منابع مشابه
The Well-Rounded Linear Function
The generic linear function ax + b of a real variable, with a, b, x ∈ R, is usually evaluated as a scale function (product) followed by a translation (sum). Our main result shows that when such a function is variously combined with rounding functions (floor and ceiling), exactly 67 inequivalent rounded generic linear functions result, of which 38 are integer-valued and 29 are not. Several relat...
متن کاملOn Well-rounded Ideal Lattices
We investigate a connection between two important classes of Euclidean lattices: well-rounded and ideal lattices. A lattice of full rank in a Euclidean space is called well-rounded if its set of minimal vectors spans the whole space. We consider lattices coming from full rings of integers in number fields, proving that only cyclotomic fields give rise to well-rounded lattices. We further study ...
متن کاملMinimality of the Well-rounded Retract
We prove that the well-rounded retract of SOn \ SLn R is a minimal SLn Z-invariant spine.
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Nematodes pervade Earth's biosphere and occupy innumerable ecological niches. The role of Caenorhabditis elegans as a model for developmental processes has encouraged us to cultivate a second nematode, Pristionchus pacificus, as a comparative counterpoint to address questions in development, behavior and ecology in nematode evolution. We hope that this endeavor, now more than a decade underway,...
متن کاملWell - Rounded Integral Lattices in Dimension Two
A lattice is called well-rounded if its minimal vectors span the corresponding Eucildean space. In this paper we completely describe well-rounded full-rank sublattices of Z 2 , as well as their determinant and minima sets. We show that the determinant set has positive density, deriving an explicit lower bound for it, while the minima set has density 0. We also produce formulas for the number of...
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ژورنال
عنوان ژورنال: Science
سال: 1961
ISSN: 0036-8075,1095-9203
DOI: 10.1126/science.134.3488.1393