On the Decompositions of a Quantum State

We classify all the decompositions of a quantum state as a weighted sum of one dimensional projectors. In particular we describe explicitly the set of irreducible decompositions. The physical interest in this problem rests on the possibility of interpreting the decomposition in terms of a classical mixture.     

Quantum theory of measurement and the modal interpretations of quantum mechanics

Several variants of the modal interpretation of quantum mechanics have been introduced and discussed in recent years. In this paper we present a study of the mathematical foundations of such an interpretation in the framework of the quantum theory of measurement.     

Quantum mechanics andp-adic numbers

We study the possibility of representing the proposition lattice associated with a quantum system by a linear vector space with coefficients from ap-adic field. We find inconsistencies if the lattice is assumed, as usual, to be irreducible, complete, orthocomplemented, atomic, and weakly modular.     

Interacting wakes of two normal flat plates an investigation based on phase averaging of LDA signals

The flow around two bluff bodies in tandem is an interesting phenomenon whose nature strongly depends on the distance between the bodies. In this work oil smoke visualizations of the flow around two normal flat plates in tandem configuration are compared with phase averaged Laser Doppler Anemometry measurements of the flow field for a full period. Phase averaging is exploited to resolve the mean time evolution of the flow and the signal from a single constant temperature hot wire probe is employed as phasing reference. The flow-field information obtained from visualizations agrees well with quantitative indications provided by measures, and the comparison allows to precisely understand what information can be extracted from simple visualizations. As a result, new insight in flow mechanism is obtained from the analysis of the flow data showing that, for the analyzed plate distance, the gap between the two plates behaves substantially as a cavity while the vortex formation process takes place in the wake region behind the aft plate.     

SiO2-B2O3 xerogels: The problem of boron leaching

Borosilicate materials are of interest for many technological applications. Whereas sol-gel techniques are well suited for the preparation of these materials, the nominal concentration of boron is often not maintained, and a considerable amount of boron is lost during the preparation procedure. In this work we deal with the synthesis of borosilicate systems in order to analyse the problem of the boron loss. Different sol-gel precursors of B₂O₃ were explored and organically modified silicon alcoxide were tested, in addition P₂O₅ co-doping was proposed. IR spectroscopy, differential Scanning Calorimetry, Thermogravimetry and ICP-OES analyses were performed. Sol-gel synthesis of SiO₂-B₂O₃ xerogels with a high boron content (> 18 wt.%) was successfully obtained by employing trimethoxyboroxine and 3-aminopropyltriethoxysilane.     

Square-integrability modulo a subgroup

We prove a weak form of the Frobenius reciprocity theorem for locally compact groups. As a consequence, we propose a definition of square-integrable representation modulo a subgroup that clarifies the relations between coherent states, wavelet transforms and covariant localisation observables. A self-contained proof of the imprimitivity theorem for covariant positive operator-valued measures is given.

     

Conditional probabilities on orthomodular lattices

A definition of generalized probability on an orthomodular lattice which includes as particular cases the classical probability space and non-commutative probability theory on a von Neumann algebra is proposed. In this generalized structure the problem of conditioning with respect to Boolean σ-subalgebras is examined.     

Generalized Orthogonality Relations and <Emphasis Type="Italic">SU</Emphasis>(1,1)-Quantum Tomography

We present a mathematically precise derivation of some generalized orthogonality relations for the discrete series representations of SU(1,1). These orthogonality relations are applied to derive tomographical reconstruction formulas. Their physical interpretation is also discussed. We are very pleased to dedicate this paper to Pekka Lahti, for his sixtieth birthday. In particular, one of us (G.C.) would like to remember a long lasting fraternal friendship that goes well beyond the (rather narrow) borders of Quantum Mechanics.     

Force measurements on cell repellant and cell adhesive alginic acid coated surfaces

The atomic force microscope (AFM) was used to acquire force versus distance curves between the cantilever tip and samples bearing a surface overlayer of covalently linked alginic acid. The alginic acid coating resists cell-adhesion in in vitro experiments involving a normal and a tumor cell line. However, the surface becomes cell adhesive when alginic acid coated samples are subjected to glow discharge treatment. Force curves show in both cases the typical features resulting from the interaction between the cantilever tip and a hydrophilic, compressible polymer overlayer, suggesting that in both cases a diffuse interface with water exists. Following some recent findings on oligoethyleneglycol-terminated self-assembled-monolayers, it is suggested that conformational and molecular aspects of hydrophilic surface layers, rather than steric repulsion effects, could play a significant role in the mechanism that controls resistance to bio-adhesion.