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A NOTE ON WITT RINGS OF 2-FOLD FULL RINGS

  • Cho, In-Ho;Kim, Jae-Gyeom
    • Bulletin of the Korean Mathematical Society
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    • v.22 no.2
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    • pp.121-126
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    • 1985
  • D.K. Harrison [5] has shown that if R and S are fields of characteristic different from 2, then two Witt rings W(R) and W(S) are isomorphic if and only if W(R)/I(R)$^{3}$ and W(S)/I(S)$^{3}$ are isomorphic where I(R) and I(S) denote the fundamental ideals of W(R) and W(S) respectively. In [1], J.K. Arason and A. Pfister proved a corresponding result when the characteristics of R and S are 2, and, in [9], K.I. Mandelberg proved the result when R and S are commutative semi-local rings having 2 a unit. In this paper, we prove the result when R and S are 2-fold full rings. Throughout this paper, unless otherwise specified, we assume that R is a commutative ring having 2 a unit. A quadratic space (V, B, .phi.) over R is a finitely generated projective R-module V with a symmetric bilinear mapping B: V*V.rarw.R which is nondegenerate (i.e., the natural mapping V.rarw.Ho $m_{R}$ (V, R) induced by B is an isomorphism), and with a quadratic mapping .phi.:V.rarw.R such that B(x,y)=(.phi.(x+y)-.phi.(x)-.phi.(y))/2 and .phi.(rx)= $r^{2}$.phi.(x) for all x, y in V and r in R. We denote the group of multiplicative units of R by U(R). If (V, B, .phi.) is a free rank n quadratic space over R with an orthogonal basis { $x_{1}$, .., $x_{n}$}, we will write < $a_{1}$,.., $a_{n}$> for (V, B, .phi.) where the $a_{i}$=.phi.( $x_{i}$) are in U(R), and denote the space by the table [ $a_{ij}$ ] where $a_{ij}$ =B( $x_{i}$, $x_{j}$). In the case n=2 and B( $x_{1}$, $x_{2}$)=1/2, we reserve the notation [ $a_{11}$, $a_{22}$] for the space.the space.e.e.e.

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CLASSIFICATION OF CLIFFORD ALGEBRAS OF FREE QUADRATIC SPACES OVER FULL RINGS

  • Kim, Jae-Gyeom
    • Bulletin of the Korean Mathematical Society
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    • v.22 no.1
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    • pp.11-15
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    • 1985
  • Manddelberg [9] has shown that a Clifford algebra of a free quadratic space over an arbitrary semi-local ring R in Brawer-Wall group BW(R) is determined by its rank, determinant, and Hasse invariant. In this paper, we prove a corresponding result when R is a full ring.Throughout this paper, unless otherwise specified, we assume that R is a commutative ring having 2 a unit. A quadratic space (V, B, .phi.) over R is a finitely generated projective R-module V with a symmetric bilinear mapping B: V*V.rarw.R which is non-degenerate (i.e., the natural mapping V.rarw.Ho $m_{R}$(V,R) induced by B is an isomorphism), and with a quadratic mapping .phi.: V.rarw.R such that B(x,y)=1/2(.phi.(x+y)-.phi.(x)-.phi.(y)) and .phi.(rx) = $r^{2}$.phi.(x) for all x, y in V and r in R. We denote the group of multiplicative units of R by U9R). If (V, B, .phi.) is a free rank n quadratic space over R with an orthogonal basis { $x_{1}$,.., $x_{n}$}, we will write < $a_{1}$,.., $a_{n}$> for (V, B, .phi.) where the $a_{i}$=.phi.( $x_{i}$) are in U(R), and denote the space by the table [ $a_{ij}$ ] where $a_{ij}$ =B( $x_{i}$, $x_{j}$). In the case n=2 and B( $x_{1}$, $x_{2}$)=1/2 we reserve the notation [a $a_{11}$, $a_{22}$] for the space. A commutative ring R having 2 a unit is called full [10] if for every triple $a_{1}$, $a_{2}$, $a_{3}$ of elements in R with ( $a_{1}$, $a_{2}$, $a_{3}$)=R, there is an element w in R such that $a_{1}$+ $a_{2}$w+ $a_{3}$ $w^{2}$=unit.TEX>=unit.t.t.t.

