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THE SYMMETRY OF spin DIRAC SPECTRUMS ON RIEMANNIAN PRODUCT MANIFOLDS

  • HONG, KYUSIK;SUNG, CHANYOUNG
    • Journal of the Korean Mathematical Society
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    • v.52 no.5
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    • pp.1037-1049
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    • 2015
  • It is well-known that the spectrum of a $spin^{\mathbb{C}}$ Dirac operator on a closed Riemannian $spin^{\mathbb{C}}$ manifold $M^{2k}$ of dimension 2k for $k{\in}{\mathbb{N}}$ is symmetric. In this article, we prove that over an odd-dimensional Riemannian product $M^{2p}_1{\times}M^{2q+1}_2$ with a product $spin^{\mathbb{C}}$ structure for $p{\geq}1$, $q{\geq}0$, the spectrum of a $spin^{\mathbb{C}}$ Dirac operator given by a product connection is symmetric if and only if either the $spin^{\mathbb{C}}$ Dirac spectrum of $M^{2q+1}_2$ is symmetric or $(e^{{\frac{1}{2}}c_1(L_1)}{\hat{A}}(M_1))[M_1]=0$, where $L_1$ is the associated line bundle for the given $spin^{\mathbb{C}}$ structure of $M_1$.

강릉연안 토종 다시마의 양식 연구

  • 김형근;박중구
    • Proceedings of the Korean Aquaculture Society Conference
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    • 2003.10a
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    • pp.147-148
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    • 2003
  • 동해안의 강릉 연안에 자생하는 토종 다시마인 개다시마는 산업적으로 개발의 여지가 매우 크다. 그러나 천연 자원량에 의존하고 있는 가공산업은 해황에 따라 원료 공급이 좌우되는 불안정성을 가지고 있어서 이 식물의 산업적 생산량을 확보하기 위한 방안으로 대량양식의 필요성이 대두되고 있다. 본 연구는 동해안 토종 다시마인 개다시마의 종묘생산기술 개발을 위해서 항온배양기와 실내수조배양을 실시하고 바다 가이식 양성에 의한 환경적응성 실험을 수행하였다. 연구 방법은 2001년 10월에 강릉연안 수심 20m에서 분포하는 개다시마 군락의 모조로부터 유주자액을 받아 온도 5, 10, 15, 20, $25^{\circ}C$, 조도 40, 80, 120 $\mu$mol m$^{-2}$ s$^{-1}$의 조건에서 6주간 정치배양하였다. 유주자의 발아 및 아포체 생장 실험 이후 바다 가이식 및 양성실험은 2002년 1~2월까지 1개월간 실시하였다. 유주자의 발아 및 아포체 형성은 1$0^{\circ}C$, 120$\mu$mo1 m$^{-2}$ s$^{-1}$에서 배양 2주만에 가장 먼저 아포체의 발아가 관찰되었으며, 이후 15$^{\circ}C$와 5$^{\circ}C$에서 순차적으로 아포체의 발아가 이루어졌다. 2$0^{\circ}C$는 80, 120$\mu$mol m$^{-2}$ s$^{-1}$에서 소수의 아포체만이 관찰되었으며, $25^{\circ}C$에서는 아포체가 형성되지 않았다. 아포체는 1$0^{\circ}C$에서 가장 좋은 생장을 보였고, 15$^{\circ}C$와 1$0^{\circ}C$에서는 비슷한 생장을 나타냈으며, 2$0^{\circ}C$에서는 80$\mu$mol m$^{-2}$ s$^{-1}$에서만 아포체의 형성이 관찰되어 가장 낮은 생장을 보였다. 동일 온도에서는 조도에 따른 생장의 차이가 많이 났는데, 40$\mu$mol m$^{-2}$ s$^{-1}$에서 가장 좋은 생장을 나타냈다. 80과 120$\mu$mol m$^{-2}$ s$^{-1}$에서는 120$\mu$mol m$^{-2}$ s$^{-1}$이 약간 좋은 생장을 보였지만 큰 차이는 나지 않았다. 생장이 가장 좋은 조건은 1$0^{\circ}C$, 40$\mu$mol m$^{-2}$ s$^{-1}$으로 엽장 1.28mm까지 생장했다. 전체적으로 수심이 깊은 곳에 서식하는 특성상 저수온과 저조도에서 좋은 생장 경향을 보였다. 실내배양을 통해 얻은 엽장 약 1~2mm의 종묘를 2002년 1월말에 삼척 호산에 위치한 바다 양성장에서 종묘들과 함께 2주간 수심별로 가이식(수온 12$^{\circ}C$)을 실시한 결과, 수심 1m에서 좋게 나타나 엽장이 약 5mm정도 생장하였다. 수심 0m에서는 강한 조도에 의해 엽상체가 사그라드는 기형이 나타났으며, 수심 5m에서는 엽상체의 기형이나 생장의 차이는 없었지만, 색택이 약간 바랜 것을 볼 수 있었다. 종합적으로 볼 때 종묘의 관리나 생장에는 수심 1~2m가 양호할 것으로 생각된다. 바다 가이식을 통해 엽장 5mm의 종묘로 생장시킨 후 바로 본양성장에 씨줄감기를 하여 양성을 실시하였다 양성 1개월 후 엽상체는 약 2~3cm, 최대 4~5cm까지 생장하였다. 이를 통해 강릉연안 토종 다시마인 개다시마에 대한 종묘 생산과 대량 양성의 가능성을 확인하였다.

