scholarly journals A modification of Fitzgerald's characterization of primitive polynomials over a finite field

2008 ◽  
Vol 14 (1) ◽  
pp. 85-91 ◽  
Author(s):  
Vichian Laohakosol ◽  
Umarin Pintoptang
Keyword(s):  
Finite Field ◽  
Primitive Polynomials

scholarly journals On accurate high-order numerical derivatives computations for quantum chemistry purposes

2018 ◽  
Keyword(s):  
Quantum Chemistry ◽  
Finite Field ◽  
Numerical Differentiation ◽  
Field Method ◽  
High Order ◽  
Parameter Choice ◽  
Derivatives Of ◽  
Finite Field Method ◽  
Account Electron

Various molecular parameters in quantum chemistry could be computed as derivatives of energy over different arguments. Unfortunately, it is quite complicated to obtain analytical expression for characteristics that are of interest in the framework of methods that account electron correlation. Especially it relates to the coupled cluster (CC) theory. In such cases, numerical differentiation comes to rescue. This approach, like any other numerical method has empirical parameters and restrictions that require investigation. Current work is called to clarify the details of Finite-Field method usage for high-order derivatives calculation in CC approaches. General approach to the parameter choice and corresponding recommendations about numerical steadiness verification are proposed. As an example of Finite-Field approach implementation characterization of optical properties of fullerene passing process through the aperture of carbon nanotorus is given.

LOGICAL CHARACTERIZATION OF RECOGNIZABLE SETS OF POLYNOMIALS OVER A FINITE FIELD

2011 ◽  
Vol 22 (07) ◽  
pp. 1549-1563 ◽  
Author(s):  
MICHEL RIGO ◽  
LAURENT WAXWEILER
Keyword(s):  
Finite Field ◽  
Order Theory ◽  
Ring Of Integers ◽  
First Order ◽  
Polynomial Coefficients ◽  
Bounded Number ◽  
First Order Theory ◽  
Ring Of Polynomials

The ring of integers and the ring of polynomials over a finite field share a lot of properties. Using a bounded number of polynomial coefficients, any polynomial can be decomposed as a linear combination of powers of a non-constant polynomial P playing the role of the base of the numeration. Having in mind the theorem of Cobham from 1969 about recognizable sets of integers, it is natural to study P-recognizable sets of polynomials. Based on the results obtained in the Ph.D. thesis of the second author, we study the logical characterization of such sets and related properties like decidability of the corresponding first-order theory.

A Characterization of the n × n Matrices over a Finite Field

1973 ◽  
Vol 80 (6) ◽  
pp. 670-672
Author(s):  
J. V. Brawley ◽  
L. Carlitz
Keyword(s):  
Finite Field

scholarly journals A characterization of the Jacobi logarithms of a finite field

2001 ◽  
Vol 231 (1-3) ◽  
pp. 295-302 ◽  
Author(s):  
A.D. Keedwell
Keyword(s):  
Finite Field
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