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Formation of Multi-Component Boride Coatings Containing V and/or Cr and Evaluation of Their Properties (바나듐 및 크롬을 포함하는 다 성분 Boride 코팅의 생성 및 특성 평가)

  • Lee, Euiyeol;Yoon, Sanghyun;Kim, Jongha
    • Journal of the Korean institute of surface engineering
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    • v.49 no.2
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    • pp.211-217
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    • 2016
  • Boride coating applied on steam turbine parts of power plants has provided good particle erosion resistance under temperature of $550^{\circ}C$, but it isn't able to protect the parts effectively any more in ultra super critical (USC) steam turbine which is being operated up to temperature of $650^{\circ}C$. To ensure stable durability for USC steam turbine parts, an alternative coating replacing boride coating should be developed. In this study, multi-component boride coatings containing elements such as chromium (Cr) and vanadium (V) were formed on base metal (B50A365B) using thermochemical treatment method called by pack cementation. The thermochemical treatments involve consecutive diffusion of boron(B) and Cr or/and V using pack powders containing diffusion element sources, activators and diluents. The top layer of Cr-boride coating is primarily consisted of $Cr_2B_3$ and $Cr_5B_3$, while that of V-boride coating is mostly consisted of $VB_2$ and $V_2B_3$. The (Cr,V)-boride coating is consisted of $Cr_2B_3$, $Cr_5B_3$ and $V_2B_3$ mostly. The top surfaces of 3 multi-component boride coatings show hardness of $3200-3400H_v$, which is much higher than that of boride, about $1600-2000H_v$. In 5 wt.% NaCl solution immersion tests, the multi-component boride coatings show much better corrosion resistance than boride coating.

Evidence for VH Gene Replacement in Human Fetal B Cells

  • Lee, Jisoo;Cho, Young Joo;Lipsky, Peter E.
    • IMMUNE NETWORK
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    • v.2 no.2
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    • pp.79-85
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    • 2002
  • Background: In contrast to evidences of Ig H chain receptor editing in transformed cell lines and transgenic mouse models, there has been no direct evidence that this phenomenon occurs in human developing B cells. Methods: $V_HDJ_H$ rearrangements were obtained from genomic DNA of individual $IgM^-$ B cells from liver and $IgM^+B$ cells from bone marrow of 18 wk of gestation human fetus by PCR amplification and direct sequencing. Results: We found three examples of H chain receptor editing from $IgM^+$ and $IgM^-human$ fetal B cells. Two types of $V_H$ replacements were identified. The first involved $V_H$ hybrid formation, in which part of a $V_H$ gene from the initial VDJ rearrangement is replaced by part of an upstream $V_H$ gene at the site of cryptic RSS. The second involved a gene conversion like replacement of CDR2, in which another $V_H$ gene donated a portion of its CDR2 sequence to the initial VDJ rearrangement. Conclusion: These data provide evidence of receptor editing at the H chain loci in developing human B cells, and also the first evidence of a gene conversion event in human Ig genes.

Ground-based and On-satellite Observations of Be and B Stars (인공위성관측과 지상관측에 의한 Be성과 B성의 연구)

  • 정장해
    • Journal of Astronomy and Space Sciences
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    • v.5 no.1
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    • pp.9-18
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    • 1988
  • Gamma Cassiopeae has been observe at Yonsei University Observatory(YUO) for 31 nights in the period 1983-1987 and a total of 312 UBV observations(104 in each colour) was secured. Light curves of ${\gamma}$ Cas in V, B-V, and U-B have been constructed with the YUO data; among them we present selected light curves of 5 different long nights. Discussed are the general photometric behaviour of ${\gamma}$ Cas, especially in connection with B-V changes, V/R variations of $H\alpha$ and H$\beta$, and high velocity narrow component(hvnc) exhibited in the far UV. Six spectral image sets of $\varepsilon$Per archived on IUE satellite are reduced and their line profiles in C IV and Si IV resonance lines are analyzed to find out any change, but the evidence is unlikely.

