Boundary blow-up for differential equations with indefinite weight

We obtain results of existence and multiplicity of solutions for the second-order equation x″+q(t)g(x)=0, with x(t) defined for all t∈]0,1[ and such that x(t)→+∞ as t→0⁺ and t→1⁻. We assume g having superlinear growth at infinity and q(t) possibly changing sign on [0,1].     

On some recent proposals for testing macrorealism versus quantum mechanics

In order to evaluate its relevance, we reconsider critically the recent proposal by Leggett and Garg to test macrorealism against quantum mechanics by resorting to experiments involving noninvasive measurement processes on a SQUID. Our conclusion is that, in spite of the fact that the proposed experiment would neither constitute a test of macrorealism nor a test of macrocontextuality, a simplified form of it represents a (presumably) feasible experiment permitting a direct test of macroscopic quantum coherence. We also analyze the proposal from the point of view of the recent attempts to build up model theories allowing to take, within a purely quantum framework, a macrorealistic position about natural phenomena, i.e., the socalled dynamical reduction models and we stress that the proposed experiment has no relevance for the dynamical reduction program, as developed so far. However consideration of the SQUID system allows one to test other possible dynamical mechanisms leading to the objectification of macroproperties which could, in principle, be operative. We also briefly sketch experimental procedures to be followed to get all relevant information concerning macrocoherence.     

On a new stochastic global optimization algorithm based on censored observations

In this paper a new algorithm is proposed for global optimization problems. The main idea is that of modifying a standard clustering approach by sequentially sampling the objective function while adaptively deciding an appropriate sample size. Theoretical as well as computational results are presented.     

Phase transitions in N—n-propylpyridinium-TCNQ2 and N—n-butylpyridinium-TCNQn at high pressures

The electrical resistivity of N-n-propylpyridinium-TCNQ₂ (NPPy-TCNQ₂) and N-n-butylpyridinium-TCNQ_n (NBPy-TCNQ_n) has been measured as a function of temperature and pressure. Phase transitions in these salts have been studied at high pressures. The transition temperature (T_c) in NPPy-TCNQ₂ at atmospheric pressure increased with increasing pressure at the rate of dT_c/dP = + 12.0 degkbar^?1. The value of volume change calculated from the Clapeylon-Clausius relation was + 4.4 cm³ mol^?1. The electrical resistivity along the a- and c-axis increased with increasing pressure below 7 kbar. This anomalous electrical behaviour is closely related to the crystal structure of NPPy-TCNQ₂. The resistivity dropped sharply at about 11 kbar. This abrupt change may be due to a new pressure induced phase transition.The T_c of the NBPy-TCNQ_n increased remarkably with increasing pressure up to 0.7 kbar, above which the phase transition disappeared. The phase transitions of N-n-alkyl-substituted pyridinium TCNQ salts depend strongly on the nature of cations.     

Large deviations and Lifshitz singularity of the integrated density of states of random Hamiltonians

We consider the integrated density of states (IDS) ρ_∞(λ) of random Hamiltonian H_ω=?Δ+V_ω, V_ω being a random field on ? ^d which satisfies a mixing condition. We prove that the probability of large fluctuations of the finite volume IDS |Λ|^?1ρ(λ, H_Λ(ω)), Λ ? ? ^d , around the thermodynamic limit ρ_∞(λ) is bounded from above by exp {?k|Λ|},k>0. In this case ρ_∞(λ) can be recovered from a variational principle. Furthermore we show the existence of a Lifshitztype of singularity of ρ_∞(λ) as λ → 0⁺ in the case where V_ω is non-negative. More precisely we prove the following bound: ρ_∞(λ)≦exp(?kλ^?d/2) as λ → 0⁺ k>0. This last result is then discussed in some examples.     

Sequential stopping rules for the multistart algorithm in global optimisation

In this paper a sequential stopping rule is developed for the Multistart algorithm. A statistical model for the values of the observed local maxima of an objective function is introduced in the framework of Bayesian non-parametric statistics. A suitablea-priori distribution is proposed which is general enough and which leads to computationally manageable expressions for thea-posteriori distribution. Sequential stopping rules of thek-step look-ahead kind are then explicitly derived, and their numerical effectiveness compared.     

Evolution of Classical and Quantum States in the Groupoid Picture of Quantum Mechanics

The evolution of states of the composition of classical and quantum systems in the groupoid formalism for physical theories introduced recently is discussed. It is shown that the notion of a classical system, in the sense of Birkhoff and von Neumann, is equivalent, in the case of systems with a countable number of outputs, to a totally disconnected groupoid with Abelian von Neumann algebra. The impossibility of evolving a separable state of a composite system made up of a classical and a quantum one into an entangled state by means of a unitary evolution is proven in accordance with Raggio’s theorem, which is extended to include a new family of separable states corresponding to the composition of a system with a totally disconnected space of outcomes and a quantum one.     

Computer-aided design of nanostructured materials containing trisaza-bridged [60]fullerene

A novel fullerene-based building block for the synthesis of nanostructured materials has been designed with the aid of electronic structure theory calculations and molecular modeling. The building block consists of four trisaza-bridged C₆₀ fullerene molecules linked to a central cubane (C₈) unit. Each C₆₀ unit is located on the vertex of a tetrahedron with edge of 2.2 nm. One possible packing mode of the building blocks to yield the nanostructured material is suggested.