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THE COMPUTATION METHOD OF THE MILNOR NUMBER OF HYPERSURFACE SINGULARITIES DEFINED BY AN IRREDUCIBLE WEIERSTRASS POLYNOMIAL $z^n$+a(x,y)z+b(x,y)=0 in $C^3$ AND ITS APPLICATION

  • Kang, Chung-Hyuk
    • Bulletin of the Korean Mathematical Society
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    • v.26 no.2
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    • pp.169-173
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    • 1989
  • Let V={(x,y,z):f=z$^{n}$ -npz+(n-1)q=0 for n .geq. 3} be a compled analytic subvariety of a polydisc in $C^{3}$ where p=p(x,y) and q=q(x,y) are holomorphic near (x,y)=(0,0) and f is an irreducible Weierstrass polynomial in z of multiplicity n. Suppose that V has an isolated singular point at the origin. Recall that the z-discriminant of f is D(f)=c(p$^{n}$ -q$^{n-1}$) for some number c. Suppose that D(f) is square-free. then we prove that by Theorem 2.1 .mu.(p$^{n}$ -q$^{n-1}$)=.mu.(f)-(n-1)+n(n-2)I(p,q)+1 where .mu.(f), .mu. p$^{n}$ -q$^{n-1}$are the corresponding Milnor numbers of f, p$^{n}$ -q$^{n-1}$, respectively and I(p,q) is the intersection number of p and q at the origin. By one of applications suppose that W$_{t}$ ={(x,y,z):g$_{t}$ =z$^{n}$ -np$_{t}$ $^{n-1}$z+(n-1)q$_{t}$ $^{n-1}$=0} is a smooth family of complex analytic varieties near t=0 each of which has an isolated singularity at the origin, satisfying that the z-discriminant of g$_{t}$ , that is, D(g$_{t}$ ) is square-free. If .mu.(g$_{t}$ ) are constant near t=0, then we prove that the family of plane curves, D(g$_{t}$ ) are equisingular and also D(f$_{t}$ ) are equisingular near t=0 where f$_{t}$ =z$^{n}$ -np$_{t}$ z+(n-1)q$_{t}$ =0.}$ =0.

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KRONECKER FUNCTION RINGS AND PRÜFER-LIKE DOMAINS

  • Chang, Gyu Whan
    • Korean Journal of Mathematics
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    • v.20 no.4
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    • pp.371-379
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    • 2012
  • Let D be an integral domain, $\bar{D}$ be the integral closure of D, * be a star operation of finite character on D, $*_w$ be the so-called $*_w$-operation on D induced by *, X be an indeterminate over D, $N_*=\{f{\in}D[X]{\mid}c(f)^*=D\}$, and $Kr(D,*)=\{0\}{\cup}\{\frac{f}{g}{\mid}0{\neq}f,\;g{\in}D[X]$ and there is an $0{\neq}h{\in}D[X]$ such that $(c(f)c(h))^*{\subseteq}(c(g)c(h))^*$}. In this paper, we show that D is a *-quasi-Pr$\ddot{u}$fer domain if and only if $\bar{D}[X]_{N_*}=Kr(D,*_w)$. As a corollary, we recover Fontana-Jara-Santos's result that D is a Pr$\ddot{u}$fer *-multiplication domain if and only if $D[X]_{N_*} = Kr(D,*_w)$.

Asn124 of Cel5A from Hypocrea jecorina not only provides the N-glycosylation site but is also essential in maintaining enzymatic activity

  • Qin, Yuqi;Qu, Yinbo
    • BMB Reports
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    • v.47 no.5
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    • pp.256-261
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    • 2014
  • To investigate the function of N-glycosylation of Cel5A (endoglucanase II) from Hypocrea jecorina, two N-glycosylation site deletion Cel5A mutants (rN124D and rN124H) were expressed in Saccharomyces cerevisiae. The weights of these recombinant mutants were 54 kDa, which were lower than that of rCel5A. This result was expected to be attributed to deglycosylation. The enzyme activity of rN124H was greatly reduced to 60.6% compared with rCel5A, whereas rN124D showed slightly lower activity (10%) than that of rCel5A. rN124D and rN124H showed different thermal stabilities compared with the glycosylated rCel5A, especially at lower pH value. Thermal stabilities were reduced and improved for rN124D and rN124H, respectively. Circular dichroism spectroscopy showed that the modification of secondary structure by mutation may be the reason for the change in enzymatic activity and thermal stability.

