A basis for the ring of doubly integer-valued polynomials.
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E.G. Straus, Demetrios Brizolis (1976)
Journal für die reine und angewandte Mathematik
Andrew Yingst (2014)
Colloquium Mathematicae
Consider an experiment with d+1 possible outcomes, d of which occur with probabilities . If we consider a large number of independent occurrences of this experiment, the probability of any event in the resulting space is a polynomial in . We characterize those polynomials which arise as the probability of such an event. We use this to characterize those x⃗ for which the measure resulting from an infinite sequence of such trials is good in the sense of Akin.
Joshua Harrington, Lenny Jones (2013)
Colloquium Mathematicae
Let , where . We show that f(x) and f(x²) are irreducible over ℚ. Moreover, the upper bound of on the coefficients of f(x) is the best possible in this situation.
Andrzej Schinzel (1991)
Mathematica Slovaca
Everest, Graham, Ward, Thomas (1998)
Experimental Mathematics
Sury, B. (2004)
Integers
Martha Allen, Michael Filaseta (2003)
Acta Arithmetica
Georges Rhin (2004)
Colloquium Mathematicae
We give lower bounds for the Mahler measure of totally positive algebraic integers. These bounds depend on the degree and the discriminant. Our results improve earlier ones due to A. Schinzel. The proof uses an explicit auxiliary function in two variables.
Martha Allen, Michael Filaseta (2004)
Acta Arithmetica
Hungerbühler, Norbert, Specker, Ernst (2006)
Integers
Qiang Wu (2003)
Journal de théorie des nombres de Bordeaux
Using refinement of an algorithm given by Habsieger and Salvy to find integer polynomials with smallest sup norm on [0, 1] we extend their table of polynomials up to degree 100. For the degree 95 we find a new exceptionnal polynomial which has complex roots. Our method uses generalized Müntz-Legendre polynomials. We improve slightly the upper bound for the integer transfinite diameter of [0, 1] and give elementary proofs of lower bounds for the exponents of some critical polynomials.
Petros S. Stefaneas (1995)
Δελτίο της Ελληνικής Μαθηματικής Εταιρίας
Michal Vavroš (2002)
Acta Mathematica et Informatica Universitatis Ostraviensis
Daniel Davies (1996)
Colloquium Mathematicae
Xiangdong Yang, Caifeng Yi, Jin Tu (2011)
Annales Polonici Mathematici
Let p(z) be a polynomial of the form , . We discuss a sufficient condition for the existence of zeros of p(z) in an annulus z ∈ ℂ: 1 - c < |z| < 1 + c, where c > 0 is an absolute constant. This condition is a combination of Carleman’s formula and Jensen’s formula, which is a new approach in the study of zeros of polynomials.
Andrzej Schinzel, J. Wójcik (1971)
Acta Arithmetica
Schauz, Uwe (2010)
The Electronic Journal of Combinatorics [electronic only]
Michael Filaseta, Joshua Harrington (2012)
Acta Arithmetica
Pakovich, F. (2007)
Integers
Sophie Depeyre (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
We present in this paper a stability study concerning finite volume schemes applied to the two-dimensional Maxwell system, using rectangular or triangular meshes. A stability condition is proved for the first-order upwind scheme on a rectangular mesh. Stability comparisons between the Yee scheme and the finite volume formulation are proposed. We also compare the stability domains obtained when considering the Maxwell system and the convection equation.
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