Chow forms of congruences

1997 ◽  
Vol 121 (1) ◽  
pp. 31-37
Author(s):  
LUIS GIRALDO ◽  
IGNACIO SOLS
Keyword(s):  
Differential Equations ◽  
Complex Space ◽  
Grassmann Variety ◽  
First Results ◽  
Chow Forms ◽  
Integral Surface

Let V be a 4-dimensional complex space. A congruence Y is an integral surface of the Grassmann variety G = Gr(2, 4) of 2-dimensional subspaces V2 of V (we denote by Vi a subspace of V of dimension i). They have been extensively studied by both classical and modern geometers. We bring to their study the tool of Chow forms, characterizing them by differential equations, following the program of M. Green and I. Morrison [3]. The first results in this direction are due to Cayley ([1], [2]) and are rederived in [3]. Our results share much of the geometrical flavour of Cayley's.

scholarly journals Analysis of Obata’s Differential Equations on Pointwise Semislant Warped Product Submanifolds of Complex Space Forms via Ricci Curvature

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Amira A. Ishan
Keyword(s):  
Differential Equations ◽  
Ricci Curvature ◽  
Warped Product ◽  
Complex Space ◽  
Space Forms ◽  
Geometric Conditions ◽  
Isometric To A Sphere ◽  
Complex Space Forms

The present paper studies the applications of Obata’s differential equations on the Ricci curvature of the pointwise semislant warped product submanifolds. More precisely, by analyzing Obata’s differential equations on pointwise semislant warped product submanifolds, we demonstrate that, under certain conditions, the base of these submanifolds is isometric to a sphere. We also look at the effects of certain differential equations on pointwise semislant warped product submanifolds and show that the base is isometric to a special type of warped product under some geometric conditions.

scholarly journals Characterization of Skew CR-Warped Product Submanifolds in Complex Space Forms via Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Ibrahim Al-Dayel ◽  
Meraj Ali Khan
Keyword(s):  
Euclidean Space ◽  
Differential Equations ◽  
Warped Product ◽  
Complex Space ◽  
Space Form ◽  
Space Forms ◽  
Geometric Conditions ◽  
Complex Space Forms ◽  
The Impact

Recently, we have obtained Ricci curvature inequalities for skew CR-warped product submanifolds in the framework of complex space form. By the application of Bochner’s formula on these inequalities, we show that, under certain conditions, the base of these submanifolds is isometric to the Euclidean space. Furthermore, we study the impact of some differential equations on skew CR-warped product submanifolds and prove that, under some geometric conditions, the base is isometric to a special type of warped product.

Discussion of the Oblique Rotator Model Cases Of 108 Aqr and x Serp.

1976 ◽  
Vol 32 ◽  
pp. 577-588
Author(s):  
C. Mégessier ◽  
V. Khokhlova ◽  
T. Ryabchikova
Keyword(s):  
Mathematical Formulation ◽  
The Other ◽  
Rotator Model ◽  
Oblique Rotator ◽  
First Results

My talk will be on the oblique rotator model which was first proposed by Stibbs (1950), and since received success and further developments. I shall present two different attempts at describing a star according to this model and the first results obtained in the framework of a Russian-French collaboration in order to test the precision of the two methods. The aim is to give the best possible representation of the element distributions on the Ap stellar surfaces. The first method is the mathematical formulation proposed by Deutsch (1958-1970) and applied by Deutsch (1958) to HD 125248, by Pyper (1969) to α2CVn and by Mégessier (1975) to 108 Aqr. The other one was proposed by Khokhlova (1974) and used by her group.

Meridional Circulation, Turbulence, and Diffusion Processes in Stars

1976 ◽  
Vol 32 ◽  
pp. 109-116 ◽  
Author(s):  
S. Vauclair
Keyword(s):  
Convection Zone ◽  
Diffusion Processes ◽  
Meridional Circulation ◽  
Diffusion Time ◽  
Work In Progress ◽  
First Results ◽  
Stellar Envelopes ◽  
And Diffusion ◽  
Turbulence And Diffusion ◽  
Hr Diagram

This paper gives the first results of a work in progress, in collaboration with G. Michaud and G. Vauclair. It is a first attempt to compute the effects of meridional circulation and turbulence on diffusion processes in stellar envelopes. Computations have been made for a 2 Mʘstar, which lies in the Am - δ Scuti region of the HR diagram.Let us recall that in Am stars diffusion cannot occur between the two outer convection zones, contrary to what was assumed by Watson (1970, 1971) and Smith (1971), since they are linked by overshooting (Latour, 1972; Toomre et al., 1975). But diffusion may occur at the bottom of the second convection zone. According to Vauclair et al. (1974), the second convection zone, due to He II ionization, disappears after a time equal to the helium diffusion time, and then diffusion may happen at the bottom of the first convection zone, so that the arguments by Watson and Smith are preserved.

