Action of the Cremona group on a noncommutative ring

The Cremona group acts on the field of two independent commutative variables over complex numbers. We provide a noncommutative algebra that is an analog of a noncommutative field of two independent variables and prove that the Cremona group embeds in a group of outer automorphisms of this algebra. We give two proofs of it, the first proof is technical, the second one is conceptual and proceeds through a construction of a birational invariant of an algebraic variety from its bounded derived category of coherent sheaves.     

On choosing a reference redox system for electrochemical measurements: a cautionary tale

The potential of a quasi-reference electrode can be determined by introducing an internal reference redox system (IRRS) which comprises either the oxidizable or reducible form of a reversible (and, ideally, outer-sphere) redox couple and then observing the cyclic voltammetric responses. The objective is to choose the IRRS so that the cyclic voltammetric response for the simultaneously present electroactive analyte system (ANS) can be observed independently of the IRRS response. We identify three fundamental paradigms describing the relative positioning of the IRRS and ANS on the potential scale, the operative redox components for the IRRS and ANS, and the starting potential (E _start), reversing potential (E _rev), and ending potential (E _end) for the cyclic voltammetric scan as follows: paradigm A, an optimal paradigm which can produce completely independent cyclic voltammetric responses for the IRRS or for ANS; paradigm B, a less-than-optimal paradigm which can produce an independent cyclic voltammetry (CV) response for the ANS or a mixed response for the IRRS with that response on top of the ANS response; paradigm C, a problematic paradigm that can produce an independent CV response for the IRRS or a mixed response for the ANS with that response on top of the IRRS response; and any mixed response produces a thermodynamically favored redox cross-reaction which couples the IRRS and ANS systems and which can complicate the analysis of the ANS and IRRS responses. The conclusion is that paradigm C is to be avoided.     

Synthesis of Drim-7,9(11)-diene and Its Hydroxylated Derivatives

This article describes a new efficient synthesis of drim-7,9(11)-diene and its hydroxylated derivates from drim-8-en-7-one. Reduction of this ketone with NaBO₄ in the presence of CeCl₃ · 7H₂O afforded regio- and stereoselectively drim-8-en-7β-ol in a high yield. Its dehydration with H₂SO₄ under mild conditions led to drim-7,9(11)-diene. Noncatalytic oxidation of drim-7,9(11)-diene with OsO₄ and the catalytic oxidation with the pair OsO₄–NMO gave, in a high yield, depending on conditions, driman-7β,8β,9α,11-tetraol or its mixture with drim-7-en-9α,11-diol and drim-9(11)-en-7α,8α-diol. Under optimal conditions the total yield of these diols reached 89%. The separate, noncatalytic oxidation of drim-7-en-9α,11-diol and of drim-9(11)-en-7α,8α-diol with OsO₄ afforded driman-7α,8α,9α,11-tetraol.     

One-pot synthesis of 1-substituted-5-alkylselanyl-1H-tetrazoles from isoselenocyanates: unexpected formation of N-alkyl-N-arylcyanamides and (Z)-Se-alkyl-N-cyano-N,N′-diarylisoselenoureas

1-Substituted-5-alkylsulfanyl-1H-tetrazoles are well known class of organic substances with various applications in medicinal chemistry or photographic industry. Their selenium analogues, 1-substituted-5-alkylselanyl-1H-tetrazoles are, however, much less explored because of the lack of suitable methods for their preparation. In this work we investigated the synthesis of 1-alkyl/aryl-5-alkylselanyl-1H-tetrazoles from synthetically available alkyl/arylisoselenocyanates. One-pot reactions of arylisoselenocyanates with sodium azide and alkylating agent led to the target 5-alkylselanyl-1-aryl-1H-tetrazoles but also to interesting side products, namely N-alkyl-N-arylcyanamides and (Z)-Se-alkyl-N-cyano-N,N′-diarylisoselenoureas. Nevertheless, when alkylisoselenocyanates were utilized as the substrates, the reactions led exclusively to the formation of 1-alkyl-5-alkylselanyl-1H-tetrazoles in good yields. This simple one-pot procedure brings new possibilities for the preparation of variously substituted selenium compounds. It also opens the way to further investigations of selenium isosteres of the widely utilized 5-thiotetrazole moiety in biomedical applications.     

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.     

Molecular mobility and transport in polymer membranes and polyelectrolyte multilayers

Polyelectrolyte multilayers prepared by the layer-by-layer technique provide an efficient way to generate planar structures of tailored surface charge and hydrophobicity, which are used as membranes for pervaporation. The use of polyelectrolyte multilayers to form the membrane permits tailoring the surface charge of the membrane and, thus, selectivity; at the same time, it reduces fouling of the membrane by adsorption of organic matter. Pulsed field gradient (PFG) nuclear magnetic resonance has been used to investigate the diffusion of probe molecules into polymer systems. Evaluation of the apparent diffusion coefficient in porous poly(amide) results in a pore size of 4 microm, as found in electron micrographs. For the pore size obtained for polyelectrolyte multilayers, no equivalent pores could be found in microscopy. Propagators for the diffusion of propanol and propanol-water mixture into multilayers reveal that there might be selective interaction of probe molecules with the polyelectrolyte system.     

Methane Pyrolysis for Hydrogen Production: Specific Features of Using Molten Metals

Russian Journal of Applied Chemistry - Published data on noncatalytic pyrolysis of natural gas in molten metals are analyzed. The most illustrative results obtained in the past two decades are...     

Transversals in Uniform Hypergraphs with Property (p,2)

Dedicated to the memory of Paul Erdős Let f(r,p,t) (p > t >= 1, r >= 2) be the maximum of the cardinality of a minimum transversal over all r-uniform hypergraphs possessing the property that every subhypergraph of with p edges has a transversal of size t. The values of f(r,p,2) for p = 3, 4, 5, 6 were found in [1] and bounds on f(r,7,2) are given in [3]. Here we prove that for large p and huge r. Received September 23, 1999 RID="*" ID="*" This work was partially supported by the grant 99-01-00581 of the Russian Foundation for Fundamental Research and the Dutch–Russian Grant NWO-047-008-006.