• Journal of the Korean Chemical Society
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• v.22 no.2
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• pp.67-77
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• 1978

MO's of a complex are expanded in terms of the set of Shull-Lowdin functions based on a single point, the nucleus of central metal ion, and the result was interpreted from the viewpoint of perturbation theory. We find that even in the case of $[NiF_6]^{4-}$, which has relatively small covalency, excited configurations with high orbital angular momentum are considerably mixed into $e_g$ and $t_{2g}$, orbitals of central metal ion, and that the distortions in these orbitals differ from each other. Therefore it is concluded that the energy difference between $e^*_g$ and $t^*_{2g}$, orbitals evaluated in the MO scheme has little meaning of the unique parameter 10Dq in the crystal field theory, and that such a unique parameter cannot be defined in a rigorous sense in the MO scheme.

• Journal of Astronomy and Space Sciences
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• v.29 no.2
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• pp.151-161
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• 2012

An intensive analysis of 148 timings of V700 Cyg was performed, including our new timings and 59 timings calculated from the super wide angle search for planets (SWASP) observations, and the dynamical evidence of the W UMa W subtype binary was examined. It was found that the orbital period of the system has varied over approximately $66^y$ in two complicated cyclical components superposed on a weak upward parabolic path. The orbital period secularly increased at a rate of $+8.7({\pm}3.4){\times}10^{-9}$ day/year, which is one order of magnitude lower than those obtained by previous investigators. The small secular period increase is interpreted as a combination of both angular momentum loss (due to magnetic braking) and mass-transfer from the less massive component to the more massive component. One cyclical component had a $20.^y3$ period with an amplitude of $0.^d0037$, and the other had a $62.^y8$ period with an amplitude of $0.^d0258$. The components had an approximate 1:3 relation between their periods and a 1:7 ratio between their amplitudes. Two plausible mechanisms (i.e., the light-time effects [LTEs] caused by the presence of additional bodies and the Applegate model) were considered as possible explanations for the cyclical components. Based on the LTE interpretation, the minimum masses of 0.29 $M_{\odot}$ for the shorter period and 0.50 $M_{\odot}$ for the longer one were calculated. The total light contributions were within 5%, which was in agreement with the 3% third-light obtained from the light curve synthesis performed by Yang & Dai (2009). The Applegate model parameters show that the root mean square luminosity variations (relative to the luminosities of the eclipsing components) are 3 times smaller than the nominal value (${\Delta}L/L_{p,s}{\approx}0.1$), indicating that the variations are hardly detectable from the light curves. Presently, the LTE interpretation (due to the third and fourth stars) is preferred as the possible cause of the two cycling period changes. A possible evolutionary implication for the V700 Cyg system is discussed.

• Journal of Astronomy and Space Sciences
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• v.28 no.3
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• pp.163-172
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• 2011

An intensive analysis of 185 timings of WZ Cep, including our new three timings, was made to understand the dynamical picture of this active W UMa-type binary. It was found that the orbital period of the system has complexly varied in two cyclical components superposed on a secularly downward parabola over about 80y. The downward parabola, corresponding to a secular period decrease of $-9.{^d}97{\times}10^{-8}y^{-1}$, is most probably produced by the action of both angular momentum loss (AML) due to magnetic braking and mass-transfer from the massive primary component to the secondary. The period decrease rate of $-6.^{d}72{\times}10^{-8}y^{-1}$ due to AML contributes about 67% to the observed period decrease. The mass flow of about $5.16{\times}10^{-8}M_{\odot}y^{-1}$ from the primary to the secondary results the remaining 33% period decrease. Two cyclical components have an $11.^{y}8$ period with amplitude of $0.^{d}0054$ and a $41.^{y}3$ period with amplitude of $0.^{d}0178$. It is very interesting that there seems to be exactly in a commensurable 7:2 relation between their mean motions. As the possible causes, two rival interpretations (i.e., light-time effects (LTE) by additional bodies and the Applegate model) were considered. In the LTE interpretation, the minimum masses of $0.30M_{\odot}$ for the shorter period and $0.49M_{\odot}$ for the longer one were calculated. Their contributions to the total light were at most within 2%, if they were assumed to be main-sequence stars. If the LTE explanation is true for the WZ Cep system, the 7:2 relation found between their mean motions would be interpreted as a stable 7:2 orbit resonance produced by a long-term gravitational interaction between two tertiary bodies. In the Applegate model interpretation, the deduced model parameters indicate that the mechanism could work only in the primary star for both of the two period modulations, but could not in the secondary. However, we couldn't find any meaningful relation between the light variation and the period variability from the historical light curve data. At present, we prefer the interpretation of the mechanical perturbation from the third and fourth stars as the possible cause of two cycling period changes.