Nickel-catalyzed Asymmetric Alkylation of Some Chiral and Achiral Allylic Alcohols. Preliminary communication

[(?) (R)-1,2-bis (Diphenylphosphino)-1-phenylethane]nickel (II) chloride was found to catalyze the asymmetric alkylation of some chiral and achiral allylic alcohols with Grignard reagents, leading to the formation of optically active olefins. Enantiomer discrimination of the substrate takes place in the alkylation of chiral allylic alcohols.     

Synthesis of new 1,2,3-triazolo[1,2-a]benzotriazole derivatives or substituted 2,3-benzo-1,3a,6,6a-tetraazapentalenes. II

This paper continues the synthesis of new 1,2,3-triazolo[1,2-a]benzotriazoles or 2,3-benzo-1,3a,6,6a-tetrazapentalenes to submit to biological assays. The derivatives were obtained by deoxycyclization reactions of appropriate nitrophenyl-1,2,3-triazole derivatives and by thermal decomposition of appropriate azidophenyl-1,2,3-triazoles (Schemes 1 and 2). Some attempts to extend these synthetic routes to the preparation of 1,2,4-triazolo[1,2-a]benzotriazoles (Scheme 3) and 1,2,3-triazolo[1,2-b]-4H-1,2,3-benzo-triazines (Scheme 4) completely failed.     

New 1,2,3‐triazolo[4,5‐e]1,2,4‐triazolo[4,3‐c]pyrimidine derivatives II

The 7‐chloro‐3‐(2‐chlorobenzyl)‐ and 7‐chloro‐3‐(2‐fluorobenzyl)‐1,2,3‐triazolo[4,5‐d]pyrimidines ( 1 and 4 ), by nucleophilic replacement with some hydrazides, gave the corresponding 7‐hydrazidoderivatives ( 2a‐e and 5a‐e ). These, by heating in Dowtherm, underwent an intramolecular cyclization to form the new tricyclic 7‐substituted‐3‐(2‐chlorobenzyl)‐ and 3‐(2‐fluorobenzyl)‐1,2,3‐triazolo[4,5‐e]1,2,4‐triazolo[4,3‐c]pyrimidines ( 3a‐d and 6a‐d ). The 7‐hydrazino‐3‐(2‐chlorobenzyl)‐ and 7‐hydrazino‐3‐(2‐fluorobenzyl)‐triazolo‐pyrimidines ( 9a and 9b ) were also prepared via the corresponding mercapto ( 7a and 7b ) and thiomethyl ( 8a and 8b ) derivatives.     

Synthesis of some 3,7-disubstituted quino[3,2-c][1,8]naphthyridines

The preparation of some 3,7-disubstituted-5,6-dihydroquino[3,2-c][1,8]naphthyridines ( 6 ) by the condensation of 7-substituted-2,3-dihydro-1,8-naphthyridin-4-(1H)ones ( 5 ) with o-aminoacetophenone or o-aminobenzophenone is described. All the 5,6-dihydroderivatives 6 were transformed into the fully aromatic compounds 7 by heating with nitrobenzene. Only a few quino[3,2-c][1,8]naphthyridines were previously described.     

1,2,3-Triazolo[4,5-d]-1,2,4-triazolo[4,3-b]pyridazines

Some new 1,2,3-triazolo[4,5-d]-1,2,4-triazolo[4,3-b]pyridazines were prepared starting from the corresponding 1,2,3-triazolo[4,5-d]pyridazines via the formation of the 1,2,4-triazole ring, by condensation of an appropriate monocarbon fragment with the 4-hydrazino substituent and the nitrogen atom in the 5 position of the heterocycle. Condensation of 4-phenylhydrazino substituted derivatives with formic acid gave zwitterionic compounds.     

New N6‐substituted 8‐alkyl‐2‐phenylmethylsulfanyl‐adenines. II

Title compounds bearing substituents on C(2), C(6) and C(8) were prepared from a newly synthesized pyrimidine derivative 11. The new pyrimidine 11 was generated from compound 2 through two different synthetic schemes. In one pathway, compound 2 was nitrosated, reduced and alkylated to produce com pounds 9 , 10 and 11 respectively (Scheme). In an alternate route using compound 2 as the starting material, a coupling reaction using the diazonium salt derived from p‐methylaniline afforded the azo derivative 7 , which was subsequently alkylated and reductively cleaved to form compounds 8 and 11 respectively (See Scheme). Compound 11 was annulated to the corresponding hypoxanthine derivatives 12–14 ; compounds 12 and 13 were chlorinated with phosphorus oxychloride, then reacted with amines to yield compound 17 and 20 respectively. Compounds 21 , 22 and 23 were obtained by oxidation of the corresponding sulfide as depicted in Scheme. Alkylation of the thiol function of 1 gave a mixture of 3 and 4. Compound 3 was chlo rinated to 5. Nitration of 5 resulted in electrophilic aromatic substitution of the aryl ring and concomitant oxidation of the sulfide to the sulfoxide, producing 6.     

Noise- and inertia-induced inhomogeneity in the distribution of small particles in fluid flows

The dynamics of small spherical neutrally buoyant particulate impurities immersed in a two-dimensional fluid flow are known to lead to particle accumulation in the regions of the flow in which vorticity dominates over strain, provided that the Stokes number of the particles is sufficiently small. If the flow is viewed as a Hamiltonian dynamical system, it can be seen that the accumulations occur in the nonchaotic parts of the phase space: the Kolmogorov-Arnold-Moser tori. This has suggested a generalization of these dynamics to Hamiltonian maps, dubbed a bailout embedding. In this paper we use a bailout embedding of the standard map to mimic the dynamics of neutrally buoyant impurities subject not only to drag but also to fluctuating forces modeled as white noise. We find that the generation of inhomogeneities associated with the separation of particle from fluid trajectories is enhanced by the presence of noise, so that they appear in much broader ranges of the Stokes number than those allowing spontaneous separation. (c) 2002 American Institute of Physics.     

Algebraic Isomorphisms and Finite Distributive Subspace Lattices

Let L₁ and L₂ be finite distributive subspace lattices on realor complex Banach spaces. It is shown that every rank-preservingalgebraic isomorphism of AlgL₁ onto AlgL₂ is quasi-spatiallyinduced. If the algebraic isomorphism in question is known onlyto preserve the rank of rank one operators, then it inducesa lattice isomorphism between L₁ and L₂.     

Large Deviation Approach to the Randomly Forced Navier--Stokes Equation

The random forced Navier--Stokes equation can be obtained as a variational problem of a proper action. By virtue of incompressibility, the integration over transverse components of the fields allows to cast the action in the form of a large deviation functional. Since the hydrodynamic operator is nonlinear, the functional integral yielding the statistics of fluctuations can be practically computed by linearizing around a physical solution of the hydrodynamic equation. We show that this procedure yields the dimensional scaling predicted by K41 theory at the lowest perturbative order, where the perturbation parameter is the inverse Reynolds number. Moreover, an explicit expression of the prefactor of the scaling law is obtained.