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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Two little known forms of child labour in Turkey are examined. The process through which these children are made to work has parallels with the experiences of slaves. First, a longstanding practice from Northwestern Turkey of parents hiring children to better-off farmers is examined. Further, a more recent problem is examined where children are trafficked to big cities and forced to join crimin...
متن کاملHermite Constant and Extreme Forms for Algebraic Number Fields
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...
متن کاملSome Extreme Forms Defined in Terms of Abelian Groups
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...
متن کاملCheeger's Inequalities for General Symmetric Forms and Existence Criteria for Spectral Gap
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