How One can Repair Non-integrable Kahan Discretizations. II. A Planar System with Invariant Curves of Degree 6

Mathematical Physics, Analysis and Geometry - In this paper, we develop the dressing method to study the modified Camassa-Holm equation with the help of reciprocal transformation and the associated...     

Scalar Perturbations in Inflationary Models Based on the Non-Linear Sigma Model

The inflationary models based on the non-linear sigma model with the self-coupling potential are considered. The slow-roll solutions for long-wavelength inhomogeneities in general two-component chiral models and diagonal three-component chiral model of a special case are obtained. Scalar perturbations are calculated for two examples.     

Extension of the range of resonator scanning spectrometer into submillimeter band and some perspectives of its further developments

Extension of the working frequency of modern resonator spectrometers into submillimeter wave range is described. Experimental record of atmospheric absorption spectrum covering 45-370 GHz range is demonstrated for the first time, and measured water vapor J′_{ka′, kc′}-J_{ka, kc} = 5_1,5-4_2,2 at 325 GHz line parameters are presented. For the first time pressure lineshift for the 325-GHz water vapor line is measured. Further extension of working range is discussed. New estimations of physical limits of time needed for measurements of absorption in the whole Backward Wave Oscillator (BWO) range are given for phase continuous synthesizer regime. Basic schemes of fast broadband continuous phase synthesized sources are discussed. Verification of the previous measurements of water vapor 3_1,3-2_2,0 at 183 GHz line parameters is presented. Comparisons with ringdown resonator spectrometers are given.     

Cycloaddition of fluorinated oxazoles

Cycloaddition reactions of polyfluorinated 1,3-oxazoles with cyclic and acyclic alkenes were studied. The results of these reactions were interpreted using quantum chemical calculations. An unusual product, viz., fluorine-containing acylpyrrole, was studied by X-ray diffraction. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1630–1635, July, 2005.     

Synthesis and properties of sym-triazene derivatives 12. Synthesis of 2,4-bis(trichloromethyl)-6-substituted sym-triazenes containing a sterically hindered phenol group

6-Substituted 2,4-bis(trichloromethyl)-sym-triazet:es containing the 2,6-di-tert-butylphenol group are synthesized by simultaneous cyclotrimerization of trichloroacetonitrile with the nitrile or thiocyanate derivative of the sterically hindered phenol in the presence of gaseous HCl. Significant amounts of 2,4,6-tris(trichloromethyl)-sym-triazene are formed as a byproduct.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, pp. 240–243, February, 1994. Original article submitted January 19, 1994.     

Beta-sheet preferences from first principles

The natural amino acids have different preferences of occurring in specific types of secondary protein structure. Simulations are performed on periodic model beta-sheets of 14 different amino acids, at the level of density functional theory, employing the generalized gradient approximation. We find that the statistically observed beta-sheet propensities correlate very well with the calculated binding energies. Analysis of the calculations shows that the beta-sheet propensities are determined by the local flexibility of the individual polypeptide strands.