• Journal of The Korean Astronomical Society
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• v.12 no.1
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• pp.41-70
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• 1979

From $B\ddot{o}hm$-Vitense's atmospheric model calculations, the relations, [$T_e$, (B-V)] and [B.C, (B-V)] with respect to heavy element abundance were obtained. Using these relations and evolutionary model calculations of Rood, and Sweigart and Gross, analytic expressions for some physical parameters relating to the C-M diagrams of globular clusters were derived, and they were applied to 21 globular clusters with observed transition periods of RR Lyrae variables. More than 20 different parameters were examined for each globular cluster. The derived ranges of some basic parameters are as follows; $Y=0.21{\sim}0.33,\;Z=1.5{\times}10^{-4}{\sim}4.5{\times}10^{-3},\;age,\;t=9.5{\sim}19{\times}10^9$ years, mass for red giants, $m_{RG}=0.74m_{\odot}{\sim}0.91m_{\odot}$, mass for RR Lyrae stars, $m_{RR}=0.59m_{\odot}{\sim}0.75m_{\odot}$, the visual magnitude difference between the turnoff point and the horizontal branch (HB), ${\Delta}V_{to}=3.1{\sim}3.4(<{\Delta}V_{to}>=3.32)$, the color of the blue edge of RR Lyrae gap, $(B-V)_{BE}=0.17{\sim}0.21=(<(B-V)_{BE}>=0.18),\;[\frac{m}{L}]_{RR}=-1.7{\sim}-1.9$, mass difference of $m_{RR}$ relative to $m_{RG},(m_{RG}-m_{RR})/m_{RG}=0.0{\sim}0.39$. It was found that the ranges of derived parameters agree reasonably well with the observed ones and those estimated by others. Some important results obtained herein can be summarized as follows; (i) There are considerable variations in the initial helium abundance and in age of globular clusters. (ii) The radial gradient of heavy element abundance does exist for globular clusters as shown by Janes for field stars and open clusters. (iii) The helium abundance seems to have been increased with age by massive star evolution after a considerable amount (Y>0.2) of helium had been attained by the Big-Bang nucleosynthesis, but there is not seen a radial gradient of helium abundance. (iv) A considerable amount of heavy elements ($Z{\sim}10{-3}$) might have been formed in the inner halo ($r_{GC}$<10 kpc) from the earliest galactic co1lapse, and then the heavy element abundance has been slowly enriched towards the galactic center and disk, establishing the radial gradient of heavy element abundance. (v) The final galactic disk formation might have taken much longer by about a half of the galactic age than the halo formation, supporting a slow, inhomogeneous co1lapse model of Larson. (vi) Of the three principal parameters controlling the morphology of C-M diagrams, it was found that the first parameter is heavy clement abundance, the second age and the third helium abundance. (vii) The globular clusters can be divided into three different groups, AI, BI and CII according to Z, Y an d age as well as Dickens' HB types. BI group clusters of HB types 4 and 5 like M 3 and NGC 7006 are the oldest and have the lowest helium abundance of the three groups. And also they appear in the inner halo. On the other hand, the youngest AI clusters have the highest Z and Y, and appear in the innermost halo region and in the disk. (viii) From the result of the clean separations of the clusters into three groups, a three dimensional classification with three parameters, Z, Y and age is prsented. (ix) The anomalous C-M diagrams can be expalined in terms of the three principal parameters. That is, the anomaly of NGC 362 and NGC 7006 is accounted for by the smaller age of the order of $1{\sim}2{\times}10^9$ years rather than by the helium abundance difference, compared with M 3. (x) The difference in two Oosterhoff types I and II can be explained in terms of the mean mass difference of RR Lyrae variables rather than in terms of the helium abundance difference as suggested by Stobie. The mean mass of the variables in Oosterhoff type I clusters is smaller by $0.074m_{\odot}$ which is exactly consistent with Rood's estimate. Since it was found that the mean mass of RR Lyrae stars increases with decreasing Z, the two Oosterhoff types can be explained substantially by the metal abundance difference; the type II has Z<$3.4{\times}10^{-4}$, and the type I has higher Z than the type II.

