• Title/Summary/Keyword: $Z_2$

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A Kohn-nirenberg example using lower degree

  • Yi, Jeong-Seon
    • Communications of the Korean Mathematical Society
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    • v.11 no.1
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    • pp.81-87
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    • 1996
  • We will construct polynomials of degree 6 in z and $\bar{z}$ on $C^2$ which gives, via its coefficient $\beta$ as a parameter, a family of pseudoconvex domains $\Omega_\beta$ in $C^2$ with the origin being a boundary point, and show that the domains $\Omega_\beta$ has no peak functions of class $c^1$ at the origin and has no holomorphic support functions for $1 \leq \beta < \frac{9}{5}$.

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SOME IDENTITIES OF DEGENERATE GENOCCHI POLYNOMIALS

  • Lim, Dongkyu
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.2
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    • pp.569-579
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    • 2016
  • L. Carlitz introduced higher order degenerate Euler polynomials in [4, 5] and studied a degenerate Staudt-Clausen theorem in [4]. D. S. Kim and T. Kim gave some formulas and identities of degenerate Euler polynomials which are derived from the fermionic p-adic integrals on ${\mathbb{Z}}_p$ (see [9]). In this paper, we introduce higher order degenerate Genocchi polynomials. And we give some formulas and identities of degenerate Genocchi polynomials which are derived from the fermionic p-adic integrals on ${\mathbb{Z}}_p$.

Stereochemical Induction in the Generation of 1-Chloro-1-phenyl-2-neopentylsilene

  • Bok Ryul Yoo;Il Nam Jung;Myong Euy Lee;Chang Hwan Kim
    • Bulletin of the Korean Chemical Society
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    • v.12 no.5
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    • pp.517-520
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    • 1991
  • The reaction of dichlorophenylvinylsilane with tert-butyllithium in hydrocarbon solvents at room temperature or below generated the Z and E-isomers of 1-chloro-1-phenyl-2-neopentylsilene. The intermediates were trapped by cyclopentadiene, anthracene and methoxytrimethylsilane to give a consistent 90/10 ratio for the Z-silene to E-silene adduct. This result was interpreted as an evidence for stereochemical induction in the silene generation reaction.

ON SUFFICIENT CONDITIONS FOR CARATHÉODORY FUNCTIONS WITH THE FIXED SECOND COEFFICIENT

  • Kwon, Oh Sang
    • Honam Mathematical Journal
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    • v.41 no.2
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    • pp.227-242
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    • 2019
  • In the present paper, we derive several sufficient conditions for $Carath{\acute{e}}odory$ functions in the open unit disk ${\mathbb{D}}:=\{z{\in}{\mathbb{C}}:{\mid}z{\mid}<1\}$ under the constraint that the second coefficient of the function is preassigned. And, we obtain some sufficient conditions for strongly starlike functions in ${\mathbb{D}}$.

The influence of gonadotropin-releasing hormone agonists on anthropometric change in girls with central precocious puberty

  • Yoon, Jong Wan;Park, Hyun A;Lee, Jieun;Kim, Jae Hyun
    • Clinical and Experimental Pediatrics
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    • v.60 no.12
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    • pp.395-402
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    • 2017
  • Purpose: The potential effect of gonadotropin-releasing hormone agonist (GnRHa) treatment on the weight of girls with central precocious puberty (CPP) remains a controversy. We investigated anthropometric changes during and after GnRHa treatment among girls with CPP. Methods: This retrospective study evaluated data from 127 girls with CPP who received GnRHa treatment for ${\geq}2years$. Height, weight, and body mass index (BMI) values were compared at the baseline (visit 1), after 1 year of GnRHa treatment (visit 2), the end of GnRHa treatment (visit 3), and 6-12 months after GnRHa discontinuation (visit 4). Results: The height z score for chronological age (CA) increased continuously between visit 1 and visit 4. No significant differences were observed in BMI z score for CA between visits 1 and 4. However, an increasing trend in the BMI z score for bone age (BA) was observed between visits 1 and 4. The numbers of participants who were of normal weight, overweight, and obese were 97, 22, and 8, respectively, at visit 1, compared to 100, 16, and 11, respectively, at visit 4 (P=0.48). Conclusion: Among girls with CPP, the overall BMI z score for CA did not change significantly during or after GnRHa treatment discontinuation, regardless of their BMI status at visit 1. However, the BMI z score for BA showed an increasing trend during GnRHa treatment and a decreasing trend after discontinuation. Therefore, long-term follow-up of BMI changes among girls with CPP is required until they attain adult height.

