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SUMS OF (p<sup>r</sup> + 1)-TH POWERS IN THE POLYNOMIAL RING F<sub>p</sub><sub>m</sub>[T]
Car, Mireille Korean Mathematical Society 2012 대한수학회지 Vol.49 No.6
Let $p$ be an odd prime number and let F be a finite field with $p^m$ elements. We study representations and strict representations of polynomials $M{\in}F$[T] by sums of ($p^r$ + 1)-th powers. A representation $$M=M_1^k+{\cdots}+M_s^k$$ of $M{\in}F$[T] as a sum of $k$-th powers of polynomials is strict if $k$ deg $M_i<k$ + degM.
ABOUT THE PERIOD OF BELL NUMBERS MODULO A PRIME
Car, Mireille,Gallardo, Luis H.,Rahavandrainy, Olivier,Vaserstein, Leonid N. Korean Mathematical Society 2008 대한수학회보 Vol.45 No.1
Let p be a prime number. It is known that the order o(r) of a root r of the irreducible polynomial $x^p-x-l$ over $\mathbb{F}_p$ divides $g(p)=\frac{p^p-1}{p-1}$. Samuel Wagstaff recently conjectured that o(r) = g(p) for any prime p. The main object of the paper is to give some subsets S of {1,...,g(p)} that do not contain o(r).
SUMS OF (pr + 1)-TH POWERS IN THE POLYNOMIAL RING F pm[T]
Mireille Car 대한수학회 2012 대한수학회지 Vol.49 No.6
Let p be an odd prime number and let F be a finite field with pm elements. We study representations and strict representations of polynomials M 2 F[T] by sums of (pr + 1)-th powers. A representation M = Mk 1 + · · · +Mk s of M 2 F[T] as a sum of k-th powers of polynomials is strict if k degMi <k + degM.
About the period of Bell numbers modulo a prime
Mireille Car,Luis H. Gallardo,Olivier Rahavandrainy,Leonid N. Vaserstein 대한수학회 2008 대한수학회보 Vol.45 No.1
Let p be a prime number. It is known that the order o(r) of a root r of the irreducible polynomial xp-x-1 over Fp divides g(p) = [수식]. Samuel Wagstaff recently conjectured that o(r) = g(p) for any prime p. The main object of the paper is to give some subsets S of {1,...,g(p)} that do not contain o(γ).
Tihomir Car,Krešimir Salamon,Nikola Radić,Jovica Ivkov 대한금속·재료학회 2019 METALS AND MATERIALS International Vol.25 No.5
Some of mechanical, electrical, and thermal properties of the Al–(Nb, Mo, Ta, W) binary thin films which are importantfor the stability and usability of the amorphous alloys were examined. Samples were prepared by magnetron depositiontechnique in wide range of composition onto various substrates held at room temperature. Different experimental techniqueswere used for the characterization of samples. The results of structural relaxation and crystallization measurements underisochronal conditions are compared with the results of measurements of micro/nano hardness and strain in the films. Fromthe micro/nano hardness measurement, the elastic deformation energy fraction is calculated. The elastic deformation energyfraction is correlated with the various results obtained from electrical resistivity measurements under isochronal conditions. Particular emphasis was placed on the Al–Mo amorphous alloys. It turns out that elastic deformation energy fraction becomesimportant indicator and phenomenological correlation parameter between various physical properties of examined films