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.     

Darstellung,Struktur und Reaktionsfähigkeit einiger Metall(I)- und-(II)-Derivate des Diäthylphosphono-Acetons

Metalation of diethylphosphono-acetone (DÄPA) with potassium or lithium in benzene and with KNH₂, LiNH₂, or calcium in liquid ammonia afforded the metal derivatives ofDEPA, which were isolated in a pure state. Their structure has been investigated by i.r.- and¹H n.m.r.-spectroscopy. In solution metallotropic conversion of thecis-enolate chelates intotrans-enolates and C-forms occurs. The reactivity of these metal derivatives towards some alkylating and acylating reagents as well towards carbonyl compounds has been investigated.

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Diese Mitteilung ist z. T. Inhalt der Diplomarbeit vonI. Velinov, Univ. Sofia (1968).     

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.     

Reconstruction of scattering properties of rough air-dielectric boundary

The article is devoted to elaboration of the method of reconstruction of rough surface scattering properties. The object with rough surface is made of transparent dielectric material. Typically these properties are described with bi-directional scattering distribution function (BSDF). Direct measurement of such function is either impossible or very expensive. The suggested solution provides physically reasonable method for the rough surface BSDF reconstruction. The method is based on Monte-Carlo ray tracing simulation for BSDF calculation. Optimization technique is further applied to correctly reconstruct the BSDF. The results of the BSDF reconstruction together with measurement results are presented in the article as well.     

Olefin Synthesis via,the Li-Derivative of N,N,N′,N′-Tetramethyldimides of Arylmethanephosphonic Acids

Abstract

The high erythro-stereoselective reaction of Li-tetramethyldiamides of arylmethanephosphonic acids with carbonyl compounds is used for synthesis of (Z)-alkenes by thermolysis of the erythro-adducts as well as in acidic media.     

2,5-Dihydro-1,2-oxaphosphole Derivatives in the Reaction of 3,3-Disubstituted Allenylphosphonic Amidoesters with Electrophilic Reagents

Abstract

The reaction of 3,3-disubstituted allenylphosphonic amidoesters with halogenes, sulfenyl and selenenylchlorides proceeds with five-membered heterocyclization and formation of 2-N,N-dialkylamino-2,5-dihydro-1,2-oxaphosphole 2-oxides:     

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.