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Arbitrarily Tight Bounds On The Distribution Of Smooth Integers
 Proceedings of the Millennial Conference on Number Theory
, 2002
"... This paper presents lower bounds and upper bounds on the distribution of smooth integers; builds an algebraic framework for the bounds; shows how the bounds can be computed at extremely high speed using FFTbased powerseries exponentiation; explains how one can choose the parameters to achieve ..."
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This paper presents lower bounds and upper bounds on the distribution of smooth integers; builds an algebraic framework for the bounds; shows how the bounds can be computed at extremely high speed using FFTbased powerseries exponentiation; explains how one can choose the parameters to achieve any desired level of accuracy; and discusses several generalizations.
ABSTRACT By
, 1995
"... Interest in understanding how brownrot fungi decay wood has received increasing interest in recent years because of a need to identify novel targets that can be inhibited for the next generation of antifungal wood preservatives. Brownrot fungi are unique in that they can degrade holocellulose (cel ..."
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Interest in understanding how brownrot fungi decay wood has received increasing interest in recent years because of a need to identify novel targets that can be inhibited for the next generation of antifungal wood preservatives. Brownrot fungi are unique in that they can degrade holocellulose (cellulose and hemicellulose) in wood without first removing the lignin. Furthermore, they degrade holocellulose in an unusual manner, causing a rapid decrease in degree of polymerization at low weight loss. Despite the increased research effort the mechanism of brownrot decay remains unclear and, furthermore, this research has not provided biochemical targets for inhibition and development of new wood preservatives. In viewing the brownrot literature, it became apparent that many of the beliefs about brownrot decomposition of wood are based more on tradition or conjecture than on facts. These myths tend to cloud our understanding of brownrot decay and as a result may contribute to a misdirection of research efforts. The purpose of this paper is to attempt to identify and clarify some of these misconceptions about brownrot decay that have become dogma. Keywords: Brownrot, wood decay, oxidation, Fenton reaction, oxalic acid, oxalate decarboxylase
Squarefree Integers Without Large Prime Factors In Short Intervals
"... We show that for every > 0 and > 0 there are squarefree integers that are free of prime factors > X in the interval [X X + X 1 2 + ] for all large enough X. The approach used is a simple variant of the methods used by Balog [Ba87] and by Harman [Har91] in their study of smooth integers in s ..."
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We show that for every > 0 and > 0 there are squarefree integers that are free of prime factors > X in the interval [X X + X 1 2 + ] for all large enough X. The approach used is a simple variant of the methods used by Balog [Ba87] and by Harman [Har91] in their study of smooth integers in short intervals.
ANOTHER NOTE ON SMOOTH NUMBERS IN SHORT INTERVALS
"... Abstract. We prove that, for any positive constants δ and ε and every large enough x, the interval [x, x+ x(log x)7/3+δ] contains numbers whose all prime factors are smaller than xε. 1. ..."
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Abstract. We prove that, for any positive constants δ and ε and every large enough x, the interval [x, x+ x(log x)7/3+δ] contains numbers whose all prime factors are smaller than xε. 1.
ACTA ARITHMETICA
"... Integers without large prime factors in short intervals and arithmetic progressions by Glyn Harman (Cardiff) 1. Introduction. Let Ψ(x, u) denote the number of integers up to x having all their prime factors no more than u in size. Write Ψ(x, u; a, q) for the number of such integers congruent to a (m ..."
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Integers without large prime factors in short intervals and arithmetic progressions by Glyn Harman (Cardiff) 1. Introduction. Let Ψ(x, u) denote the number of integers up to x having all their prime factors no more than u in size. Write Ψ(x, u; a, q) for the number of such integers congruent to a (mod q). Many authors have studied these functions ([4], [7], [9], [12], [13], [15] for example), either for