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The Action of ATP on Phospholipase $A_2$Activation in C6 Cells (C6세포에서 phospholipase $A_2$활성에 대한 ATP의 작용)

  • 심상수;김명준;윤신희;김창종;조양혁
    • YAKHAK HOEJI
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    • v.45 no.4
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    • pp.413-418
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    • 2001
  • To investigate action of ATP on ischemia-induced brain injury, we measured phospholipase $A_2$activity and nitric oxide (NO) production in C6 cells. ATP alone did not have any influence on phospholipase $A_2$activity but increased NO production. Glutamate (1 mM) significantly increased phospholipase $A_2$activity whereas did not increased NO production. ATP significantly inhibited phospholipase $A_2$activation induced by 0.1 $\mu$M A23187, 1 mM glutamate and 1 mM $H_2O$$_2$, but did not inhibited 1 $\mu$M PMA-induced phospholipase $A_2$activation. From the above results, it is suggested that the action of ATP in C6 cells has dual actions, such as the inhibition of agonist-induced phospholipase $A_2$activation and the increase of NO production.

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Effect of Light Intensity, Temperature and $CO_2$ Concentration on Photosynthesis in Hovenia dulcis Thunb. (광도, 온도 및 $CO_2$의 농도가 헛개나무의 광합성에 미치는 영향)

  • Lee, Kang-Soo;Choi, Sun-Young
    • Korean Journal of Medicinal Crop Science
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    • v.10 no.1
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    • pp.1-4
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    • 2002
  • This study was carried out to know the effect of light intensity, temperature and $CO_2$ concentration on photosynthesis and transpiration in Hovenia dulcis Thunb. Light compensation point was $2.4\;{\mu}mol\;m^{-2}\;s^{-1}$ and light saturation point was $1033\;{\mu}mol\;m^{-2}\;s^{-1}$. The optimum temperature for photosynthesis was $25^{\circ}C$ at $1000\;{\mu}mol\;m^{-2}\;s^{-1}$ light intensity. $CO_2$ compensation point was 67 vpm and $CO_2$ saturation point was 707 vpm. Transpiration rate was increased to about $2\;mmol\;m^{-2}\;s^{-1}$ with increasing of light intensity to $1750\;{\mu}mol\;m^{-2}\;s^{-1}$ and to above $4\;mmol\;m^{-2}\;s^{-1}$ with increasing of temperature from $18^{\circ}C$ to $36^{\circ}C$. however It was gradually reduced as $CO_2$ concentration increased from 21 vpm to 800 vpm.

