Symmetries and conservation laws of Navier-Stokes equations

All the symmetries and conservation laws of Navier-Stokes equations are calculated.     

Symmetries and conservation laws of Kadomtsev-Pogutse equations

Kadomtsev-Pogutse equations are of great interest from the viewpoint of the theory of symmetries and conservation laws and, in particular, enable us to demonstrate their potentials in action. This paper presents, firstly, the results of computations of symmetries and conservation laws for these equations and the methods of obtaining these results. Apparently, all the local symmetries and conservation laws admitted by the considered equations are exhausted by those enumerated in this paper. Secondly, we point out some reductions of Kadomtsev-Pogutse equations to more simpler forms which have less independent variables and which, in some cases, allow us to construct exact solutions. Finally, the technique of solution deformation by symmetries and their physical interpretation are demonstrated.     

Efficacy of Biologically Active Food Supplements for People with Atherosclerotic Vascular Changes

The current paper deals with the development of a new biologically active food supplement (BAFS) aimed at treating atherosclerosis. Since atherosclerosis is considered to be a disease of aging, the composition of the supplement includes such essential minerals as magnesium and potassium, which are commonly used to prevent atherosclerosis, as well as vitamins C, E and the B-group vitamins in order to address the needs of the elderly. The authors outline the supplement-manufacturing technology and discuss the clinical trial undertaken by patients, aged about 60 years, with peripheral atherosclerosis. The research methodology focuses on studying the effectiveness of the developed supplement by assessing the influence of the active ingredients on treating metabolic disorders. To establish the efficacy of the supplement, blood tests, ultrasound and physical examinations were applied. The combination therapy resulted in improved metabolism and an overall better performance of the cardiovascular system; therefore, the BASF can be recommended as part of combination therapy to prevent and treat atherosclerotic and age-related changes in blood vessels.     

Cohomological uniqueness of the Cauchy problem solutions for the Einstein equation

In this paper we analyze the Cauchy problem for the Einstein equation in the case of a non-characteristic initial hypersurface. To find the correct notions for the characteristic and Cauchy data we introduce a complex, which we call the Einstein complex. Then the Cauchy problem acquires correctness in terms of the associated spectral sequence. We define the Cauchy data in such way that they allow us to reconstruct a cohomologously unique formal solution.     

Synthesis and Therapeutic Use of Dimephosphone

Abstract

The synthesis of dimephosphone (1) was carried out on Pudovik's reaction.     

Combined Crossed Molecular Beams and Ab Initio Study of the Bimolecular Reaction of Ground State Atomic Silicon (Si; 3P) with Germane (GeH4; X1A1)

The chemical dynamics of the elementary reaction of ground state atomic silicon (Si; ³P) with germane (GeH₄; X¹A₁) were unraveled in the gas phase under single collision condition at a collision energy of 11.8±0.3 kJ mol⁻¹ exploiting the crossed molecular beams technique contemplated with electronic structure calculations. The reaction follows indirect scattering dynamics and is initiated through an initial barrierless insertion of the silicon atom into one of the four chemically equivalent germanium-hydrogen bonds forming a triplet collision complex (HSiGeH₃; ³ i1 ). This intermediate underwent facile intersystem crossing (ISC) to the singlet surface (HSiGeH₃; ¹ i1 ). The latter isomerized via at least three hydrogen atom migrations involving exotic, hydrogen bridged reaction intermediates eventually leading to the H₃SiGeH isomer i5 . This intermediate could undergo unimolecular decomposition yielding the dibridged butterfly-structured isomer ¹ p1 (Si(μ-H₂)Ge) plus molecular hydrogen through a tight exit transition state. Alternatively, up to two subsequent hydrogen shifts to i6 and i7 , followed by fragmentation of each of these intermediates, could also form ¹ p1 (Si(μ-H₂)Ge) along with molecular hydrogen. The overall non-adiabatic reaction dynamics provide evidence on the existence of exotic dinuclear hydrides of main group XIV elements, whose carbon analog structures do not exist.     

Ab initio method for calculating electron-phonon scattering times in semiconductors: application to GaAs and GaP

We propose a fully ab initio approach to calculate electron-phonon scattering times for excited electrons interacting with short-wavelength (intervalley) phonons in semiconductors. Our approach is based on density functional perturbation theory and on the direct integration of electronic scattering probabilities over all possible final states with no ad hoc assumptions. We apply it to the deexcitation of hot electrons in GaAs, and calculate the lifetime of the direct exciton in GaP, both in excellent agreement with experiments. Matrix elements of the electron-phonon coupling, and their dependence on the wave vector of the final state and on the phonon modes, are shown to be crucial ingredients of the evaluation of electron-phonon scattering times.     

Gas Phase Formation of Methylgermylene (HGeCH3)

The methylgermylene species (HGeCH₃; X¹A′) has been synthesized via the bimolecular gas phase reaction of ground state methylidyne radicals (CH) with germane (GeH₄) under single collision conditions in crossed molecular beams experiments. Augmented by electronic structure calculations, this elementary reaction was found to proceed through barrierless insertion of the methylidyne radical in one of the four germanium-hydrogen bonds on the doublet potential energy surface yielding the germylmethyl (CH₂GeH₃; X²A′) collision complex. This insertion is followed by a hydrogen shift from germanium to carbon and unimolecular decomposition of the methylgermyl (GeH₂CH₃; X²A′) intermediate by atomic hydrogen elimination leading to singlet methylgermylene (HGeCH₃; X¹A′). Our investigation provides a glimpse at the largely unknown reaction dynamics and isomerization processes of the carbon-germanium system, which are quite distinct from those of the isovalent carbon system thus providing insights into the intriguing chemical bonding of organo germanium species on the most fundamental, microscopic level.     

Driving defect modes of Bose-Einstein condensates in optical lattices

We present an approximate analytical theory and direct numerical computation of defect modes of a Bose-Einstein condensate loaded in an optical lattice and subject to an additional localized (defect) potential. Some of the modes are found to be remarkably stable and can be driven along the lattice by means of a defect moving following a steplike function defined by the period of Josephson oscillations and the macroscopic stability of the atoms.     

Ni olivine: thermal behavior of liebenbergite

The synthetic samples of nickel olivine were measured in the temperature range 100–630 K by the X-ray powder diffraction method. Temperature dependencies of molar volumes and coefficients of bulk thermal expansion of liebenbergite were determined. Interpolation and extrapolation of the experimental data were performed by the procedure based on the Debye–Mie–Gruneisen theory of solid body in the range from 50 to 2000 K, and the Gruneisen coefficient and Debye temperature were calculated. Heat capacity and its behavior in accordance with temperature were evaluated.