The Analytical Solutions of 2D Stationary Broadwell Kinetic Model

The present communication is devoted to the calculation of some explicit stationary solutions of the four-velocity Broadwell kinetic model in two spatial dimensions. The method of the truncated Painlevé expansion is employed and two classes of solutions are constructed. It is shown that these solutions satisfy the special boundary value problem in a rectangle.     

Cyclic products of the Ugi reaction of aldehydo and keto carboxylic acids: chemoselective modification

A method for the chemoselective reduction of Ugi-type lactam amides at the lactam carbonyl functionality with borane complexes has been developed. The novel reduction products can be further manipulated synthetically to yield various novel N- and C-terminally active unnatural amino acid building blocks.     

Minimal parabolic quantum groups in twist deformations

Study of parabolic twist deformations in the exponential coordinates faces serious difficulties. We demonstrate how to deal with this problem using the dual-group approach. The properties of the deformed symmetries can be easily disclosed when the deformed costructure is formulated in the dual-group terms.     

Study of benzene sorption in H-ZSM-5 zeolite under catalytic conditions

The equilibrium of the sorption of benzene in an H-ZSM-5 zeolite has been investigated in the temperature range of 100-400°С and at partial pressures 0.11÷0.57 аtm. The data on the sorption under these conditions could be fitted with the Langmuir isotherms taking into account a linear decrease in heats of sorption with the increase in the sorbate loading. The equilibrium constants and heat of the sorption have been determined. This revised version was published online in June 2006 with corrections to the Cover Date.     

On the Lieb-Thirring Constant on the Torus

Mathematical Notes -     

Synthesis of heterocyclic compounds possessing the 4H-thieno[3,2-b]pyrrole moiety

A series of novel heterocyclic combinatorial libraries containing 4H-thieno[3,2-b]pyrrole, thieno[2',3':4,5]-pyrrol[1,2-d][1,2,4]triazine and thieno[2',3':4,5]pyrrolo[1,2-a]pyrazine heterocyclic moieties were obtained by parallel solution-phase synthesis. Key steps include different reactions of initial alkyl 4H-thieno[3,2-b]-pyrrole-5-carboxylates, such as alkylation with alkylating agents; transformation of the carboxylate group into different reactive functionalities, followed by reactions with electrophilic species; intramolecular cyclizations; and amide bond formation. Simple manual techniques for parallel reactions were coupled with easy purification procedures to give high-purity final products.     

Anhydrous mono- and dinuclear tris(quinolinolate) complexes of scandium: the missing structures of rare earth metal 8-quinolinolates

The first monomeric anhydrous scandium tris(8-quinolinolate) complex 1 with the 2-amino-8-quinolinolate ligands and the Sc(2)Q(6) dinuclear complex 2 with the unsubstituted 8-quinolinolate ligands have been synthesized and characterized by X-ray analysis and DFT calculations. The intramolecular hydrogen bonds appear to be responsible for the unique monomeric structure of complex 1. The DFT-based analysis of the electron density topology reveals the (3,-1) critical points corresponding to the O···H and N···H bonds. The two scandium atoms in compound 2 are inequivalent due to different ligand surroundings. They are coordinated by seven (5O, 2N) and eight (4O, 4N) ligand atoms. The increase in the coordination number is accompanied by a decrease in the positive charge of the metal atom as evidenced by the DFT calculations.