q-polymatroids and their relation to rank-metric codes

Journal of Algebraic Combinatorics - It is well known that linear rank-metric codes give rise to q-polymatroids. Analogously to matroid theory, one may ask whether a given q-polymatroid is...     

Phase behavior and chain dynamics of elastin-like peptides versus amino acid sequences

Journal of Thermal Analysis and Calorimetry - Elastin fibrillogenesis is conditioned by multiple self-assembly processes. Previous studies have evidenced the crucial influence of amino acid...     

Influence of homocysteine on the physical structure and molecular mobility of elastin network in cultured arteries

The thermal and dielectric properties of the elastin network were investigated in arteries cultured with physiological and pathological concentrations of homocysteine, an aminoacid responsible of histological impairments in human arteries. The glass transition of this amorphous protein was investigated by Differential Scanning Calorimetry (DSC). To explore the molecular dynamics of the elastin network in the nanometer range, we used Thermally Stimulated Currents (TSC), a dielectric technique running at low frequency and measuring the dipolar reorientations in proteins subjected to a static electrical field. Combining TSC and DSC experiments with determination of the activation parameters of relaxation times reveals the molecular mobility of the proteins. The major differences in the relaxation behavior of elastin between arteries cultured with physiological and pathological concentrations of homocysteine are discussed.     

General covariant derivatives for general connections

In this paper we introduce the general covariant derivatives of vertical-valued tensor fields with respect to a general connection on a fibered manifold and a classical connection on the base. We prove that the general covariant derivatives satisfy the general Ricci and the general Bianchi identities.     

An Algebraic Approach to Physical Scales

This paper is aimed at introducing an algebraic model for physical scales and units of measurement. This goal is achieved by means of the concept of “positive space” and its rational powers. Positive spaces are “semi-vector spaces” on which the group of positive real numbers acts freely and transitively through the scalar multiplication. Their tensor multiplication with vector spaces yields “scaled spaces” that are suitable to describe spaces with physical dimensions mathematically. We also deal with scales regarded as fields over a given background (e.g., spacetime).     

Thermal and vibrational characterization of human skin

For a better understanding of the molecular and organizational changes in human dermis, biophysical methods were tested. The aim of this study was to find suitable and reproducible biomarkers for further clinical studies on intrinsic and extrinsic aging of dermis. Thermoporometry, hydric organization and thermal transitions of fresh and frozen skins were determined by differential scanning calorimetry (DSC). Fourier transform infrared spectroscopy (FTIR) was used to identify the absorption bands of the dermis especially in the 1800–1000 cm^?1 zone and to discriminate between the different secondary structures of proteins. A widening of the pore size distribution is evidenced with freezing, but there is no significant difference between the hydric organization and the endothermic collagen denaturation of fresh and frozen skins. The global FTIR spectra and the second derivative spectra in the scanned zone are also identical in fresh and frozen dermis, validating the storage protocol. DSC and FTIR are well-suited techniques to characterize human skin, giving accurate results with high reproducibility. The acquisition of thermal and vibrational biomarkers of the skin at the mesoscale and nanoscale contributes to its better knowledge and is promising for further studies on skin aging.     

Higher order valued reduction theorems for classical connections

We generalize reduction theorems for classical connections to operators with values in k-th order natural bundles. Using the 2nd order valued reduction theorems we classify all (0,2)-tensor fields on the cotangent bundle of a manifold with a linear (non-symmetric) connection. This paper has been supported by the Grant Agency of the Czech Republic under the Project number GA 201/02/0225.     

Natural operations with projectable tangent valued forms on a fibred manifold

Summary Let p: EB be a fibred manifold. Then, we consider the sheaf (E)=(B)P(E) of (local) projectable tangent valued forms on E, where (B) is the sheaf of (local) differential forms on B andP(E) is the sheaf of (local) projectable vector fields on E. The Frölicher-Nijenhuis bracket makes (E) to be a sheaf of graded Lie algebras [18]. In this paper we study all natural R -bilinear operations on (E) which are of Frölicher-Nijenhuis type. By using the analytical method of [16], we prove that there is a three-parameter family of such operators on (E). As a consequence, we obtain a result on the unicity of the covariant differential of tangent valued forms and of the curvature associated with a given connection on E. All manifolds and mappings are assumed to be infinitely differentiable.This paper has been written during the author's visit at the Institute of Applied Mathematics «Giovanni Sansone». Florence, Italy. The author would like to thank ProfessorMarco Modugno for his kind hospitality and for stimulating discussions.