REMARKS ON FINITE FIELDS III

  • Kang, Shinwon
    • Bulletin of the Korean Mathematical Society
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    • v.23 no.2
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    • pp.103-111
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    • 1986
  • In [2] and [3], the Shinwon polynomial S$_{n}$(x) of order n is defined and studied in some details. In this paper we will define the general Shinwon polynomial S$_{n}$(a,x) and the Dickson polynomial D$_{n}$(a,x) of the second kind of order n which is a slightly changed form of the Dickson polynomial g$_{n}$(a,x), and show that D$_{n}$(a,x) is closely related to S$_{n}$(a,x).EX> n/(a,x).

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The Sound Velocity and Attenuation Coefficient of the Marine Surface Seciments in the nearshore area, Korea (韓半島 沿近海底 表層堆積物에서의 音波傳達速度와 減衰係數)

  • 김성;석봉출
    • 한국해양학회지
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    • v.20 no.2
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    • pp.10-21
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    • 1985
  • The sound velocity (compressional wave) and attenuation coefficient in the marine surface sediments in the nearshore areas off the Pohang, Pusan, Yeosu and Kunsan were investigated in terms of the geotechnical properties of the marine surface sediments in the water depth range of 10-50 meters. The marine surface sediments in the study areas are variable, that is, sand to clay. Due to the various four different study area, the sound velocities and attenuation coefficients in the surface sediment facies vary 1,44m/sec to 1,510m/sec in velocity and 0.82dB/m to 3.70dB/m in coefficient respectively. In fact, the sound velocity increases with increasing of density and mean grain sizes of the sediments, and however, with decreasing of porosith. The correlation equations between the sound velocith and geotechnical properties of mean grain size, density, and porosity were expressed as the following: Vp=1512.28406-9.16083(Mz)+0.20795(Mz)$\^$2/, Vp=1876.15527-597.50397(d)+210.48375(d)$\^$2/, Vp=1559.47217-2.09266(n)$\^$2/. where Vp is sound velocity, Mz is mean grain size, d is density, and m is porosity, respectively. However, the relationship between the attenuation and geotechnical properties were different from that of sound velocity and geotchnical properties. Furthermore, the correlation equations between attenuation coefficient and geotechnical properties were expressed as the following: a=1.85217+0.67197(Mz)-0.09035 (Mz)$\^$2/, a=48.87859+58.21721(d)-16.3.143(d)$\^$2/, a=2.06765+0.07215(n)-0.00111(n)$\^$2/, where a is attenuation coefficient. The high attenuation appeared in the silty sand through fine sand facies in sediment and k values in these facies were in the range of 0.86 to 0.89 dB/m/KHz.

Robustness Evaluation of GaN Low-Noise Amplifier in Ka-band (Ka-대역 GaN 저잡음 증폭기의 강건성 평가)

  • Lee, Dongju;An, Se-Hwan;Joo, Ji-Han;Kwon, Jun-Beom;Kim, Younghoon;Lee, Sanghun;Seo, Mihui;Kim, Sosu
    • The Journal of the Institute of Internet, Broadcasting and Communication
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    • v.22 no.6
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    • pp.149-154
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    • 2022
  • Due to high power capabilities and high linearity of GaN devices, GaN Low-Noise Amplifiers (LNAs) without a limiter can be implemented in order to improve noise figure and reduce chip area in radar receivers. In this paper, a GaN LNA is presented for Ka-band radar receivers. The designed LNA was realized in a 150-nm GaN HEMT process and measurement results show that the voltage gain of >23 dB and the noise figure of <6.5 dB including packaging loss in the target frequency range. Under the high-power stress test, measured gain and noise figure of the GaN LNA is degraded after the first stress test, but no more degradation is observed under multiple stress tests. Through post-stress noise and s-parameter measurements, we verified that the GaN LNA is resilient to pulsed input power of ~40 dBm.

Carbohydrate Structure of N- and O-linked Oligosaccharides of Human Erythropoietin Expressed in Chinese Hamster Ovary Cells

  • Lee, Dong-Eok;Ha, Byung-Jhip;Kim, Suk-Joon;Park, Ji-Sook;Yoo, Ree-Ann;Oh, Myung-Suk;Kim, Hyun-Su
    • BMB Reports
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    • v.29 no.3
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    • pp.266-271
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    • 1996
  • A recombinant human erythropoietin (EPO), expressed in Chinese hamster ovary (CHO) cells, is glycosylated at Asn 24, Asn 38, Asn 83, and Ser 126. After release of the N-linked carbohydrate chains by $peptide-N^{4}-(N-acetyl-{\beta}-glucosaminyl)$ asparagine amidase F, the oligosaccharides were analyzed by FACE (Fluorophore-Assisted Carbohydrate Electrophoresis). The O-linked carbohydrate chain was separated by hydrazine, and analyzed by FACE. The monosacccharide composition of recombinant EPO showed man nose, fucose, galactose, N-acetylglucosamine, N-acetylneuraminic acid, and a trace of N-acetylgalactosamine, which are typical monosaccharides in the glycoproteins from the CHO cell. Sequences of N-linked and O-linked oligosaccharides were determined. The structure and composition of oligosaccharides attached to recombinant human EPO, expressed in the CHO cell, are identical to the reported oligosaccharide structure in human EPO isolated from urine.

