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.     

Metastable phase in the quantum Hall ferromagnet

Time-dependent capacitance measurements reveal an unstable phase of electrons in gallium arsenide quantum well that occurs when two Landau levels with opposite-spin are brought close to degeneracy by applying a gate voltage. This phase emerges below a critical temperature and displays a peculiar non-equilibrium dynamical evolution. The relaxation dynamics is found to follow a stretched-exponential behaviour and correlates with hysteresis loops observed by sweeping the magnetic field. These experiments indicate that metastable randomly distributed magnetic domains with peculiar excitations are involved in the relaxation process in a way that is equivalently tunable by a change in gate voltage or temperature.     

On a model of phase relaxation for the hyperbolic Stefan problem

In this paper we study a model of phase relaxation for the Stefan problem with the Cattaneo–Maxwell heat flux law. We prove an existence and uniqueness result for the resulting problem and we show that its solution converges to the solution of the Stefan problem as the two relaxation parameters go to zero, provided a relation between these parameters holds.     

Generation of analytic semigroups by degenerate elliptic operators

We consider the generation of analytic semigroups by degenerate elliptic operators satisfying a uniform H?rmander condition under homogeneous Dirichlet boundary conditions. Received January 12, 1996     

5-vinylisoxazole

Cycloaddition of fulminic acid to 1-butyn-3-ol gave a mixture of 5-α-hydroxyethylisoxazole (I) and 4-α-hydroxyethylisoxazole (II) in the ratio 9:1. By the dehydration of 1, 5-vinylisoxazole (III) was obtained. Compound III has also been prepared by cyclization of 4-penten-2-ynal as well as its diethylacetal with hydroxylamine hydrochloride; in both instances no isomers have been obtained. Compound III spontaneously polymerizes even at room temperature yielding a polymer still containing isoxazole rings.     

The use of “actinometer” gases in optical diagnostics of plasma etching mixtures: SF6-O2

The spectroscopic emission intensities from excited F atoms in SF₆-O₂ discharges at 1 torr have been correlated to the densities of atoms in their ground electronic state by measuring the excitation efficiencies of the electrons in the energy range 11 to 17 eV with a method which essentially consists in the analysis of the emission of Ar or N₂, added as actinometer gases to the discharge mixtures. The general applicability of the method has been tested by a direct titration of F atoms with chlorine. The spectroscopic analysis has allowed the determination of useful information on the trends of both the electron densities and their energies as a function of the oxygen percent in the feed.     

Chemical Composition and Evaluation of Insecticidal Activity of Calendula incana subsp. maritima and Laserpitium siler subsp. siculum Essential Oils against Stored Products Pests

The problems of the environment and human health related to the use of synthetic and broad-spectrum insecticides have increasingly motivated scientific research on different alternatives and among these, the use of green systems, such as essential oils, have been explored. Several species of the Apiaceae and Asteraceae families, aromatic herbs rich in secondary bioactive metabolites, are used in the industrial field for pharmaceutical, cosmetic, and food purposes. Different essential oils extracted from some species of these families have shown acute toxicity and attractive and/or repellent effects towards different insects. In our work, we investigated the toxic potential of Calendula incana subsp. maritima and Laserpitium siler subsp. siculum essential oils against four insect species, Sitophilus oryzae, Lasioderma serricorne, Necrobia rufipes, and Rhyzoperta dominica, which are common pests of stored products. The composition of both oils, extracted by hydrodistillation from the aerial parts of the two plants, was evaluated by GC×GC-MS. Calendula incana subsp. maritima essential oil was rich in oxygenated sesquiterpenoids, such as cubebol (35.39%), 4-epi-cubebol (22.99%), and cubenol (12.77%), while the Laserpitium siler subsp. siculum essential oil was composed mainly of monoterpene hydrocarbons, such as β-phellandrene (42.16%), limonene (23.87%), and β-terpinene (11.80%). The toxicity Petri dish bioassays indicated that C. maritima oil killed a mean of 65.50% of S. oryzae and 44.00% of R. dominica adults, indicating a higher biocidal activity in comparison with L. siculum oil, while toward the other species, no significant differences in mortality were recorded. Calendula maritima oil could be, then, considered a promising candidate for further tests as an alternative biocide toward S. oryzae and R. dominica. The possibility that the relatively high content of oxygenated sesquiterpenoids in C. maritima essential oil determines its higher biocidal activity is discussed.