• Korean Journal of Optics and Photonics
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• v.11 no.1
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• pp.1-5
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• 2000

We define the basic minimal coupling Hamiltonian of the atomic systems in the Coulomb guage and show that this Hamiltonian yields the correct equations of motion for the operators of interest. Using the unitary transformation and making the dipole approximation, we calculate the effect of polarization of the dipoles on the interaction Hamiltonian of the system. ystem.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.553-568
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• 2010

By making use of minimax theory and pseudo $Z_p$ index theory, some results on the existence and multiplicity of periodic solutions with minimal period to nonconvex superquadratic discrete Hamiltonian systems are obtained.

• Bulletin of the Korean Mathematical Society
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• v.44 no.3
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• pp.415-418
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• 2007

In this note we show the relationship between the period of a isochronous center of a planar Hamiltonian system and the Gauss curvature of the surface S = (x, y, H(x, y)) where H is the energy function of the system.

• Korean Journal of Mathematics
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• v.17 no.3
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• pp.331-340
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• 2009

We show the existence of nonconstant periodic solution for the nonlinear Hamiltonian systems with some nonlinearity. We approach the variational method. We use the critical point theory and the variational linking theory for strongly indefinite functional.

• Journal of information and communication convergence engineering
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• v.12 no.1
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• pp.39-45
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• 2014

A numerical method for solving Hamiltonian equations is said to be symplectic if it preserves the symplectic structure associated with the equations. Various symplectic methods are widely used in many fields of science and technology. A symplectic method preserves an approximate Hamiltonian perturbed from the original Hamiltonian. It theoretically supports the effectiveness of symplectic methods for long-term integration. Although it is also related to long-term integration, numerical stability of symplectic methods have received little attention. In this paper, we consider explicit symplectic methods defined for Hamiltonian equations with Hamiltonians of the special form, and study their numerical stability using the harmonic oscillator as a test equation. We propose a new stability criterion and clarify the stability of some existing methods that are visually based on the criterion. We also derive a new method that is better than the existing methods with respect to a Courant-Friedrichs-Lewy condition for hyperbolic equations; this new method is tested through a numerical experiment with a nonlinear wave equation.

• Journal of KIISE:Computer Systems and Theory
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• v.30 no.7_8
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• pp.434-444
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• 2003

In this paper, we consider the hamiltonian properties of m$\times$n (m$\geq$2, n$\geq$3) mesh networks with two wraparound edges on the first row and last row, called M$_2$(m, n), in the presence of a faulty node or link. We prove that M$_2$(m, n) with odd n is hamiltonian-connected and 1-fault hamiltonian. In addition, we prove that M$_2$(m, n) with even n is strongly hamiltonian laceable and 1-vertex fault tolerant strongly hamiltonian laceable.

• Journal of the Korean Mathematical Society
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• v.48 no.6
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• pp.1143-1152
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• 2011

The existence of periodic solutions for the planar Hamiltonian systems with positively homogeneous Hamiltonian is discussed. The asymptotic expansion of the Poincar$\acute{e}$ map is calculated up to higher order and some sufficient conditions for the existence of periodic solutions are given in the case when the first order term of the Poincar$\acute{e}$ map is identically zero.

• Bulletin of the Korean Chemical Society
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• v.6 no.5
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• pp.309-311
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• 1985

When a molecule is perturbed by an external field, the perturbed moecue can be described as a doubly perturbed system. Hartree-Fock operator in the absence of the field is the zeroth order Hamiltonian, and a correlation operator and the external field operator are perturbations. The effective Hamiltonian, which is a projection of the total Hamiltonian onto a small finite subspace (usually a valence space), has been formally derived. The influence of the external field to the molecular Hamiltonian itself has been examined within an effective Hamiltonian framework. The first order effective expectation values, for instance electromagnetic transition amplitudes, between valence states are found to be easily calculated - by simply taking matrix elements of the effective external field operator. Implications of the terms in perturbation expansion are discussed.

• Structural Engineering and Mechanics
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• v.61 no.5
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• pp.657-661
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• 2017

In this paper, it has been tried to propose a new semi analytical approach for solving nonlinear vibration of conservative systems. Hamiltonian approach is presented and applied to high nonlinear vibration systems. Hamiltonian approach leads us to high accurate solution using only one iteration. The method doesn't need any small perturbation and sufficiently accurate to both linear and nonlinear problems in engineering. The results are compared with numerical solution using Runge-Kutta-algorithm. The procedure of numerical solution are presented in detail. Hamiltonian approach could be simply apply to other powerfully non-natural oscillations and it could be found widely feasible in engineering and science.

• Journal of Korea Society of Industrial Information Systems
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• v.6 no.3
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• pp.20-28
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• 2001

In this paper, we present an efficient path-based multicast algorithm in wormhole-routed mesh networks. Our algorithm is based on a network partitioning strategy that uses two Hamiltonian paths. In the previous studies, only on a network partitioning strategy that uses two Hamiltonian paths. In the previous studies, only one Hamiltonian path was used. Thus messages traverse mire horizontal channels than vertical ones, leading to earlier network congestion. By incorporating additional vertical Hamiltonian path as well as the horizontal Hamiltonian path, messages are distributed evenly as much as possible, thus making network evenly as much as possible, thus making network performance better. We prove that this algorithm is deadlock-free. And by extensive simulations, we show that this algorithm is superior to the previous ones by 15∼20%.