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Effects of Different Dietary Oil and d-Limonene on Histopathological and Biochemical Changes in Experimental Hepatocarcinogenesis (식이지방의 종류 및 d-Limonene 투여가 간 발암과정에 미치는 영향)

  • 이미숙;김정희
    • Journal of Nutrition and Health
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    • v.33 no.1
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    • pp.23-32
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    • 2000
  • The purpose of this study was to investigate the effcts of n-3, n-6 fatty arid and d-limonene on histopathological and biochemical changes in experimental rat hepatocarcinogenesis. To attain the above objectives, weanling Sprague-Dawley female rats were intraperitoneally injected twice with a dose of diethylnitrosamine(DEN, 50mg/kg body weight) and after 1 week 0.05% phenobarbital was provided with water. Sardine oil rich in n-3 fatty acids and corn oil rich in n-6 fatty acids were fed at 15% by weight and 5% d-limonene was added to the diet in each group. Ten weeks or 20 weeks after DEN treatment, rats were sacrifirced. The formation of glutathione S-transferase placental form positive(GST-P$\^$+/) foci was significantly decreased by the treatment of either sardine oil or d-limonene HMG-CoA reductase activity was not affected by dietary oils and d-limonene. Protein kinase C (PKC) activity was decreased by either sardine oil or d-limonene. Particularly d-limonene decreased the membrane PKC activity. Membrane Cholesterol/Phospholipid(Chol/PL) ratio was significantly decreased by d-limonene in sardine oil group. The data showed that GST-P$\^$+/ foci number was positively correlated with membrane PKC activity and serum cholesterol and negatively correlated with liver cholesterol level. These results suggest informations about the correlation between histopathological and biochemical changes such as cholesterol metabolism and PKC activity in experimental hepatocarcinogenesis and thereby can elucidate the possible mechanism related to the cancer inhibition.(Korean J Nutrition 33(1) : 23-32, 2000)

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High performance X-band power amplifier MMIC using a 0.25 ㎛ GaN HEMT technology (0.25 ㎛ GaN HEMT 기술을 이용한 우수한 성능의 X-대역 전력 증폭기)

  • Lee, Bok-Hyung;Park, Byung-Jun;Choi, Sun-Youl;Lim, Byeong-Ok;Go, Joo-Seoc;Kim, Sung-Chan
    • Journal of IKEEE
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    • v.23 no.2
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    • pp.425-430
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    • 2019
  • This work describes the design and characterization of a X-band power amplifier (PA) monolithic microwave integrated circuit (MMIC) using a $0.25{\mu}m$ gate length gallium nitride (GaN) high electron mobility transistor (HEMT) technology. The developed X-band power amplifier MMIC has small signal gain of over 22.7 dB and saturated output power of 43.02 dBm (20.04 W) over the entire band of 9 to 10 GHz. Maximum saturated output power is a 43.84 dBm (24.21 W) at 9.5 GHz. Its power added efficiency (PAE) is 41.0~51.24% and the chip dimensions are $3.7mm{\times}2.3mm$, generating the output power density of $2.84W/mm^2$. The developed GaN power amplifier MMIC is expected to be applied in a variety of X-band radar applications.

AN EXTREMAL PROBLEM ON POTENTIALLY $K_{r,r}$-ke-GRAPHIC SEQUENCES

  • Chen, Gang;Yin, Jian-Hua
    • Journal of applied mathematics & informatics
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    • v.27 no.1_2
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    • pp.49-58
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    • 2009
  • For $1{\leq}k{\leq}r$, let ${\sigma}$($K_{r,r}$ - ke, n) be the smallest even integer such that every n-term graphic sequence ${\pi}$ = ($d_1$, $d_2$, ..., $d_n$) with term sum ${\sigma}({\pi})$ = $d_1$ + $d_2$ + ${\cdots}$ + $d_n\;{\geq}\;{\sigma}$($K_{r,r}$ - ke, n) has a realization G containing $K_{r,r}$ - ke as a subgraph, where $K_{r,r}$ - ke is the graph obtained from the $r\;{\times}\;r$ complete bipartite graph $K_{r,r}$ by deleting k edges which form a matching. In this paper, we determine ${\sigma}$($K_{r,r}$ - ke, n) for even $r\;({\geq}4)$ and $n{\geq}7r^2+{\frac{1}{2}}r-22$ and for odd r (${\geq}5$) and $n{\geq}7r^2+9r-26$.

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