Congruence classes of Frenet curves in complex quadrics

Congruent classes of Frenet curves of order 2 in the complex quadric are studied, obtaining that each congruence class is a level set of a family of certain smooth functions, that are generalizations of isoparametric functions on the unit sphere in the tangent space of the complex quadric.     

On closed sets of relational constraints and classes of functions closed under variable substitutions

Pippenger’s Galois theory of finite functions and relational constraints is extended to the infinite case. The functions involved are functions of several variables on a set A and taking values in a possibly different set B, where any or both of A and B may be finite or infinite. Received April 30, 2004; accepted in final form February 8, 2005.     

Empirical consequences of the scientific construction: The program of local hidden-variables theories in quantum mechanics

We claim that physics has been constructed because three “philosophical” principles have been respected, namely, realism, locality, and consistency. These principles lead to an interpretation of quantum mechanics (QM) in terms of local hidden-variables theories (LHV). In order to prove that LHV have not been refuted, we analyze the empirical proofs of Bell's inequalities and we argue that none is loophole-free. Then we propose a restricted QM that does not contain measurement postulates and that does not claim that all state vectors (self-adjoint operators) are states (observables). The contradiction of such restricted QM with Bell's inequality cannot be shown as a theorem, but only by the design of a loophole-free experiment. Finally, we argue that noise has been underestimated in quantum theory. It does not appear in QM, but it is essential in quantum field theory. We conjecture that noise will prevent the violation of Bell's inequality.     

Dimethyl carbonate synthesis and other oxidative reactions using alkyl nitrites

The oxidative reactions using the alkyl nitrites (RONO) as an oxidant have been developed by Ube Industries, Ltd. In the alkyl nitrite reactions, substrates such as CO andyor unsaturated- andyor carbonyl-compounds are oxidized over the palladium catalysts in no direct contact with molecular oxygen. The dimethyl carbonate (DMC), dialkyl oxalates and other useful chemicals are synthesized efficiently under moderate conditions by the alkyl nitrite reactions.     

Spectrofluorimetric determination of 5-hydroxyindoles with benzylamine or 3,4-dimethoxybenzylamine as a selective fluorogenic reagent.

A spectrofluorimetric method has been developed for the sensitive and selective determination of 5-hydroxyindoles; the method is based on the reaction of 5-hydroxyindoles in a weakly alkaline solution (pH 9.0) with aromatic methylamines in the presence of potassium hexacyanoferrate(III) and dimethyl sulphoxide; the compounds produced fluoresce intensely in an alkaline solution (pH 11-12). Of the eight aromatic methylamines tested, benzylamine and 3,4-dimethoxybenzylamine were found to be the most favourable fluorogenic reagents in terms of sensitivity and reactivity. The methods with benzylamine and 3,4-dimethoxybenzylamine permit the determination of 5-hydroxyindoles at concentrations as low as 22-72 pmol ml-1 and 1.0-2.4 nmol ml-1, respectively.