• Journal for History of Mathematics
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• v.21 no.4
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• pp.1-10
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• 2008

In this paper, we investigate the part dealing with algebra in Hong Gil Ju's GiHaSinSul to analyze his algebraic structure. The book consists of three parts. In the first part SangChuEokSan, he just renames Die jie hu zheng(疊借互徵) in Shu li jing yun to SangChuEokSan and adds a few examples. In the second part GaeBangMongGu, he obtains the following identities: $$n^2=n(n-1)+n=2S_{n-1}^1+S_n^0;\;n^3=n(n-1)(n+1)+n=6S_{n-1}^2+S_n^0$$; $$n^4=(n-1)n^2(n+1)+n(n-1)+n=12T_{n-1}^2+2S_{n-1}^1+S_n^0$$; $$n^5=2\sum_{k=1}^{n-1}5S_k^1(1+S_k^1)+S_n^0$$ where $S_n^0=n,\;S_n^{m+1}={\sum}_{k=1}^nS_k^m,\;T_n^1={\sum}_{k=1}^nk^2,\;and\;T_n^2={\sum}_{k=1}^nT_k^1$, and then applies these identities to find the nth roots $(2{\leq}n{\leq}5)$. Finally in JabSwoeSuCho, he introduces the quotient ring Z/(9) of the ring Z of integers to solve a system of congruence equations and also establishes a geometric procedure to obtain golden sections from a given one.

• Korean Journal of Crystallography
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• v.6 no.1
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• pp.36-42
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• 1995

Two types of single crystals of the title compound [6-(2-pyridyl)-3, 5-hexadiyn-ol, PyHxD] were obtained by solution of n-hexane/CH2C12 and n-hexane/Et2O, and their molecular conformations are proved identical in spite of different of space groups; C22H18N2O2 (I), Mr=343.70, Monoclinic, Pa, a=14.595(2), b=5.413(2), c=12.218(2)Å, β=96.86(1)°, V=958.3Å3, Z=2, Dx=1.19 Mgm-3, λ(MoKα)=0.71069Å, μ=0.072mm-1, F(000)=360.0, T=292K, R=0.104 for 756 unique observed reflections. An asymmetric unit contains a dimer connected by two N-H…O intermolecular hydrogen bonds. C11H9NO (II), Mr=171.85, Monoclinic, P21/a, a=14.611(2), b=5.423(6), c=12.191(2)Å, β=96.89(1)°, V=959.0Å3, Z=4, Dx=1.19 Mgm-3, λ(MoKα)=0.71069Å, μ=0.072mm-1, F(000)=360.0, T=293K, R=0.066 for 824 unique observed reflection. The structural asymmetric unit contains a molecule, but two N-H…O hydrogen bonds related by controsymmetry make the molecules form a dimer. In both structure, the dihedral angle between the planar pyridyl ring and the plane defined by C(10)-C(11)-O connected by linear diyne chain is approximately normal, and the molecules are stacked along b-axis with the unit repeat of b-axis.

• Advances in materials Research
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• v.5 no.2
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• pp.93-105
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• 2016

KNN-based ceramics modified with small amounts of $Bi_4Zr_3O_{12}$ (BiZ) has been synthesized using high-throughput experimentation (HTE). The results from X-ray diffraction show that for samples with base composition $(K_{0.5}Na_{0.5})NbO_3$ (KNN), the phase present changes from orthorhombic to pseudo-cubic with more than 0.2 mol% BiZ addition; for samples with base composition $(K_{0.48}Na_{0.48}Li_{0.04})(Nb_{0.9}Ta_{0.1})O_3$ (KNNLT), the phase present changes from a mixture of orthorhombic and tetragonal symmetry to pseudo-cubic with more than 0.4 mol % while for samples with base composition $(K_{0.48}Na_{0.48}Li_{0.04})(Nb_{0.86}Ta_{0.1}Sb_{0.04})O_3$ (KNNLST), the phase present is tetragonal with <0.3 mol% BiZ addition and transforms to pseudo-cubic with more dopant addition. The microstructures of the samples show that addition of BiZ decreases the average grain size and increases the volume of pores at the grain boundaries. The values of dielectric constant for KNN and KNNLT compositions increase slightly with BiZ addition while that for KNNLST decreases gradually with BiZ addition. The dielectric loss values are between 0.02 and 0.04 for KNNLT and KNNLST compositions while they are ~ 0.05 for KNN samples. The resistivity values increases with BiZ addition and values in the range of $10^{10}{\Omega}cm$ and $10^{12}{\Omega}cm$ are obtained. The piezoelectric charge coefficient ($d{^*}_{33}$) is highest for KNNLST samples and decreases gradually from ~400 pm/V to ~100 pm/V with BiZ addition.

