• Title/Summary/Keyword: K

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WEYL'S THEOREM AND TENSOR PRODUCT FOR OPERATORS SATISFYING T*k|T2|Tk≥T*k|T|2Tk

  • Kim, In-Hyoun
    • Journal of the Korean Mathematical Society
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    • v.47 no.2
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    • pp.351-361
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    • 2010
  • For a bounded linear operator T on a separable complex infinite dimensional Hilbert space $\mathcal{H}$, we say that T is a quasi-class (A, k) operator if $T^{*k}|T^2|T^k\;{\geq}\;T^{*k}|T|^2T^k$. In this paper we prove that if T is a quasi-class (A, k) operator and f is an analytic function on an open neighborhood of the spectrum of T, then f(T) satisfies Weyl's theorem. Also, we consider the tensor product for quasi-class (A, k) operators.

LOCALLY CONFORMAL KÄHLER MANIFOLDS AND CONFORMAL SCALAR CURVATURE

  • Kim, Jae-Man
    • Communications of the Korean Mathematical Society
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    • v.25 no.2
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    • pp.245-249
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    • 2010
  • We show that on a compact locally conformal K$\ddot{a}$hler manifold $M^{2n}$ (dim $M^{2n}\;=\;2n\;{\geq}\;4$), $M^{2n}$ is K$\ddot{a}$hler if and only if its conformal scalar curvature k is not smaller than the scalar curvature s of $M^{2n}$ everywhere. As a consequence, if a compact locally conformal K$\ddot{a}$hler manifold $M^{2n}$ is both conformally flat and scalar flat, then $M^{2n}$ is K$\ddot{a}$hler. In contrast with the compact case, we show that there exists a locally conformal K$\ddot{a}$hler manifold with k equal to s, which is not K$\ddot{a}$hler.

An Improvement of Distance Relay Technique Reliability using Elman Network (Elman Network를 이용한 거리계전기법의 신뢰성 향상)

  • Jung, H.S.;Lee, J.J.;Shin, M.C.;Lee, B.K.;Park, C.W.;Jang, S.I.
    • Proceedings of the KIEE Conference
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    • 2000.07a
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    • pp.212-214
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    • 2000
  • The distance relay technique used for transmission line protection operates overreach and underreach to the self protection region because the power system becomes complex and fault conditions are different. To solve these problems, this paper describes new technique to set the reliable self protection lesion. The trip region of the quadrilateral distance relay is set by training of multi layer recurrent elman network. The proposed network is able to reach the trip zone for the fault impedance, fault initial angle and source impedance variance correctly.

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TATE-SHAFAREVICH GROUPS AND SCHANUEL'S LEMMA

  • Yu, Hoseog
    • Honam Mathematical Journal
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    • v.39 no.2
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    • pp.137-141
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    • 2017
  • Let A be an abelian variety defined over a number field K and let L be a finite Galois extension of K. Let III(A/K) and III(A/L) denote, respectively, the Tate-Shafarevich groups of A over K and over L. Let $Res_{L/K}(A)$ be the restriction of scalars of A from L to K and let B be an abelian subvariety of $Res_{L/K}(A)$ defined over K. Assuming that III(A/L) is finite, we compute [III(B/K)][III(C/K)]/[III(A/L)], where [X] is the order of a finite abelian group X and the abelian variety C is defined by the exact sequence defined over K $0{\longrightarrow}B{\longrightarrow}Res_{L/K}(A){\longrightarrow}C{\longrightarrow}0$.

Eukaryotic DNAJ/K Database: A Comprehensive Phylogenomic Analysis Platform for the DNAJ/K Family

  • Cheong, Kyeongchae;Choi, Jaehyuk;Choi, Jaeyoung;Park, Jongsun;Jang, Suwang;Lee, Yong-Hwan
    • Genomics & Informatics
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    • v.11 no.1
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    • pp.52-54
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    • 2013
  • Proteins in DNAJ/K families are ubiquitous, from prokaryotes to eukaryotes, and function as molecular chaperones. For systematic phylogenomics of the DNAJ/K families, we developed the Eukaryotic DNAJ/K Database (EDD). A total of 12,908 DNAJs and 4,886 DNAKs were identified from 339 eukaryotic genomes in the EDD. Kingdom-wide comparison of DNAJ/K families provides new insights on the evolutionary relationship within these families. Empowered by 'class', 'cluster', and 'taxonomy' browsers and the 'favorite' function, the EDD provides a versatile platform for comparative genomic analyses of DNAJ/K families.