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 -     

On the applicability of deep-level transient spectroscopy for the investigation of deep centers in silicon created by fast neutron irradiation

Deep-Level Transient Spectroscopy (DLTS) measurements were carried out on silicon p⁺nn⁺ diodes before and after irradiation with fast neutrons at room temperature with fluences 5.5×10¹¹ and 1.0×10¹² n/cm². It was found out, that all preexisting defects decreased their amplitudes during irradiation, while only one defect, identified as a single-charged divacancy, increased in amplitude. An interpretation is proposed in terms of the cluster model, and the applicability of the DLTS is discussed.     

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.     

Raman and parametric emission from excited states induced by collisions

A collisional energy transfer in the wings of Na 3p and between Na₂ A ¹ _u ⁺ and na 3p states has been used to excite a number of stimulated emissions in the near-ir region of 800–850 nm. The detailed study reveals Raman and parametric emission involving 3p, 3d, 4p, and 4d levels of Na. Two tunable dye lasers in the visible provide the pump waves.     

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.     

On kinetics of the photodissociation iodine laser

The kinetics of iodine laser amplifiers is examined by solving the time evolution equations of chemical kinetics during optical pumping. The pumping radiation intensity is modelled by a black body of the temperature varying in time (corresponding to the flash lamp pulse). A brief comparison is made of pumping effects by long and short light pulses. Pumping by the long pulse is studied in more detail and it is found that there exists an optimum pulse strength beyond which the inversion in the laser mixture no longer grows appreciably, only its lifetime is shortened. In this connection the effect of pyrolysis of the alkyliodide molecule is also discussed. The pyrolysis is found to occur under very strong illumination, but it does not interfere with the photolytic decomposition and the optimum laser action. Finally, the influence of the reaction rate constants is studied in a systematic way and only few of them are found to carry real weight.The authors are obliged to Drs. S. V. Kuznetsova and A. I. Maslov who were consulted on the values of the reaction constants and who also drew our attention to some of the references.     

Sublimation enthalpy of dye molecules measured using fluorescence

We present an in-flight fluorescence detection scheme for molecular beams which is applied to determine the enthalpy of sublimation of dye molecules. We investigate tetraphenylporphyrin (TPP), porphine, and nile red, which are believed to be suitable candidates for molecular de Broglie wave interferometry. The measured values are H(sub)(TPP)=142+/-3 kJ/mol, H(sub)(porphine)=87+/-3 kJ/mol, and H(sub)(nile red)=66+/-2 kJ/mol. For TPP, sublimation enthalpies differ in the literature by more than a factor of 2. Our measurements confirm a value at the lower end of this scale. We discuss changes in the character of the molecular flow with the source temperature as a prime reason for discrepancies in the published data.     

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.