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A Variable-Gain Low-Voltage LNA MMIC Based on Control of Feedback Resistance for Wireless LAN Applications (피드백 저항 제어에 의한 무선랜용 가변이득 저전압구동 저잡음 증폭기 MMIC)

  • Kim Keun Hwan;Yoon Kyung Sik;Hwang In Gab
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.29 no.10A
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    • pp.1223-1229
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    • 2004
  • A variable-gain low-voltage low noise amplifier MMIC operating at 5GHz frequency band is designed and implemented using the ETRI 0.5$\mu\textrm{m}$ GaAs MESFET library process. This low noise amplifier is designed to have the variable gain for adaptive antenna array combined in HIPERLAN/2. The feedback circuit of a resistor and channel resistance controlled by the gate voltage of enhancement MESFET is proposed for the variable-gain low noise amplifier consisted of cascaded two stages. The fabricated variable gain amplifier exhibits 5.5GHz center frequency, 14.7dB small signal gain, 10.6dB input return loss, 10.7dB output return loss, 14.4dB variable gain, and 2.98dB noise figure at V$\_$DD/=1.5V, V$\_$GGl/=0.4V, and V$\_$GG2/=0.5V. This low noise amplifier also shows-19.7dBm input PldB, -10dBm IIP3, 52.6dB SFDR, and 9.5mW power consumption.

Sensitivity Improvement of 3-D Hall Sensor using Anisotropic Etching and Ni/Fe Thin Films (트랜치 구조를 갖는 3차원 홀 센서의 감도 개선에 관한 연구)

  • 이지연;최채형
    • Journal of the Microelectronics and Packaging Society
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    • v.8 no.4
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    • pp.17-23
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    • 2001
  • The 3-D Hall sensor has two horizontal magnetic field sensing parts ($\chi$, y components) and one vertical magnetic field sensing part (z component). For conventional, 3-D Hall sensor it is general that the sensitivity for $B_{z}$ is about 1/10 compared with those for $B_\chi$ or $B_y$. Therefore, in this work, we proposed 3-D Hall sensor with new structure. We have increased the sensitivity about 6 times to form the trench using anisotropic etching. And we have increased the sensitivity for the $B_z$ by 80% compared with those of $B_\chi$ and$B_y$ using deposition of the ferromagnetic thin films on the bottom surface of the wafer to concentrate the magnetic fluxes. When the input current was 3 mA, sensitivities of the fabricated sensor with Ni/Fe film for $B_\chi, B_y$ and $B_{z}$ were measured as 120.1 mV/T, 111.7 mV/T, 95.3 mV/T, respectively. The measured linearity of the sensor was within $\pm$3% of error.

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Experimental Study on the Expression of Hair Growth Related Factors after Bee Venom Acupuncture Therapy (봉독약침요법(蜂毒藥鍼療法)에 의한 발모관련 인자들의 발현에 대한 연구)

