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 Application of neuron networks of deep learning for exposures editing of digital phonograms

2020 ◽  
Vol 65 (4) ◽  
pp. 506-512
Author(s):  
V. I. Solovyov ◽  
O. V. Rybalskiy ◽  
V. V. Zhuravel ◽  
V. K. Zheleznyak
Keyword(s):  
Deep Learning ◽  
Binary Classification ◽  
Maximum Size ◽  
Maximum Efficiency ◽  
Correct Classification ◽  
Digital Audio ◽  
Neuron Networks ◽  
Effective System ◽  
Further Development

Possibility of creation of effective system, which is intended for exposure of tracks of editing in digital phonograms and is built on the basis of neuron networks of the deep learning, is experimentally proven. Sense of experiment consisted in research of ability of the systems on the basis of such networks to expose pauses with tracks of editing. The experimental array of data is created in a voice editor from phonograms written on the different apparatus of the digital audio recording (at frequency of discretisation 44,1 kHz). A preselection of pauses was produced from it, having duration from 100 мs to a few seconds. From 1000 selected pauses the array of fragments of pauses is formed in the automatic (computer) mode, from which the arrays of fragments of pauses of different duration are generated by a dimension about 100 000. For forming of array of fragments of pauses with editing, the chosen pauses were divided into casual character parts in arbitrary correlation. Afterwards, the new pauses were created from it with the fixed place of editing. The general array of all fragments of pauses was broken into training and test arrays. The maximum efficiency, achieved on a test array in the process of educating, was determined. In general case this efficiency is determined by the maximum size of probability of correct classification of fragments with editing and fragments without editing. Scientifically reasonable methodology of exposure of signs of editing in digital phonograms is offered on the basis of neuron networks of the deep learning. The conducted experiments showed that the construction of the effective system is possible for the exposure of such tracks. Further development of methodology must be directed to find the ways to increase the probability of correct binary classification of investigated pauses.

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.

Generalized Artin'S Conjecture for Primitive Roots and Cyclicity Mod of Elliptic Curves Over Function Fields

1995 ◽  
Vol 38 (2) ◽  
pp. 167-173 ◽  
Author(s):  
David A. Clark ◽  
Masato Kuwata
Keyword(s):  
Finite Field ◽  
Prime Ideal ◽  
Elliptic Curve ◽  
Elliptic Curves ◽  
Function Field ◽  
Function Fields ◽  
Artin's Conjecture ◽  
Primitive Roots

AbstractLet k = Fq be a finite field of characteristic p with q elements and let K be a function field of one variable over k. Consider an elliptic curve E defined over K. We determine how often the reduction of this elliptic curve to a prime ideal is cyclic. This is done by generalizing a result of Bilharz to a more general form of Artin's primitive roots problem formulated by R. Murty.

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