The Copenhagen Variant of the Modal Interpretation and Quantum theory of measurement

The implications of the Copenhagen Variant of the Modal Interpretation of Quantum Mechanics are studied in the context of the quantum theory of measurement. Two formulations of this interpretation are discussed. Both of them imply specifications of the notion of measurement which go beyond the minimal calibration condition of a measurement. The weaker one implies some algebraic and topological constrains on the measurement coupling, whereas the stronger formulation of the same interpretation implies that measurements are necessarily of the first kind.     

The measurement statistics interpretation of quantum mechanics: Possible values and possible measurement results of physical quantities

Starting with the Born interpretation of quantum mechanics, we show that the quantum theory of measurement, supplemented by the strong law of large numbers, leads to a measurement statistics interpretation of quantum mechanics. A probabilistic characterization of the spectrum of a physical quantity is given, and an analysis of the notions of possible values and possible measurement results is carried out.     

Quantum mechanics of the quaternionic Hilbert spaces based upon the imprimitivity theorem

We survey the realization of quantum mechanics in quaternionic Hilbert spaces following the methods of Mackey, who examined the complex and real cases exploiting the imprimitivity theorem. We show that there exists a unique unitary skew-adjoint operator which commutes with all the observables. This operator not only plays the role of the imaginary unit in the complex case, but allows a complexification of the Hilbert space by the choice of any quaternionic imaginary unit. Difficulties in the definition of time reversal, however, arise because of the properties of the quaternionic field. The introduction of an extra imaginary unit, commuting with the others, is suggested in order to implement time reversal properly. In the Appendix we give the proof of the imprimitivity theorem, in the quaternionic case, that we use in the paper.     

Atomic force microscopy evaluation of aqueous interfaces of immobilized hyaluronan

Hyaluronan (HA) was immobilized on aminated glass surfaces in three different ways: by simple ionic interaction and by covalent linking at low density and at full density. In agreement with previous reports, in vitro experiments show that the outcome of fibroblast adhesion tests is markedly affected by the details of the coupling procedure, suggesting that different interfacial forces are operating at the aqueous/HA interface in the three cases investigated. The interfacial properties of the HA-coated surfaces were probed by force-distance curves obtained with the atomic force microscope (AFM). This approach readily shows significant differences among the tested samples, which are directly related to the coupling strategy and to results of cell adhesion tests. In particular, the range of interaction between the tip and the surface is much lower when HA is covalently linked than when it is ionically coupled, suggesting a more compact surface structure in the former case. Increasing HA surface density minimizes the interaction force between the surface and the AFM tip, likely reflecting more complete shielding by the HA chains of the underlying substrate. In summary, these measurements clearly show the different nature of the aqueous interfaces tested, and underline the role of this analytical approach in the development and control of finely tuned biomaterial surfaces.     

Incorporation of Boron in Mesoporous Bioactive Glass Nanoparticles Reduces Inflammatory Response and Delays Osteogenic Differentiation

Mesoporous bioactive glass nanoparticles (MBG) are multifunctional building blocks for tissue regeneration and nanomedicine applications. Incorporation of biologically active ions can endow MBG with additional functionalities toward promoted therapeutic effects. Here, boron is incorporated into MBG by using a sol–gel approach. The concentration of boron incorporated is controllable by tuning the amount of boron precursor. Two types of boron-doped MBG, namely 10B- and 15B-MBG (5.8 and 6.5 mol% of B₂O₃, respectively) are synthesized. Boron incorporation does not significantly influence the particle morphology. All synthesized particles exhibit a sphere-like shape with a size ranging from 100 to 300 nm. 10B- and 15B-MBG show large specific surface area (346 and 320 m² g⁻¹, respectively) and pore volume. Both boron-doped MBG exhibit remarkable in vitro bioactivity and noncytotoxicity. Boron incorporation is shown to reduce the inflammatory response linked to macrophages as indicated by downregulated expression of pro-inflammatory genes. However, boron incorporation delays the osteogenic differentiation in osteoblasts as indicated by the downregulated expression of pro-osteogenic genes. The results demonstrate the promising potential of using boron-doped MBG to modulate inflammatory response for bone regeneration under inflammatory conditions, as shown in this study for the first time.     

On discrete frames associated with semidirect products

For groups which are the semidirect product of some vector group with a unimodular group we prove that the existence of a discrete frame obtained from an at-most countable set of vectors through the action of a given unitary representation implies that the representation in use has to be square-integrable.     

On the quantum theory of sequential measurements

The quantum theory of sequential measurements is worked out and is employed to provide an operational analysis of basic measurement theoretical notions such as coexistence, correlations, repeatability, and ideality. The problem of the operational definition of continuous observables is briefly revisited, with a special emphasis on the localization observable. Finally, a brief overview is given of possible applications of the theory to various fields and problems in quantum physics.     

Ideal,first-kind measurements in a proposition-state structure

Let be an orthomodular lattice and a strongly ordering set of probability measures on such that supports of measures exist in . Then we show the existence of a set of mappings of into that are physically interpretable as ideal, first-kind measurements.     

Mathematical foundations of classical embeddings of quantum mechanical state spaces

In this paper we review the basic mathematical properties that allow the embedding of quantum state spaces into spaces of classical probability measures. In particular, the precise topological structures used for these immersions are described.     

Brownian rotational relaxation and power absorption in magnetite nanoparticles

We present a study of the power absorption efficiency in several magnetite-based colloids, to asses their potential as magnetic inductive hyperthermia (MIH) agents. Relaxation times τ$\tau$ were measured through the imaginary susceptibility component χ^″(T)${\chi }^{″}(T)$, and analyzed within Debye's theory of dipolar fluid. The results indicated Brownian rotational relaxation and allowed to calculate the hydrodynamic radius close to the values obtained from photon correlation. The study of the colloid performances as power absorbers showed no detectable increase of temperature for dextran-coated Fe₃O₄ nanoparticles, whereas a second Fe₃O₄-based dispersion of similar concentration could be heated up to 12 K after 30 min under similar experimental conditions. The different power absorption efficiencies are discussed in terms of the magnetic structure of the nanoparticles.