Involutions for upper triangular matrix algebras

In this paper we describe completely the involutions of the first kind of the algebra UT_n(F) of n×n upper triangular matrices. Every such involution can be extended uniquely to an involution on the full matrix algebra. We describe the equivalence classes of involutions on the upper triangular matrices. There are two distinct classes for UT_n(F) when n is even and a single class in the odd case.Furthermore we consider the algebra UT₂(F) of the 2×2 upper triangular matrices over an infinite field F of characteristic different from 2. For every involution *, we describe the *-polynomial identities for this algebra. We exhibit bases of the corresponding ideals of identities with involution, and compute the Hilbert (or Poincaré) series and the codimension sequences of the respective relatively free algebras.Then we consider the *-polynomial identities for the algebra UT₃(F) over a field of characteristic zero. We describe a finite generating set of the ideal of *-identities for this algebra. These generators are quite a few, and their degrees are relatively large. It seems to us that the problem of describing the *-identities for the algebra UT_n(F) of the n×n upper triangular matrices may be much more complicated than in the case of ordinary polynomial identities.     

Higher order bad loci

Zero-schemes on smooth complex projective varieties, forcing all elements of ample and free linear systems to be reducible, are studied. Relationships among the minimal length of such zero-schemes, the positivity of the line bundle associated with the linear system, and the dimension of the variety are established. Bad linear spaces are also investigated.     

Error estimate for the approximation of nonlinear conservation laws on bounded domains by the finite volume method

In this paper we derive a priori and a posteriori error estimates for cell centered finite volume approximations of nonlinear conservation laws on polygonal bounded domains. Numerical experiments show the applicability of the a posteriori result for the derivation of local adaptive solution strategies.

     

A fractal analysis of skin pigmented lesions using the novel tool of the variogram technique

The incidence of the cutaneous malignant melanoma is increasing rapidly in the world [Ferlay J, Bray F, Pisani P, et al. GLOBOCAN 2000: Cancer incidence, mortality and prevalence worldwide, Version 1.0 IARC Cancer Base no. 5. Lyon: IARC Press, 2001]. The therapeutic address requires a method having high sensitivity and capability to diagnose such disease at an early stage. We introduce a new diagnostic method based on non-linear methodologies. In detail we suggest that fractal as well as noise and chaos dynamics are the most important components responsible for genetic instability of melanocytes. As consequence we introduce the new technique of the variogram and of fractal analysis extended to the whole regions of interest of skin in order to obtain parameters able to identify the malignant lesion. In a preliminary analysis, satisfactory results are reached.     

Organometallic complexes in ascidian embryonic development: II. Effects on different stages and larvae

The effects of the organometallic compounds Bu₂Sn-D -(?;)sorbitol, Bu₂Sn-D -(+)glucose, Bu₂Sn-D -(?)fructose and Bu₂Sn-D -(+)glyceraldehyde were tested in vivo on different stages of Ascidian development, larval movement and metamorphosis. Organotin(IV) complexes are organometallic compounds widely used as industrial biocides, antifouling agents and agricultural fungicides and are toxic to a range of organisms. Two-cell stage embryos, if incubated for one hour in the organotin (IV) solutions, stopped the cleavage, which was restored when they were transferred into normal sea water. The gastrula stage was seriously affected in 10^?4mol dm^?3 solutions of the above-mentioned complexes: 85% of the embryos were anomalous neurulae with open neural folds, 5% were twisted larvae. The gastrulae, when incubated for 1 h in 10^?5mol dm^?3 solutions, developed twisted larvae in ovular envelopes and immobile larvae with twisted tails. Larvae treated with 10^?4mol dm^?3 and 10^?5 mol dm^?3 Bu₂Sn-D -(?)sorbitol, Bu₂Sn-D -(+)glucose and Bu₂Sn-D -(+)glyceraldehyde solutions stopped swimming, did not metamorphose and afterwards underwent cytolysis. An initial hyperactivity of circular movements, followed by immobility, was observed in the larvae incubated in Bu₂Sn-D -(?;)fructose.     

Crystal-field induced dipoles in heteropolar crystals I: Concept

The electrostatic part of the internal energy of heteropolar crystals is largely assumed to be purely of the Coulomb or monopole type. Here, it is argued, ions in a crystal lattice may not only bear a net charge, but also higher electrostatic moments. This applies explicitly for dipole moments. Dipoles are assumed to occur only for ions on lattice sites where the point symmetry allows a non-vanishing crystal electric field to cause a polarization. Infinite lattice sums that account for the electrostatic interaction between point charges and dipoles are given, with the Madelung constant being the first of them in a more general Taylor expansion. An expression for the binding energy of heteropolar solids is hereby presented. The share due to induced dipoles is always negative if dipole-dipole interactions are neglected, i.e. it increases the strength of crystal binding. The concept, which is developed for crystals of arbitrary symmetry is explained on the basis of the examples (i) sphalerite (ZnS), (ii) pyrite (FeS₂), (iii) rutile (TiO₂), and (iv) orthorhombic La₂CuO₄.     

On commutativity in point-reflection geometries

To any spatial point-reflection geometry there corresponds a determined commutative kinematic space.Dedicated to Professor Raphael Artzy on his 80^th birthday.Research supported by the NATO Scientific Affairs Division grant CRG 900103.