Criteria for extreme forms
نویسندگان
چکیده
منابع مشابه
On extreme forms in dimension 8
A theorem of Voronoi asserts that a lattice is extreme if and only if it is perfect and eutactic. Very recently the classification of the perfect forms in dimension 8 has been completed [5]. There are 10916 perfect lattices. Using methods of linear programming, we are able to identify those that are additionally eutactic. In lower dimensions almost all perfect lattices are also eutactic (for ex...
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In this paper we consider a generalization to algebraic number fields of the classical Hermite constant γ n . For this constant we extend the well-known Minkowski bound and study the notion of extreme forms in this setting. Let us briefly recall the definition of Hermite’s constant. Let (a ij ) be a positive definite symmetric real n¬n matrix and let f(x " ,... ,x n ) ̄3 ij a ij x i x j be its a...
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On the other hand, no one has yet constructed a sequence of forms for which yn{f) is unbounded, let alone of order n, as n -> oo. We have therefore thought it worthwhile to describe, in some detail, a new class of extreme forms yielding values yn{f) of order n% for suitable large n. More specifically, corresponding to each N = 2 (n = 2, 3, . . .) and to each sequence of integers Ao, Xv . . ., X...
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In this paper, some new forms of the Cheeger’s inequalities are established for general (maybe unbounded) symmetric forms (Theorem 1.1 and Theorem 1.2), the resulting estimates improve and extend the ones obtained by Lawler and Sokal (1988) for bounded jump processes. Furthermore, some existence criteria for spectral gap of general symmetric forms or general reversible Markov processes are pres...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 1959
ISSN: 0004-9735
DOI: 10.1017/s1446788700025027