Note on Projective Differential Line Geometry

1989 ◽  
pp. 191-193
Author(s):  
Shing-Shen Chern
Keyword(s):  
Line Geometry ◽  
Differential Line

Note on Projective Differential Line Geometry

1989 ◽  
pp. 191-193
Author(s):  
Shiing-shen Chern
Keyword(s):  
Line Geometry ◽  
Differential Line

Differential Line Geometry

1955 ◽  
Vol 39 (328) ◽  
pp. 160
Author(s):  
T. J. Willmore ◽  
V. Hlavaty ◽  
H. Levy
Keyword(s):  
Line Geometry ◽  
Differential Line

scholarly journals Book Review: Differential line geometry

1955 ◽  
Vol 61 (4) ◽  
pp. 348-352
Author(s):  
Alice T. Schafer
Keyword(s):  
Line Geometry ◽  
Differential Line

AN INTERPRETATION OF LINE GEOMETRY ON PROJECTIVE PLANE

1994 ◽  
Vol 27 (1) ◽  
Author(s):  
Edwin Kozniewski
Keyword(s):  
Projective Plane ◽  
Line Geometry

scholarly journals Spectrum radial velocity analyser (SERVAL)

2017 ◽  
Vol 609 ◽  
pp. A12 ◽  
Author(s):  
M. Zechmeister ◽  
A. Reiners ◽  
P. J. Amado ◽  
M. Azzaro ◽  
F. F. Bauer ◽  
...  
Keyword(s):  
Radial Velocity ◽  
Line Width ◽  
Active Regions ◽  
High Signal ◽  
Chromatic Index ◽  
Visual Channel ◽  
Low Mass Stars ◽  
Differential Line ◽  
Spectral Diagnostics ◽  
Low Mass

Context. The CARMENES survey is a high-precision radial velocity (RV) programme that aims to detect Earth-like planets orbiting low-mass stars. Aims. We develop least-squares fitting algorithms to derive the RVs and additional spectral diagnostics implemented in the SpEctrum Radial Velocity AnaLyser (SERVAL), a publicly available python code. Methods. We measured the RVs using high signal-to-noise templates created by coadding all available spectra of each star. We define the chromatic index as the RV gradient as a function of wavelength with the RVs measured in the echelle orders. Additionally, we computed the differential line width by correlating the fit residuals with the second derivative of the template to track variations in the stellar line width. Results. Using HARPS data, our SERVAL code achieves a RV precision at the level of 1 m/s. Applying the chromatic index to CARMENES data of the active star YZ CMi, we identify apparent RV variations induced by stellar activity. The differential line width is found to be an alternative indicator to the commonly used full width half maximum. Conclusions. We find that at the red optical wavelengths (700–900 nm) obtained by the visual channel of CARMENES, the chromatic index is an excellent tool to investigate stellar active regions and to identify and perhaps even correct for activity-induced RV variations.

XVIII.—The Invariant Theory of Forms in Six Variables relating to the Line Complex

1927 ◽  
Vol 46 ◽  
pp. 210-222 ◽  
Author(s):  
H. W. Turnbull
Keyword(s):  
Invariant Theory ◽  
Line Geometry ◽  
Five Dimensions ◽  
Ordinary Space ◽  
Homogeneous Coordinates ◽  
Plücker Coordinates ◽  
Algebraic Theories ◽  
Straight Line ◽  
Image Position ◽  
Theory Of Forms

It is well known that the Plücker coordinates of a straight line in ordinary space satisfy a quadratic identitywhich may also be considered as the equation of a point-quadric in five dimensions, if the six coordinates Pij are treated as six homogeneous coordinates of a point. Projective properties of line geometry may therefore be treated as projective properties of point geometry in five dimensions. This suggests that certain algebraic theories of quaternary forms (corresponding to the geometry of ordinary space) can best be treated as algebraic theories of senary forms: that is, forms in six homogeneous variables.

The Effect of Line Geometry on Void Growth in Thin, Narrow Aluminum Lines

1991 ◽  
Vol 226 ◽  
Author(s):  
P. Borgesen ◽  
J. K. Lee ◽  
M. A. Korhonen ◽  
C.-Y. Li
Keyword(s):  
Stress Relaxation ◽  
Void Growth ◽  
Room Temperature ◽  
Line Geometry

AbstractThe stress induced growth of individual voids in passivated Al-lines at room temperature was monitored in-situ without removing the passivation. The kinetics was strongly influenced by variations in line gec.etry, even over distances of many Am, indicating variations in the stress relaxation as well.

Spacetime Algebra and Line Geometry

1996 ◽  
pp. 449-457
Author(s):  
Johannes G. Maks
Keyword(s):  
Line Geometry ◽  
Spacetime Algebra

scholarly journals Characterizations of the $G_2(4)$ and $L_3(4)$ Near Octagons

10.37236/8476 ◽  
2021 ◽  
Vol 28 (4) ◽  
Author(s):  
Bart De Bruyn
Keyword(s):  
Generalized Quadrangle ◽  
Line Geometry ◽  
Near Polygon ◽  
Generalized Polygon ◽  
Generalized Hexagon ◽  
Split Cayley Hexagon ◽  
Point Line ◽  
Line Spread

A triple $(\mathcal{S},S,\mathcal{Q})$ consisting of a near polygon $\mathcal{S}$, a line spread $S$ of $\mathcal{S}$ and a set $\mathcal{Q}$ of quads of $\mathcal{S}$ is called a polygonal triple if certain nice properties are satisfied, among which there is the requirement that the point-line geometry $\mathcal{S}'$ formed by the lines of $S$ and the quads of $\mathcal{Q}$ is itself also a near polygon. This paper addresses the problem of classifying all near polygons $\mathcal{S}$ that admit a polygonal triple $(\mathcal{S},S,\mathcal{Q})$ for which a given generalized polygon $\mathcal{S}'$ is the associated near polygon. We obtain several nonexistence results and show that the $G_2(4)$ and $L_3(4)$ near octagons are the unique near octagons that admit polygonal triples whose quads are isomorphic to the generalized quadrangle $W(2)$ and whose associated near polygons are respectively isomorphic to the dual split Cayley hexagon $H^D(4)$ and the unique generalized hexagon of order $(4,1)$.

An introduction to line geometry with applications

1999 ◽  
Vol 31 (1) ◽  
pp. 3-16 ◽  
Author(s):  
Helmut Pottmann ◽  
Martin Peternell ◽  
Bahram Ravani
Keyword(s):  
Line Geometry
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