• 대한수학회지
• /
• 제35권2호
• /
• pp.449-463
• /
• 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.

• 대한수학회보
• /
• 제56권6호
• /
• pp.1601-1615
• /
• 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.

• 대한수학회보
• /
• 제56권3호
• /
• pp.703-728
• /
• 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.

• 대한수학회논문집
• /
• 제26권4호
• /
• pp.649-660
• /
• 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.

• Nonlinear Functional Analysis and Applications
• /
• 제29권3호
• /
• pp.649-672
• /
• 2024

This paper explores the significance and implications of fixed point results related to orbital contraction as a novel form of contraction in various fields. Theoretical developments and theorems provide a solid foundation for understanding and utilizing the properties of orbital contraction, showcasing its efficacy through numerous examples and establishing stability and convergence properties. The application of orbital contraction in control systems proves valuable in designing resilient and robust control strategies, ensuring reliable performance even in the presence of disturbances and uncertainties. In the realm of financial modeling, the application of fixed point results offers valuable insights into market dynamics, enabling accurate price predictions and facilitating informed investment decisions. The practical implications of fixed point results related to orbital contraction are substantiated through empirical evidence, numerical simulations, and real-world data analysis. The ability to identify and leverage fixed points grants stability, convergence, and optimal system performance across diverse applications.

• 대한수학회지
• /
• 제45권6호
• /
• pp.1505-1521
• /
• 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].

• 대한수학회지
• /
• 제37권5호
• /
• pp.657-664
• /
• 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.

• 한국세라믹학회지
• /
• 제42권5호
• /
• pp.304-307
• /
• 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
• /
• 제13권1호
• /
• pp.131-138
• /
• 1997

• Bulletin of the Korean Chemical Society
• /
• 제14권1호
• /
• pp.101-107
• /
• 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.