Hamiltonian group actions on symplectic Deligne–Mumford stacks and toric orbifolds

We develop differential and symplectic geometry of differentiable Deligne–Mumford stacks (orbifolds) including Hamiltonian group actions and symplectic reduction. As an application we construct new examples of symplectic toric DM stacks.     

From dynamic modulus via different relaxation spectra to relaxation and creep functions

The main goal of the paper is to compare predictive power of relaxation spectra found by different methods of calculations. The experimental data were obtained for a new family of propylene random copolymers with 1-pentene as a comonomer. The results of measurements include flow curves, viscoelastic properties, creep curves and rubbery elasticity of copolymer melts. Different relaxation spectra were calculated using independent methods based on different ideas. It lead to various distributions of relaxation times and their “weights”. However, all of them correctly describe the frequency dependencies of dynamic modulus. Besides, calculated spectra were used for finding integral characteristics of viscoelastic behaviour of a material (Newtonian viscosity, the normal stress coefficient, steady-state compliance). In this sense all approaches are equivalent, though it appears impossible to estimate instantaneous modulus. The most crucial arguments in estimating the results of different approaches is calculating the other viscoelastic function and predicting behaviour of a material in various deformation modes. It is the relaxation and creep functions. The results of relaxation curve calculations show that all methods used give rather similar results in the central part of the curves, but the relaxation curves begin to diverge when approaching the high-time (low-frequency) boundary of the relaxation curves. The distributions of retardation times calculated through different approaches also appear very different. Meanwhile, predictions of the creep curves based on these different retardation spectra are rather close to each other and coincide with the experimental points in the wide time range. Relatively slight divergences are observed close to the upper boundary of the experimental window. All these results support the conclusion about a rather free choice of the relaxation time spectrum in fitting experimental data and predicting viscoelastic behaviour of a material in different deformation modes. Received: 15 March 2000 Accepted: 18 September 2000     

Degradation of synthetic restoration materials in heterogenous systems

By the method of the optical spectrsocopy of diffuse reflection in the region 0.5–5.0 eV, accelerated aging of pigment compositions with synthetic materials used in restoration of paint layers of paintings is investigated. Composition containing pigments zinc and titanium oxides (white pigments), chromium oxide and copper carbonate (green pigments), and iron oxide (brown pigment) and reinforcing materials vinyl acetate-ethylene copolymer, fluorolon F-42L, and polyvinyl alcohol are investigated. It is established that the appearance of color in pigment impregnation and subsequent heating is observed only in the compositions of reinforcing materials with white pigments and occurs as a result of heterogeneous reactions that lead to the formation in the pigment of color centers bonded by oxygen vacancies. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 4, pp. 518–522, July–August, 1997.     

Submillimeter electron-nuclear excitation spectra in CsCdBr3:Ln3+ (Ln=Tm, Ho) crystals

The ESR spectra of single and pair impurity centers of thulium and holmium ions in CsCdBr₃:Tm³⁺ and CsCdBr₃:Ho³⁺ crystals are measured in the frequency range 160-400 GHz. Analysis of the characteristic features of the hyperfine structure of the ESR lines and analysis of the variations in the spectra as a function of the temperature and external magnetic field shows that the Ln³⁺ ions substitute for Cd²⁺ ions and predominantly form symmetric pair centers of the type Ln³⁺-(vacancy at a neighboring Cd²⁺ site)-Ln³⁺. The ESR spectra of CsCdBr₃: Ln³⁺ crystals are used to make a positive identification of the optical spectra of selective laser excitation. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 7, 535–540 (10 April 1997)     

Nuclear spin-lattice relaxation in germanium single crystals

The temperature dependence of the spin-lattice relaxation time corresponding to the inelastic scattering of phonons by the⁷³Ge quadrupole moment in Ge single crystals is calculated in the framework of the adiabatic bond charge model. The results obtained agree with the experimental data.     

Photochemistry of spiropyrans of the dithiolane series with polycondensed chromene fragments

It has been shown on the basis of determinations of the values of the quantum yields of the photocoloration of spiropyrans of the 1,3-dithiolane and benzo1,3-dithiolane series that the annelation of a benzene ring in the chromene part of the molecule results in an increase in the efficiency of photocoloration and an increase in the stability of the merocyanine forms of the compounds investigated.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 11, pp. 2504–2510, November, 1989.     

Quiver varieties and Lusztig's algebra

We study preprojective algebras of graphs and their relationship to module categories over representations of quantum SL(2). As an application, ADE quiver varieties of Nakajima are shown to be subvarieties of the variety of representations of a certain associative algebra introduced by Lusztig.     

Quantitative study of the photostability of spiropyrans

A quantitative method of determining the quantum yield of irreversible photodegradation (_C) of photochromic spiropyrans (SPP) was proposed for the first time. The _C of a large number of SPP of different types (with a different heterocyclic part) were determined. It was shown that for all of the SPP studied (except for dithiolane SPP), _C is almost independent of the heterocyclic part and is determined by the structure of the chromene part of the SPP. In addition to photodegradation, photooxidation takes place as a result of the reaction of the triplet state of the closed form of the SPP with O₂ for nitrosubstituted SPP of all types. The value of _C is determined by the efficiency of the reaction of isomer X of the colored form with the solvent or impurities, i.e., the lifetime of this isomer.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 2, pp. 290–298, February, 1990.     

Rheology of the Melt of Acrylonitrile–Styrene Copolymer Modified with Montmorillonite

The rheological properties of the acrylonitrile–styrene copolymer modified with hydrophobized montmorillonite Cloisite 30B and composites are studied in a wide range of shear rates and shear frequencies at a temperature of 230°C. It is shown that the filler insignificantly affects the viscoelastic properties of the compositions, but the viscosity of composite melts considerably increases at low shear rates and monotonically grows with increasing concentration, whereas at high shear rates the effective viscosity declines appreciably in the concentration range of about 0.3 vol %.