On the Validity of Clauser and Horne Factorizability

The Clauser–Horne approach used to derive experimentally measurable quantities for performing experiments on EPR paradox based on Type-I Spontaneous Parametric Down Conversion (SPDC) sources is discussed. It is proved that in this case the deduced Bell's type inequality does not correctly express separability and causality. A deeper analysis of the problem shows that the Clauser–Horne hypothesis of factorizability of joint detection probability cannot be considered so general as to describe this physical situation.     

The rotational-conformational distribution of 2,2'-bithienyl in liquid crystals

We have investigated the distribution of conformations and orientations for a simple internal rotor molecule, 2,2'-bithienyl dissolved in liquid crystal solvents, by re-analysing published proton dipolar coupling data with the maximum entropy internal order method (MEIO). We show that detailed, model independent, conformational information can be obtained when data of sufficiently high quality are available. We also propose a novel and convenient representation method for the orientational-conformational coupling.     

Certification of nitrate in spinach powder reference material SPIN-1 by high-precision isotope dilution GC–MS

A high-precision exact-matching quadruple isotope dilution method (ID⁴MS) was employed for the quantitation of nitrate in an air-dried spinach powder Certified Reference Material (CRM). The analyte was extracted in hot water following addition of ¹⁵NO\({}_{3}^{-}\) internal standard. The blend was then treated with sulfamic acid to remove nitrite and with triethyloxonium tetrafluoroborate to promote aqueous conversion of nitrate into volatile EtONO₂. The derivative was analyzed by headspace GC–MS with 3-min elution time. The method performance was validated with a series of tests which demonstrated adequate selectivity and ruggedness. This method supported the development of novel SPIN-1 CRM giving a modest contribution to its uncertainty (u_char = 0.85%). With respect to previous attempts, the SPIN-1 was proven stable, homogeneous (u_hom = 0.44%), and suitable for spinach monitoring under EU regulations. On dried basis, the nitrate content of SPIN-1 was found to be 22.53 ± 0.43 mg/g (U_c = 1.9%, k = 2). The material was also used in an inter-laboratory study where four laboratories employed a total of ten measurement methods.

SPIN-1 Certified Reference Material for nitrate in spinach powder

     

SYNTHESIS AND THERMAL REARRANGEMENT OF 2-ALKOXYCARBONYL-3-ALKYL-4H-BENZO[b][1,4]THIAZINES

Abstract

The title compounds (4b-d) together with the benzothiazolines (5b-d) have been obtained by a reaction between 2,2′-dithiodianiline (1) and β-keto esters (2b-d). The reaction between 1 and the β-keto ester 2a gives 1,4-benzothiazine 3a in addition to the benzothiazoline 5a.

It has been established that the 1,4-benzothaizines 4b-d undergo an acid-catalysed thermal rearrangement involving a [1,3] shift of the sulfur atom, giving rise to the isomeric 1,4-benzothiazines 3b-d.     

On the continuous extension of Adams–Bashforth methods and the event location in discontinuous ODEs

The interpolation polynomial in the $k$-step Adams–Bashforth method may be used to compute the numerical solution at off grid points. We show that such a numerical solution is equivalent to the one obtained by the Nordsieck technique for changing the step size. We also provide an application of this technique to the event location in discontinuous differential systems.     

Adducts of 2-aminothiophenol with acetylenic nitriles or esters and their conversion into benzothiazoles and/or 1,4-benzothiazines

The reaction between 2-aminothiophenol 1 and acetylenic nitriles or esters 2a-d leads to the vinyl thio-ethers 3a-d. The conversion of 3 into benzothiazoles 8 and/or 1,4-benzothiazines 9 , in boiling dimethyl sulfoxide, has been achieved. A possible pathway involving benzothiazolines 5 as key intermediates is suggested.     

A generalization of a conservativity theorem for classical versus intuitionistic arithmetic

A basic result in intuitionism is Π⁰₂‐conservativity. Take any proof p in classical arithmetic of some Π⁰₂‐statement (some arithmetical statement ?x.?y.P(x, y), with P decidable). Then we may effectively turn p in some intuitionistic proof of the same statement. In a previous paper [1], we generalized this result: any classical proof p of an arithmetical statement ?x.?y.P(x, y), with P of degree k, may be effectively turned into some proof of the same statement, using Excluded Middle only over degree k formulas. When k = 0, we get the original conservativity result as particular case. This result was a by‐product of a semantical construction. J. Avigad of Carnegie Mellon University, found a short, direct syntactical derivation of the same result, using H. Friedman's A‐translation. His proof is included here with his permission. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)