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

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.

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 $(4,1)$.

Finding an improved amorphous-silicon x-ray flat-panel detector configuration for the in-line geometry

2013 ◽  
Vol 58 (7) ◽  
pp. 2305-2324 ◽  
Author(s):  
M F Fast ◽  
A Teymurazyan ◽  
G Pang ◽  
U Oelfke ◽  
J A Rowlands
Keyword(s):  
Amorphous Silicon ◽  
Line Geometry ◽  
Flat Panel ◽  
X Ray ◽  
Flat Panel Detector

Structure Evolution in Plated Cu Films

2005 ◽  
Vol 863 ◽  
Author(s):  
D.P. Field ◽  
NJ Park ◽  
PR Besser ◽  
JE Sanchez
Keyword(s):  
Film Thickness ◽  
Grain Growth ◽  
Texture Evolution ◽  
Structural Evolution ◽  
Similar Process ◽  
Structure Evolution ◽  
Line Geometry ◽  
Strong Function ◽  
Cu Films ◽  
Line Widths

AbstractStructure evolution in plated Cu films is a function of sublayer stacking, film thickness, plating chemistry, plating parameters, and temperature. The present work examines grain growth and texture evolution in annealed plated Cu on a 25 nm thick Ta sublayer for films of 480 and 750 nm in thickness. These results are compared against those obtained from damascene Cu lines fabricated from a similar process, using a series of line widths. The results show that the initial structures of the plated films are similar, with slightly weaker (111) texture, a higher fraction of twin boundaries, and larger grains in the thicker films. The microstructure of the Cu within the trench constraints is a strong function of line geometry with the propensity for twin boundary development controlling structural evolution.

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