• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.6
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• pp.853-859
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• 2001

This paper describes the extended topological clean up procedures to improve the quality of unstructured triangular meshes. As a postprocessing step, topological improvement procedures are applied both for elements that are interior to the mesh and for elements connected to the boundary and then Laplacian-like smoothing is used by default. Previous clean up algorithms are limited to eliminate the nodes of degree 3,4,8,9,10 and pairs of nodes of degree 5. In this study, new clean up algorithms which minimize the triple connection structures combined with degree 5 and 7 (ie ; 5-7-5, 7-7-5, 7-5-7 etc) are added. The suggested algorithms are applied to two example meshes to demonstrate the effectiveness of the approach in improving element quality in a finite element mesh.

• East Asian mathematical journal
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• v.24 no.3
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• pp.213-221
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• 2008

In this paper, a new class of fuzzy topological spaces called ordered fuzzy pre-extremally disconnected spaces is introduced. Tietze extension theorem for ordered fuzzy pre-extremally disconnected spaces has been discussed as in [9] besides proving several other propositions and lemmas.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.25 no.6
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• pp.559-567
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• 2012

A level set based topological shape optimization method for nonlinear structure considering hyper-elastic problems is developed. To relieve significant convergence difficulty in topology optimization of nonlinear structure due to inaccurate tangent stiffness which comes from material penalization of whole domain, explicit boundary for exact tangent stiffness is used by taking advantage of level set function for arbitrary boundary shape. For given arbitrary boundary which is represented by level set function, a Delaunay triangulation scheme is used for current structure discretization instead of using implicit fixed grid. The required velocity field in the actual domain to update the level set equation is determined from the descent direction of Lagrangian derived from optimality conditions. The velocity field outside the actual domain is determined through a velocity extension scheme based on the method suggested by Adalsteinsson and Sethian(1999). The topological derivatives are incorporated into the level set based framework to enable to create holes whenever and wherever necessary during the optimization.

• Korean Journal of Mathematics
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• v.5 no.2
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• pp.169-176
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• 1997

The purpose of this note is to compare two known results related to the lifting problem of an action of a topological group G on a G-space X to a coverring space of X.

• Honam Mathematical Journal
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• v.21 no.1
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• pp.157-169
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• 1999

For a k-connected inverse system $({\scr{X}},\;*)=((X_{\lambda},\;*),p_{{\lambda}{{\lambda}}^{\prime}},\;{\Lambda})$ of pointed topological spaces and pointed preserving weak fibrations, inducting epimorphic chain maps, over a directed set, we show that the homotopy group ${\pi}_k(lim{\scr{X}},\;*)$ of the inverse limit is isomorphic to the integral homology group $$H_k(lim{\scr{X}};\mathbb{Z})$. Using the result of S. $Marde{\check{s}}i{\acute{c}}$, we prove that the group of pure extension $Pext(colimH^n({\scr{X}},\;A)$ is isomorphic to the group of extension $Ext({\Delta}({\lambda}),\;Hom(H^n({\scr{X}}),\;A))$.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.4
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• pp.281-284
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• 2009

In [8], we introduced the concept of fuzzy r-minimal structure which is an extension of smooth fuzzy topological spaces and fuzzy topological spaces in Chang's sense. And we also introduced and studied the fuzzy r-M continuity. In this paper, we introduce the concepts of fuzzy r-minimal compactness on fuzzy r-minimal compactness and nearly fuzzy r-minimal compactness, almost fuzzy r-minimal spaces and investigate the relationships between fuzzy r-M continuous mappings and such types of fuzzy r-minimal compactness.

• Journal of the Korean Institute of Intelligent Systems
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• v.2 no.1
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• pp.3-16
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• 1992

In this paper, we establish the conceptes of compactifications of a L-fuzzy topological space and a order relation in these compactifications. This order is a preorder. The existemce problem and the uniqueness problem of the largest compactifications are closely related to the mapping extension problem. We give out the largest compactifications and show the non-uniqueness of the largest compactifications in the preorder for a kind of spaces. Moreover, under some natural assumptions of separation axioms, we prove that the preorder is just a partial order, thus it ensures the uniqueness of the largest compactification. In addition. the related discussion involves the special properties of fuzzy product space, the latter seems to be independent interesting.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.659-675
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• 2023

Let K be an algebraically closed field of characteristic 0 and let f be a non-fibered planar quadratic polynomial map of topological degree 2 defined over K. We assume further that the meromorphic extension of f on the projective plane has the unique indeterminacy point. We define the critical pod of f where f sends a critical point to another critical point. By observing the behavior of f at the critical pod, we can determine a good conjugate of f which shows its statue in GIT sense.

• East Asian mathematical journal
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• v.39 no.3
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• pp.349-354
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• 2023

The motivation in this paper comes from the recent results about Bell inequalities and topological insulators from group theory. Symmetries which are interested in group theory could be mainly used to find material structures. In this point of views, we study group extending by adding one relator which is easily called an equation. So a relative group extension by a adding relator is aspherical if the natural injection is one-to-one and the group ring has no zero divisor. One of concepts of asphericity means that a new group by a adding relator is well extended. Also, we consider that several equations and relative presentations over torsion-free groups are related to zero divisors.

• Journal of the Korean Mathematical Society
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• v.46 no.3
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• pp.643-656
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• 2009

The family of demi-linear mappings between topological vector spaces is a meaningful extension of the family of linear operators. We establish equicontinuity results for demi-linear mappings and develop the usual theory of distributions and the usual duality theory.