scholarly journals Determination of a type of permutation binomials over finite fields

2015 ◽  
Vol 147 ◽  
pp. 14-23 ◽  
Author(s):  
Xiang-Dong Hou ◽  
Stephen D. Lappano
Keyword(s):  
Finite Fields

scholarly journals Combinatorics on Finite Fields: the Sign Repartition for the Quadratic Residues

2014 ◽  
Vol 22 (1) ◽  
pp. 41-44
Author(s):  
Şerban Bărcănescu
Keyword(s):  
Finite Fields ◽  
Class Number ◽  
Quadratic Extensions ◽  
Quadratic Residues

AbstractIn the present paper we present the equivalence between the combinatorial determination of the sign repartition for the quadratic residues and non-residues to the computation of the class number of certain quadratic extensions of the field of rationals.

scholarly journals Construction and Determination of Irreducible Polynomials in Galois elds, GF(2m)

2019 ◽  
pp. 1-6
Author(s):  
Abraham Aidoo ◽  
Kwasi Baah Gyam ◽  
Fengfan Yang
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Monic Polynomial ◽  
Galois Field ◽  
Irreducible Polynomials ◽  
Primitive Polynomials

This work is about Construction of Irreducible Polynomials in Finite fields. We defined some terms in the Galois field that led us to the construction of the polynomials in the GF(2m). We discussed the following in the text; irreducible polynomials, monic polynomial, primitive polynomials, eld, Galois eld or nite elds, and the order of a finite field. We found all the polynomials in $$F_2[x]$$ that is, $$P(x) =\sum_{i=1}^m a_ix^i : a_i \in F_2$$ with $$a_m \neq 0$$ for some degree $m$ whichled us to determine the number of irreducible polynomials generally at any degree in $$F_2[x]$$.

Polynomials for Kloosterman Sums

2007 ◽  
Vol 50 (1) ◽  
pp. 71-84 ◽  
Author(s):  
S. Gurak
Keyword(s):  
Finite Fields ◽  
Complete System ◽  
Kloosterman Sums ◽  
Multiplicative Inverse ◽  
Rational Field ◽  
Image Position ◽  
Explicit Determination

AbstractFix an integer m > 1, and set ζm = exp(2πi/m). Let denote the multiplicative inverse of x modulo m. The Kloosterman sums , satisfy the polynomialwhere the sum and product are taken over a complete system of reduced residues modulo m. Here we give a natural factorization of fm(x), namely,where σ runs through the square classes of the group of reduced residues modulo m. Questions concerning the explicit determination of the factors (or at least their beginning coefficients), their reducibility over the rational field Q and duplication among the factors are studied. The treatment is similar to what has been done for period polynomials for finite fields.

Galactic orbits of stars

1966 ◽  
Vol 25 ◽  
pp. 93-97
Author(s):  
Richard Woolley
Keyword(s):  
Globular Cluster ◽  
Potential Field ◽  
High Velocity ◽  
Velocity Vector ◽  
Variable Stars ◽  
The Sun ◽  
Proper Motions ◽  
Rr Lyrae ◽  
The Galaxy

It is now possible to determine proper motions of high-velocity objects in such a way as to obtain with some accuracy the velocity vector relevant to the Sun. If a potential field of the Galaxy is assumed, one can compute an actual orbit. A determination of the velocity of the globular clusterωCentauri has recently been completed at Greenwich, and it is found that the orbit is strongly retrograde in the Galaxy. Similar calculations may be made, though with less certainty, in the case of RR Lyrae variable stars.

Distance to SN 1987A and the LMC

1999 ◽  
Vol 190 ◽  
pp. 549-554
Author(s):  
Nino Panagia
Keyword(s):  
Angular Size ◽  
Large Magellanic Cloud ◽  
Magellanic Cloud ◽  
Light Curves ◽  
Distance Modulus ◽  
Absolute Size ◽  
Sn 1987A

Using the new reductions of the IUE light curves by Sonneborn et al. (1997) and an extensive set of HST images of SN 1987A we have repeated and improved Panagia et al. (1991) analysis to obtain a better determination of the distance to the supernova. In this way we have derived an absolute size of the ringRabs= (6.23 ± 0.08) x 1017cm and an angular sizeR″ = 808 ± 17 mas, which give a distance to the supernovad(SN1987A) = 51.4 ± 1.2 kpc and a distance modulusm–M(SN1987A) = 18.55 ± 0.05. Allowing for a displacement of SN 1987A position relative to the LMC center, the distance to the barycenter of the Large Magellanic Cloud is also estimated to bed(LMC) = 52.0±1.3 kpc, which corresponds to a distance modulus ofm–M(LMC) = 18.58±0.05.

International determination of the total motion of the pole

1961 ◽  
Vol 13 ◽  
pp. 29-41
Author(s):  
Wm. Markowitz
Keyword(s):  
Secular Motion ◽  
The Future

A symposium on the future of the International Latitude Service (I. L. S.) is to be held in Helsinki in July 1960. My report for the symposium consists of two parts. Part I, denoded (Mk I) was published [1] earlier in 1960 under the title “Latitude and Longitude, and the Secular Motion of the Pole”. Part II is the present paper, denoded (Mk II).

Time and Latitude in South Africa

1972 ◽  
Vol 1 ◽  
pp. 27-38
Author(s):  
J. Hers
Keyword(s):  
South Africa ◽  
Cape Town ◽  
Astronomical Observations ◽  
Royal Observatory ◽  
The Republic ◽  
Astronomical Determination ◽  
Limited Accuracy ◽  
Better Than

In South Africa the modern outlook towards time may be said to have started in 1948. Both the two major observatories, The Royal Observatory in Cape Town and the Union Observatory (now known as the Republic Observatory) in Johannesburg had, of course, been involved in the astronomical determination of time almost from their inception, and the Johannesburg Observatory has been responsible for the official time of South Africa since 1908. However the pendulum clocks then in use could not be relied on to provide an accuracy better than about 1/10 second, which was of the same order as that of the astronomical observations. It is doubtful if much use was made of even this limited accuracy outside the two observatories, and although there may – occasionally have been a demand for more accurate time, it was certainly not voiced.

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