Minimal Axiomatization in Modal Logic

We consider the problem of finding, in the ambit of modal logic, a minimal characterization for finite Kripke frames, i.e., a formula which, given a frame, axiomatizes its theory employing the lowest possible number of variables and implies the other axiomatizations. We show that every finite transitive frame admits a minimal characterization over K4, and that this result can not be extended to K.     

Experimental tests of bell inequalities. Are all local models really excluded?

Bell inequality tests performed by atomic cascade experiments always make use of a coincidence counting electronics. It is shown that such electronics can act as a “source of nonlocality” in the correlation function, even if every phenomenon involved is perfectly local. A simple example illustrating this situation is given.     

Almost everywhere convergence of riesz means on certain noncompact symmetric spaces

Summary Let G/K be a rank one or complex non compact symmetric space of dimension l. We prove that if f L^p, 1p2, the Riesz means of order z of f with respect to the eigenfunction expansion of the Laplacian converge to falmost everywhere for Re(z)>(l, p). The critical index (l, p) is the same as in the classical result of Stein in the Euclidean case.The first author was supported by funds of the Ministero della Pubblica Istruzione. The work was done while the second author was a member of the Mathematical Sciences Research Institute at Berkeley, with a fellowship from the Consiglio Nazionale delle Ricerehe.     

New synthesis of optically active 5-isoxazolidinones and beta-amino acids

A new simple and stereoselective synthesis of 5-isoxazolidinones based on the reaction of lithiated 2-isopropyl-2-oxazolines with nitrones is described. A chiral version of such a methodology allows the preparation of highly enantioenriched 5-isoxazolidinones which are useful precursors for the synthesis of beta-amino acids     

“Normal” and “cine” substitution in the thioalkoxy-dehalogenation of halogenobenzofurazans—III: Investigation on the solvent effect

The reaction of 4-chloro- and 4-chloro-7-deuteriobenzofurazan with MeS^-, isopropyl-S^-, and t-Butyl-S^- in different alcohols as solvents has been investigated. In going from methanol through isopropanol to t-butanol, a progressive decrease of the contribution of the cine-substitution as compared with the normal substitution pathway has been found. By proceeding in the same order, a decrease of the ratio and $\text{k}\text{MeS}{}^{\mathrm{?}}\text{k}{}_{\mathrm{<mtext>t</mtext>}}$-ButylS^? has also been observed.     

Electrochemical Reduction of Ellman's Reagent: A Novel Selective Detection Protocol for Thiol Compounds

Herein we detail a novel approach to the detection of total sulfhydryl thiol species based on an electrochemical adaptation of the classical Ellman's reaction. The ability to electrochemically reduce the nitro moieties of both the parent 5,5‐dithiobis(2‐nitrobenzoic acid) (DTNB) and the resulting 5‐thio‐2‐nitrobenzoic acid (TNBA) species provides a selective means of detecting thiol compounds. The use of the reductive sweep means that electrode passivation as a result of oxidative electrochemical procedures can be avoided and the selectivity improved through positioning the analytical signal within a region where few interferences reside. The electrochemical protocol enables the detection of the thiols in both acidic and basic media, which the colorimetric method is unable to do.     

Oxazolinyloxiranyllithium-mediated stereoselective synthesis of alpha-epoxy-beta-amino acids

[reaction: see text] The stereoselective synthesis of novel alpha-epoxy-beta-amino acids is described by a route that combines the chemistry of oxazolinyloxiranyllithiums with that of nitrones. The intermediate trioxadiazadispiro[2.0.4.3]undecanes 4 have been isolated and converted by hydrolysis into epoxy-5-isoxazolidinones 5 which can be transformed into the alpha-epoxy-beta-amino acids 8 by N-O reduction.     

Grignard reagent induced self-condensation of benzoxazoles: synthesis of benzoxazolylalkyl alkyl ketones

2-Alkylbenzoxazoles $\text{1}$ undergo clean Claisen-type self-condensation upon treatment with $\text{n}$-BuMgBr and quenching with aqueous NH₄Cl to give $\text{5}$. In contrast, quenching of the reaction with aqueous HCl furnishes quite good yields of the benzoxazolylalkyl alkyl ketones $\text{8}$.     

An efficient route to tetrahydronaphthols via addition of ortho-lithiated stilbene oxides to alpha,beta-unsaturated fischer carbene Complexes

[reaction: see text] A stereoselective/stereospecific synthesis of polysubstituted tetrahydronaphthols based on the Michael addition of ortho-lithiated stilbene oxides to alpha,beta-unsaturated Fischer carbene complexes followed by an unusual cyclization of the corresponding intermediate in a 6-endo-tet mode is described.