• Honam Mathematical Journal
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• v.32 no.3
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• pp.375-387
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• 2010

The paper studies an existence problem of a (generalized) universal covering space over a digital wedge with a compatible adjacency. In algebraic topology it is well-known that a connected, locally path connected, semilocally simply connected space has a universal covering space. Unlike this property, in digital covering theory we need to investigate its digital version which remains open.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.479-494
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• 2017

We construct various examples of simply connected minimal complex surfaces of general type with $p_g=0$ and $K^2=1,2$ using ${\mathbb{Q}}$-Gorenstein smoothing method.

• The Pure and Applied Mathematics
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• v.22 no.4
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• pp.359-364
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• 2015

We present smooth simply connected closed 4k-dimensional manifolds N := N_k, for each k ∈ {2, 3, ⋯}, with distinct symplectic deformation equivalence classes [[ω_i]], i = 1, 2. To distinguish [[ω_i]]’s, we used the symplectic Z invariant in [4] which depends only on the symplectic deformation equivalence class. We have computed that Z(N, [[ω₁]]) = ∞ and Z(N, [[ω₂]]) < 0.

• Communications of the Korean Mathematical Society
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• v.29 no.4
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• pp.549-554
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• 2014

We present a smooth simply connected closed eight dimensional manifold with distinct symplectic deformation equivalence classes [[${\omega}_i$]], i = 1, 2 such that the symplectic Z invariant, which is defined in terms of the scalar curvatures of almost K$\ddot{a}$hler metrics in [5], satisfies $Z(M,[[{\omega}_1]])={\infty}$ and $Z(M,[[{\omega}_2]])$ < 0.

• Structural Engineering and Mechanics
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• v.34 no.5
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• pp.549-561
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• 2010

In this paper, free vibration analyses of a parallel placed twin pipe system simulated by simply supported-simply supported and fixed-fixed Euler-Bernoulli beams resting on Winkler elastic soil are presented. The motion of the system is described by a homogenous set of two partial differential equations, which is solved by a simulation method called the Differential Transform Method (DTM). Free vibrations of an elastically connected twin pipe system are realized by synchronous and asynchronous deflections. The results of the presented theoretical analyses for simply supported Euler-Bernoulli beams are compared with existing ones in open literature and very good agreement is demonstrated.

• Communications of the Korean Mathematical Society
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• v.13 no.1
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• pp.109-121
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• 1998

Let X,Y be connected, locally connected, semilocally simply connected and $f,g : X \to Y$ be a pair of maps. We find an upper bound of the Reidemeister number R(f,g) by using the regular coverig spaces.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.267-278
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• 2009

As a survey-type article, the paper reviews the recent results on a (generalized) universal covering space in digital covering theory. The recent paper [19] established the generalized universal (2, k)-covering property which improves the universal (2, k)-covering property of [3]. In algebraic topology it is well-known that a simply connected and locally path connected covering space is a universal covering space. Unlike this property, in digital covering theory we can propose that a generalized universal covering space has its intrinsic feature. This property can be useful in classifying digital covering spaces and in studying a shortest k-path problem in data structure.

• Korean Journal of Mathematics
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• v.14 no.1
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• pp.65-70
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• 2006

In this article, we mention some subsequent developments of the theory of cluster sets, and present a new boundary cluster set for a simply connected domain in the complex plane and its applications.

• Journal of the Korean Mathematical Society
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• v.40 no.6
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• pp.1015-1029
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• 2003

In this paper, we study a connected, simply connected homogeneous Kahler surface with distinct constant Ricci eigenvalues, and specify the local structure of them.

• Communications of the Korean Mathematical Society
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• v.35 no.2
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• pp.653-666
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• 2020

In this paper, when G is a connected and simply connected nilpotent Lie group of dimension less than or equal to four, we study the uniform lattices Γ of G up to isomorphism and then we study the structure of the automorphism group Aut(Γ) of Γ from the viewpoint of splitting as a natural extension.