• 대한수학회지
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• 제42권1호
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• pp.65-83
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• 2005

In this paper, we prove that the two well-known natural normalizations of Hamiltonian functions on the symplectic manifold ($M,\;{\omega}$) canonically relate the action spectra of different normalized Hamiltonians on arbitrary symplectic manifolds ($M,\;{\omega}$). The natural classes of normalized Hamiltonians consist of those whose mean value is zero for the closed manifold, and those which are compactly supported in IntM for the open manifold. We also study the effect of the action spectrum under the ${\pi}_1$ of Hamiltonian diffeomorphism group. This forms a foundational basis for our study of spectral invariants of the Hamiltonian diffeomorphism in [8].

• Bulletin of the Korean Chemical Society
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• 제24권6호
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• pp.809-811
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• 2003

This brief review contains surveys of both four-component and two-component relativistic molecular theories. First the four-component relativistic approach is reviewed. Emphasis is placed on efficient computational schemes for the four-component Dirac-Hartree-Fock and Dirac-Kohn-Sham methods. Next, in the twocomponent relativistic framework, two relativistic Hamiltonians, RESC and higher-order Douglas-Kroll (DK), are introduced. An illustrative application is shown for the relativistic study on valence photoelectron spectrum of OsO₄. The developing four-component relativistic and approximate quasi-relativistic methods have been packed in a program suite named REL4D.

• 대한수학회논문집
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• 제11권4호
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• pp.1137-1145
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• 1996

A Steinhaus graph is a labelled graph whose adjacency matrix $A = (a_{i,j})$ has the Steinhaus property : $a_{i,j} + a{i,j+1} \equiv a_{i+1,j+1} (mod 2)$. We consider random Steinhaus graphs with n labelled vertices in which edges are chosen independently and with probability $\frac{1}{2}$. We prove that almost all Steinhaus graphs are Hamiltonian like as in random graph theory.

• 한국진공학회:학술대회논문집
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• 한국진공학회 2000년도 제18회 학술발표회 논문개요집
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• pp.118-118
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• 2000

We investigate Frohlich-like electron--optical-phonon interactionsin uniaxial crytals based on the macroscopic dielectric continuum model. In general, the optical-phonon branches support mixed longitudinal and transverse modes due to the anisotropy. For heterostructures with double interfaces and superlattices, it is known that confined, interface, and half-space optical phonon modes exist in zincblende cystals. In uniaxial structures, additional propagating modes may exist in wurtzite heterosystems due to anisotropic phonon dispersion. This is especially the case when the dielectric properties of the adjacent heterostructure materials do not differ substantially. The dispersion relations and the interaction Hamiltonians for each of these modes are derived.

• 대한수학회보
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• 제54권6호
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• pp.2043-2051
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• 2017

Consider a sequence of compactly supported Hamiltonian diffeomorphisms ${\phi}_k$ of an exact symplectic manifold, all of which are "graphical" in the sense that their graphs are identified by a Darboux-Weinstein chart with the image of a one-form. We show by an elementary argument that if the ${\phi}_k$ $C^0$-converge to the identity, then their Calabi invariants converge to zero. This generalizes a result of Oh, in which the ambient manifold was the two-disk and an additional assumption was made on the Hamiltonians generating the ${\phi}_k$. We discuss connections to the open problem of whether the Calabi homomorphism extends to the Hamiltonian homeomorphism group. The proof is based on a relationship between the Calabi invariant of a $C^0$-small Hamiltonian diffeomorphism and the generalized phase function of its graph.

• Journal of information and communication convergence engineering
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• 제12권1호
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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.

• Bulletin of the Korean Chemical Society
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• 제17권2호
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• pp.192-198
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• 1996

We present a theoretical formulation of diffusion process on solid surface based on multidimensional transition state theory (TST). Surface diffusion of single adatom results from hopping processes on corrugated potential surface and is affected by surface vibrations of surface atoms. The rate of rare events such as hopping between lattice sites can be calculated by transition state theory. In order to include the interactions of the adatom with surface vibrations, it is assumed that the coordinates of adatom are coupled to the bath of harmonic oscillators whose frequencies are those of surface phonon modes. When nearest neighbor surface atoms are considered, we can construct Hamiltonians which contain terms for interactions of adatom with surface vibrations for the well minimum and the saddle point configurations, respectively. The escape rate constants, thus the surface diffusion parameters, are obtained by normal mode analysis of the force constant matrix based on the Hamiltonian. The analysis is applied to the diffusion coefficients of W, Ir, Pt and Ta atoms on the bcc(110) plane of W in the zero-coverage limit. The results of the calculations are encouraging considering the limitations of the model considered in the study.

• Bulletin of the Korean Chemical Society
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• 제6권3호
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• pp.168-170
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• 1985

The pairing properties of electronic structure are investigated from ab initioists' point of view. Numerical results of exact ab initio effective valence shell Hamiltonian are compared with simple semiempirical Hamiltonian calculations. In the oxygen atom case it was found that effective three-electron interaction terms break the similarity between electron-states and hole-states. With the trans-butadiene as an example the pairing theorem was studied. Even for alternant hydrocarbons, the deviation from the pairing was found to be enormous. The pairing theorem, which is usually stated for semiempirical Hamiltonians, is not valid when the exact effective Hamiltonian is considered. The present study indicates that comparisons between the pairing theorem of semiempirical methods and ab initio effective Hamiltonian give important information on the accuracy of semiempirical methods.

• Nonlinear Functional Analysis and Applications
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• 제29권2호
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• pp.527-543
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• 2024

In the realm of differential games and bioeconomic modeling, where intricate systems and multifaceted interactions abound, we explore the precision and efficiency of the Chebyshev Tau method (CTM). We begin with the Weierstrass Approximation Theorem, employing Chebyshev polynomials to pave the way for solving intricate bioeconomic differential games. Our case study revolves around a three-player bioeconomic differential game, unveiling a unique open-loop Nash equilibrium using Hamiltonians and the FilippovCesari existence theorem. We then transition to numerical implementation, employing CTM to resolve a Three-Point Boundary Value Problem (TPBVP) with varying degrees of approximation.

• 한국전기전자재료학회논문지
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• 제11권4호
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• pp.267-273
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• 1998

The band structures of $Si_{1-x}Ge_x$ layers grown on $Si_{1-y}Ge_y$ substrate are calculated using k$\cdot$p and strain Hamiltonians. The hole drift mobilities in the plane direction are then calculated by taking into account the screening effect and the density-of-states of the impurity band. When $Si_{1-x}Ge_x$ is grown on Si substrate, the mobilities of (110) and (111) $Si_{1-x}Ge_x$ layers are larger than that of (001) $Si_{1-x}Ge_x$. However, due to the large defect and surface scattering, (110) and (111) $Si_{1-x}Ge_x$ layers may not be useful for the development of the fast device. Meanwhile, when Si is grown on $Si_{1-y}Ge_y$ substrate, the mobilities of (001) and (110) Si layers are greatly enhanced. Based on the amount of defect and the surface scattering, it is expected that Si grown on (001) $Si_{1-y}Ge_y$ substrate, where the Ge contents is larger than 10%(y>0.1), has the highest mobility.