On the Existence and Uniqueness of the Solution to the Cauchy Problem for a System of Integral Equations Describing the Motion of a Rarefied Mass of a Self-Gravitating Gas

Computational Mathematics and Mathematical Physics - The Cauchy problem for a system of nonlinear Volterra-type integral equations that describes, in Lagrangian coordinates, the motion of a finite...     

Methacrylate-containing polymer compounds for dentistry

Methacrylate-containing oligosilsesquioxanes were synthesized by acidohydrolytic copolycondensation of γ-methacryloyloxypropyltrimethoxysilane and phenyltrimethoxysilane in a mixture of bismethacrylate monomers, 2,2-bis[4-(2-hydroxy-3-methacryloyloxypropyl)phenyl]propane and triethylene glycol dimethacrylate, and were characterized by NMR spectroscopy and MALDI-TOF mass spectrometry. Performing the process in the bismethacrylate medium favors formation of uniform blends. Their introduction in an amount of 3 wt % into filled methacrylate dental composites considerably improves the physicomechanical characteristics of these composites.     

Phonon spectrum softening near temperatures of superconducting and structural transitions in HTSC ceramic “1-2-3”

Anomalous behavior of the Mössbauer factorf for iron and tin impurity atoms in the ceramic of the 1-2-3 composition indicates a phonon softening nearT _c andT _t≈190 K.     

Wavelet algorithm for solving integral equations of molecular liquids. A test for the reference interaction site model

A new efficient method is developed for solving integral equations based on the reference interaction site model (RISM) of molecular liquids. The method proposes the expansion of site-site correlation functions into the wavelet series and further calculations of the approximating coefficients. To solve the integral equations we have applied the hybrid scheme in which the coarse part of the solution is calculated by wavelets with the use of the Newton-Raphson procedure, while the fine part is evaluated by the direct iterations. The Coifman 2 basis set is employed for the wavelet treatment of the coarse solution. This wavelet basis set provides compact and accurate approximation of site-site correlation functions so that the number of basis functions and the amplitude of the fine part of solution decrease sufficiently with respect to those obtained by the conventional scheme. The efficiency of the method is tested by calculations of SPC/E model of water. The results indicated that the total CPU time to obtain solution by the proposed procedure reduces to 20% of that required for the conventional hybrid method.     

Rearrangement of the crystal structure during solid-phase elimination of solvate acetic acid fromN′-(5-nitrofurfurylidene)isonicotinic hydrazide monohydrate

A new crystal modification ofN-(5-nitrofurfurylidene)isonicotinic hydrazide (1) was studied by IR spectroscopy and X-ray structural analysis. The compound studied is the product of solid-phase desolvation of solvate hydrate1 of the composition [MeCOOH · 1 · H₂O]. Spontaneous elimination of solvate acetic acid results in complex overall rearrangement of the crystal structure and formation of a new system of intermolecular hydrogen bonds. The crystal hydrate of 1 : 1 composition (1c) was formed from compound1. In the crystal structure of1c molecules1 are linked in infinite chains through intermolecular C=O...W...H-N hydrogen bonds. The second hydrogen atom of the molecule of the crystallization water is involved in formation of an intermolecular O-H...N(Py) hydrogen bond with the nitrogen atom of the pyridine ring of the molecule of the adjacent chain.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 2501–2505, October, 1996.     

Nature of the metal-nonmetal transition in metal-ammonia solutions. I. Solvated electrons at low metal concentrations

Using a theory of polarizable fluids, we extend a variational treatment of an excess electron to the many-electron case corresponding to finite metal concentrations in metal-ammonia solutions (MAS). We evaluate dielectric, optical, and thermodynamical properties of MAS at low metal concentrations. Our semianalytical calculations based on a mean-spherical approximation correlate well with the experimental data on the concentration and temperature dependencies of the dielectric constant and the optical absorption spectrum. The properties are found to be mainly determined by the induced dipolar interactions between localized solvated electrons, which result in the two main effects: the dispersion attractions between the electrons and a sharp increase in the static dielectric constant of the solution. The first effect creates a classical phase separation for the light alkali metal solutes (Li, Na, K) below a critical temperature. The second effect leads to a dielectric instability, i.e., polarization catastrophe, which is the onset of metallization. The locus of the calculated critical concentrations is in a good agreement with the experimental phase diagram of Na-NH(3) solutions. The proposed mechanism of the metal-nonmetal transition is quite general and may occur in systems involving self-trapped quantum quasiparticles.     

Differential equations of program motions of a mechanical system

We obtain all types and forms of differential equations describing the program motions of a mechanical system both for ideal and nonideal primary constraints. We find the forms of differential equations of motion that significantly simplify the mathematical transformations required to obtain them in explicit form.