Creep Rupture Due to Molybdenum Rich $M_6C$ Carbide in 1.0Cr-1.0Mo-0.25V Steel Weldment (1.0Cr-1.0Mo-0.25V강 용접부의 $M_6C$ 탄화물에 의한 크립 파단)

  • O, Yeong-Geun;Kim, Byeong-Cheol;Gang, Gye-Myeong;Min, Tae-Guk
    • Korean Journal of Materials Research
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    • v.6 no.12
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    • pp.1257-1262
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    • 1996
  • 1.0Cr-1.0Mo-0.25V강 용접부의 크립 파단 시험시 파단 발생 원인에 관한 연구가 시행되었다. 파괴는 Intercritical Heat Affected Zone에서 발생하였으며 파단면에서 구상의조대한 M6C탄화물이 발견되었다. 모재는 molybdenum 주성분의 M2C, vanadium 주성분의 M4C3 및 chromium 주성분의 M23C6와 M7C3 탄화물이 존재하였다. 모의 실험 결과 준안정 상태인 M2C 탄화물은 85$0^{\circ}C$, 10oh에서 안정한 M6C탄화물로 변태하였다. M6C 탄화물은 주변의 molybdenum 농도를 떨어뜨려 강도의 저하를 가져오며 크립 기공의 발생 원인을 제공하였다.

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Preparation of B4C-Al2O3 Composite Powder by Self-propagation High-temperature Synthesis(SHS) Process under High Pressure (고압 자전 고온반응 합성법에 의한 B4C-Al2O3복합분말 제조)

  • 임경란;강덕일;김창삼
    • Journal of the Korean Ceramic Society
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    • v.40 no.1
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    • pp.18-23
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    • 2003
  • Composite powder of$B_4C-A1_2O_3$was prepared from a mixed powder of$B_2O_3/A1/C$by SHS under argon pressure instead of using a chemical furnace. A mixture of$B_2O_3,$Al and C powder (equivalent amounts to the reaction,$2B_2O_3+4A1+C=B_4C+2A1_2O_3)$was ball milled for 2 h. The mixed powder was placed in a SHS reactor and filled with 10 atm of argon gas and ignited. The inner and outer products were the same by XRD analysis. It was consisted of a composite powder of$B_4C-A1_2O_3$without $AlB_{12}/C_2$which was always produced using a chemical furnace. The composite powder was about$60~100{mu}m$size which was composed of crystalline particles of about 0.3~l${mu}m$size. But when 15 atm of argon was employed, partial sintering took place to give rise hard composite powder of$15~25{mu}m$$B_4C$with $0.1~0.2{mu}m$$A1_2O_3.$

A Study on the Optimum coating thickness of $TiC-A1_2O_3$ coated cemented carbide tool ($TiC-A1_2O_3$ 피복초경공구의 최적피복두께에 관한 연구)

  • 김정두
    • Journal of the Korean Professional Engineers Association
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    • v.21 no.1
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    • pp.5-12
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    • 1988
  • The purpose of this paper is to investigate on the optimum coating thickness layer of TiC-Al$_2$O$_3$ coated cemented carbide tool. Chemical Vapor Deposition (CVD) of a thick film of TiC-A1$_2$O$_3$ on a cemented carbide produces an intermediate layer, $1.5mutextrm{m}$, 4.5${\mu}{\textrm}{m}$, 7.5${\mu}{\textrm}{m}$ 10.5${\mu}{\textrm}{m}$, 4 kind of TiC between the substrate and the $1.5mutextrm{m}$ constant thick A1$_2$O$_3$ coating. Experiments were carried out with the test relationship between coating thickness and shear angle, surface roughness, cutting force, microphotograph of crater wear, flank wear, tool life. From the experimental results, it was found that the optimum coating thickness of TiC-A1$_2$O$_3$ is 6${\mu}{\textrm}{m}$. Although the coating thickness layer 9${\mu}{\textrm}{m}$. 12${\mu}{\textrm}{m}$ have a much loger tool wear than an 3${\mu}{\textrm}{m}$, 6${\mu}{\textrm}{m}$ coating tool in cutting condition feed 0.05mm/rev, and the condition of feed 0.2mm/rev, 0.3mm/rev has upon in the shot time phenomenon of chipping.

