A method for calculating invariant subspaces of symmetric hyperbolic equations

An algorithm is constructed for calculating invariant subspaces of symmetric hyperbolic systems arising in electromagnetic, acoustic, and elasticity problems. Discrete approximations are calculated for subspaces that correspond to minimal eigenvalues and smooth eigenfunctions. Difficulties related to the presence of an infinite-dimensional kernel in the differential operator are successfully handled. The efficiency of the algorithm is demonstrated using acoustics equations.     

S1←S0 vibronic spectra and the vapor-state molecular structure of propanal and 2-methylpropanal

The vapor-state absorption spectra have been recorded for propanal PA and 2-methylpropanal MP with path lengths up to 120 m. The initial points in the S₁S₀ electronic transitions have been identified together with various fundamental vibrational frequencies of the PA and MP conformers. They contain nonplanar aldehyde groups in the S₁ states with inversion potential barriers of about 600 cm^–1. The parameters of the internal-rotation potential functions in the S₁ states have been determined, and the corresponding potential functions in the S₀ states have been refined.Chemical Faculty, Lomonosov Moscow University. Translated from Zhurnal Strukturnoi Khimii, Vol. 34, No. 1, pp. 20–25, January–February, 1993.     

S1←S0 Vibronic spectra and the structure of acetyl fluoride-h3 and acetyl fluoride-d3 molecules

UV absorption spectra of acetyl fluoride-h₃ and -d₃ (CH₃COF and CD₃COF) molecules in the region of S₁S₀ electronic transitions are investigated. The origins (0⁰ ₀ or 14^0± ₀) of these transitions are observed at 39912 and 39904 cm^–1, respectively, and some of the fundamental frequencies of these molecules in the s₀ and S₁ states are determined. In particular, the systems of torsion and inversion (out-of-plane C=O vibrations) energy levels are studied. The geometric parameters of an acetyl fluoride-h₃ molecule in the S₁ state are estimated by the theoretical simulation of the rotational contours of the 0⁰ ₀ (14^0± ₀) band. These data are used to evaluate the potential barriers to internal rotation in the S₀ and S₁ states, which were found to be 360 and 560 cm^–1 for acetyl fluoride-h₃ and 380 and 770 cm^–1 for acetyl fluoride-d₃, respectively, as well as the potential barriers to inversion in the S₁ states, which were found to be 2090 and 2370 cm^–1 for acetyl fluoride-h₃ and acetyl fluoride-d₃, respectively.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 11, pp. 1957–1964, November, 1994.In conclusion, the authors would like to acknowledge T. S. Kuznetsova for the synthesis and purification of the AF samples.The research presented here was supported in part by the International Science Foundation under grant No. MJ 1000.     

Reinterpretation of the fluorescence excitation spectrum of hexafluorobiacetyl in a supersonic jet

The results of the analysis of the fluorescence excitation spectrum of trans-hexafluorobiacetyl published earlier are revised. New values of torsion frequencies and potential barriers of internal rotation of the CF₃ group in the ground and excited states of the molecule are obtained. A procedure for calculating the probabilities of torsional vibronic transitions of molecules is described. Translated fromZhurnal Struktumoi Khirnii, Vol. 38, No. 2, pp. 293–302, March–April, 1997.     

Application of vibronic spectroscopy to conformational analysis. Investigations of molecules of carbonyl compounds

Application of vibronic spectroscopy to the conformational analysis of molecules in the ground and excited electronic states is reviewed. The basic concepts of the method as well as its methodological and technical aspects are discussed. The abilities of vibronic spectroscopy are exemplified by the results obtained for molecules of carbonyl compounds.The review is based on a report at the Vibrational Spectroscopy Conference dedicated to the 80th birthday of B. I. Stepanov (Minsk, Belarus', October 3–5, 1993).Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 783–791, May, 1994.This work was performed with the partial financial support of the Russian.Universities State Program.     

Symmetrization of the nonlinear system of gas dynamics equations

We describe a method for representing the nonlinear system of gas dynamics equations in quasilinear form with symmetric coefficient matrices and, moreover, with a positive definite matrix at the time derivative.     

Vibronic spectra, ab initio calculations, and structures of conformationally non-rigid molecules of oxalyl halides in the ground and lowest excited electronic states - Part VI: Oxalyl bromide (COBr)2 and summary

The structure of oxalyl bromide (COBr)₂ in the ground and four lowest excited electronic states was theoretically investigated using the CASPT2/cc-pVTZ-DK method. Structural information obtained allowed the reassignment of the and vibronic absorption spectra. Generalization of oxalyl halide structural data for the ground and excited electronic states is presented.     

Shock structure in a viscoelastic medium with a nonlinear dependence of the Maxwellian viscosity on the parameters of the material

The shock-profile structure in a viscoelastic medium with a nonlinear dependence of the Maxwellian viscosity (a quantity inverse to the tangential stress-relaxation time ) on the substance parameters is investigated in this paper on the basis of a model proposed in [1]. The presence of such a dependence of the relaxation time permitted the extraction of sections with an abrupt change in the quantities on the profile, called plastic waves, by using additional relationships. The model of the isotropic medium used is characterized by an equation of state in the form of a dependence of the density of the internal energy E per unit mass on the strain-tensor invariants and the entropy S.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 101–108, September–October, 1974.