Two-Variable Identities in Groups and Lie Algebras

We study two-variable Engel-like relations and identities characterizing finite-dimensional solvable Lie algebras and, conjecturally, finite solvable groups and introduce some invariants of finite groups associated with such relations. Bibliography: 29 titles.     

The role of a vector-valued field in multidimensional universe geometry

For a model of the multidimensional universe we take a smooth manifold S which under the action of a compact Lie group G fibres into orbits of the same type G/H acquiring the structure of a fibre bundle with typical fibre G/H and base-the orbit space S/G (identified with the four-dimensional spacetime). The notion of a connection form on the fibre bundle SS/G is defined and its role for some geometrical structures on S is considered. In the framework of a theory of G-invariant tensor-type fields on S, it is shown that -being itself a field of this type-determines a dimensional reduction of the objects on S to objects on S/G.     

Study on the Kinetics of Non-isothermal Dehydration of Alkaline Earth Metal Selenites

The dehydration kinetics of crystallohydrates of beryllium, magnesium and calcium selenites were studied under non-isothermal conditions. The values of the activation energy of dehydration, the pre-exponential factor in Arrhenius equation and the change of entropy for the formation of the activated complex were calculated using the calculation procedure of Coats and Redfern. Thermal stability and activation energy of dehydration of the crystallohydrates were found to increase by the same order. The relationships observed were interpreted using Klopman’s generalized perturbation theory of chemical reactivity. The same theory was applied to explain the differences in the IR spectra of the selenite crystallohydrates studied.     

Thermal and calorimetric investigations on crystalline hydrates of barium hydroxide and their deuterated analogues

The thermal decompositions of Ba(OH)₂ · 8H₂O, Ba(OH)₂ · 8D₂O, Ba(OH)₂ · H₂O and Ba(OH)₂ · D₂O were studied and the phase transitions were identified by DSC and DTA methods. The corresponding enthalpy changes were determined and compared with those calculated from the thermodynamic data. A decrease of the thermal stability was demonstrated for the deuterated crystal hydrates in comparison with the normal ones.

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Zusammenfassung Die thermische Zersetzung von Ba(OH)₂ · 8H₂O, Ba(OH)₂ · 8D₂O, Ba(OH)₂ · H₂O und Ba(OH)₂ · D₂O wurde untersucht. Phasenübergänge wurden mittels DSC und DTA ermittelt. Die entsprechenden Enthalpieveränderungen wurden bestimmt und mit den aus thermodynamischen Daten berechneten Werten verglichen. Die deuterierten Kristallhydrate sind thermisch weniger stabil als die leichtes Kristallwasser enthaltenden Verbindungen.

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()₂ · 8₂, ()₂ · 8D₂O, Ba(OH)₂·H₂O Ba(OH)₂·D₂O. , . .

     

Potassium Fluoride Promoted Reaction of 3-Acylsubsti-Tuted 2H-1-Benzopyran-2-Ones with Acid Anhydrides. An Improved Method for the Synthesis of 4-(2-Oxoalkyl)-2H-Chroman-2-Ones. Part III1

The reaction of 3-acylsubstituted 2H-1-benzo-pyran-2-ones 1, 5 and 11a-c with acid anhydrides in the presence of potassium fluoride (KF)/molecular sieves 4A gives the 4-(2-oxoalkyl)-2-oxochromans 2, 6 and 12a-c as the main products. Also the 3-carboxylic acid derivatives, such as esters and N,N-dialkylamides, of 2H-1-benzopyran-2-one (11d-g) react with isobutyric acid anhydride in the presence of KF/molecular sieves 4A to give the corresponding 2-oxochroman-4-acetic acid derivatives.     

Polarization reflection holographic gratings in azobenzene-containing gelatine films

We have written polarization reflection holograms in an azobenzene-containing material. Two waves with circular polarization were used to record the gratings; the light resulting from their overlap induces chirality in the samples. The holographic reflection of the polarization gratings has the properties of Bragg reflection in cholesteric liquid crystals.     

Photoinduced dichroism in lightsensitive suspension layers of As2S3 dispersed in gelatin

The absorption edge shift and the spectra of the dichroism in suspension layers of As₂S₃ dispersed in gelatin induced by a linearly polarized laser light are measured. The results are compared to the photoinduced changes in evaporated As₂S₃ layers.     

On Clarkson's inequality,type and cotype for the Edmunds-Triebel logarithmic spaces

We show that the (p, p') Clarkson's inequality holds in the Edmunds-Triebel logarithmic spaces A_q(logA)_b,q A_{\theta}({\log}A)_{b,q} and in the Zygmund spaces L_p(logL)_b(W) L_p({\log}L)_b(\Omega) , for b ? \mathbbR b \in \mathbb{R} and for suitable 1 ￡ p ￡ 2 1 \leq p \leq 2 . As a consequence of these results we also obtain some new information about the types and the cotypes of these spaces.     

Polarisation-sensitive optical elements in azobenzene polyesters and peptides

In this article, we describe fabrication of polarisation holographic optical elements in azobenzene polyesters. Both liquid crystalline and amorphous side-chain polyesters have been utilised. Diffractive optical elements such as lenses and gratings that are sensitive to the polarisation of the incident light have been fabricated with polarisation holography. Computer-generated optical elements and patterns have also been written with a single polarised laser beam. Recording of polarisation defects enabling easy visualisation is also shown to be feasible in azobenzene polyesters.     

Influence of the type of light polarization on photoinduced processes

We investigate the influence of the type of light polarization (linear or circular) on the efficiency of non-linear optical processes in photoanisotropic materials. A theoretical model of photoprocesses in materials in which optical non-linearity is related to absorbing centres with intrinsic linear anisotropy is constructed. Theoretical calculations show that the photostationary concentration of the photoproducts (and the mean values of the non-linear changes in optical constants) in these materials is higher if the exciting light is circularly polarized. Experimental results on non-linear processes in samples of fluorescein incorporated in orthoboric acid and in azodye/polymer layers are in good agreement with the theory. This revised version was published online in November 2006 with corrections to the Cover Date.