Quantum Conservative Gates for Finite-Valued Logics

We introduce some conservative gates for finite-valued logics which are able to realize all the main connectives of the many-valued logics of ?ukasiewicz, the MV-algebras of Chang and Brower–Zadeh algebras. After a brief exposition of the motivations for this work, the gates are defined and their properties are explored. Finally, a possible quantum realization of them is proposed, using three techniques: a “brute force” method--an extension of the Conditional Quantum Control argument, and a new technique which we call the Constants Method. For all these techniques, the unitary operator which describes the gate is a sum of local operators.     

Brouwer-Zadeh (Fuzzy-intuitionistic) posets for unsharp quantum mechanics

The partial ordered structure which plays for unsharp quantum mechanics the same role of orthomodular lattices for ordinary quantum mechanics is introduced. Differently from the unsharp case, in which one can identify quantum propositions (i.e., Hilbert space subspaces) with yes-no devices (i.e., orthogonal projections) they are tested by, in the unsharp case this identification is broken down: every quantum generalized proposition (i.e., pair of mutually orthogonal subspaces) is tested by many different yes-no devices (i.e., Hilbert space effects). The set of all quantum effects has a structure of Brouwer-Zadeh poset, canonically embeddable in a (minimal) Brouwer-Zadeh lattice, whereas the set of all quantum generalized propositions has a structure of Brouwer-Zadeh complete lattice.A Brouwer-Zadeh poset is defined as a partially ordered structure equipped with two nonusual orthocomplementations: a regular degenerate (Zadeh or fuzzy-like) one and a weak (Brouwer or intuitionistic-like) one linked by an interconnection rule. Using these two orthocomplementations it is possible to introduce the two modal-like operators of necessity and possibility.     

Physical content of preparation-question structures and Brouwer-Zadeh lattices

We give a criterion to compare the physical content of different mathematical structures derived from a preparation-question structure. Then this criterion is used in order to compare the physical content of the (Jauch-Piron's) property lattice with the physical content of the poset of testable properties. We prove that for complete preparation-question structures these two structures carry the same physical content; moreover the set of testable properties has the algebraic structure of the Brouwer-Zadeh lattice. For more general preparation-question structures the physical content of the poset of testable property can be larger than that of the property lattice. Physically relevant examples of the possible cases are given.     

Unusual volumetric and hydration behavior of the catanionic system sodium undecenoate: sodecyltrimethylammonium bromide

Following the studies on the effect of double bonds in the surfactant hydrophobic tail on the formation of mixed surfactant aggregates, we studied the viscosity and density of the system Sodium 10-undecenoate (SUD)–decyltrimethylammonium bromide (DTAB)–water. We found that the partial molar volume (pmv) and intrinsic viscosity of both, micellised and unmicellised mixtures, are non-ideal, dependent on the mixture composition and related to structural changes in micelles. These phenomena are caused by the presence of the double bond at the distal extreme of the SUD molecule, which has some affinity with water by formation of hydrogen bonds. In particular, as far as we know, this is the first report on non-ideal behavior of the pmv in mixed micelles.     

The aqueous cationic system sodium undecenoate-dodecyltrimethylammonium bromide at low concentration

The aqueous sodium undecenoate (SUD) –dodecyltrimethylammonium bromide (DTAB) catanionic system was studied at low concentration. The system did not precipitate, even at a 1:1 SUD:DTAB proportion, but showed the formation of a coacervate in a range of surfactant mixture compositions. Micelles have a preferential composition of 0.37 mole fraction of SUD. This behavior is attributed to the presence of the double bond at the distal extreme of the SUD molecule, which can form hydrogen bonds with water. Consequently, the –CH=CH₂ group is situated at the interface between the hydrocarbon micelle core and water, reducing the interfacial free energy. Structural computations demonstrate that the mentioned SUD proportion produces complete coverage of the micelle surface by the double bonds.     

