• Journal of The Korean Astronomical Society
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• v.29 no.1
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• pp.19-30
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• 1996

We have examined consequences of strong tidal encounters between a neutron star and a normal star using SPH as a possible formation mechanism of isolated recycled pulsars in globular clusters. We have made a number of SPH simulations for close encounters between a main-sequence star of mass ranging from 0.2 to 0.7 $M_\bigodot$ represented by an n=3/2 poly trope and a neutron star represented by a point mass. The outcomes of the first encounters are found to be dependent only on the dimensionless parameter $\eta'{\equiv}(m/(m+ M))^{1/2}(\gamma_{min}/R_{MS})^{3/2}(m/M)^{{1/6)}$, where m and M are the mass of the main-sequence star and the neutron star, respectively, $\gamma_{min}$ the minimum separation between two stars, and $R_{MS}$ the size of the main-sequence star. The material from the (at least partially) disrupted star forms a disk around the neutron star. If all material in the disk is to be acctreted onto the neutron star's surface, the mass of the disk is enough to spin up the neutron star to spin period of 1 ms.

• Journal of The Korean Astronomical Society
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• v.40 no.4
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• pp.153-155
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• 2007

We have analyzed H and $K_s$-band images of the Arches cluster obtained using the NIRC2 instrument on Keck with the laser guide star adaptive optics (LGS AO) system. With the help of the LGS AO system, we were able to obtain the deepest ever photometry for this cluster and its neighborhood, and derive the background-subtracted present-day mass function (PDMF) down to $1.3M_{\bigodot}$ for the 5"-9" annulus of the cluster. We find that the previously reported turnover at $6M_{\bigodot}$ is simply due to a local bump in the mass function (MF), and that the MF continues to increase down to our 50 % completeness limit ($1.3M_{\bigodot}$) with a power-law exponent of ${\Gamma}$ = -0.91 for the mass range of 1.3 < M/$M_{\bigodot}$ < 50. Our numerical calculations for the evolution of the Arches cluster show that the ${\Gamma}$ values for our annulus increase by 0.1-0.2 during the lifetime of the cluster, and thus suggest that the Arches cluster initially had ${\Gamma}$ of $-1.0{\sim}-1.1$, which is only slightly shallower than the Salpeter value.

• Journal of Astronomy and Space Sciences
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• v.27 no.1
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• pp.1-10
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• 2010

The distance distribution in our planetary system has been a controversial matter. Two kinds of important issues on Titius-Bode's relation have been discussed up to now: one is if there is a simple mathematical relation between distances of natural bodies orbiting a central body, and the other is if there is any physical basis for such a relation. We have examined, by applying it to exo-planetary systems, whether Titius-Bode's relation is exclusively applicable to our solar system. We study, with the $X^2$ test, the distribution of period ratios of two planets in multiple planet systems by comparing it with that derived from not only Titius-Bode's relation but also other forms of it. The $X^2$ value between the distribution of the orbital period derived from Titius-Bode's relation and that observed in our Solar system is 12.28 (dof=18) with high probability, i.e., 83.3 %. The value of $X^2$ and probability resulted from Titius-Bode's relation and observed exo-planetary systems are 21.38 (dof=26) and 72.2 %, respectively. Modified forms we adopted seem also to agree with the planetary system as favorably as Titius-Bode's relation does. As a result, one cannot rule out the possibility that the distribution of the ratio of orbiting periods in multiple planet systems is consistent with that derived from Titius-Bode's relation. Having speculated Titius-Bode's relation could be valid in exo-planetary systems, we tentatively conclude it is unlikely that Titius-Bode's relation explains the distance distribution in our planetary system due to chance. Finally, we point out implications of our finding.

• Publications of The Korean Astronomical Society
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• v.35 no.1
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• pp.1-16
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• 2020

We report a calendar sheet for the 31st year of the reign of King Gojong (1894) (hereafter, calendar sheet 1894) in Korea, which calendrical data in a single page. This calendar sheet 1894 is composed of 14 rows by 14 columns (about 190 cells), and various calendrical data are recorded such as the sexagenary circle of the first day in each month, 24 solar terms, full moon day. In this paper, we compare calendrical data of 1894 calendar sheet with those of the almanac based on the Shixian calendar (hereafter, annual almanac) of the same year. Our findings are as follows. First, we find that the year is expressed using the reign-year of the king of the Joseon dynasty differently from using the reign-style of China in the annual almanac those times. Other calendar days of this calendar sheet are the same as those of the annual almanac in term of lunar dates, 24 solar terms, sexagenary days and so forth. Second, we find that the calendar sheet 1894 contains memorial days for 64 lineally ancestors of the Joseon royal family. These royal memorial days appears in the annual almanac two years later (i.e., 1896). Third, as the most distinctive feature, we find that the symbol of 工 kept every two cells. It was found that the cells can be filled with three days as the maximum number of days and then are labelled the same symbol 工 every second cell. This feature allows us to get the first year in which this kind of calendar sheet was published. It is conjectured one of 11 years, such as 1845, 1846, 1847, 1873, 1874, 1875, 1876, 1877, 1878, 1879 or 1880. We also think that the format of the calendar sheet 1894 has influenced on the Daehan-Minryeok (Korean civil calendar sheet) of 1920.

• Journal for History of Mathematics
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• v.25 no.4
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• pp.53-67
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• 2012

Today, it is necessary to calculate orbits with high accuracy in space flight. The key words of Poincar$\acute{e}$ in celestial mechanics are periodic solutions, invariant integrals, asymptotic solutions, characteristic exponents and the non existence of new single-valued integrals. Poincar$\acute{e}$ define an invariant integral of the system as the form which maintains a constant value at all time $t$, where the integration is taken over the arc of a curve and $Y_i$ are some functions of $x$, and extend 2 dimension and 3 dimension. Eigenvalues are classified as the form of trajectories, as corresponding to nodes, foci, saddle points and center. In periodic solutions, the stability of periodic solutions is dependent on the properties of their characteristic exponents. Poincar$\acute{e}$ called bifurcation that is the possibility of existence of chaotic orbit in planetary motion. Existence of near exceptional trajectories as Hadamard's accounts, says that there are probabilistic orbits. In this context we study the eigenvalue problem in early 20th century in three body problem by analyzing the works of Darwin, Bruns, Gyld$\acute{e}$n, Sundman, Hill, Lyapunov, Birkhoff, Painlev$\acute{e}$ and Hadamard.