منابع مشابه
Polynomials That Are Positive on an Interval
This paper discusses representations of polynomials that are positive on intervals of the real line. An elementary and constructive proof of the following is given: If h(x), p(x) ∈ R[x] such that {α ∈ R | h(α) ≥ 0} = [−1, 1] and p(x) > 0 on [−1, 1], then there exist sums of squares s(x), t(x) ∈ R[x] such that p(x) = s(x) + t(x)h(x). Explicit degree bounds for s and t are given, in terms of the ...
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A theorem of S.D. Cohen gives a characterization for Dickson polynomials of the second kind that permutes the elements of a finite field of cardinality the square of the characteristic. Here, a different proof is presented for this result. 1. Permutation polynomials of finite fields. In recent years cryptographers became interested in finding polynomials that induce a bijection of a finite fiel...
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Dickson polynomials which are permutations are interesting combinatorial objects and well studied. In this paper, we describe Dickson polynomials of the first kind in F2[x] that are involutions over finite fields of characteristic 2. Such description is obtained using modular arithmetic’s tools. We give results related to the cardinality and the number of fixed points (in the context of cryptog...
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Extremal trigonometric polynomials with two fixed leading coefficients deviated least from zero on an interval shorter than period are found. The complete solution splits into three different cases, one of them uses elliptic functions, and two others use only elementary functions. (Published in Journal of Approximation Theory,Volume 168, April 2013, Pages 18-32). Weighted analogues (rational tr...
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It is proved that, if F (x) be a cubic polynomial with integral coefficients having the property that F (n) is equal to a sum of two positive integral cubes for all sufficiently large integers n, then F (x) is identically the sum of two cubes of linear polynomials with integer coefficients that are positive for sufficiently large x. A similar result is proved in the case where F (n) is merely a...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2000
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-00-02595-2