• Journal of KIISE
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• v.43 no.10
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• pp.1073-1078
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• 2016

(${\delta}$, ${\gamma}$)-matching for strings over integer alphabets can be applied to such fields as musical melody and share prices on stock markets. In this paper, we define ${\delta}$-approximate periods and ${\gamma}$-approximate periods of strings over integer alphabets. We also present two $O(n^2)$-time algorithms, each of which finds minimum ${\delta}$-approximate periods and minimum ${\gamma}$-approximate periods, respectively. Then, we provide the experimental results of execution times of both algorithms.

• Journal of KIISE
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• v.44 no.8
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• pp.760-766
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• 2017

Repetitive strings have been studied in diverse fields such as data compression, bioinformatics and so on. Recently, two problems of approximate periods of strings over integer alphabets were introduced, finding minimum ${\delta}-approximate$ periods and finding minimum ${\gamma}-approximate$ periods. Both problems can be solved in $O(n^2)$ time when n is the length of the string. In this paper, we present two parallel algorithms for solving the above two problems in O(n) time using $O(n^2)$ threads, respectively. The experimental results show that our parallel algorithms for finding minimum ${\delta}-approximate$ (resp. ${\gamma}-approximate$) periods run approximately 19.7 (resp. 40.08) times faster than the sequential algorithms when n = 10,000.

• 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.