scholarly journals A Characterization of Balanced Rational Normal Surface Scrolls in Terms of Their Osculating Spaces II.

1992 ◽  
Vol 70 ◽  
pp. 204 ◽  
Author(s):  
E. Ballico ◽  
R. Piene ◽  
H. -s. Tai
Keyword(s):  
Normal Surface ◽  
Osculating Spaces

scholarly journals The Abel map for surface singularities III: Elliptic germs

2021 ◽  
Author(s):  
János Nagy ◽  
András Némethi
Keyword(s):  
General Theory ◽  
Present Note ◽  
Affine Subspace ◽  
Normal Surface ◽  
Rational Homology ◽  
Surface Singularities ◽  
Abel Map ◽  
Appl Math ◽  
Rational Homology Sphere

AbstractThe present note is part of a series of articles targeting the theory of Abel maps associated with complex normal surface singularities with rational homology sphere links (Nagy and Némethi in Math Annal 375(3):1427–1487, 2019; Nagy and Némethi in Adv Math 371:20, 2020; Nagy and Némethi in Pure Appl Math Q 16(4):1123–1146, 2020). Besides the general theory, by the study of specific families we wish to show the power of this new method. Indeed, using the general theory of Abel maps applied for elliptic singularities in this note we are able to prove several key properties for elliptic singularities (e.g. the statements of the next paragraph), which by ‘old’ techniques were not reachable. If $$({\widetilde{X}},E)\rightarrow (X,o)$$ ( X ~ , E ) → ( X , o ) is the resolution of a complex normal surface singularity and $$c_1:{\mathrm{Pic}}({\widetilde{X}})\rightarrow H^2({\widetilde{X}},{\mathbb {Z}})$$ c 1 : Pic ( X ~ ) → H 2 ( X ~ , Z ) is the Chern class map, then $${\mathrm{Pic}}^{l'}({\widetilde{X}}):= c_1^{-1}(l')$$ Pic l ′ ( X ~ ) : = c 1 - 1 ( l ′ ) has a (Brill–Noether type) stratification $$W_{l', k}:= \{{\mathcal {L}}\in {\mathrm{Pic}}^{l'}({\widetilde{X}})\,:\, h^1({\mathcal {L}})=k\}$$ W l ′ , k : = { L ∈ Pic l ′ ( X ~ ) : h 1 ( L ) = k } . In this note we determine it for elliptic singularities together with the stratification according to the cycle of fixed components. E.g., we show that the closure of any $$W(l',k)$$ W ( l ′ , k ) is an affine subspace. For elliptic singularities we also characterize the End Curve Condition and Weak End Curve Condition in terms of the Abel map, we provide several characterization of them, and finally we show that they are equivalent.

Measurement of normal surface displacements for the characterization of rectangular acoustic array elements

1984 ◽  
Vol 76 (2) ◽  
pp. 516-524 ◽  
Author(s):  
R. L. Jungerman ◽  
P. Bennett ◽  
A. R. Selfridge ◽  
B. T. Khuri‐Yakub ◽  
G. S. Kino
Keyword(s):  
Normal Surface ◽  
Surface Displacements ◽  
Acoustic Array

Tissue printing for scanning electron microscopy and microanalysis

1993 ◽  
Vol 51 ◽  
pp. 140-141
Author(s):  
Barbara A. Reine
Keyword(s):  
Critical Point ◽  
Chemical Constituents ◽  
Plant Cells ◽  
Plant Morphology ◽  
Specimen Preparation ◽  
Normal Surface ◽  
Tissue Printing ◽  
Critical Point Drying ◽  
Scanning Electron

The study of plant morphology and plant cells in the scanning electron microscope is often compromised by the limitations of specimen preparation techniques. Simple natural dehydration usually results in unacceptable shrinkage and distortion of the normal surface morphology of plant cells. Chemical fixation followed by critical point drying or some substitute for critical point drying such as Peldri II or HMDS (hexamethyldisilazane) improves morphological results but still imparts artifacts, adds chemical constituents to the specimen, and requires the use of toxic chemicals, a hood, and much time.One technique that eliminates many of these disadvantages and is even suitable for specimen preparation in the field is tissue printing. For low magnification imaging and chemical analysis its “elegant simplicity” (2) is compelling. Historically, the application of tissue printing has been in connection with optical microscopy (1,2). However, this technique works very well for low magnification SEM and associated elemental characterization of residues by x-ray microanalysis.

Tangent Spaces of a Normal Surface with Hyperelliptic Sections

1984 ◽  
Vol 36 (1) ◽  
pp. 131-143
Author(s):  
W. L. Edge
Keyword(s):  
Normal Curve ◽  
Normal Surface ◽  
Osculating Spaces ◽  
Del Pezzo ◽  
Image Position ◽  
Rational Normal Curve

A rational normal curve C of order n in [n] has, at each point P, a nest of osculating spacesas P moves on C the [n — 2] generates a primal Dn-1 of order 2n — 2.Hilbert [3] found the multiplicities on Dn-1 not only of the vμ+1 generated by Dμ for each lesser value of μ but also those of all submanifolds common to these various Dμ.A surface Φ in higher space has, as explained [4] by del Pezzo, a nest of tangent spacesof respective dimensionsthey raise the problem of finding the orders of manifolds generated by them and the multiplicity of each on the higher manifolds to which it belongs: the task does not seem to have been attempted, but it may well be eased if Φ is rational and normal.

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.

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

1973 ◽  
Vol 31 ◽  
pp. 132-133 ◽  
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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