Synthesis of an Aspartame Precursor Using Thermolysin in Organic Two-Phase System (유기용매 이상계에서 Thermolysin에 의한 아스파탐 전구체 생산)

  • 이인영;안경섭;이선복
    • Microbiology and Biotechnology Letters
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    • v.20 no.1
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    • pp.61-67
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    • 1992
  • The synthesis of N-benzyloxycarbonyl-L-aspartyl-L-phenylalanine methyl ester(ZAPM), a precursor of aspartame, from N-benzyloxycarbonyl-L-aspartic acid(Z-Asp) and L-phenylalanine methyl ester hydrochloride(L-PM-HCl) was investigated in ethylacetate-MES buffer two-phase system using thermolysin. In organic two-phase system, the degree of spontaneous hydrolysis of L-PM. HCl was significantly reduced with increasing the volume ratio of organic to aqueous phase. Stability of thermolysin in organic two-phase system was found to be higher than that in MES buffer solution. More than 90% of initial enzyme activity was maintained after 10 days of incubation in case that the volume of organic phase was equal to that of buffer phase, while the half life of thermolysin was about 2 days in aqueous buffer solution. The results of partitioning of substrates and product in organic two-phase system showed that the difference in partition coefficients between substrates and product was maximum at pH 5.5. The optimal pH for 2-APM synthesis in organic two-phase system was found to be 5.5-5.8, which is consistent with the value expected from the partition experiments. As the concentration of substrates was increased the conversion yield of Z-APM was increased with concomitant reduction of L-PMqHC1 hydrolysis. In case that the concentration of L-PM-HCl and Z-Asp were 160 mM and 80 mM respectively, the conversion yield of Z-APM reached 90% after 28 hrs of reaction. The yield obtained at different volume ratio of organic phase compares well with the predicted equilibrium constant in biphasic system.

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GRB 100905A at the Epoch of Re-ionization

  • Im, Myung-Shin;Jeon, Yi-Seul;Jang, Min-Sung;Choi, Chang-Su;Kang, Eu-Gene;Jun, Hyun-Sung;Urata, Yuji;Huang, Kui-Yun;Kruehler, Thomas;Sakamoto, Taka;Gehrels, Neil;Choi, Philip I.;Larger Collaboration, Larger Collaboration
    • The Bulletin of The Korean Astronomical Society
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    • v.37 no.1
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    • pp.32.2-32.2
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    • 2012
  • Gamma Ray Bursts (GRBs) are the most energetic events in the universe, and are known to arise from the death of massive stars in many cases. Their extreme brightness makes it possible to detect them at very high redshift (z > 6.5), well into the epoch of re-ionization, providing us with an opportunity to investigate the deaths of the first stars when the universe was much younger than 1 Gyr. Here, we report the discovery of GRB 100905A, a GRB at $z$ - 7.5 (age of the universe at 700 Myr). Our observation revealed a strong spectral break between z and J band, allowing us to estimate its photometric redshift. Its gamma-ray light curve shows a very short duration of about 0.7 sec, the shortest duration event at z > 5. Investigation of this and three other known GRBs at z > 6.5 reveals that they are all short duration bursts. This is puzzling, considering that GRBs from death of massive stars do not show short duration. We suggest two possible explanations for this: (i) the BAT light curves of the high redshift GRBs suffered from observational selection effect where we are only observing the very tip of the light curve; (ii) the stars in the early universe had a peculiar nature that are different from ordinary stars at lower redshifts.