Investigation of cluster layers of small netal particles by TEM, SEM, EELS and by photoacoustic spectroscopy

1990 ◽  
Vol 48 (4) ◽  
pp. 250-251
Author(s):  
H. Seiler ◽  
U. Haas ◽  
K.H. Körtje
Keyword(s):  
Bulk Material ◽  
High Vacuum ◽  
Optical Methods ◽  
Metal Particles ◽  
Silver Particles ◽  
Low Loss ◽  
Plasmon Excitation ◽  
First Results ◽  
Diffraction Patterns ◽  
Small Metal Particles

The physical properties of small metal particles reveal an intermediate position between atomic and bulk material. Especially Ag has shown pronounced size effects. We compared silver layers evaporated in high vacuum with cluster layers of small silver particles, evaporated in N2 at a pressure of about 102 Pa. The investigations were performed by electron optical methods (TEM, SEM, EELS) and by Photoacoustic (PA) Spectroscopy (gas-microphone detection).The observation of cluster layers with TEM and high resolution SEM show small silver particles with diameters of about 50 nm (Fig. 1 and Figure 2, respectively). The electron diffraction patterns of homogeneous Ag layers and of cluster layers are similar, whereas the low loss EELS spectra due to plasmon excitation are quite different. Fig. 3 and Figure 4 show first results of EELS spectra of a cluster layer of small silver particles on carbon foil and of a homogeneous Ag layer, respectively.

Towards 1-Ångstrom-resolution STEM

1993 ◽  
Vol 51 ◽  
pp. 996-997
Author(s):  
H.S. von Harrach ◽  
D.E. Jesson ◽  
S.J. Pennycook
Keyword(s):  
High Resolution ◽  
Field Emission ◽  
Phase Contrast ◽  
Spherical Aberration ◽  
A Priori ◽  
Dark Field ◽  
Image Resolution ◽  
Objective Lens ◽  
Annular Dark Field ◽  
First Results

Phase contrast TEM has been the leading technique for high resolution imaging of materials for many years, whilst STEM has been the principal method for high-resolution microanalysis. However, it was demonstrated many years ago that low angle dark-field STEM imaging is a priori capable of almost 50% higher point resolution than coherent bright-field imaging (i.e. phase contrast TEM or STEM). This advantage was not exploited until Pennycook developed the high-angle annular dark-field (ADF) technique which can provide an incoherent image showing both high image resolution and atomic number contrast.This paper describes the design and first results of a 300kV field-emission STEM (VG Microscopes HB603U) which has improved ADF STEM image resolution towards the 1 angstrom target. The instrument uses a cold field-emission gun, generating a 300 kV beam of up to 1 μA from an 11-stage accelerator. The beam is focussed on to the specimen by two condensers and a condenser-objective lens with a spherical aberration coefficient of 1.0 mm.

Imaging of polymer single crystals in low-voltage, high-resolution scanning electron microscopy

1990 ◽  
Vol 48 (4) ◽  
pp. 1106-1107
Author(s):  
W.W. Adams ◽  
G. Price ◽  
A. Krause
Keyword(s):  
Electron Microscopy ◽  
Scanning Electron Microscopy ◽  
High Resolution ◽  
Single Crystals ◽  
Low Voltage ◽  
Polymer Surface ◽  
Beam Current ◽  
Image Features ◽  
First Results ◽  
Scanning Electron

It has been shown that there are numerous advantages in imaging both coated and uncoated polymers in scanning electron microscopy (SEM) at low voltages (LV) from 0.5 to 2.0 keV compared to imaging at conventional voltages of 10 to 20 keV. The disadvantages of LVSEM of degraded resolution and decreased beam current have been overcome with the new generation of field emission gun SEMs. In imaging metal coated polymers in LVSEM beam damage is reduced, contrast is improved, and charging from irregularly shaped features (which may be unevenly coated) is reduced or eliminated. Imaging uncoated polymers in LVSEM allows direct observation of the surface with little or no charging and with no alterations of surface features from the metal coating process required for higher voltage imaging. This is particularly important for high resolution (HR) studies of polymers where it is desired to image features 1 to 10 nm in size. Metal sputter coating techniques produce a 10 - 20 nm film that has its own texture which can obscure topographical features of the original polymer surface. In examining thin, uncoated insulating samples on a conducting substrate at low voltages the effect of sample-beam interactions on image formation and resolution will differ significantly from the effect at higher accelerating voltages. We discuss here sample-beam interactions in single crystals on conducting substrates at low voltages and also present the first results on HRSEM of single crystal morphologies which show some of these effects.

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