• Title, Summary, Keyword: o-minimal

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SPACELIKE MAXIMAL SURFACES, TIMELIKE MINIMAL SURFACES, AND BJÖRLING REPRESENTATION FORMULAE

  • Kim, Young-Wook;Koh, Sung-Eun;Shin, Hea-Yong;Yang, Seong-Deog
    • Journal of the Korean Mathematical Society
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    • v.48 no.5
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    • pp.1083-1100
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    • 2011
  • We show that some class of spacelike maximal surfaces and timelike minimal surfaces match smoothly across the singular curve of the surfaces. Singular Bj$\"{o}$rling representation formulae for generalized spacelike maximal surfaces and for generalized timelike minimal surfaces play important roles in the explanation of this phenomenon.

ON G-INVARIANT MINIMAL HYPERSURFACES WITH CONSTANT SCALAR CURVATURE IN S5

  • So, Jae-Up
    • Communications of the Korean Mathematical Society
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    • v.17 no.2
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    • pp.261-278
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    • 2002
  • Let G = O(2) $\times$ O(2) $\times$O(2) and let M$^4$be closed G-invariant minimal hypersurface with constant scalar curvature in S$^{5}$ . If M$^4$has 2 distinct principal curvatures at some point, then S = 4. Moreover, if S > 4, then M$^4$does not have simple principal curvatures everywhere.

A THEOREM OF G-INVARIANT MINIMAL HYPERSURFACES WITH CONSTANT SCALAR CURVATURES IN Sn+1

  • So, Jae-Up
    • Honam Mathematical Journal
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    • v.31 no.3
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    • pp.381-398
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    • 2009
  • Let $G\;=\;O(k){\times}O(k){\times}O(q)$ and let $M^n$ be a closed G-invariant minimal hypersurface with constant scalar curvature in $S^{n+1}$. Then we obtain a theorem: If $M^n$ has 2 distinct principal curvatures at some point p, then the square norm of the second fundamental form of $M^n$, S = n.

HEWITT REALCOMPACTIFICATIONS OF MINIMAL QUASI-F COVERS

  • Kim, Chang Il;Jung, Kap Hun
    • Korean Journal of Mathematics
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    • v.10 no.1
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    • pp.45-51
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    • 2002
  • Observing that a realcompactification Y of a space X is Wallman if and only if for any non-empty zero-set Z in Y, $Z{\cap}Y{\neq}{\emptyset}$, we will show that for any pseudo-Lindel$\ddot{o}$f space X, the minimal quasi-F $QF({\upsilon}X)$ of ${\upsilon}X$ is Wallman and that if X is weakly Lindel$\ddot{o}$, then $QF({\upsilon}X)={\upsilon}QF(X)$.

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Fast Training of Structured SVM Using Fixed-Threshold Sequential Minimal Optimization

  • Lee, Chang-Ki;Jang, Myung-Gil
    • ETRI Journal
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    • v.31 no.2
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    • pp.121-128
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    • 2009
  • In this paper, we describe a fixed-threshold sequential minimal optimization (FSMO) for structured SVM problems. FSMO is conceptually simple, easy to implement, and faster than the standard support vector machine (SVM) training algorithms for structured SVM problems. Because FSMO uses the fact that the formulation of structured SVM has no bias (that is, the threshold b is fixed at zero), FSMO breaks down the quadratic programming (QP) problems of structured SVM into a series of smallest QP problems, each involving only one variable. By involving only one variable, FSMO is advantageous in that each QP sub-problem does not need subset selection. For the various test sets, FSMO is as accurate as an existing structured SVM implementation (SVM-Struct) but is much faster on large data sets. The training time of FSMO empirically scales between O(n) and O($n^{1.2}$), while SVM-Struct scales between O($n^{1.5}$) and O($n^{1.8}$).

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