• Journal of the Korean Applied Science and Technology
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• v.18 no.3
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• pp.214-232
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• 2001

CTA ester bonds in TG molecules were not attacked by pancreatic lipase and lipases produced by microbes such as Candida cylindracea, Chromobacterium viscosum, Geotricum candidium, Pseudomonas fluorescens, Rhizophus delemar, R. arrhizus and Mucor miehei. An aliquot of total TG of all the seed oils and each TG fraction of the oils collected from HPLC runs were deuterated prior to partial hydrolysis with Grignard reagent, because CTA molecule was destroyed with treatment of Grignard reagent. Deuterated TG (dTG) was hydrolyzed partially to a mixture of deuterated diacylglycerols (dDG), which were subsequently reacted with (S)-(+)-1-(1-naphthyl)ethyl isocyanate to derivatize into dDG-NEUs. Purified dDG-NEUs were resolved into 1, 3-, 1, 2- and 2, 3-dDG-NEU on silica columns in tandem of HPLC using a solvent of 0.4% propan-1-o1 (containing 2% water)-hexane. An aliquot of each dDG-NEU fraction was hydrolyzed and (fatty acid-PFB ester). These derivatives showed a diagnostic carboxylate ion, $(M-1)^{-}$, as parent peak and a minor peak at m/z 196 $(PFB-CH_{3})^{-}$ on NICI mass spectra. In the mass spectra of the fatty acid-PFB esters of dTGs derived from the seed oils of T. kilirowii and M. charantia, peaks at m/z 285, 287, 289 and 317 were observed, which corresponded to $(M-1)^{-}$ of deuterized oleic acid ($d_{2}-C_{18:0}$), linoleic acid ($d_{4}-C_{18:0}$), punicic acid ($d_{6}-C_{18:0}$) and eicosamonoenoic acid ($d_{2}-C_{20:0}$), respectively. Fatty acid compositions of deuterized total TG of each oil measured by relative intensities of $(M-1)^-$ ion peaks were similar with those of intact TG of the oils by GLC. The composition of fatty acid-PFB esters of total dTG derived from the seed oils of T. kilirowii are as follows; $C_{16:0}$, 4.6 mole % (4.8 mole %, intact TG by GLC), $C_{18:0}$, 3.0 mole % (3.1 mole %), $d_{2}C_{18:0}$, 11.9 mole % (12.5 mole %, sum of $C_{18:1{\omega}9}$ and $C_{18:1{\omega}7}$), $d_{4}-C_{18:0}$, 39.3 mole % (38.9 mole %, sum of $C_{18:2{\omega}6}$ and its isomer), $d_{6}-C_{18:0}$, 41.1 mole % (40.5 mole %, sum of $C_{18:3\;9c,11t,13c}$, $C_{18:3\;9c,11t,13r}$ and $C_{18:3\;9t,11t,13c}$), $d_{2}-C_{20:0}$, 0.1 mole % (0.2 mole % of $C_{20:1{\omega}9}$). In total dTG derived from the seed oils of M. charantia, the fatty acid components are $C_{16:0}$, 1.5 mole % (1.8 mole %, intact TG by GLC), $C_{18:0}$, 12.0 mole % (12.3 mole %), $d_{2}-C_{18:0}$, 16.9 mole % (17.4 mole %, sum of $C_{18:1{\omega}9}$), $d_{4}-C_{18:0}$, 11.0 mole % (10.6 mole %, sum of $C_{18:2{\omega}6}$), $d_{6}-C_{18:0}$, 58.6 mole % (57.5 mole %, sum of $C_{18:3\;9c,11t,13t}$ and $C_{18:3\;9c,11t,13c}$). In the case of Aleurites