scholarly journals Classification of Elliptic Cubic Curves OverThe Finite Field of Order Nineteen

2016 ◽  
Vol 13 (4) ◽  
Keyword(s):  
Finite Field ◽  
Cubic Curves

scholarly journals Classification of Elliptic Cubic Curves Over The Finite Field of Order Nineteen

2016 ◽  
Vol 13 (4) ◽  
pp. 846-852
Author(s):  
Baghdad Science Journal
Keyword(s):  
Finite Field ◽  
Elliptic Curve ◽  
Maximum Size ◽  
Cubic Curves ◽  
Projective Equivalence

Plane cubics curves may be classified up to isomorphism or projective equivalence. In this paper, the inequivalent elliptic cubic curves which are non-singular plane cubic curves have been classified projectively over the finite field of order nineteen, and determined if they are complete or incomplete as arcs of degree three. Also, the maximum size of a complete elliptic curve that can be constructed from each incomplete elliptic curve are given.

scholarly journals Cubic Curves Over the Finite Field of Order Twenty-Five

2021 ◽  
Vol 1818 (1) ◽  
pp. 012079
Author(s):  
S. H. Naji ◽  
E. B. Al-Zangana
Keyword(s):  
Finite Field ◽  
Cubic Curves

scholarly journals Nilpotent orbits of exceptional Lie algebras over algebraically closed fields of bad characteristic

1985 ◽  
Vol 38 (3) ◽  
pp. 330-350 ◽  
Author(s):  
D. F. Holt ◽  
N. Spaltenstein
Keyword(s):  
Finite Field ◽  
Lie Algebras ◽  
Closed Field ◽  
Nilpotent Orbits ◽  
Reductive Algebraic Group ◽  
Exceptional Lie Algebras ◽  
Closed Fields ◽  
Characteristic 3 ◽  
Algebraically Closed Fields

AbstractThe classification of the nilpotent orbits in the Lie algebra of a reductive algebraic group (over an algebraically closed field) is given in all the cases where it was not previously known (E7 and E8 in bad characteristic, F4 in characteristic 3). The paper exploits the tight relation with the corresponding situation over a finite field. A computer is used to study this case for suitable choices of the finite field.

scholarly journals Cubic Arcs in the Projective Plane Over a Finite Field of Order Twenty Three

2019 ◽  
Vol 54 (6) ◽  
Author(s):  
Najm A.M. Al-Seraji ◽  
Asraa A. Monshed
Keyword(s):  
Finite Field ◽  
Projective Plane ◽  
Coding Theory ◽  
Finite Projective Plane ◽  
Cubic Curves ◽  
The Subject

In this research we are interested in finding all the different cubic curves over a finite projective plane of order twenty-three, learning which of them is complete or not, constructing the stabilizer groups of the cubics in, studying the properties of these groups, and, finally, introducing the relation between the subject of coding theory and the projective plane of order twenty three.

Affine cubic functions

1979 ◽  
Vol 85 (3) ◽  
pp. 387-401 ◽  
Author(s):  
C. T. C. Wall
Keyword(s):  
Singularity Theory ◽  
Essential Difference ◽  
Parallel Study ◽  
Cubic Curves ◽  
Level Curves ◽  
The Subject ◽  
Coordinate Geometry

Although the classification of affine cubic curves was undertaken by Newton(4), in one of the first major exercises ever in coordinate geometry (see Cayley(2) for a fuller account), a parallel study of cubic functions seems not to have been contemplated till recently. The essential difference is that a function f defines a pencil of curves – its level curves – which have to be considered simultaneously. The author's interest in the subject arose from problems in singularity theory (concerning canonical stratifications), and a later paper in the series will have applications of this kind. Here we study the simplest case as an introduction. Our techniques are entirely classical, but the results are hard to find elsewhere. In later papers we intend to study cubic functions on ℝ2, and on ℂ3.

scholarly journals TOWARDS A CLASSIFICATION OF FINITE FIELD THEORIES

1994 ◽  
Vol 09 (27) ◽  
pp. 2555-2567
Author(s):  
PETER GRANDITS
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Finite Field ◽  
Field Theories ◽  
Quantum Field ◽  
Particle Content ◽  
Finiteness Conditions ◽  
Gauge Groups ◽  
Yukawa Couplings

We consider the finiteness conditions on the Yukawa couplings of a general quantum field theory for gauge groups SU (n)(n>6) and a rather general particle content. It is shown that in the class of theories considered (149 different particle contents), only two models are able to fulfill the finiteness conditions. Only one of these is supersymmetric. For the nonsupersymmetric one the appropriate Yukawa couplings are constructed explicitly.

The classification of small weakly minimal sets. III: Modules

1988 ◽  
Vol 53 (3) ◽  
pp. 975-979 ◽  
Author(s):  
Steven Buechler
Keyword(s):  
Finite Field ◽  
Algebraic Closure ◽  
Morley Rank ◽  
Minimal Sets

AbstractTheorem A. Let M be a left R-module such that Th(M) is small and weakly minimal, but does not have Morley rank 1. Let A = acl(∅) ⋂ M and I = {r ∈ R: rM ⊂ A}. Notice that I is an ideal.(i) F = R/Iis a finite field.(ii) Suppose that a, b0,…,bn, ∈ M and . Then there are s, ri ∈ R, i ≤ n, such that sa + Σi≤nribi ∈ A and s ∉ I.It follows from Theorem A that algebraic closure in M is modular. Using this and results in [B1] and [B2], we obtainTheorem B. Let M be as in Theorem A. Then Vaught's conjecture holds for Th(M).

scholarly journals Classification of cubic surfaces with twenty-seven lines over the finite field of order thirteen

2017 ◽  
Vol 4 (1) ◽  
pp. 37-50 ◽  
Author(s):  
Anton Betten ◽  
James W. P. Hirschfeld ◽  
Fatma Karaoglu
Keyword(s):  
Finite Field ◽  
Cubic Surfaces

scholarly journals The affine classification of cubic curves

1988 ◽  
Vol 18 (3) ◽  
pp. 655-664 ◽  
Author(s):  
D.A. Weinberg
Keyword(s):  
Cubic Curves
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