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.     

Palladium(II) and platinum(II)-C(3)-substituted 2,2′-bipyridines

Reaction of Pd(OAc)₂ with HL¹ and HL² (HL¹=6-iso-propyl-2,2-bipyridine; HL²=6-neo-pentyl-2,2-bipyridine), followed by treatment with LiCl or KI, gives [PdCl(L¹)]₂, (1), [PdCl(L²)]₂ (2), and [PdI(L²)]₂ (3), respectively. The chloride bridge in complexes1 and2 is split by PPh³ to give the mononuclear species PdCl(L¹)(PPh₃) (4) and PdCl(L²)(PPh₃) (5). Spectroscopic data provide evidence for coordination of the deprotonated ligands through a nitrogen and the C₍₃₎ atom of the 6-substituted pyridine. An analogous platinum complex PtCl(L³)(SMe₂) (6) (HL³=6-tert-butyl-2,2-bipyridine) was obtained from trans-PtClMe(SMe₂)₂ and HL³. The crystal structures of compounds1 and6 have been solved by X-ray diffraction analysis.Dipartimento di Chimica, Universita di Sassari, via Vienna 2, I-07100 Sassari, Italy; Dipartimento di Chimica Strutturale e Stereochimica Inorganica, Universita di Milano, Centro CNR, I-20133 Milano, Italy; Published in Khimiya Geterotsiklicheskikh Soedinenii, No. 8, pp. 1127–1137, August, 1999.     

Stochastic Bounds for the Sparre Andersen Process

In this paper we define two stochastic processes that are smaller and greater in usual stochastic order than the Sparre Andersen process. We derive, as a consequence, upper and lower bounds of its marginal distributions, and of the distributions of its first passage times above fixed thresholds. We also present a generalization of these stochastic bounds for risk processes perturbed by diffusion.AMS 2000 Subject Classification: 60K10, 60E15Partially supported by the italian PRIN-Cofin 2004 “Stochastic models in mathematical finance” (F. Pellerey) and PRIN-Cofin 2003 “Numerical, analytical and simulation methods with reference to reliability in neuronal signal transmission” (C. Zucca).     

Fuzzy events and fuzzy logics in classical information systems

Classical information systems are introduced in the framework of measure and integration theory. The measurable characteristic functions are identified with the exact events while the fuzzy events are the real measurable functions whose range is contained in the unit interval. Two orthogonality relations are introduced on fuzzy events, the first linked to the fuzzy logic and the second to the fuzzy structure of partial a Baer¹-ring. The fuzzy logic is then compared with the “empirical” fuzzy logic induced by the classical information system. In this context, quantum logics could be considered as those empirical fuzzy logics in which it is not possible to have preparation procedures which provide physical systems whose “microstate” is always exactly defined.     

An Unsharp Logic from Quantum Computation

Logical gates studied in quantum computation suggest a natural logical abstraction that gives rise to a new form of unsharp quantum logic. We study the logical connectives corresponding to the following gates: the Toffoli gate, the NOT and the $\sqrt {NOT} $ (which admit of natural physical models). This leads to a semantic characterization of a logic that we call quantum computational logic (QCL).     

A Monte Carlo Method for the Simulation of First Passage Times of Diffusion Processes

A reliable Monte Carlo method for the evaluation of first passage times of diffusion processes through boundaries is proposed. A nested algorithm that simulates the first passage time of a suitable tied-down process is introduced to account for undetected crossings that may occur inside each discretization interval of the stochastic differential equation associated to the diffusion. A detailed analysis of the performances of the algorithm is then carried on both via analytical proofs and by means of some numerical examples. The advantages of the new method with respect to a previously proposed numerical-simulative method for the evaluation of first passage times are discussed. Analytical results on the distribution of tied-down diffusion processes are proved in order to provide a theoretical justification of the Monte Carlo method.     

Survival,Extinction and Approximation of Discrete-time Branching Random Walks

We consider a general discrete-time branching random walk on a countable set X. We relate local, strong local and global survival with suitable inequalities involving the first-moment matrix M of the process. In particular we prove that, while the local behavior is characterized by M, the global behavior cannot be completely described in terms of properties involving M alone. Moreover we show that locally surviving branching random walks can be approximated by sequences of spatially confined and stochastically dominated branching random walks which eventually survive locally if the (possibly finite) state space is large enough. An analogous result can be achieved by approximating a branching random walk by a sequence of multitype contact processes and allowing a sufficiently large number of particles per site. We compare these results with the ones obtained in the continuous-time case and we give some examples and counterexamples.     

State of supported rhodium nanoparticles for methane catalytic partial oxidation (CPO): FT-IR studies

The effect of pretreatments as well as of rhodium precursor and of the support over the morphology of Rh nanoparticles were investigated by Fourier transform infrared (FT-IR) spectroscopy of adsorbed CO. Over a Rh/alumina catalyst, both metallic Rh particles, characterized by IR bands in the range 2070-2060 cm-1 and 1820-1850 cm-1, and highly dispersed rhodium species, characterized by symmetric and asymmetric stretching bands of RhI(CO)2 gem-dicarbonyl species, are present. Their relative amount changes following pretreatments with gaseous mixtures, representative of the catalytic partial oxidation (CPO) reaction process. The Rh metal particle fraction decreases with respect to the Rh highly dispersed fraction in the order CO approximately CO/H2 > CH4/H2O, CH4/O2 > CH4 > H2. The metal particle dimensions decrease in the order CH4/O2 > H2 > CH4/H2O > CO > CO/H2. Grafting from a carbonyl rhodium complex also increases the amount and the dimensions of Rh0 particles at the catalyst surface. Increasing the ratio (extended rhodium metal particles/highly dispersed Rh species) allows a shorter conditioning process. The surface reconstruction phenomena going on during catalytic activity are related to this effect.