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.     

The Asymptotics of Spectral Gaps of a 1D Dirac Operator with Cosine Potential

Letters in Mathematical Physics -     

Tau Function Solutions to a q-Deformation of the KP Hierarchy

We construct tau-function solutions to the q-KP hierarchy as deformations of classical tau functions.     

Enhanced specificity of bacterial spore identification by oxidation and mass spectrometry

Addition of an oxidizing agent (e.g., hydrogen peroxide) to intact spores selectively and completely oxidizes Met-containing biomarker proteins by formation of Met sulfoxides. This reaction increases the masses of the biomarker proteins observed in matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS) of Bacillus spores by Deltam = (16 x n) Da, where n is the number of Met residues in the sequence of each individual protein. The procedure is very rapid, and can be performed in situ (i.e., on the MALDI target). It confirms the identity of individual biomarkers by comparing the number of Met amino acids from the experimentally determined mass shifts with predictions for n from the tentative amino acid sequence for each protein. In turn, accurate determination of n for several biomarkers allows rapid validation of the initial spore identification by MALDI-MS.     

Thermal analysis of diazo pigments

The differential-thermal and thermogravimetric analysis of eight derivatives of 1,4-bis-(8′-hydroxy-3′,6′-disulpho-1′-naphthyl)-benzenediamide showed that these compounds have a marked exothermic effect, with maxima in the temperature range 290–340°C. The 4-nitroaniline derivative was found to undergo a blast-like decomposition in the temperature interval 285–295°C, reflected by large steps in the TG curves. The thermal analysis of diazo pigments permits determination of their applicability at higher temperatures.     

Thermal analysis of disazo pigments

The differential-thermal and thermogravimetric analysis of eight derivatives of 1,4-bis-(5-hydroxy-7-sulpho-2naphthyl)-benzenediamide showed that these compounds have a marked exothermic effect, with maxima in the temperature range 280–330°C. The derivative of 4-nitroaniline-2-sulphonic acid were found to undergo a blast-like decomposition in the temperature intervals 255–265°C and 285–290°C, which is reflected by large steps in their TG curves.The thermal analysis of disazo pigments permits determination of their applicability at higher temperatures.

---

Zusammenfassung Die DT- und TG- Analyse von acht Derivaten von 1,4-bis-(5-Hydroxy-7-sulpho-2naphthyl)-benzoldiamid zeigte, dass diese Verbindungen mit einem Maximum im Temperaturbereich 280–330°C einen eindeutigen exothermen Effekt aufweisen. Derivate mit 4-Nitroanilin-2-sulfonsäure zeigen eine explosionsartige Zersetzung im Temperaturintervall 255–265°C und 285–290°C, was sich in den TG-Kurven in einer großen Stufe wiederspiegelt.Die Thermoanalyse von Bisazopigmenten ermöglicht eine Ermittlung ihrer Anwendbarkeit für höhere Temperaturen.

     

Chemometrical approaches to evaluate analytical data from aquatic macrophytes and marine algae

The possibility of using aquatic macrophytes and algae as bioindicators of water pollution is investigated. The use of cluster analysis enables the treatment of the analytical data in a global way, revealing hidden clusters of similar behaviour between various biological species or sampling sites. A great number of species was collected from four rivers and fourteen coastal sites in Greece and were analysed for zinc, copper, cadmium, lead and manganese. The analytical data obtained were treated by hierarchical clustering, for marine algae and aquatic macrophytes separately.     

Environmetric modeling of emission sources for dry and wet precipitation from an urban area

Monitoring data from chemical analysis of rainwater and aerosol samples collected in an urban area have been interpreted by the use of environmetric approaches. An attempt was done to compare the data set structures of both type of precipitation and to estimate the contribution of different anthropogenic and naturally occurring emission sources to the total mass of the wet and dry precipitation. It was found that three latent factors explaining over 80% of the total variance of the set are responsible for the rainwater set structure-'sea spray', 'soil dust', and 'anthropogenic'. Only two were the latent factors explaining the dominant part of the variance in the case of aerosol samples-'anthropogenic' and 'natural'. It is shown that the anthropogenic influence for aerosol samples is more complex that that of rainwater samples and represents interaction between typical anthropogenic sources and natural emitters. Additionally, a source apportioning using multiple regression on absolute principal component scores is performed in order to obtain qualitative information about the impact of the different identified emission sources on the urban environment.     

CTI: A novel charge-related topological index with low degeneracy

A new type of topological index is proposed. Its definition is based on the concept of atomic charge distributions in organic molecules. Introduction of electronic in addition to purely topologic factors allows consideration of heteroatom-containing structures as well. It is demonstrated that the index has a low degree of degeneracy, thus suggesting it can be used for coding chemical structures, discrimination of redundancies in structure generation programs, and studies of quantitative structure-activity relationships for heteroatom-containing structures.     

Observations on toxicologically relevant arsenic in urine in adult offspring of families with Balkan Endemic Nephropathy and controls by batch hydride generation atomic absorption spectrometry

The aim of this study was to develop a method for the characterization of internal exposure to arsenic, which is thought to play a role in the development of a kidney disease, known as Balkan Endemic Nephropathy, typical for a district in Bulgaria, and to investigate whether the As body burden differs in the offspring versus control individuals. For this case study, an analytical procedure for the determination of toxicologically relevant arsenic (the sum of arsenite, arsenate, monomethylarsonate, and dimethylarsinate) in urine by batch-type hydride generation atomic absorption spectrometry was developed. Optimization experiments for levelling off the sensitivity of inorganic arsenic and its mono- and dimethylated species in dilute HCl–L-cysteine medium were performed. The limit of detection for hydride forming arsenic fraction was 0.5?ng As, i.e. 0.25?µg?L^?1 in 10?mL of 1?+?4 v/v diluted urine. The relative standard deviation was typically 1.5–1.8% for aqueous solution and 2–6% for urine samples at 1.0?µg?L^?1 As. The sample throughput rate was 15?h^?1. No statistical correlation and cross-correlation between individuals case-control and sex at 95% confidence were found: controls (n?=?99), mean 3.5?±?2.1 (SD), range 0.9–10.4, median 3.0?µg?L^?1 As and cases (n?=?102), mean 3.6?±?2.2 (SD), range 0.5–11.0, median 3.2?µg?L^?1 As. On the basis of this study, arsenic can be excluded as a factor involved in BEN development.