Cosmological models based on a statistical system of scalar charged degenerate fermions and an asymmetric Higgs scalar doublet

Theoretical and Mathematical Physics - On the basis of the general relativistic statistical and kinetic theory, a consistent closed cosmological model is formulated. It is based on a statistical...     

Synthesis of magnesium dicyclopentadienide catalyzed by titanium and vanadium derivatives

Synthesis of magnesium dicyclopentadienide from metal and cyclopentadiene in THF is effectively catalyzed by the derivatives of vanadium and titanium. The kinetics of the synthesis, as well as thermodynamic parameters of reagents adsorption on the magnesium surface, have been determined. The process catalyzed by titanium derivatives is accompanied by the quantitative hydrogenation of cyclopentadiene to cyclopentene whereas the catalysis by vanadium derivatives leads to hydrogen gas evolution. A number of reaction intermediates including Cp₂TiCl, Cp₂TiH₂MgCl, Cp₂Ti(cyclo‐C₅H₇) and Cp₂V, were identified by the electron spin resonance method. The equilibrium constants, enthalpies and entropies of adsorption of metal halides on the magnesium surface were calculated. Copyright © 2001 John Wiley & Sons, Ltd.     

Comments on “On stability of switched homogeneous nonlinear systems” by Lijun Zhang, Sheng Liu, and Hai Lan [J. Math. Anal. Appl. 334 (1) (2007) 414-430]

We show that the proof of the results obtained in the above paper is wrong since it is based on lemma which is not true. Therefore the results of the paper cannot be considered as true ones.     

Effect of substituents and hydrogen bonding on barrier heights in dehydration reactions of carbon and silicon geminal diols

Activation barrier heights for the dehydration reaction of geminal carbinols and silanediols R'R″X(OH)(2) (X = C, Si) were estimated at the B3LYP and MP2 levels of theory employing Dunning's correlation-consistent triple-zeta basis sets. It was shown that the barrier height for carbon derivatives steadily decreases upon substitution by R groups, usually termed as electron-donating, such as alkyl and amino groups. Substitution by electron-withdrawing groups leads, however, only to small changes in barrier heights compared to that of methanediol. A similar tendency was also found for silicon derivatives, but high activation barriers of this reaction remain even for amino group substituted silanediols. Introduction of additional water molecules into the reactive space of carbinol dehydration drastically reduces barrier heights and brings the transition state energy for methanediol close to the experimental value. The difference between dehydration barrier heights for both methanediol and carbinols with electron-rich substituents becomes well-defined for dimeric species. The higher acidity of the hydroxyl group protons in molecules containing halogens and C==O groups brings about a noticeable growth in the dehydration barrier heights of these compounds. This difference in barrier heights for oligomeric species may be the reason for the stability of carbinols with electron-rich substituents.     

On Solution of the Integrable Initial Boundary Value Problem for KdV Equation on the Semi-axis

This paper is concerned with the Korteweg-de Vries (KdV) equation on the right semi-axis. The initial boundary value problem with inhomogeneous integrable boundary conditions is studied. We show that, under some conditions on the initial data the problem has a solution and provide the procedure for constructing this solution. The procedure is based on the inverse spectral method and consists of several steps reducing to either solving some linear problems or calculations via some explicit formulas.     

On the Existence of Homoclinic Orbits in Nonautonomous Second-Order Differential Equations

Mathematical Notes - or the second-order differential equation ẍ + f(t) ẋ + g(t)x = 0, the method of Lyapunov functions is used to obtain sufficient conditions for the existence of...     

Structure and vibrational spectra of Ti(IV) hydroxides and their clusters with expanded titanium coordination. DFT study

Equilibrium structures of H(4-n)Ti(OH)n (n = 2-4) molecules and the Ti(OH)4 dimer and trimers were optimized at the B3LYP level of theory. Theoretical vibrational frequencies of TiO stretching modes obtained with several basis sets were compared with the existing experimental frequencies of these vibrations, and the 6-31+G(d) set was chosen for cluster calculations. Only one energy minimum was found for the [Ti(OH)4](2) dimer, but two isomers without symmetry elements stabilized by internal hydrogen bonds and two isomers, belonging to C(s) and C(i) point groups, with free OH groups were found as minima at the [Ti(OH)4](3) potential energy surface. The structure with the linear arrangement of hexacoordinated titanium atoms in the Ti3O12 skeleton may be proposed for trimeric species observed in liquid titanium alkoxides as the only structure satisfying experimental spectroscopic evidence about the presence of center of inversion in these species. Frequency changes of TiO4 modes which accompany the oligomer formation are predicted and discussed.     

Open tube combustion method of organic samples for stable carbon isotope analysis

A simple and effective method for the conversion of organic carbon into carbon dioxide for analysis of stable carbon isotopes (delta(13)C) in samples of various organic substances, soils, sedimentary rocks, oils and volatile organic liquids is presented. The conversion of organic carbon of the samples is carried out in a quartz reactor connected to a vacuum line for CO(2) freezing and purification. A solid organic sample mixed with CuO is placed at the reactor bottom and the reactor is subsequently filled with granular CuO. One end of the CuO column is preheated to 850 degrees C while the other end of the column in contact with the sample is kept at ambient temperature. Heating of the sample (850 degrees C) and the remainder of the column is then performed. The preheated part of the column provides efficient conversion of carbon into CO(2). The reactor for the conversion of volatile liquid organic compounds is filled with granular CuO. The column of CuO is heated to 850 degrees C. Samples of volatile liquids are introduced into the reactor through a septum using a microsyringe. Complete conversion takes 10 min for solid samples and 3 min for volatile liquids. The precision of the delta(13)C analysis for solid and volatile liquid organic substances is +/-0.1 per thousand and +/-0.04 per thousand, respectively.     

Mechanism of the Catalytic Activity of Nucleophiles in the Stepwise Hydrolysis and Condensation Reactions of Tetramethoxysilane

Active ingredients : A model for the simplest hydrolysis reaction is applied to all stages of stepwise hydrolysis and condensation taking place during a sol–gel process. The picture shows the molecular structures of the transition states of the ammonia‐ (left) and OH^?‐promoted (right) condensation reactions of two Si(OH)₄ molecules, including an additional water molecule.