Boundary characterization of holomorphic isometric embeddings between indefinite hyperbolic spaces

In this paper, we continue our investigations giving the characterization of weights for two-weight Hardy inequalities to hold on general metric measure spaces possessing polar decompositions. Since there may be no differentiable structure on such spaces, the inequalities are given in the integral form in the spirit of Hardy’s original inequality. This is a continuation of our paper (Ruzhansky & Verma 2018. Proc. R. Soc. A 475 , 20180310 ( doi:10.1098/rspa.2018.0310 )) where we treated the case p ≤ q . Here the remaining range p > q is considered, namely, 0 < q < p , 1 < p < ∞. We give several examples of the obtained results, finding conditions on the weights for integral Hardy inequalities on homogeneous groups, as well as on hyperbolic spaces and on more general Cartan–Hadamard manifolds. As in the first part of this paper, we do not need to impose doubling conditions on the metric.

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Morphological Characterization of Mycobacteriophage R1

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100051281 ◽

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.

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AEM analysis of crystallization in Ti-based amorphous alloys

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100075142 ◽

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.

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Characterization of Coherent, Ordered Precipitates in Nickel-Base Alloys

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100071168 ◽

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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The Use of Advanced Analytical Techniques for Characterization of the Chemical, Physical, and Crystallographic Nature of a Surface

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100071107 ◽

1973 ◽

Vol 31 ◽

pp. 132-133 ◽

Cited By ~ 1

Author(s):

R. E. Herfert

Keyword(s):

Surface Characterization ◽

Analytical Techniques ◽

X Ray Diffraction ◽

Depth Of Penetration ◽

X Ray ◽

The Past ◽

Transmission Electron ◽

Scanning Electron

Studies of the nature of a surface, either metallic or nonmetallic, in the past, have been limited to the instrumentation available for these measurements. In the past, optical microscopy, replica transmission electron microscopy, electron or X-ray diffraction and optical or X-ray spectroscopy have provided the means of surface characterization. Actually, some of these techniques are not purely surface; the depth of penetration may be a few thousands of an inch. Within the last five years, instrumentation has been made available which now makes it practical for use to study the outer few 100A of layers and characterize it completely from a chemical, physical, and crystallographic standpoint. The scanning electron microscope (SEM) provides a means of viewing the surface of a material in situ to magnifications as high as 250,000X.

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