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Dependence of Halo Properties on Galactic Potentials

  • Kim, Youngkwang;Lee, Young Sun;Beers, Timothy C.
    • The Bulletin of The Korean Astronomical Society
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    • v.42 no.2
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    • pp.51.1-51.1
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    • 2017
  • We present the dependence of halo properties on two different Galactic potentials: the $St{\ddot{a}}ckel$ potential and the Milky Way-like potential known as "Galpy". Making use of the Sloan Digital Sky Survey Data Release 12 (SDSS DR12), we find that the shape of the metallicity distribution and rotation velocity distribution abruptly changes at 15 kpc of $Z_{max}$ (the maximum distance of stellar orbit above or below the Galactic plane) and 32 kpc of $r_{max}$ (the maximum distance of an orbit from the Galactic center) in the $St{\ddot{a}}ckel$, which indicates that the transition from the inner to outer halo occurs at those distances. When adopting the $St{\ddot{a}}ckel$ potential, stars with $Z_{max}$ > 15 kpc show a retrograde motion of $V_{\phi}=-60km\;s^{-1}$, while stars with $r_{max}$ > 32 kpc show $V_{\phi}=-150km\;s^{-1}$. If we impose $V_{\phi}$ < $-150km\;s^{-1}$ to the stars with $Z_{max}$> 15 kpc or $r_{max}$> 32, we obtain the peak of the metallicity distribution at [Fe/H] = -1.9 and -1.7 respectively. However, there is the transition of the metallicity distribution at $Z_{max}=25kpc$, whereas there is no noticeable retrograde motion in the Galpy. The reason for this is that stars with high retrograde motion in the $St{\ddot{a}}ckel$ potential are unbound and stars with low rotation velocity reach to larger region of $Z_{max}$ and $r_{max}$ due to shallower potential in the Galpy. These results prove that as the adopted Galactic potential can affect the interpretation of the halo properties, it is required to have a more realistic Galactic potential for the thorough understanding of the dichotomy of the Galactic halo.

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Migration Activity of Chicken Gonadal Primordial Germ Cells (gPGCs) and Post-transfer Localization of LacZ-transfected gPGCs in the Embryonic Gonads

  • Jeong, D.K.;Han, J.Y.
    • Asian-Australasian Journal of Animal Sciences
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    • v.15 no.9
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    • pp.1227-1231
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    • 2002
  • A powerful tool for chicken transgenesis could be established by employing a germline chimera production through primordial germ cell transplantation. This study was conducted to examine whether foreign gene-transfected gonadal primordial germ cells (gPGCs) have a migration activity into the gonad after transfer to recipient embryos. In Experiment 1, gPGCs of Korean Ogol Chicken were retrieved from 5.5-day-old embryos and subsequently transferred to the dorsal aorta of 2.5-day-old White Leghorn embryos after being labeled with PKH26 fluorescent dye. To confirm migration activity after transplantation, recipient embryos were sacrificed and examined on 3 days after transfer. Sex determination was concomitantly undertaken to examine whether sex of recipient embryos could affect the migration activity of gPGCs. All of embryonic gonads examined showed positive signals with PKH26 fluorescence and W-chromosome specific band by polymerase chain reaction (PCR) was detected in male embryos when gPGCs with ZW chromosome were transferred to recipient embryos. In Experiment 2, retrieved gPGCs were transfected with LacZ gene-containing cytomegalovirus promoter ($pCMV{\beta}$) by electroporation and subsequently transferred to recipient embryos. LacZ gene expression was identified in the gonads of 6 or 10-day-old recipient embryos and hatched-chicks. A total of 20 embryos and 12 hatched-chicks were examined and 11 of them (10 embryos and one hatched chicken; 11/32=34.4%) expressed $\beta$-galactosidase, a marker substance of LacZ gene. The results of this study demonstrated that foreign gene-transfected gPGCs can migrate and settle down into the gonad after being transferred into the blood vessel of the recipient embryos. This established technique will contribute to developing a peer biotechnology for transgenic chicken.