scholarly journals Characterization of the rational homogeneous space associated to a long simple root by its variety of minimal rational tangents

2019 ◽  
Author(s):  
Jaehyun Hong ◽  
Jun-Muk Hwang
Keyword(s):  
Homogeneous Space ◽  
Simple Root ◽  
Rational Homogeneous Space

Two-Weight Norm Inequality and Carleson Measure in Weighted Hardy Spaces

1992 ◽  
Vol 44 (6) ◽  
pp. 1206-1219 ◽  
Author(s):  
Dangsheng Gu
Keyword(s):  
Homogeneous Space ◽  
Hardy Spaces ◽  
Maximal Operator ◽  
Carleson Measure ◽  
Norm Inequality ◽  
Doubling Measure ◽  
Weight Norm Inequality ◽  
Weighted Hardy Spaces

AbstractLet (X, ν, d) be a homogeneous space and let Ω be a doubling measure on X. We study the characterization of measures μ on X+ = X x R+ such that the inequality , where q < p, holds for the maximal operator Hvf studied by Hörmander. The solution utilizes the concept of the “balayée” of the measure μ.

scholarly journals Grouptheoretical Characterization of Projective Space and Conformal Space

1953 ◽  
Vol 5 ◽  
pp. 59-74
Author(s):  
Minoru Kurita
Keyword(s):  
Projective Space ◽  
Homogeneous Space ◽  
Homogeneous Spaces ◽  
Rotation Group ◽  
Conformal Space ◽  
Inversive Geometry ◽  
Full Rotation

In this paper we characterize a projective space and a conformal space, namely a space of inversive geometry of point and sphere, from the standpoint of a homogeneous space. In such spaces a covariant differential of a vectorfield is not a vector, contrary to the case stated in my previous paper “On the vector in homogeneous spaces.” (This journal vol. 5. This paper will be referred to as [1] below.) But when we restrict a rotation about a point to a certain subgroup of the full rotation group, we get a covariant differential which is also a vector, and this situation holds good in a general homogeneous space.

scholarly journals A new characterization of the Bruhat decomposition

1982 ◽  
Vol 86 ◽  
pp. 131-153 ◽  
Author(s):  
Yoshifumi Kato
Keyword(s):  
Homogeneous Space ◽  
Parabolic Subgroup ◽  
Lie Group ◽  
Dimensional Subspace ◽  
Factor Space ◽  
Bruhat Decomposition ◽  
Maximal Parabolic Subgroup ◽  
Grassmann Variety ◽  
Simply Connected

By an algebraic homogeneous space, we mean the factor space X = G/P, where G is a simply-connected, complex, semi-simple Lie group and P is a parabolic subgroup of G. Many typical manifolds such as the projective spaces and the Grassmann varieties belong to this class of manifolds. For instance, the Grassmann variety G(k, n) can be expressed as SL(n + 1, C)/P, where P is a maximal parabolic subgroup of SL(n + 1, C) leaving a suitable k + 1 dimensional subspace invariant. In this paper, we devote ourselves to study the Bruhat decomposition of an algebraic homogeneous space X = G/P.

scholarly journals Geometric characterization of continuously defective elastic crystals

2021 ◽  
pp. 108128652110587
Author(s):  
Marek Z. Elżanowski
Keyword(s):  
Homogeneous Space ◽  
Kinematic Model ◽  
Geometric Characterization ◽  
Geometric Structures ◽  
Elastic Crystals

We show how some differential geometric structures associated with a concept of a homogeneous space appear naturally in a kinematic model of continuously distributed defects in an elastic crystal solid and discuss how one can use them to describe the defectiveness of such a continuum.

scholarly journals Pseudo-differential operators on homogeneous spaces of compact and Hausdorff groups

2019 ◽  
Vol 31 (2) ◽  
pp. 275-282 ◽  
Author(s):  
Vishvesh Kumar
Keyword(s):  
Homogeneous Space ◽  
Closed Subgroup ◽  
Differential Operators ◽  
Homogeneous Spaces ◽  
Trace Class ◽  
Necessary And Sufficient Condition ◽  
Pseudo Differential Operators ◽  
Hausdorff Group ◽  
Necessary And Sufficient

AbstractLet G be a compact Hausdorff group and let H be a closed subgroup of G. We introduce pseudo-differential operators with symbols on the homogeneous space {G/H}. We present a necessary and sufficient condition on symbols for which these operators are in the class of Hilbert–Schmidt operators. We also give a characterization of and a trace formula for the trace class pseudo-differential operators on the homogeneous space {G/H}.

scholarly journals Fano manifolds containing a negative divisor isomorphic to a rational homogeneous space of Picard number one