  • Kim, Ho-Il;Kim, Cheong-Moo;Shin, Hyun-Jong;Lee, Chang-Hyun
    • Journal of Physiology & Pathology in Korean Medicine
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    • v.25 no.3
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    • pp.496-502
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    • 2011
  • The present study was undertaken to investigate the effect of bee venom acupuncture therapy on the hair follicle growth by macroscopic, microscopic and immunohistochemical observation of skin 10 and 17 days after treatment. The results were as follows : Macroscopic hair follicle growth of 0.2 ml S.B.V. acupuncture treated group was more prominent than those of 0.1 ml S.B.V. acupuncture treated group and control group. Microscopic observation indicated that the hair follicle growth of control group reached anagen phase IV of hair growing cycle, and that of 0.1 ml and 0.2 ml S.B.V. acupuncture treated groups reached anagen phase VI and catagen, respectively. Immunohistochemical observations of the expression of various cytokines, enzymes and receptors in association with hair follicle cycle after local treatment of S.B.V. acupuncture therapy are as follows: Expression of fibroblast growth factor was more intense in epidermis and outer root sheath in 0.2 ml S.B.V. acupuncture treated group than that of 0.1 ml S.B.V. acupuncture treated group and control group. Expression of epidermal growth factor was more intense in bulge and outer root sheath in 0.2 ml S.B.V. acupuncture treated group than that of 0.1 ml S.B.V. acupuncture treated group and control group. Expression of c-kit receptor was more intense in epidermis, bulge and outer root sheath in 0.2 ml S.B.V. acupuncture treated group than that of control group. Expression of vascular endothelial growth factor was more intense in epidermis, bulge and outer root sheath in 0.2 ml S.B.V. acupuncture treated group than that of control group. Expression of protein kinase C-${\alpha}$ was more intense in epidermis, bulge and outer root sheath in 0.2 ml S.B.V. acupuncture treated group than control group. It is concluded that bee venom acupuncture therapy promoted the expression of various cytokines, enzymes and receptors related to the hair growth cycle for hair growth. This findings indicates that bee venom acupuncture therapy is applicable to the treatment of hair loss.

A Study on the Channeling Effect of Ultra Low Energy B, P and As Ion Implant to Form Ultra-Shallow Junction of Semiconductor Device (초미세 접합형성을 위한 극 저 에너지 B, P 및 As 이온주입시 채널링 현상에 관한연구)

  • 강정원;황호정
    • Journal of the Korean Institute of Telematics and Electronics D
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    • v.36D no.3
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    • pp.27-33
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    • 1999
  • We have investigated the ultra-low energy B, P, and As ion implantation using upgraded MDRANGE code to study formation of nanometer junction depths. Even at the ultra-low energies simulated in this paper, it was revealed that ion channeling should be carefully considered. It was estimated that ion channelings have much effect on dopant profiles when B ion implant energies were more than 500 eV, P more than 2 keV and As approximately more than 4 keV. When we compared 2-dimensional dopant profiles of 1 keV B with that of tilted one, 2 keV P with tilt, and 5 keV As with tilt, we could find that most channeling cases occurred not lateral directions but depth directions.

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The Effect of the Ligand's Spin-Orbit Coupling on the Zero-Field Splitting in the Low Spin Octahedral Ti(Ⅲ), V(Ⅲ), Fe(Ⅲ) and Ni(Ⅱ) Complexes (리간드의 Spin-Orbit Coupling이 작은 스핀팔면체 Ti(Ⅲ), V(Ⅲ), Fe(Ⅲ) 및 Ni(Ⅱ) 착물의 Zero-Field Splitting에 미치는 영향)

  • Ahn Sangwoon;Lee Kee Hag
    • Journal of the Korean Chemical Society
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    • v.23 no.2
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    • pp.65-74
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    • 1979
  • An effect of the spin-orbit coupling interaction of ligand orbitals on the ground state for octahedral $[Ti(Ⅲ)A_3B_3]$, $ [V(Ⅲ)A_3B_3]$, $ [Fe(Ⅲ)A_3B_3]$ and $ [Ni(Ⅱ)A_3B_3]$ type complexes has been investigated in this work, applying the degenerate perturbation theory. The wave functions are not affected but the energy level splitting for the ground state of these complexes by the spin-orbit coupling interaction of ligand orbitals. The extent of effect on the energy level splitting for the ground state is decreased in order Ti(Ⅲ) > V(Ⅲ) > Fe(Ⅲ).

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