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].     

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].     

Specifics of Interaction of Acetone Molecules with Quasi-free Electrons: Analysis of Positron Annihilation Characteristics in Aqueous and Alcoholic Acetone Solutions

The yields of formation of radiolytic hydrogen (H₂) and orthopositronium (o-Ps) in aqueous and alcoholic acetone solutions were experimentally determined. A decrease in the o-Ps yield with an increase in the acetone concentration is much weaker than the decline in the yield of solvated electrons (e^– _s) under picosecond pulse radiolysis conditions. In contrast, the decrease in the o-Ps yield is minimal in higher alcohols where the inhibiting action of acetone e^– _s is most pronounced. These findings seem to contradict the conventional concepts of Ps formation via the intratrack reaction of positron recombination with a track electron (e^–), which competes with the reaction of e^– scavenging by dissolved acetone molecules. This contradiction can be eliminated, assuming that the scavenging of e^– by acetone begins from the formation of the weakly bound transient state (CH₃)₂CO···e^– capable of donating e^– to a positron. This opens up an additional pathway for the formation of the Ps atom.     

E-cadherin expression is biochemical marker in cervical intraepithelial neoplasia

The expression of E-cadherin has been investigated by the immunohistochemical method. The expression of E-cadherin is considered as a biomarker of junctions of intercellular adhesion in tissues samples with cervical intraepithelial neoplasias. The quantitative avidin-biotin-peroxidase method was used to estimate the expression. Precancer lesions, i.e., cervical intraepithelial neoplasias, CIN 1, 2, 3, precede invasive cancer of the cervix uteri by several years, the prognosis of which is variable in terms of regression and progression into invasive cancer. The expression of E-cadherin has been analyzed in cervical tissues of patients with various grades of CIN and microinvasive cancer (81 samples), as well as patients without CIN (ten samples). The sharp, statistically significant decrease in the expression of E-cadherin in CIN3 has been recorded compared to CIN1, CIN2, and the normal epithelium. It is reasonable to use this marker to assess the grade of the lesion and develop an individual prognosis of CIN progression. The data present a new way to construct pharmaceuticals based on compounds that influence E-cadherin expression.     

On a convective flow of a binary mixture in a vertical layer

Under study is an invariant solution of the equations of thermal diffusive convection which describes a stationary process of a binary mixture flow in a vertical layer under the action of the pressure gradient and the buoyancy force that depends nonlinearly on temperature and concentration. Some general properties of this solution are established and an existence theorem is proved. Analysis of the numerical solution of the problem is carried out in the cases of a power-law and exponential dependence of the buoyancy force on its argument.