Local-in-time well-posedness of a regularized mathematical model for silicon MESFET

We prove the local-in-time well-posedness of the initial boundary value problem for a system of quasilinear equations. This system is used for finding numerical stationary solutions of the hydrodynamical model of charge transport in the silicon MESFET (metal semiconductor field effect transistor). The initial boundary value problem has the following peculiarities: the quasilinear system is not a Cauchy-Kovalevskaya-type system; the boundary is a non-smooth curve and has angular points; nonlinearity of the problem is mainly connected with squares of gradients of the unknown functions. By using a special representation for the solution of a model problem we reduce the original problem to an integro-differential system. The local-in-time existence of a weakened generalized solution of this system is then proved by the fixed-point argument.     

Synthesis of unsymmetrical phosphorus-containing macrocycles on the basis of hydroquinone, 4,4′-(propane-2,2-diyl)diphenol,and resorcinol

Bisphosphorylation of hydroquinone and 4,4′-(propane-2,2-diyl)diphenol was performed for the first time in ethyl acetate. The bisphosphorylated products were used in molecular assembly of unsymmetrical phosphorus(III)-containing macrocycles consisting of hydroquinone and 2,2-bis(p-hydroxyphenyl)propane or resorcinol fragments. The macrocyclic compound based on hydroquinone and 2,2-bis(p-hydroxyphenyl)-propane was subjected to oxidation and sulfurization to obtain the corresponding phosphorus(V) derivatives. Its biological activity was also studied.     

Influence of steric hindrance on luminescence anisotropy of resonance dipole–dipole transfer of electronic excitation energy

An orientation factor is calculated and the effect of steric hindrance in the donor and acceptor molecules is found for the efficiency of resonance dipole–dipole transfer of electronic energy. General expressions for the acceptor luminescence anisotropy under such conditions in isotropic media (gases and liquids) are obtained taking into account orientational relaxation in ensembles of donors and acceptors. It is shown that the luminescence anisotropy of an acceptor with significant steric hindrance can increase by more than an order of magnitude compared with the case with no hindrance.     

Incompressible Polymer Fluid Flow Past a Flat Wedge

A problem of an incompressible polymer fluid flow past an infinite flat wedge is considered. The flow moves parallel to the plane of symmetry of the wedge and normal to the wedge rib. It is demonstrated that two surfaces of strong discontinuities are needed for the no-slip condition to be satisfied on the wedge surface. Steady solutions of the problem are studied, and the flow is shown to be asymmetric with respect to the plane of symmetry of the wedge.     

Heterylimidazoles

The condensation of heterocyclic aldehydes with aromatic -diketones in the presence of ammonium acetate in acetic acid has given 4,5-diaryl-2-quinolinylimidazoles and 4,5-diaryl-2-(acridin-9-yl) imidazoles. The oxidation of the latter with K₃Fe(CN)₆ in an alkaline medium has given the corresponding biimidazolyls, which possess photochromic and thermochromic properties.For Communication I, see [1].Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 8, pp. 1105–1108, August, 1973.     

Cell proliferation in normal and malignant transformed cells: thermodynamic model of signal transduction

We present a new thermodynamic model for the mechanism of activation and regulation of cell proliferation in the G1 stage. In this model, the interactions between growth factors and transmembrane proteins play a crucial role in cell growth control for a normal tissue-culture system. We calculate a phase diagram of normal and malignant transformed states of a cell signal transduction system. We propose thermodynamic reasons why cancer cells can continually grow without activation by the growth factors.     

Some mathematical properties of radiating gas model obtained with a variable Eddington factor

Some mathematical properties of the model for a radiating gas obtained with a variable Eddington factor are studied.In particular we discuss the problem of symmetrization and the derivation of so-called a priori estimates for the quasilinear equations describing the model.