• Journal of the Korean Mathematical Society
• /
• v.54 no.1
• /
• pp.117-139
• /
• 2017

This paper presents a systematic study for theoretical aspects of a unified approach to the abstract relative Fourier transforms over canonical homogeneous spaces of semi-direct product groups with Abelian normal factor. Let H be a locally compact group, K be a locally compact Abelian (LCA) group, and ${\theta}:H{\rightarrow}Aut(K)$ be a continuous homomorphism. Let $G_{\theta}=H{\ltimes}_{\theta}K$ be the semi-direct product of H and K with respect to ${\theta}$ and $G_{\theta}/H$ be the canonical homogeneous space (left coset space) of $G_{\theta}$. We introduce the notions of relative dual homogeneous space and also abstract relative Fourier transform over $G_{\theta}/H$. Then we study theoretical properties of this approach.

• Journal of the Korean Mathematical Society
• /
• v.41 no.1
• /
• pp.51-64
• /
• 2004

Q-reflexive locally convex spaces are spaces where $\widehat{\bigotimes}_{n,s,\pi}\;{E_e}^{"}\;and\;\overline{{(P(^nE),\;\taub)_i}^'}$ are isomorphic in a canonical way for every n. We investigate properties and find examples of such spaces.

• Journal of Mechanical Science and Technology
• /
• v.17 no.12
• /
• pp.1922-1927
• /
• 2003

Nonlinear normal mode (NNM) vibration, in a nonlinear dual mass Hamiltonian system, which has 6$\^$th/ order homogeneous polynomial as a nonlinear term, is studied in this paper. The existence, bifurcation, and the orbital stability of periodic motions are to be studied in the phase space. In order to find the analytic expression of the invariant curves in the Poincare Map, which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space, Whittaker's Adelphic Integral, instead of the direct integration of the equations of motion or the Birkhoff-Gustavson (B-G) canonical transformation, is derived for small value of energy. It is revealed that the integral of motion by Adelphic Integral is essentially consistent with the one obtained from the B-G transformation method. The resulting expression of the invariant curves can be used for analyzing the behavior of NNM vibration in the Poincare Map.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2001.11b
• /
• pp.799-804
• /
• 2001

Nonlinear normal mode (NNM) vibration, in a nonlinear dual mass Hamiltonian system, which has 6th order homogeneous polynomial as a nonlinear term, is studied in this paper. The existence, bifurcation, and the orbital stability of periodic motions are to be studied in the phase space. In order to find the analytic expression of the invariant curves in the Poincare Map, which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space, Whittaker's Adelphic Integral, instead of the direct integration of the equations of motion or the Birkhotf-Gustavson (B-G) canonical transformation, is derived for small value of energy. It is revealed that the integral of motion by Adelphic Integral is essentially consistent with the one obtained from the B-G transformation method. The resulting expression of the invariant curves can be used for analyzing the behavior of NNM vibration in the Poincare Map.

• Journal of KSNVE
• /
• v.9 no.1
• /
• pp.196-205
• /
• 1999

The existence. bifurcation. and the orbital stability of periodic motions, which is called nonlinear normal mode, in a nonlinear dual mass Hamiltonian system. which has 6th order homogeneous polynomial as a nonlinear term. are studied in this paper. By direct integration of the equations of motion. Poincare Map. which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space. is obtained. And via the Birkhoff-Gustavson canonical transformation, the analytic expression of the invariant curves in the Poincare Map is derived for small value of energy. It is found that the nonlinear system. which is considered in this paper. has 2 or 4 nonlinear normal modes depending on the value of nonlinear parameter. The Poincare Map clearly shows that the bifurcation modes are stable while the mode from which they bifurcated out changes from stable to unstable.

• Journal of The Korean Astronomical Society
• /
• v.39 no.3
• /
• pp.73-80
• /
• 2006

We analyze the extinction law towards several B1V stars-members of our Galaxy, searching for possible discrepancies from the galactic average extinction curve. Our photometric data allow to build extinction curves in a very broad range: from extreme UV till infrared. Two-colour diagrams, based on the collected photometric data from the ANS UV satellite, published UBV measurements and on the infrared 2MASS data of the selected stars, are constructed. Slopes of the fitted straight lines are used to build the average extinction curve and to search for discrepant objects. The selected stars have also been observed spectroscopically from the Terskol and ESO Observatories; these spectra allow to check their Sp/L's. The spectra of only about 30% of the initially selected objects resemble closely that of HD144470, considered as the standard of B1 V type. Other spectra either show some emission features or belong clearly to another spectral types. They are not used to build the extinction curve. Two-colour diagrams, constructed for the selected B1 V stars, showing no emission stellar features, prove that the interstellar extinction law is homogeneous in the Galaxy. Both the shape of the curve and the total-to-selective extinction ratio do not differ from the galactic average and the canonical value(3.1) respectively. The circumstellar emissions usually cause some discrepancies from the average interstellar extinction law; the discrepancies observed in the extraterrestrial ultraviolet, usually follow some misclassifications.