• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.449-463
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• 1998

In this paper we introduce the notions of orbital Lipschitz stability (in variation) and orbital exponential asymptotic stability (in variation) of $C^{r}$ dynamical systems (or $C^{r}$ diffeomor-phisms) on Riemannian manifolds, and study the embedding problem of those concepts in $C^{r}$ dynamical systems.stems.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1601-1615
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• 2019

We show the existence of ground state and orbital stability of standing waves of nonlinear $Schr{\ddot{o}}dinger$ equations with singular linear potential and essentially mass-subcritical power type nonlinearity. For this purpose we establish the existence of ground state in $H^1$. We do not assume symmetry or monotonicity. We also consider local and global well-posedness of Strichartz solutions of energy-subcritical equations. We improve the range of inhomogeneous coefficient in [5, 12] slightly in 3 dimensions.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.703-728
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• 2019

Considered herein is the orbital stability in the energy space $H^1({\mathbb{R}})$ of a decoupled sum of N peakons for a Camassa-Holm-type equation with quartic nonlinearity, which admits single peakon and multi-peakons. Based on our obtained result of the stability of a single peakon, then combining modulation argument with monotonicity of local energy $H^1$-norm, we get the stability of the sum of N peakons.

• Communications of the Korean Mathematical Society
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• v.26 no.4
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• pp.649-660
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• 2011

S. M. Saperstone and M. Nishihama [6] had showed both continuity and stability of the orbital and limit set maps, K(x) and L(x), where K and L are considered as maps from X to $2^X$. The main purpose of this paper is to extend continuity and stability for dynamical systems to general dynamical systems.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1505-1521
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• 2008

In this paper, we give a characterization of the structurally stable vector fields via the notion of orbital inverse shadowing. More precisely, it is proved that the $C^1$ interior of the set of $C^1$ vector fields with the orbital inverse shadowing property coincides with the set of structurally stable vector fields. This fact improves the main result obtained by K. Moriyasu et al. in [15].

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.657-664
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• 2000

A new concept of stability that includes Lyapunov and orbital stabilities and leads to concepts in between them is discussed in terms of a given topology of the function space. The criteria for such new concepts to hold are investigted employing suitably Lyapunov-like functions and the comparison principle.

• Journal of the Korean Ceramic Society
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• v.42 no.5 s.276
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• pp.304-307
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• 2005

The possible configurations of hydroxyl group in hexagonal hydroxyapatite were identified through molecular orbital calculation. The molecular orbital interaction between O and H in hydroxyl column was analyzed using charge variation and Bond Overlap Population (BOP). We supposed 5 kinds of O-H bond configurations as cluster types of I, II, III, IV, and V. Mulliken's population analysis was applied to evaluate ionic charges of O, H, P, and Ca ions, and BOPs (Bond Overlap Populations) in order to discuss the bond strength change by the atomic arrangement. The stability of each O-H bond configuration was analyzed using bond overlap and ionic charge.

• East Asian mathematical journal
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• v.13 no.1
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• pp.131-138
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• 1997

• Bulletin of the Korean Chemical Society
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• v.14 no.1
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• pp.101-107
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• 1993

Ab initio calculations are carried out at the 6-311G$^{**}$ level for the $C_{2v}$ interactions of Be and Li atoms with acetylene molecule. The main contribution to the deep minima on the $^3B_2\;BeC_2H_2\;and\;^2B_2 LiC_2H_2$ potential energy curves is the b_2\;(2p(3b_2)-l{\pi}_g^*(4b_2))$ interaction, the $a_1\;(2s(6a_1)-I{\pi}_u(5a_1))$ interaction playing a relatively minor role. The exo deflection of the C-H bonds is basically favored, as in the $b_2$ interaction, due to steric crowding between the metal and H atoms, but the strong in-phase orbital interaction, or mixing, of the $a_1$ symmetry hydrogen orbital with the $5a'_1,\;6a'_1,\;and\;7a'_1$ orbitals can cause a small endo deflection in the repulsive complexes. The Be complex is more stable than the Li complex due to the double occupancy of the 2s orbital in Be. The stability and structure of the $MC_2H_2$ complexes are in general determined by the occupancy of the singly occupied frontier orbitals.

• Journal of Astronomy and Space Sciences
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• v.31 no.3
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• pp.187-197
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• 2014

We have investigated the dynamical stability of the proposed companions orbiting the Algol type short-period eclipsing binary SW Lyncis (Kim et al. 2010). The two candidate companions are of stellar to substellar nature, and were inferred from timing measurements of the system's primary and secondary eclipses. We applied well-tested numerical techniques to accurately integrate the orbits of the two companions and to test for chaotic dynamical behavior. We carried out the stability analysis within a systematic parameter survey varying both the geometries and orientation of the orbits of the companions, as well as their masses. In all our numerical integrations we found that the proposed SW Lyn multi-body system is highly unstable on time-scales on the order of 1000 years. Our results cast doubt on the interpretation that the timing variations are caused by two companions. This work demonstrates that a straightforward dynamical analysis can help to test whether a best-fit companion-based model is a physically viable explanation for measured eclipse timing variations. We conclude that dynamical considerations reveal that the proposed SW Lyncis multi-body system most likely does not exist or the companions have significantly different orbital properties from those conjectured in Kim et al. (2010).