منابع مشابه
Smooth Values of the Iterates of the Euler’s Phi-function
Let φ(n) be the Euler-phi function, define φ0(n) = n and φk+1(n) = φ(φk(n)) for all k ≥ 0. We will determine an asymptotic formula for the set of integers n less than x for which φk(n) is y-smooth, conditionally on a weak form of the Elliott-Halberstam conjecture. 1.Introduction Integers without large prime factors, usually called smooth numbers, play a central role in several topics of number ...
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Let C be a closed subset of a topological space X, and let f : C → X. Let us assume that f is continuous and f(x) ∈ C for every x ∈ ∂C. How many times can one iterate f? This paper provides estimates on the number of iterations and examples of their optimality. In particular we show how some topological properties of f , C, X are related to the maximal number of iterations, both in the case of ...
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We prove an eeective mean-value theorem for the values of a non-degenerate, algebraic exponential polynomial in several variables. These objects simultaneously generalise the fundamental examples of linear recurrence sequences and sums of S-units. The proof is based on an eeective, uniform estimate for the deviation of the exponential polynomial from its expected value. This estimate is also us...
متن کاملphi-Amenable and phi-biflat Banach algebras
In this paper we study the concept of ph-biatness ofa Banach algebra A, where ph is a continuous homomorphism on A.We prove that if ph is a continuous epimorphism on A and A hasa bounded approximate identity and A is ph- biat, then A is ph-amenable. In the case where ph is an isomorphism on A we showthat the ph- amenability of A implies its ph-biatness.
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The natural DNA sequence of bacteriophage, phi X174, when analyzed as a "text" of dinucleotides, is shown to display an easily detectable degree of non-randomness by the distribution of values of dinucleotide self-information along the sequence. Self-information corresponding to occurrences of dinucleotides separated by a single nucleotide is found to be somewhat higher than the values which pr...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1979
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1979-0537079-1