Symmetries of Integrable Difference Equations on the Quad-Graph

This paper describes symmetries of all integrable difference equations that belong to the famous Adler–Bobenko–Suris classification. For each equation, the characteristics of symmetries satisfy a functional equation, which we solve by reducing it to a system of partial differential equations. In this way, all five-point symmetries of integrable equations on the quad-graph are found. These include mastersymmetries, which allow one to construct infinite hierarchies of local symmetries. We also demonstrate a connection between the symmetries of quad-graph equations and those of the corresponding Toda type difference equations.     

Antiferromagnetism of nuclear matter in the model with effective Gogny interaction

The possibility of ferromagnetic (FM) and antiferromagnetic (AFM) phase transitions in symmetric nuclear matter is analyzed within the framework of a Fermi liquid theory with effective Gogny interaction. It is shown that, at some critical density, nuclear matter with the D1S effective force undergoes a phase transition to the AFM spin state (opposite directions of neutron and proton spins). The self-consistent equations of spin-polarized nuclear matter with the D1S force have no solutions corresponding to FM spin ordering (the same direction of neutron and proton spins) and, hence, the FM transition does not appear. The AFM spin polarization parameter is found for zero and finite temperature. It is shown that the AFM spin polarization parameter of partially polarized nuclear matter at low enough temperatures increases with temperature. The entropy of the AFM spin state for some temperature range is larger than the entropy of the normal state. Nevertheless, the free energy of the AFM spin state is always less than the free energy of the normal state, and the AFM spin-polarized state is preferable for all temperatures below the critical temperature. The text was submitted by the authors in English.     

Formation of disubstituted beta-lactones using bifunctional catalysis

[reaction: see text] Acid chlorides and aromatic aldehydes react in the presence of a stoichiometric amount of a tertiary amine and catalytic amounts of a cinchona alkaloid derivative and a Lewis acid to produce beta-lactones in high diastereo- and enantioselectivity. The sense of the diastereoselectivity depends on the substitution of the acid chloride, with the reactions of aliphatic acid chlorides giving predominantly the trans-isomer and those of alkoxyacetyl chlorides favoring formation of the cis-isomer.     

Synthesis and cytotoxicity of new 2-oxo-7-phenyl-2,3-dihydrothiazolo[4,5-b]pyridine-5-carboxylic acid amides

Abstract

The synthesis and anticancer activity evaluation of new thiazolo[4,5-b]pyridine-5-carboxylic acid amides is described. The structures of the synthesized compounds were confirmed by spectroscopic data and a single crystal X-ray diffraction analysis for 2.4. The synthesized compounds were screened for their in vitro anticancer activity according to US NCI protocols. The most active 7-(4-fluorophenyl)-2-oxo-2,3-dihydrothiazolo[4,5-b]pyridine-5-carboxylic acid (4-chlorophenyl)amide 2.2 and 7-(4-chlorophenyl)-2-oxo-2,3-dihydrothiazolo[4,5-b]pyridine-5-carboxylic acid (4-chlorophenyl)amide 2.5 were screened for their cytotoxicity effects on C6 Rat glioma cells and U373 Human glioblastoma astrocytoma cells which revealed promising results comparable to temozolamide as reference control according MTT assay data.     

Fredholm boundary value problems for perturbed systems of dynamic equations on time scales

This paper offers conditions ensuring the existence of solutions of linear boundary value problems for systems of dynamic equations on time scales. Utilizing a method of Moore–Penrose pseudo‐inverse matrices leads to an analytical form of a criterion for the existence of solutions in a relevant space and, moreover, to the construction of a family of linearly independent solutions of such problems in a general case with the number of boundary conditions (defined by a linear vector functional) not coinciding with the number of unknowns of a system of dynamic equations. As an example of an application of the presented results, the problem of bifurcation of solutions of boundary value problems for systems of dynamic equations on time scales with a small parameter is considered.     

Crotonic,cynnamic, and propiolic acids motifs in the synthesis of thiopyrano[2,3-d][1,3]thiazoles via hetero-Diels–Alder reaction and related tandem processes

Various novel thiopyrano[2,3-d][1,3]thiazol-2-one-6-carboxylic acids derivatives were synthesized in 54–86% yields via hetero-Diels–Alder reactions and related acylation-based tandem processes of 5-arylidene-4-thioxo-2-thiazolidinones with crotonic, propiolic, and cynnamic acids derivatives. Stereo- and regioselectivity of cycloaddition were investigated.     

Oscillatory shear flow of polymeric systems

On the basis of the Leonov viscoelastic constitutive equation, oscillatory shear flow of elastic fluids in the linear and nonlinear regimes has been considered. The Fourier components and associated phase angles of the shear and normal components of the elastic strain tensor have been found as functions of frequency and deformation amplitude in the range usually employed in experiment, and are presented in a form convenient for further rheological applications. In the linear case, the results correspond to many known theories. In the nonlinear case, the theoretical results have been compared with experiments, on different polymeric systems, with very good agreement being obtained for the shear stress in polymeric solutions but only qualitative agreement for the shear stress and first normal-stress difference in polymer melts.     

On the structure of IO n

We study the structure of the semigroup IO _n of all order-preserving partial bijections on an n-element set. For this semigroup we describe maximal subsemigroups, maximal inverse subsemigroups, automorphisms and maximal nilpotent subsemigroups. We also calculate the maximal cardinality for the nilpotent subsemigroups in IO _n which happens to be given by the n-th Catalan number.     

Facile one-pot synthesis of 5-aryl/heterylidene-2-(2-hydroxyethyl- and 3-hydroxypropylamino)-thiazol-4-ones via catalytic aminolysis

A multicomponent synthetic approach for 5-aryl/heterylidene-2-(2-hydroxyethylamino)- and 2-(3-hydroxypropylamino)-thiazol-4-ones starting from 2-thioxothiazolidin-4-one or 2-methylsulfanylthiazol-4-one was developed. The proposed method involves simultaneous aminolysis of 2-thioxo- or 2-methylsulfanyl groups and Knoevenagel condensation with (hetero)aromatic aldehydes using 2-aminoethanol or 3-aminopropan-1-ol as catalysts. Side-chain prototropic amino–imino tautomerism was observed for target 5-ylidene-2-alkylaminothiazol-4-ones.