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.     

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.     

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.     

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.     

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.     

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. , . .

     

In Vitro Antineoplastic and Antiviral Activity and In Vivo Toxicity of Geum urbanum L. Extracts

This study evaluated the in vitro antineoplastic and antiviral potential and in vivo toxicity of twelve extracts with different polarity obtained from the herbaceous perennial plant Geum urbanum L. (Rosaceae). In vitro cytotoxicity was determined by ISO 10993-5/2009 on bladder cancer, (T-24 and BC-3C), liver carcinoma (HEP-G2) and normal embryonic kidney (HEK-293) cell lines. The antineoplastic activity was elucidated through assays of cell clonogenicity, apoptosis induction, nuclear factor kappa B p65 (NFκB p65) activation and total glutathione levels. Neutral red uptake study was applied for antiviral activity. The most promising G. urbanum extract was analyzed by UHPLC–HRMS. The acute in vivo toxicity analysis was carried out following OEDC 423. The ethyl acetate extract of aerial parts (EtOAc-AP) exhibited the strongest antineoplastic activity on bladder cancer cell lines (IC₅₀ = 21.33–25.28 µg/mL) by inducing apoptosis and inhibiting NFκB p65 and cell clonogenicity. EtOAc and n-butanol extracts showed moderate antiviral activity against human adenovirus type 5 and human simplex virus type I. Seventy four secondary metabolites (gallic and ellagic acid derivatives, phenolic acids, flavonoids, etc.) were identified in EtOAc-AP by UHPLC–HRMS. This extract induced no signs of acute toxicity in liver and kidney specimens of H-albino mice in doses up to 210 mg/kg. In conclusion, our study contributes substantially to the detailed pharmacological characterization of G. urbanum, thus helping the development of health-promoting phytopreparations.     

Influence of Gamma Irradiation on Different Phytochemical Constituents of Dried Rose Hip (Rosa canina L.) Fruits

Gamma irradiation is efficiently applied to many foods, but nevertheless there is a distinct lack of information about the changes of macro- and micronutrients (e.g., carbohydrates, lipids, organic acids, and phenolics) in dried rose hip (RH) fruits. Therefore, in this study, for the first time, the effect of gamma irradiation (10 and 25 kGy) on RH constituents is investigated. Different analytical techniques (GC-FID, HPLC-UV, HPSEC-RID, IR-FT, and SEM) are employed to examine this effect. The irradiation treatment (10 kGy) increased the glucose content by 30% and released cellobiose from RH fruits, thus revealing cellulose destruction. The extractability of total uronic acids increased from 51% (control) to 70.5% (25 kGy-irradiated), resulting in a higher pectin yield (10.8% < 12.8% < 13.4%) and molecular heterogeneity. Moreover, de-esterification was not a major effect of the irradiation-induced degradation of pectin. The sample exposure to the highest dose did not change the content of total carotenoids, β-carotene, and (un)saturated fatty acids, but it affected the tocopherols levels. Gamma rays had a negligible effect on the phenolic constituents and did not affect ORAC and HORAC antioxidant activity. In conclusion, it can be compromised that the exposition of dried RH is safe and can be successfully applied to decontaminate fruits without affecting their nutritional value and biological activity.     

Difference Equations and Discriminants for Discrete Orthogonal Polynomials

We prove that any set of polynomials orthogonal with respect to a discrete measure supported on equidistant points contained in a half line satisfy a second order difference equation. We also give a discrete analogue of the discriminant and give a general formula for the discrete discriminant of a discrete orthogonal polynomial. As an application we give explicit evaluations of the discrete discriminants of the Meixner and the Hahn polynomials. A difference analogue of the Bethe Ansatz equations is also mentioned.Research partially supported by NSF grant DMS 99-70865