fordii, $C_{16:0}$; 2.2 mole % (2.4 mole %, intact TG by GLC), $C_{18:0}$; 1.7 mole % (1.7 mole %), $d_{2}-C_{18:0}$; 5.5 mole % (5.4 mole %, sum of $C_{18:1{\omega}9}$), $d_{4}-C_{18:0}$ ; 8.3 mole % (8.5 mole %, sum of $C_{18:2{\omega}6}$), $d_{6}-C_{18:0}$; 82.0 mole % (81.2 mole %, sum of $C_{18:3\;9c,11t,13t}$ and $C_{18:3 9c,11t,13c})$. In the stereospecific analysis of fatty acid distribution in the TG species of the seed oils of T. kilirowii, $C_{18:3\;9c,11t,13r}$ and $C_{18:2{\omega}6}$ were mainly located at sn-2 and sn-3 position, while saturated acids were usually present at sn-1 position. And the major molecular species of $(C_{18:2{\omega}6})(C_{18:3\;9c,11t,13c})_{2}$ and $(C_{18:1{\omega}9})(C_{18:2{\omega}6})(C_{18:3\;9c,11t,13c})$ were predominantly composed of the stereoisomer of $sn-1-C_{18:2{\omega}6}$, $sn-2-C_{18:3\;9c,11t,13c}$, $sn-3-C_{18:3\;9c,11t,13c}$, and $sn-1-C_{18:1{\omega}9}$, $sn-2-C_{18:2{\omega}6}$, $sn-3-C_{18:3\;9c,11t,13c}$, respectively, and the minor TG species of $(C_{18:2{\omega}6})_{2}(C_{18:3\;9c,11t,13c})$ and $ (C_{16:0})(C_{18:3\;9c,11t,13c})_{2}$ mainly comprised the stereoisomer of $sn-1-C_{18:2{\omega}6}$, $sn-2-C_{18:2{\omega}6}$, $sn-3-C_{18:3\;9c,11t,13c}$ and $sn-1-C_{16:0}$, $sn-2-C_{18:3\;9c,11t,13c}$, $sn-3-C_{18:3\;9c,11t,13c}$. The TG of the seed oils of Momordica charantia showed that most of CTA, $C_{18:3\;9c,11t,13r}$, occurred at sn-3 position, and $C_{18:2{\omega}6}$ was concentrated at sn-1 and sn-2 compared to sn-3. Main TG species of $(C_{18:1{\omega}9})(C_{18:3\;9c,11t,13t})_{2}$ and $(C_{18:0})(C_{18:3\;9c,11t,13t})_{2}$ were consisted of the stereoisomer of $sn-1-C_{18:1{\omega}9}$, $sn-2-C_{18:3\;9c,11t,13t}$, $sn-3-C_{18:3\;9c,11t,13t}$ and $sn-1-C_{18:0}$, $sn-2-C_{18:3\;9c,11t,13t}$, $sn-3-C_{18:3\;9c,11t,13t}$, respectively, and minor TG species of $(C_{18:2{\omega}6})(C_{18:3\;9c,11t,13c})_{2}$ and $(C_{18:1{\omega}9})(C_{18:2{\omega}6})(C_{18:3\;9c,11t,13c})$ contained mostly $sn-1-C_{18:2{\omega6}$, $sn-2-C_{18:3\;9c,11t,13t}$, $sn-3-C_{18:3\;9c,11t,13t}$ and $sn-1-C_{18:1{\omega}9}$, $sn-2-C_{18:2{\omega}6}$, $sn-3-C_{18:3\;9c,11t,13t}$. The TG fraction of the seed oils of Aleurites fordii was mostly occupied with simple TG species of $(C_{18:3\;9c,11t,13t})_{3}$, along with minor species of $(C_{18:2{\omega}6})(C_{18:3\;9c,11t,13t})_{2}$, $(C_{18:1{\omega}9})(C_{18:3\;9c,11t,13t})_{2}$ and $(C_{16:0})(C_{18:3\;9c,11t,13t})$. The sterospecific species of $sn-1-C_{18:2{\omega}6}$, $sn-2-C_{18:3\;9c,11t,13t}$, sn-3-C_{18:3\;9c,11t,13t}$, $sn-1-C_{18:1{\omega}9}$, $sn-2-C_{18:3\;9c,11t,13t}$, $sn-3-C_{18:3\;9c,11t,13t}$ and $sn-1-C_{16;0}$, $sn-2-C_{18:3\;9c,11t,13t}$, $sn-3-C_{18:3\;9c,11t,13t}$ are the main stereoisomers for the species of $(C_{18:2{\omega}6})(C_{18:3\;9c,11t,13t})_2$, $(C_{18:1{\omega}9})(C_{18:3\;9c,11t,13t})_{2}$ and $(C_{16:0})(C_{18:3\;9c,11t,13t})$, respectively.

