Lattices generated by subspaces of the same dimension and rank in orthogonal geometry over finite fields of odd characteristic

1993 ◽  
Vol 21 (11) ◽  
pp. 4219-4252 ◽  
Author(s):  
Yuan-Ji Huo ◽  
Zhe-Xian Wan
Keyword(s):  
Finite Fields ◽  
Orthogonal Geometry

scholarly journals Frames over finite fields: Equiangular lines in orthogonal geometry

2022 ◽  
Author(s):  
Gary R.W. Greaves ◽  
Joseph W. Iverson ◽  
John Jasper ◽  
Dustin G. Mixon
Keyword(s):  
Finite Fields ◽  
Orthogonal Geometry ◽  
Equiangular Lines

scholarly journals Constructions of 112-designs from orthogonal geometry over finite fields

2016 ◽  
Vol 339 (1) ◽  
pp. 382-390 ◽  
Author(s):  
Rongquan Feng ◽  
Meng Zhao ◽  
Liwei Zeng
Keyword(s):  
Finite Fields ◽  
Orthogonal Geometry

Simulation and Contrast Analysis of tem Images of Cracks

1990 ◽  
Vol 48 (1) ◽  
pp. 578-579
Author(s):  
D. Goyal ◽  
A. H. King
Keyword(s):  
Displacement Vector ◽  
Crack Tip ◽  
Perfect Crystal ◽  
Operating Conditions ◽  
Displacement Fields ◽  
Fringe Contrast ◽  
Orthogonal Geometry ◽  
Moire Fringe ◽  
Moiré Fringe

TEM images of cracks have been found to give rise to a moiré fringe type of contrast. It is apparent that the moire fringe contrast is observed because of the presence of a fault in a perfect crystal, and is characteristic of the fault geometry and the diffracting conditions in the TEM. Various studies have reported that the moire fringe contrast observed due to the presence of a crack in an otherwise perfect crystal is distinctive of the mode of crack. This paper describes a technique to study the geometry and mode of the cracks by comparing the images they produce in the TEM because of the effect that their displacement fields have on the diffraction of electrons by the crystal (containing a crack) with the corresponding theoretical images. In order to formulate a means of matching experimental images with theoretical ones, displacement fields of dislocations present (if any) in the vicinity of the crack are not considered, only the effect of the displacement field of the crack is considered.The theoretical images are obtained using a computer program based on the two beam approximation of the dynamical theory of diffraction contrast for an imperfect crystal. The procedures for the determination of the various parameters involved in these computations have been well documented. There are three basic modes of crack. Preliminary studies were carried out considering the simplest form of crack geometries, i. e., mode I, II, III and the mixed modes, with orthogonal crack geometries. It was found that the contrast obtained from each mode is very distinct. The effect of variation of operating conditions such as diffracting vector (), the deviation parameter (ω), the electron beam direction () and the displacement vector were studied. It has been found that any small change in the above parameters can result in a drastic change in the contrast. The most important parameter for the matching of the theoretical and the experimental images was found to be the determination of the geometry of the crack under consideration. In order to be able to simulate the crack image shown in Figure 1, the crack geometry was modified from a orthogonal geometry to one with a crack tip inclined to the original crack front. The variation in the crack tip direction resulted in the variation of the displacement vector also. Figure 1 is a cross-sectional micrograph of a silicon wafer with a chromium film on top, showing a crack in the silicon.

Finite Fields

1996 ◽  
Author(s):  
Rudolf Lidl ◽  
Harald Niederreiter
Keyword(s):  
Finite Fields

Maximum Distance Separable Hankel Rhotrices over Finite Fields

2018 ◽  
Vol 43 (1-4) ◽  
pp. 13-45
Author(s):  
Prof. P. L. Sharma ◽  
◽  
Mr. Arun Kumar ◽  
Mrs. Shalini Gupta ◽  
◽  
...  
Keyword(s):  
Finite Fields ◽  
Maximum Distance ◽  
Maximum Distance Separable
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