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Lower bounds for the number of smooth values of a polynomial
, 1998
"... We investigate the problem of showing that the values of a given polynomial are smooth (i.e., have no large prime factors) a positive proportion of the time. Although some results exist that bound the number of smooth values of a polynomial from above, a corresponding lower bound of the correct ord ..."
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Cited by 3 (1 self)
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We investigate the problem of showing that the values of a given polynomial are smooth (i.e., have no large prime factors) a positive proportion of the time. Although some results exist that bound the number of smooth values of a polynomial from above, a corresponding lower bound of the correct order of magnitude has hitherto been established only in a few special cases. The purpose of this paper is to provide such a lower bound for an arbitrary polynomial. Various generalizations to subsets of the set of values taken by a polynomial are also obtained.
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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Cited by 2 (0 self)
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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
On Rough and Smooth Neighbors
, 2005
"... We study the behavior of the arithmetic functions defined by F(n) = P +(n) P−(n+ 1) and G(n) = P ..."
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We study the behavior of the arithmetic functions defined by F(n) = P +(n) P−(n+ 1) and G(n) = P