• Clinical and Experimental Pediatrics
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• v.60 no.11
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• pp.373-378
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• 2017

Purpose: The aim of this study was to investigate the statistical properties of four previously developed pediatric coronary artery z score models in healthy Korean children. Methods: The study subjects were 181 healthy Korean children, whose age ranged from 1 month to 15 years. The diameter of each coronary artery was measured using 2-dimensional echocardiography and converted to the z score in the four models (McCrindle, Olivieri, Dallaire, and Japanese model). Descriptive statistical analyses and 1-sample t tests were performed. Results: All calculated z scores had P values of ${\geq}0.050$ using the Kolmogorov-Smirnov test. The one sample t test showed that the mean z scores did not converge to zero except in 1 model, and the mean right coronary artery (RCA) z score was less than zero in all 4 models. The smaller RCA diameter in this study could be associated with the more distal measuring point used to avoid the conal branch. The percentage of subjects with extreme z score values (${\geq}2.0$ and ${\geq}2.5$) for the left main coronary artery (LMCA) seems to be higher in the Dallaire (4.9% and 3.3%) and Japanese models (7.1% and 3.8%). Conclusion: All 4 models showed statistical feasibility of normal distribution. More precise instructions would be needed for the measurement of the RCA. The higher percentage of extreme z scores for the LMCA is compatible with the basic understanding of anatomic variation in the LMCA.

• Progress in Superconductivity
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• v.1 no.1
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• pp.9-13
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• 1999

The influence of quenching temperature and annealing time on superconducting characteristics has been investigated for a $(Pb_{0.6}V_{0.4})Sr_2(Ca_{0.65}Er_{0.35})Cu_2O_z$ compound. From the resistivity measurements for samples annealed at $400^{\circ}C$ to $860^{\circ}C$ in oxygen and subsequently quenched, it is observed that $T_c$(zero) of the sample decreases with the increase of annealing temperature up to $600^{\circ}C$ and increases again beyond $700^{\circ}C$. Annealings of the sample at $860^{\circ}C$ show that $T_c$(zero) goes through a maximum of 62K with the increase of the annealing time. It is also found that $T_c$(zero) of the sample quenched from high temperature decreases when the sample is subjected to low temperature annealing below. $600^{\circ}C$ in oxygen. The experimental results indicate that the as-prepared samples contain excessive oxygen and removal of this excessive oxygen in as-prepared samples is a key factor in controlling the superconducting properties of the samples and are discussed in connection with thermal gravimetric measurements.

• Restorative Dentistry and Endodontics
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• v.27 no.5
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• pp.488-492
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• 2002

