We introduce here a new approach to the study of m-quasi-invariants. This approach consists in representing m-quasi-invariants as N tuples of invariants. Then conditions are sought which characterize such N tuples. We study here the case of S3 m-quasi-invariants. This leads to an interesting free module of triplets of polynomials in the elementary symmetric functions e1, e2, e3 which explains c...

It is proved that any non-normable Fréchet space with a semisymmetric absolute basis is isomorphic to the space ω of all scalar sequences. A similar result is shown for quasi-homogeneous absolute bases. It is also proved that any nuclear Fréchet space with a semi-subsymmetric basis is isomorphic to ω.

In this paper we address the problem of a-migrativity (for a fixed a) for semicopulas, copulas and quasi-copulas. We introduce the concept of an a-sum of semicopulas. This new concept allows us to completely characterize a-migrative semicopulas and copulas. Moreover, a-sums also provide a means to obtain a partial characterization of a-migrative quasicopulas. 2010 Elsevier Inc. All rights reser...

Generalizing orthogonal arrays, a new class of arrays called quasiorthogonal arrays, are introduced and it is shown that fractional factorial plans represented by these arrays are universally optimal under a wide class of models. Some methods of construction of quasi-orthogonal arrays are also described.

We introduce quasi-cyclic codes of index 1 1 2 , construct such codes in terms of polynomials and matrices; and prove that the quasi-cyclic codes of index 1 1 2 are asymptotically good. MSC classes: 94B05, 94B65, 15B52.

Condition (C3) is called the 2–increasing property of C, and VC ([x1, x2]× [y1, y2]) is called the C–volume of the rectangle [x1, x2]× [y1, y2]. According to Sklar’s Theorem, copulas are functions that express the rankinvariant dependence between a pair of continuous random variables and, as such, they have been largely used in statistical applications . In particular, examples of copulas are g...

When the boundary of the curve complex is connected any quasi-isometry is bounded distance from a simplicial automorphism. As a consequence, when the boundary is connected the quasi-isometry type of the curve complex determines the homeomorphism type of the surface.