Algebraic Structures Arising in Axiomatic Unsharp Quantum Physics

This article presents and compares various algebraic structures that arise in axiomatic unsharp quantum physics. We begin by stating some basic principles that such an algebraic structure should encompass. Following G. Mackey and G. Ludwig, we first consider a minimal state-effect-probability (minimal SEFP) structure. In order to include partial operations of sum and difference, an additional axiom is postulated and a SEFP structure is obtained. It is then shown that a SEFP structure is equivalent to an effect algebra with an order determining set of states. We also consider -SEFP structures and show that these structures distinguish Hilbert space from incomplete inner product spaces. Various types of sharpness are discussed and under what conditions a Brouwer complementation can be defined to obtain a BZ-poset is investigated. In this case it is shown that every effect has a best lower and upper sharp approximation and that the set of all Brouwer sharp effects form an orthoalgebra.     

Circular dichroism spectra and absolute configuration of some aryl methyl sulfoxides

The absorption and circular dichroism (CD) spectra of three aryl sulfoxides, i.e. (-)-(S)-1-naphthyl methyl sulfoxide, (S)-1, (-)-(S)-1-(2-methyl)naphthyl methyl sulfoxide, (S)-2 and (-)-(S)-9-phenanthryl methyl sulfoxide, (S)-3, have been interpreted by means of the coupled oscillator model formulated by DeVoe. Theoretical spectra have been calculated starting from input geometries provided by molecular mechanics (MMX) calculations and by employing standard spectroscopic parameters to describe the allowed transitions of the aromatic and the sulfoxide chromophores. The satisfactory agreement between the predicted and experimental spectra allows us to confirm the configurational assignment of these compounds as (-)/(S). The analysis of CD spectra, affording the right assignment of the absolute configuration (AC) of the alkyl aryl sulfoxides, then offers a practical alternative to the more complex vibrational circular dichroism spectroscopy and ab initio optical rotation calculation techniques that have been used very recently to assign the AC of (-)-2 and (-)-3.     

First example of a Sn-C bond cleaved product in the reaction of Ph3SnOSnPh3 with carboxylic acids. 3D-supramolecular network formation in the X-ray crystal structure of [Ph2Sn(OH)OC(O)(Rf)]2, Rf = 2,4,6-(CF3)3C6H2

A 1:2 reaction of Ph3SnOSnPh3 1 with RfCOOH 2 leads to the formation of [Ph2Sn(OH)OC(O)(Rf)]2 3, by means of a facile Sn-C bond cleavage process.     

Quaternionic Electron Theory: Dirac's Equation

We perform a one-dimensional complexifiedquaternionic version of the Dirac equation based oni-complex geometry. The problem of the missing complexparameters in quaternionic quantum mechanics withi-complex geometry is overcome by a nicetrick which allows us to avoid the Diracalgebra constraints in formulating our relativisticequation. A brief comparison with other quaternionicformulations is also presented.     

Neutrino Chiral Oscillations

Under certain conditions a localized wave packetexhibits Zitterbewegung. A similar phenomenon occurs forthe chirality of a massive particle. In the case ofmassive neutrinos, since they are detected via the V–A weak charged currents, thisoscillation may even explain the missingsolar neutrino experiments. The neutrino remains a masseigenstate, but contains an almost sterile right-handedcomponent. This qualitative discussion opens up a numberof interesting physical considerations.     

Axiomatic unsharp quantum theory (From Mackey to Ludwig and Piron)

On the basis of Mackey's axiomatic approach to quantum physics or, equivalently, of a state-event-probability (SEVP) structure, using a quite standard fuzzification procedure, a set of unsharp events (or effects) is constructed and the corresponding state-effect-probability (SEFP) structure is introduced. The introduction of some suitable axioms gives rise to a partially ordered structure of quantum Brouwer-Zadeh (BZ) poset; i.e., a poset endowed with two nonusual orthocomplementation mappings, a fuzzy-like orthocomplementation, and an intuitionistic-like orthocomplementation, whose set of sharp elements is an orthomodular complete lattice. As customary, by these orthocomplementations the two modal-like necessity and possibility operators are introduced, and it is shown that Ludwig's and Jauch-Piron's approaches to quantum physics are interpreted in complete SEFP. As a marginal result, a standard procedure to construct a lot of unsharp realizations starting from any sharp realization of a fixed observable is given, and the relationship among sharp and corresponding unsharp realizations is studied.     

Indium-mediated reduction of hydroxylamines to amines

[reaction: see text] A novel and simple procedure for reduction of hydroxylamines to the corresponding amines by means of indium powder in aqueous media is reported. Applicability to one-pot reactions and isoxazolidine N-O bond reduction is also demonstrated. A catalytic version of the process using 2-5% In in the presence of other metals (Zn, Al) has been successfully developed.     

The Role ofChirocephalus diaphanusin the Early Recognition of Environmental Pollution by Trace Elements

A study was undertaken to evaluate whether the fairy shrimpChirocephalus diaphanus(Crustacea: Anostraca) could be considered as a species capable of biomonitoring environmental contamination by accumulating trace elements. This preliminary investigation aimed at assessing the levels of As, Cd, Cu, Hg, Pb, Se, and Zn in natural waters as well as in adults and cysts of fairy shrimps sampled from five different sites in central Italy. Trace elements were determined by inductively coupled plasma (ICP)-based spectrometry. In particular, ICP–mass spectrometry (ICP-MS) was resorted to in most cases due to its high detection power. Pretreatment of samples (adults and cysts) consisted basically in the HNO₃-assisted microwave digestion of the material. The highest levels of trace elements were found in the anostracan cysts, with concentration ranges (μg/g) of 0.464–3.11 for As, up to 0.820 for Cd, 2.62–13.0 for Cu, 0.011–0.213 for Hg, 0.966–8.46 for Pb, 0.295–2.45 for Se, and 16.4–50.4 for Zn. On the other hand, the lowest concentrations were found in natural waters, with values close to the ICP-MS detection power for some elements. These data are probative of a bioconcentration process, the extent of which is proportional to the environmental level of each element. This may turn out to be useful in planning biological monitoring and assessing ecotoxicological consequences which might ensue from the diffusion of the exploitation of such organisms in aquaculture.