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...

We build discrete-time compactly supported biorthogonal wavelets and perfect reconstruction filter banks for any lattice in any dimension with any number of primal and dual vanishing moments. The associated scaling functions are interpolating. Our construction relies on the lifting scheme and inherits all of its advantages: fast transform, in-place calculation, and integer-to-integer transforms...

This paper presents a uni ed study of duality properties for the problem of minimizing a linear function over the intersection of an a ne space with a convex cone in nite dimension. Existing duality results are carefully surveyed and some new duality properties are established. Examples are given to illustrate these new properties. The topics covered in this paper include Gordon-Stiemke type th...

A ring is called n-perfect (n ≥ 0), if every flat module has projective dimension less or equal than n. In this paper, we show that the n-perfectness relate, via homological approach, some homological dimension of rings. We study n-perfectness in some known ring constructions. Finally, several examples of n-perfect rings satisfying special conditions are given.

Let K be a perfect field and let k ⊂ K be a subfield. In [4, Theorem 3.2], left finite dimensional simple two-sided k-central vector spaces over K were classified by arithmetic data associated to the extension K/k. In this paper, we continue to study the relationship between simple two-sided vector spaces and their associated arithmetic data. In particular, we determine which arithmetic data co...

The moment map is a mathematical expression of the concept of the conservation associated with the symmetries of a Hamiltonian system. The abstract moment map is defined from G-manifold M to dual Lie algebra of G. We will interested study maps from G-manifold M to spaces that are more general than dual Lie algebra of G. These maps help us to reduce the dimension of a manifold much more.