtain fixed point theorems, section properties and minimax inequalities.

• Communications of the Korean Mathematical Society
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• v.12 no.3
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• pp.779-788
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• 1997

In this work, using the exact separatrix map which provides an efficient way to describe dynamics near the separatrix, we study the stochastic layer near the separatrix of a one-degree-of-freedom Hamilitonian system with time periodic perturbation. Applying the twist map theory to the exact separatrix map, T. Ahn, G. I. Kim and S. Kim proved the existence of the uniformly hyperbolic invariant set(UHIS) near separatrix. Using the theorems of Bowen and Franks, we prove this UHIS has measure zero.

• Proceedings of the IEEK Conference
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• 1998.10a
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• pp.257-260
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• 1998

In this paper, we describe an IMT-2000 system architecture, a protocol stack, and basic MAP scenarios(e.g., registration, call delivery) based on the IS-41 and IS-41 and IS-751. This paper focuses on the MAP scenarios to support the IMSI which is defined for the global roaming between GSM and IS-41 Networks through the Family of System approach. This paper also deals with the design of the MAP protocol stack transported over the ATM networks and introduces the software structure of MAP in IMT-2000 MSC.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.553-574
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• 2018

In this paper, we study harmonic maps and biharmonic maps on the principal G-bundle in Kobayashi and Nomizu and also the warped product $P=M{\times}_fF$ for a $C^{\infty}$(M) function f on M studied by Bishop and O'Neill, and Ejiri.

• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.933-944
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• 1994

Let $\pi : P \to S^4$ be a principal G-bundle over $S^4$ whose the structure group G is a compact, connected, simple Lie group. Since $\pi_3(G) = \pi_4 (BG) = Z$, we can classify the principal bundle $P_k$ over $S^4$ by the map $S^4 \to BG$ of degree k. Atiyah and Jones [2] showed that $C_k = A_k/g^b_k$ is homotopy equivalent to $\Omega^3_k G \simeq \Omega^4_k BG$ where $A_k$ is the space of the all connections in $P_k$ and $g^b_k$ is the based gauge group which consists of all base point preserving automorphisms on $P_k$. Here $\Omega^nX$ is the space of all base-point preserving continuous map from $S^n$ to X. Let $M_k$ be the space of based gauge equivalence classes of all connections in $P_k$ satisfying the Yang-Mills self-duality equations, which we call the moduli space of G instantons.

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.151-158
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• 1999

Let (X, G) be a transformation group and ${\sigma}(X,x_0,G)$ the fundamental group of (X, G). In this paper, we prove that the Reidemeister number $R(f_G)$ for an endomorphism $f_G:(X,G){\rightarrow}(X,G)$ is a homotopy invariant. In particular, when any self-map $f:X{\rightarrow}X$ is homotopic to the identity map, we give some calculation of the lower bound of $R(f_G)$. Finally, we discuss commutativity and product formula for the Reidemeister number $R(f_G)$.

• Wind and Structures
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• v.2 no.1
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• pp.51-68
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• 1999

Applying and extending some preceding researches, this paper proposes a map of Italian extreme winds assigning the reference velocity, i.e., the wind velocity averaged over 10 minutes, at 10 m height, in a flat open terrain, with 50 years mean return period, depending on the site and the altitude. Furthermore, an objective criterion is formulated by which the actual values of the local wind velocity are given as a function of the reference velocity. The study has been carried out in view of the revision of the Italian Standards dealing with safety and loads and the introduction of the aeolic Italian map into Eurocode 1.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.376-379
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• 1998

We introduce the concept of a 'fuzzy' map between sets by modifying the concept of the extension principle introduced by Dubois and Prade in [1] and study their properties. Using these we generalize Goguen's and Zadeh's extension principles in [2] and [3].