• 제목/요약/키워드: nondegenerate

검색결과 54건 처리시간 0.024초

FINITENESS OF INFINITESIMAL DEFORMATIONS OF CR MAPPINGS OF CR MANIFOLDS OF NONDEGENERATE LEVI FORM

  • Cho, Chung-Ki;Han, Chong-Kyu
    • 대한수학회지
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    • 제39권1호
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    • pp.91-102
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    • 2002
  • Let M and N be CR manifolds with nondegenerate Levi forms of hypersurface type of dimension 2m + 1 and 2n + 1, respectively, where 1 $\leq$ m $\leq$ n. Let f : M longrightarrow N be a CR mapping. Under a generic assumption we construct a complete system of finite order for the infinitesimal deformations of f. In particular, we prove the space of infinitesimal deformations of f forms a finite dimensional Lie algebra.

NONDEGENERATE AFFINE HOMOGENEOUS DOMAIN OVER A GRAPH

  • Choi, Yun-Cherl
    • 대한수학회지
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    • 제43권6호
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    • pp.1301-1324
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    • 2006
  • The affine homogeneous hypersurface in ${\mathbb{R}}^{n+1}$, which is a graph of a function $F:{\mathbb{R}}^n{\rightarrow}{\mathbb{R}}$ with |det DdF|=1, corresponds to a complete unimodular left symmetric algebra with a nondegenerate Hessian type inner product. We will investigate the condition for the domain over the homogeneous hypersurface to be homogeneous through an extension of the complete unimodular left symmetric algebra, which is called the graph extension.

ON POSITIVE SEMIDEFINITE PRESERVING STEIN TRANSFORMATION

  • Song, Yoon J.
    • Journal of applied mathematics & informatics
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    • 제33권1_2호
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    • pp.229-234
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    • 2015
  • In the setting of semidefinite linear complementarity problems on $S^n$, we focus on the Stein Transformation $S_A(X):=X-AXA^T$ for $A{\in}R^{n{\times}n}$ that is positive semidefinite preserving (i.e., $S_A(S^n_+){\subseteq}S^n_+$) and show that such transformation is strictly monotone if and only if it is nondegenerate. We also show that a positive semidefinite preserving $S_A$ has the Ultra-GUS property if and only if $1{\not\in}{\sigma}(A){\sigma}(A)$.

Enhancement in quantum noise correlation between the two outputs of a nondegenerate optical amplifier with a non-vacuum state idler input

  • Kim, Chong-Hoon
    • Journal of the Optical Society of Korea
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    • 제1권1호
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    • pp.1-4
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    • 1997
  • The theoretical limit of the noise correlation between the signal and idler outputs of a nondegenerate optical parametric amplifier (NOPA) with a coherent state signal and vacuum state idler input can be enhanced if a non-vacuum coherent state idler input is employed. By choosing a balanced signal and idler input, the noise correlation is $1/{({\root}g + {\root}{g-1})}^2$, where g is the intensity gain of the NOPA, and that is superior to the prediced outputs with single signal input by approximately 3dB. The result is applicable to all the schemes that use the NOPA to produce a sub-shot noise light generation such as feed-back or feed-forward control.

반도체 광증폭기내의 Highly Nondegenerate Four-Wave Mixing에 의한 파장변환의 해석 (Analysis of wavelength conversion by highly nondegenerate four-wave mixing in a semiconductor optical amplifier)

  • 우상규;이연호
    • 한국광학회지
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    • 제10권4호
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    • pp.294-300
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    • 1999
  • 본 논문에서는 반도체 광증폭기내에서 four-wave mixing을 발생시키는 spectral hole burning을 더욱 정확하게 해석하기 위하여 밀도행렬을 기존의 방법에 비하여 정확하게 푸는 방법에 대하여 설명하고 이러한 밀도행렬에 대한 수치해석을 실시하여 그 해를 구한다. 이렇게 구한 결과를 통해 반도체 광증폭기내에서의 four-wave mixing에 의한 파장변환을 설명하는 결합 파동 방정식을 유도하고 이것의 해를 구하여 반도체 광증촉기에서의 파장변환이 어떻게 발생하는 지를 설명하고 3차 섭동을 이용하여 계산된 기존의 결과와 비교한다.

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Single Crystalline CoFe/MgO Tunnel Contact on Nondegenerate Ge with a Proper Resistance-Area Product for Efficient Spin Injection and Detection

  • Jeon, Kun-Rok;Min, Byoung-Chul;Lee, Hun-Sung;Shin, Il-Jae;Park, Chang-Yup;Shin, Sung-Chul
    • 한국자기학회:학술대회 개요집
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    • 한국자기학회 2010년도 임시총회 및 하계학술연구발표회
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    • pp.96-96
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    • 2010
  • We report the proper resistance-area products in the single crystalline bcc CoFe/MgO tunnel contact on nondegenerate n-Ge desirable for efficient spin injection and detection at room temperature. The electric properties of the crystalline CoFe(5 nm)/MgO(1.5,2.0,2.5 nm)/n-Ge(001) tunnel contacts have been investigated by I-V-T and C-V measurements. Interestingly, the tunnel contact with the 2-nm MgO exhibits the ohmic behavior with low resistance-area products, satisfying the theoretical conditions required for significant spin injection and detection. This result is ascribed to the presence of MgO layer between CoFe and n-Ge, enhancing the Schottky pinning parameter as well as shifting the charge neutrality level.

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SOME RESULTS RELATED TO DENSELY HOMOGENEOUS SPACES

  • Cho, Sung-Ki
    • 대한수학회논문집
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    • 제11권4호
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    • pp.1061-1066
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    • 1996
  • We will give an example which is a normal Hausdorff countable dense homogeneous space but not a densely homogeneous space. Next, we will give a proof for the fact that every nondegenerate component of densely homogenous spaces is open and densely homogeneous.

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EQUIVALENCE PROBLEM AND COMPLETE SYSTEM OF FINITE ORDER

  • Han, Chong-Kyu
    • 대한수학회지
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    • 제37권2호
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    • pp.225-243
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    • 2000
  • We explain the notion of complete system and how it naturally arises from the equivalence problem of G-structures. Then we construct a complete system of 3rd order for the infinitesimal CR automorphisms of CR manifold of nondegenerate Levi form.

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