2020 ◽  
Vol 31 (09) ◽  
pp. 2050066
Author(s):  
Jie Liu
Keyword(s):  
Homogeneous Space ◽  
Complete Classification ◽  
Picard Number ◽  
Fano Manifold ◽  
Fano Manifolds ◽  
Conormal Bundle ◽  
Rational Homogeneous Space

Let [Formula: see text] be an [Formula: see text]-dimensional complex Fano manifold [Formula: see text]. Assume that [Formula: see text] contains a divisor [Formula: see text], which is isomorphic to a rational homogeneous space with Picard number one, such that the conormal bundle [Formula: see text] is ample over [Formula: see text]. Building on the works of Tsukioka, Watanabe and Casagrande–Druel, we give a complete classification of such pairs [Formula: see text].

Morphological Characterization of Mycobacteriophage R1

1974 ◽  
Vol 32 ◽  
pp. 254-255
Author(s):  
B. L. Soloff ◽  
T. A. Rado
Keyword(s):  
Carbon Source ◽  
Stationary Phase ◽  
Growth Phase ◽  
Minimal Medium ◽  
Morphological Characterization ◽  
Logarithmic Growth Phase ◽  
Complete Lysis ◽  
Lysogenic Culture ◽  
Logarithmic Growth

Mycobacteriophage R1 was originally isolated from a lysogenic culture of M. butyricum. The virus was propagated on a leucine-requiring derivative of M. smegmatis, 607 leu−, isolated by nitrosoguanidine mutagenesis of typestrain ATCC 607. Growth was accomplished in a minimal medium containing glycerol and glucose as carbon source and enriched by the addition of 80 μg/ ml L-leucine. Bacteria in early logarithmic growth phase were infected with virus at a multiplicity of 5, and incubated with aeration for 8 hours. The partially lysed suspension was diluted 1:10 in growth medium and incubated for a further 8 hours. This permitted stationary phase cells to re-enter logarithmic growth and resulted in complete lysis of the culture.

AEM analysis of crystallization in Ti-based amorphous alloys

1983 ◽  
Vol 41 ◽  
pp. 270-271
Author(s):  
A.R. Pelton ◽  
A.F. Marshall ◽  
Y.S. Lee
Keyword(s):  
Magnetic Properties ◽  
Amorphous Alloys ◽  
Amorphous Materials ◽  
Isothermal Annealing ◽  
Amorphous Matrix ◽  
Nucleation And Growth ◽  
Current Interest ◽  
Amorphous Films ◽  
Electrical And Magnetic Properties

Amorphous materials are of current interest due to their desirable mechanical, electrical and magnetic properties. Furthermore, crystallizing amorphous alloys provides an avenue for discerning sequential and competitive phases thus allowing access to otherwise inaccessible crystalline structures. Previous studies have shown the benefits of using AEM to determine crystal structures and compositions of partially crystallized alloys. The present paper will discuss the AEM characterization of crystallized Cu-Ti and Ni-Ti amorphous films.Cu60Ti40: The amorphous alloy Cu60Ti40, when continuously heated, forms a simple intermediate, macrocrystalline phase which then transforms to the ordered, equilibrium Cu3Ti2 phase. However, contrary to what one would expect from kinetic considerations, isothermal annealing below the isochronal crystallization temperature results in direct nucleation and growth of Cu3Ti2 from the amorphous matrix.

Characterization of Coherent, Ordered Precipitates in Nickel-Base Alloys

1973 ◽  
Vol 31 ◽  
pp. 144-145
Author(s):  
B. H. Kear ◽  
J. M. Oblak
Keyword(s):  
Stable Phase ◽  
Nickel Base Superalloy ◽  
Alloy 718 ◽  
Commercial Alloy ◽  
Precipitate Morphology ◽  
Continuous Precipitation ◽  
Nickel Base ◽  
Base Superalloy ◽  
Strengthening Precipitate

A nickel-base superalloy is essentially a Ni/Cr solid solution hardened by additions of Al (Ti, Nb, etc.) to precipitate a coherent, ordered phase. In most commercial alloy systems, e.g. B-1900, IN-100 and Mar-M200, the stable precipitate is Ni3 (Al,Ti) γ′, with an LI2structure. In A lloy 901 the normal precipitate is metastable Nis Ti3 γ′ ; the stable phase is a hexagonal Do2 4 structure. In Alloy 718 the strengthening precipitate is metastable γ″, which has a body-centered tetragonal D022 structure.Precipitate MorphologyIn most systems the ordered γ′ phase forms by a continuous precipitation re-action, which gives rise to a uniform intragranular dispersion of precipitate particles. For zero γ/γ′ misfit, the γ′ precipitates assume a spheroidal.

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