The hydration of sodium dehydrocholate micelles

The hydration of micellised sodium dehydrocholate molecules was determined by viscosity measurements. It was found that there are 39 water molecules for each micellised surfactant molecule. About ten water molecules may be attributed to the hydration of the sodium carboxylate group. By assignation of two water molecules to each of the three carbonyl groups, the total hydration of a micellised sodium dehydrocholate molecule was estimated as about 16 water molecules. The remaining 23 water molecules per micellised sodium dehydrocholate molecule may be attributed to water trapped in the structure of micelles.     

Cobalt blood levels after total hip replacement (THR): a new follow-up study in Trieste (Italy)

Cobalt and chromium release in patients undergone a metal-on-metal total hip replacement (THR) is a matter recently discussed and whose we do not have enough information about it yet. In literature there is little data and not completely indicative, in the biological fluids and organs the amounts of released metals are different. This is also due to the fact that cobalt and chromium blood levels can change depending on physical and working activity, individual feeding and metabolism. The results obtained confirm the presence of an increase of cobalt inthe blood of patients after total hip replacement, while the chromium levels are almost alike: average values in patients operated are 4.1 +/- 1.5 microg/L for cobalt (0.3 +/- 0.1 microg/L in the control group) and 4.5 +/- 2.9 microg/L for chromium (4.7 +/- 2.4 microg/L in the control group). In spite of the cobalt values stand below the concentration generally considered dangerous, the difference between the two examined groups points out that a risk exists for the health of these patients. These results must be confirmed by further studies, providing better information and more reliable and biocompatible materials.     

Some results on BZ structures from Hilbertian unsharp quantum physics

Some algebraic structures determined by the class (þ) of all effects of a Hilbert space þ and by some subclasses of (þ) are investigated, in particular de Morgan-Brouwer-Zadeh posets [it is proved that (þ ⁿ )(n<) has such a structure], Brouwer-Zadeh ^* posets (a quite trivial example consisting of suitable effects is given), and Brouwer-Zadeh ³ posets which are both de Morgan and ^*.It is shown that a nontrivial class of effects of a Hilbert space exists which is a BZ ³ poset. An -preclusivity relation on the set of all vectors of þ is introduced, and it is shown that it satisfies the regularity condition also for [1/2, 1].     

Fuzzy quantum logic II. The logics of unsharp quantum mechanics

A survey of the main results of the Italian group about the logics of unsharp quantum mechanics is presented. In particular partial ordered structures playing with respect to effect operators (linear bounded operatorsF on a Hilbert space such that, 0¦F²) the role played by orthomodular posets with respect to orthogonal projections (corresponding to sharp effects) are analyzed. These structures are generally characterized by the splitting of standard orthocomplementation on projectors into two nonusual orthocomplementations (afuzzy-like and anintuitionistic-like) giving rise to different kinds of Brouwer-Zadeh (BZ) posets: de Morgan BZ posets, BZ^* posets, and BZ³ posets. Physically relevant generalizations of ortho-pair semantics (paraconsistent, regular paraconsistent, and minimal quantum logics) are introduced and their relevance with respect to the logic of unsharp quantum mechanics are discussed.     

The aggregation of sodium dehydrocholate in water

 We used a battery of different methods to study the association in aqueous sodium dehydrocholate (NaDHC) solutions. This salt associates by a stepwise mechanism. Below (9.6 ± 4.2) × 10⁻⁴ mol dm⁻³ there is a molecular solution with some strongly insoluble dehydrocholic acid produced by hydrolysis. Between (9.6 ± 4.2) × 10⁻⁴ and (5.2 ± 2.2) × 10⁻³ mol dm⁻³, an aggregate similar to acid soap (NaDHC.HDHC) appears and its amount and the aggregate's size increase with concentration. At =(2.20 ± 0.85) × 10⁻² mol dm⁻³ the aggregates formed have properties usually associated with true micelles, such as solubilisation of water-insoluble dyes. These aggregates increase in size with concentration and change their shape at 8 × 10⁻² mol dm⁻³, giving nonsymmetrical aggregates. The changes in the solution physicochemical properties at these concentrations may be misinterpreted and this explains the different values of the critical micelle concentration reported in the literature for substances with similar structure, such as bile salts. Received: 14 May 2001 Accepted: 10 August 2001