The purpose of this study was to evaluate the effectiveness of plasma arc curing (PAC) unit for composite and compomer curing. To compare its effectiveness with conventional quartz tungsten halogen (QTH) light curing unit, the polymerization shrinkage rates and amounts of three composites (Z100, Z250, Synergy Duo Shade) and one compomer, that had been light cured by PAC unit or QTH unit, was compared using a custome made linometer. The measurement of polymerization shrinkage was peformed after polymerization with either QTH unit or PAC unit. In case of curing with the PAC unit, the composite was light cured with Apollo 95E for 6s, the power density of which was recorded as 1350 mW/$\textrm{cm}^2$ by Coltolux Light Meter. For light curing with QTH unit, the composite was light cured for 30s with the XL2500, the power density of which was recorded as 800 mW/$\textrm{cm}^2$ by Coltolux Light Meter. The amount of linear polymerization shrinkage was recorded in the computer every 0.5s for 60s. Ten measurements were made for each material. The amount of linear polymerization shrinkage for each material in 10s and 60s which were cured with PAC or QTH unit were compared with t test. The amount of polymerization shrinkage in the tested materials were compared with 1way ANOVA with Duncan's multiple range test. As for the amounts of polymerization shrinkage in 60s, there was no difference between PAC unit and QTH unit in Z250 and Synergy Duo Shade. In Z100 and Dyract AP, it was lower when it was cured with PAC unit than when it was cured with QTH unit (p<0.05). As for the amounts of polymerization shrinkage in 10s, there was no difference between PAC unit and QTH unit in Z100 and Dyract AP. The amounts of polymerization shrinkage was significantly higher when it was cured with PAC unit in Z250 and Synergy Duo Shade (p<0.05). The amounts of polymerization shrinkage in the tested materials when they were cured with QTH unit were Z250 (6.6um) < Z100 (9.3um), Dyract AP (9.7um) < Synergy Duo Shade (11.2um) (p<0.05). The amount of polymerization shrinkage when the materials were cured with PAC unit were Dyract AP (5.6um) < Z100 (8.1um), Z250(7.0um) < Synergy Duo Shade (11.2um) (p<0.05).

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1379-1391
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• 2008

Let k be an imaginary quadratic field, ${\eta}$ the complex upper half plane, and let ${\tau}{\in}{\eta}{\cap}k,\;q=e^{{\pi}{i}{\tau}}$. For n, t ${\in}{\mathbb{Z}}^+$ with $1{\leq}t{\leq}n-1$, set n=${\delta}{\cdot}2^{\iota}$(${\delta}$=2, 3, 5, 7, 9, 13, 15) with ${\iota}{\geq}0$ integer. Then we show that $q{\frac}{n}{12}-{\frac}{t}{2}+{\frac}{t^2}{2n}{\prod}_{m=1}^{\infty}(1-q^{nm-t})(1-q^{{nm}-(n-t)})$ are algebraic numbers.

• Journal of Climate Change Research
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• v.6 no.4
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• pp.357-366
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• 2015

This study was conducted to estimate carbon stocks of Quercus serrata with drawing volume of trees in each tree height and DBH applying the suitable stem taper equation and tree specific carbon emission factors, using collected growth data from all over the country. Information on distribution area, tree number per hectare, tree volume and volume stocks were obtained from the $5^{th}$ National Forest Inventory (2006~2010), and method provided in IPCC GPG was applied to estimate carbon storage and removals. Performance in predicting stem diameter at a specific point along a stem in Quercus serrata by applying Kozak's model,$d=a_1DBH^{a_2}a_3^{DBH}X^{b_1Z^2+b_2ln(Z+0.001)+b_3{\sqrt{Z}}+b_4e^Z+b_5({\frac{DBH}{H}})}$, which is well known equation in stem taper estimation, was evaluated with validations statistics, Fitness Index, Bias and Standard Error of Bias. Consequently, Kozak's model turned out to be suitable in all validations statistics. Stem volume tables of Quercus serrata were derived by applying Kozak's model and carbon stock tables in each tree height and DBH were developed with country-specific carbon emission factors ($WD=0.65t/m^3$, BEF=1.55, R=0.43) of Quercus serrata. As a result of carbon stock analysis by age class in Quercus serrata, carbon stocks of IV age class (11,358 ha, 36.5%) and V age class (10,432; 33.5%) which take up the largest area in distribution of age class were 957,000 tC and 1,312,000 tC. Total carbon stocks of Quercus serrata were 3,191,000 tC which is 3% compared with total percentage of broad-leaved forest and carbon sequestration per hectare(ha) was 3.8 tC/ha/yr, $13.9tCO_2/ha/yr$, respectively.