• Journal of the Korean Mathematical Society
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• v.48 no.4
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• pp.749-774
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• 2011

Given a Morse function on a manifold whose moduli spaces of gradient flow lines for each action window are compact up to breaking one gets a bidirect system of chain complexes. There are different possibilities to take limits of such a bidirect system. We discuss in this note the relation between these different limits.

• Bulletin of the Korean Chemical Society
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• v.35 no.12
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• pp.3443-3446
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• 2014

We present the solution of Klein Gordon equation with new generalized Morse-like potential using SUSYQM formalism. We obtained approximately the energy eigenvalues and the corresponding wave function in a closed form for any arbitrary l state. We computed the numerical results for some selected diatomic molecules.

• Bulletin of the Korean Chemical Society
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• v.5 no.4
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• pp.145-149
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• 1984

The entropy and heat capacity are calculated for the Morse oscillator model in order to test the quality of the partition function recently deduced by two of us. It is found that these analytical expressions are more reliable than the usually accepted one and give better results in the calculation of thermodynamic properties.

• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.391-405
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• 1996

In this article, we calculate the cohomology groups of flat vector bundles on some manifolds.

• Korean Journal of Materials Research
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• v.1 no.2
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• pp.86-92
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• 1991

A potential energy function comprising a two-body potential term which is modified form Morse potential and a three-body potential term which is modified from Axilrod-Teller potential has been developed for small carbon clusters. The structural changes of small carbon clusters $C_2-C_6$ are qualitatively investigated by employing this potential energy function representing the energies of the small carbon cluster isotopes as a function of the three body intensity factor. It is found that the structure of the small carbon cluster changes from open structure to closed one, from complicated structure to simple one, and from three-dimensional structure to two-or-one dimensional one as the degree of the three-body interaction increases.

• Korean Journal of Mathematics
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• v.6 no.1
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• pp.77-85
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• 1998

In this paper we study the Hessian at critical points of energy function on Teichm$\ddot{u}$ller space T(R) and apply it to the index of minimal surfaces.

• Journal of the Korean Chemical Society
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• v.59 no.4
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• pp.358-363
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• 2015

• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.773-791
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• 2017

In this paper we introduce a notion of an attractor for local semiflows on topological spaces, which in some cases seems to be more suitable than the existing ones in the literature. Based on this notion we develop a basic attractor theory on topological spaces under appropriate separation axioms. First, we discuss fundamental properties of attractors such as maximality and stability and establish some existence results. Then, we give a converse Lyapunov theorem. Finally, the Morse decomposition of attractors is also addressed.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2003.05a
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• pp.111-115
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• 2003

Nanoindentation is simply an indentation test in which the length scale of the penetration is measured in nanometres rather than microns or millimetres, the latter being common in conventional hardness tests. Three-dimensional molecular dynamics simulations have been conducted to evaluate the nanoindentation test. Molecular dynamics simulations were carried out on single crystal copper by varying crystal orientations to investigate nano-behavior of material beneath an indenter in nanoindentation. Morse potential function was used as an interatomic force between indenter and thin film. The result of the simulation shows that crystal orientation significantly influenced the slip system, dislocation nucleation and dislocation behavior.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.10
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• pp.1754-1761
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• 2003

The atomic force microscopy (AFM) based lithographic technique has been used directly to machine material surface and fabricate nano components in MEMS (micro electro mechanical system). In this paper, three-dimensional molecular dynamics (MD) simulations have been conducted to evaluate the characteristic of deformation process at atomistic scale for nano-lithography process. Effects of specific combinations of crystal orientations and cutting directions on the nature of atomistic deformation were investigated. The interatomic force between diamond tool and workpiece of copper material was assumed to be derived from the Morse potential function. The variation of tool geometry and cutting depth was also evaluated and the effect on machinability was investigated. The result of the simulation shows that crystal plane and cutting direction significantly influenced the variation of the cutting forces and the nature of deformation ahead of the tool as well as the surface deformation of the machined surface.