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The Magnetic Relaxation Properties of DTPA-bis(4-carboxycyclohexyl) amide Paramagnetic Gd-chelates (DTPA-bis(4-carboxycyclohexyl)amide 상자성 복합체의 자기이완특성에 관한 연구)

  • Kim, In-Sung;Lee, Young-Ju;Lee, Jae-Jun;Kim, Ju-Hyun;Kim, Yoo-Kyung;Sujit, Dutta;Kim, Suk-Kyung;Kim, Tae-Jeong;Kang, Duk-Sik;Chang, Yong-Min
    • Investigative Magnetic Resonance Imaging
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    • v.10 no.1
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    • pp.20-25
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    • 2006
  • Purpose : To evaluate the NMR relaxation properties of newly developed high performance paramagnetic complexes. Materials and methods : 4-aminomethylcyclohexane carboxylic acid (0.63g, 4 mmol) was mixed with the suspension solution of DMF (15mL) and DTPA-bis-anhydride (0.71g, 2 mmol) to synthesize the ligand. The ligand was then mixed with Gd2O3 (0.18g, 0.5 mmol) to synthesize Gd-chelate. For the measurement of magnetic relaxivity of paramagnetic compounds, the compounds were diluted to 1mM and then the relaxation times were measured at 1.5T(64 MHz). Inversion-recovery pulse sequence was employed for T1 relaxation measurement and CPMG(Carr-Purcell-Meiboon-Gill) pulse sequence was employed for T2 relaxation measurement. Using MATLAB(Version 7.1) program, T1 magnetic relaxation map, R1 map, T2 magnetic relaxation map and R2 map were developed to represent magnetic relaxation time and magnetic relaxivity as image. Results : Compared to $R1=4.9mM^{-1}sec^{-1}$ and $R2=4.8mM^{-1}sec^{-1}$ of Omniscan (Gadodiamide), which is commercially available paramagnetic MR agent, R1 of SUK090(Gd-C32H74N5O24) was $12.46mM^{-1}sec^{-1}$ and R1 of SUK091(Gd-C34H78N5O24) was $12.77mM^{-1}sec^{-1}$. However, R1 of SUK092(Gd-C30H56N5O17) was decreased to $2.09mM^{-1}sec^{-1}$. In case of R2, SUK090(Gd-C32H74N5O24) was $8.76mM^{-1}sec^{-1}$ and SUK091(Gd-C34H78N5O24) was $7.60mM^{-}1sec^{-1}$ whereas SUK092(Gd-C30H56N5O17) was decreased to $1.82mM^{-1}sec^{-1}$. Conclusion : Among three new paramagnetic complexes, SUK090(Gd-C32H74N5O24) and SUK091(Gd-C34H78N5O24) showed higher T1, T2 magnetic relaxation rates than that of commercially available paramagnetic MR agent and thus expected to have more contrast enhancement effect.

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NONEXISTENCE OF A CREPANT RESOLUTION OF SOME MODULI SPACES OF SHEAVES ON A K3 SURFACE

  • Choy, Jae-Yoo;Kiem, Young-Hoon
    • Journal of the Korean Mathematical Society
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    • v.44 no.1
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    • pp.35-54
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    • 2007
  • Let $M_c$ = M(2, 0, c) be the moduli space of O(l)-semistable rank 2 torsion-free sheaves with Chern classes $c_1=0\;and\;c_2=c$ on a K3 surface X, where O(1) is a generic ample line bundle on X. When $c=2n\geq4$ is even, $M_c$ is a singular projective variety equipped with a holomorphic symplectic structure on the smooth locus. In particular, $M_c$ has trivial canonical divisor. In [22], O'Grady asks if there is any symplectic desingularization of $M_{2n}$ for $n\geq3$. In this paper, we show that there is no crepant resolution of $M_{2n}$ for $n\geq3$. This obviously implies that there is no symplectic desingularization.

HOMOGENEOUS $C^*$-ALGEBRAS OVER A SPHERE

  • Park, Chun-Gil
    • Journal of the Korean Mathematical Society
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    • v.34 no.4
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    • pp.859-869
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    • 1997
  • It is shown that for $A_{k, m}$ a k-homogeneous $C^*$-algebra over $S^{2n - 1} \times S^1$ such that no non-trivial matrix algebra can be factored out of $A_{k, m}$ and $A_{k, m} \otimes M_l(C)$ has a non-trivial bundle structure for any positive integer l, we construct an $A_{k, m^-} C(S^{2n - 1} \times S^1) \otimes M_k(C)$-equivalence bimodule to show that every k-homogeneous $C^*$-algebra over $S^{2n - 1} \times S^1)$. Moreover, we prove that the tensor product of the k-homogeneous $C^*$-algebra $A_{k, m}$ with a UHF-algebra of type $p^\infty$ has the tribial bundle structure if and only if the set of prime factors of k is a subset of the set of prime factors of pp.

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