• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.883-902
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• 2008

The main results concern with the self maps on the Klein bottle. We obtain the Reidemeister numbers and the Nielsen numbers for all self maps on the Klein bottle. In terms of the Nielsen numbers of their iterates, we totally determine the minimal sets of periods for all homotopy classes of self maps on the Klein bottle.

• The Journal of Natural Sciences
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• v.14 no.1
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• pp.1-6
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• 2004

In this paper, we calculate the Nielsen numbers of periods for maps on the Klein bottle.

• The Journal of Natural Sciences
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• v.17 no.1
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• pp.1-12
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• 2006

The main results in this paper concern the set of natural numbers correrponding to the least period of periodic orbits of a map on the Klein bottle K.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.961-971
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• 2018

We determine the sets of homotopy minimal periods of all self-maps on the Klein bottle by using a single formula for homotopy minimal periods of maps on the infra-solvmanifolds of type (R). This provides an alternate but an easy proof for the main results of [12].

• Honam Mathematical Journal
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• v.32 no.1
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• pp.73-76
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• 2010

In this paper we investigate the distances between Dehn fillings on a hyperbolic 3-manifold that yield 3-manifolds containing a M$\"{o}$bius band and a Klein bottle.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.411-419
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• 2007

In this paper, $\tilde{2}$-essential rooted maps on the Klein bottle are counted and an explicit expression with the size as a parameter is given. Further, the numbers of singular maps and the maps with one vertex on the Klein bottle are derived.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1483-1503
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• 2008

Let f : M ${\rightarrow}$ M be a self-map on the Klein bottle M. We compute the Lefschetz number and the Nielsen number of f by using the infra-nilmanifold structure of the Klein bottle and the averaging formulas for the Lefschetz numbers and the Nielsen numbers of maps on infra-nilmanifolds. For each positive integer n, we provide an explicit algorithm for a complete computation of the Nielsen type numbers $NP_n(f)$ and $N{\Phi}_{n}(f)\;of\;f^{n}$.

• Kyungpook Mathematical Journal
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• v.60 no.4
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• pp.831-837
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• 2020

Let M be the exterior of a hyperbolic link K ∪ L in a homology 3-sphere Y, such that the linking number lk(K, L) is non-zero. In this note we prove that if γ is a slope in ∂N(L) such that the manifold ML(γ) obtained by γ-Dehn filling along ∂N(L) contains a Klein bottle, then there is a bound on Δ(μ, γ), depending on the genus of K and on lk(K, L).

• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1269-1287
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• 2006

As a continuation of computing the zeta function of a regular covering graph by Mizuno and Sato in [9], we derive in this paper computational formulae for the zeta functions of a graph bundle and of any (regular or irregular) covering of a graph. If the voltages to derive them lie in an abelian or dihedral group and its fibre is a regular graph, those formulae can be simplified. As a by-product, the zeta function of the cartesian product of a graph and a regular graph is obtained. The same work is also done for a discrete torus and for a discrete Klein bottle.

• Journal of English Language & Literature
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• v.56 no.6
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• pp.1295-1310
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• 2010

In her "After Language Poetry: Innovation and Its Theoretical Discontents" in Contemporary Poetics (2007), Marjorie Perloff spotted Steve McCaffery's and Lyn Hejinian's points of reference and opacity/transparency in poetic language, and theorizes in her perspicacious insights that poetic language is not a window, to be seen through, a transparent glass pointing to something outside it, but a system of signs with its own semiological interconnectedness. Providing a critique and contextualizing Perloff's argument, the purpose of this paper is to introduce a topological model for poetry, language, and theory and further to elaborate the relation between the theory and the practice of language poetry in terms of "the revolution of language." Jacques Lacan's poetics of knowledge and of the topology of the mind, in particular, that of "extimacy," can articulate the way how language poetry problematizes the opposition between inside and outside in the substance of language itself. In fact, as signifiers always refer not to things, but to other signifiers, signifiers becomes unconscious, and can say more than they actually says. The original signifiers become unconscious through the process of repression which makes a structure of multiple and polyphonic signifying chains. Language poets use this polyphonic language of the Other at Freudian "Another Scene" and Lacan's "Other." When the reader participates the constructive meanings, the locus of the language writing transforms itself into that of the Other which becomes the open field of language. The language poet can even manage to put himself in the between-the-two, a strange place, the place of the dream and of the Unheimlichkeit (uncanny), and suture between "the outer skin of the interior" and "the inner skin of the exterior" of the impossible real of definite meaning. The objective goal of the evacuation of meaning is all the same the first aspect suggested by the aims of the experimentalism by the language poetry. The open linguistic fields of the language poetry, then, will be supplemented by The Freudian "unconscious" processes of dreams, free associations, slips of tongue, and symptoms which are composed of this polyphonic language. These fields can be properly excavated by the methods and topological mapping of the poetics of extimacy and of the klein bottle.