A variant of the pure quaternionic representation of the Navier-Stokes equation

It is shown that the three-dimensional Navier-Stokes equation for incompressible fluid can be represented as an equation including only quaternions as co-ordinate operators and variables. Only the quaternion operations such as a quaternion product and a quaternion conjugation over these variables are used.     

Eigenvalues of the antiplane-shear crack problem for a power-law material

This paper discusses the problem of finding the eigenvalue spectrum in determining the stress and strain fields at the tip of an antiplane-shear crack in a power-law material. It is shown that the perturbation method provides an analytical dependence of the eigenvalue on the material nonlinearity parameter and the eigenvalue of the linear problem. Thus, it is possible to find the entire spectrum of eigenvalues and not only the eigenvalue of the Hutchinson-Rice-Rosengren problem. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 173–180, January–February, 2008.     

Synthesis in the 2-mercaptobenzothiazole series

The reduction of some dihydrothiazolobenzothiazolium salts with sodium borohydride may take place in two directions: with the formation of thiazolidino[2, 3-b]benzathiazolines and with the cleavage of the C-S bond to give N-(-mercaptoethyl)benzothiazolines. The behavior of thiazolidino[2, 3-b]benzothiazoline under the conditions of acid and alkaline hydrolysis has been studied.For communication VI, see [1].     

Stereoselective synthesis of unnatural α-amino acid derivatives through photoredox catalysis

A protocol for stereoselective C-radical addition to a chiral glyoxylate-derived N-sulfinyl imine was developed through visible light-promoted photoredox catalysis, providing a convenient method for the synthesis of unnatural α-amino acids. The developed protocol allows the use of ubiquitous carboxylic acids as radical precursors without prior derivatization. The protocol utilizes near-stoichiometric amounts of the imine and the acid radical precursor in combination with a catalytic amount of an organic acridinium-based photocatalyst. Alternative mechanisms for the developed transformation are discussed and corroborated by experimental and computational studies.

A protocol for stereoselective C-radical addition to a chiral glyoxylate-derived N-sulfinyl imine was developed through visible light-promoted photoredox catalysis, providing a convenient method for the synthesis of unnatural α-amino acids.     

Cyanosilylation of α-butylthioacrolein

Cyanosilylation of α-butylthioacrolein with trimethylsilyl cyanide occurs as 1,2-addition. Concurrent rapid dimerization of α-butylthioacrolein occurred both in the presence and in the absence of H₂PtCl₆·6H₂O as a catalyst to give 2,5-dibutylthio-2,3-dihydro-4H-pyran-2-carbaldehyde, whose cyanosilylation afforded the corresponding cyanohydrin. The latter is prone to retrodiene degradation upon heating. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1418–1420, July, 1998.     

DIPOLE POLARIZATION RELAXATION AND MOLECULAR STRUCTURE OF MAIN-AND SIDE-CHAIN LIQUID-CRYSTALLINE POLYMERS

Molecular mobility in thermotropic polyesters and side-chain polymers with different struc-ture of mesogens and spacers has been studied by dielectrical method in dilutesolutions. The results made it possible to establish the multiplicity of dielectric relaxationtransitions which reflects the small- and large-scale types of molecular motion. It was shownthat dielectric relaxation processes occurring in accordance with local mechanism (relaxationtimes 10~(-9)--10~(-7)s. and the activation energy 10--50kJ/mol) are due to the mobility of kineticchain elements of different length within a monomer units. It was found that the dielectricrelaxation process connected with a large-scale form of molecular motion (relaxation times10~(-5)--10~(-6)s. and the activation energy 100kJ/mol) did not depend on the molecular massbut was infiuenced by factors changing the conformational state of the macromolecule. It isestablished tha the cooperative reorientation mobility of associated mesogenic fragments isthe source of the large-scale process.     

Strong intramolecular hydrogen bond N—H...O in 2-(2-acyl-1-phenylethenyl)-5-phenylpyrroles

The molecular structure of 2-(2-benzoyl-1-phenylethenyl)-5-phenylpyrrole and 2-(2-furoyl-1-phenylethenyl)-5-phenylpyrrole was studied by X-ray diffraction analysis at 110 K and quantum chemistry methods (B3LYP/6-31G*). In the crystalline state, both compounds have cyclic structures closed by strong intramolecular hydrogen bond N—H...O. Canonic zwitterionic structure contributes largely to the ground state of the molecules. This is probably due to synergism of the H-bonding and -electron interactions.     

Synthesis and properties of derivatives of 2-mercaptobenzothiazole

2,3-Dihydro-4H-[1,3]-thlazino[2,3-b]benzothiazolium chlorides have been synthesized and their reduction with sodium borohydride has given previously-unknown derivatives of (perhydro-1,3-thiazino) [2,3-b]benzothiazoline. The stability of the compounds in acid and alkaline media has been studied.For part VII, see [1].     

Addition of 1,2- and 1,3-Dithiols to 2-alkoxypropenals - a New Method for the Production of Substituted Dithiacycloalkanes

The reaction of 2-alkoxypropenals with ethane-1,2-dithiols and propane-1,3-dithiols under various conditions was studied by ¹H NMR and chromato-mass spectrometry. Under kinetically controlled conditions at 20° in the absence of catalysts the addition of dithiols takes place according to the Markovnikov rule. The primary adducts are unstable and are quickly converted into the corresponding substituted 1,4-dithiacycloheptane or 1,4-dithiane. The latter in turn can be converted under the reaction conditions or at high temperature into a thiolane derivative. The reaction of 2-ethoxypropenal with a twofold excess of ethane-1,2-dithiol at 60°C in the presence of p-toluenesulfonic acid leads to 2-methyl-2,2'-bi(dithiolane)