Thermodynamic non-additivity in disordered systems with extended phase space

Non-additivity effects in coupled dynamic-stochastic systems are investigated. It is shown that there is a mapping of the replica approach to disordered systems with finite replica indexn on Tsallis non-extensive statistics, if the average thermodynamic entropy of the dynamic subsystem differs from the information entropy for the probability distribution in the stochastic subsystem. The entropic indexq is determined by the entropy difference ΔS. In the case of incomplete information, the entropic indexq=1−n is shown to be related to the degree of lost information.     

Proof of a conjecture on the supports of Wigner distributions

In this note we prove that the Wigner distribution of an f ∈ L₂(ℝ_n) cannot be supported by a set of finite measure in ℝ_2n unless f=0. We prove a corresponding statement for cross-ambiguity functions. As a strengthening of the conjecture we show that for an f ∈ L₂(ℝ_n) its Wigner distribution has a support of measure 0 or ∞ in any half-space of ℝ_2n.     

Uniform random number generation

In typical stochastic simulations, randomness is produced by generating a sequence of independent uniform variates (usually real-valued between 0 and 1, or integer-valued in some interval) and transforming them in an appropriate way. In this paper, we examine practical ways of generating (deterministic approximations to) such uniform variates on a computer. We compare them in terms of ease of implementation, efficiency, theoretical support, and statistical robustness. We look in particular at several classes of generators, such as linear congruential, multiple recursive, digital multistep, Tausworthe, lagged-Fibonacci, generalized feedback shift register, matrix, linear congruential over fields of formal series, and combined generators, and show how all of them can be analyzed in terms of their lattice structure. We also mention other classes of generators, like non-linear generators, discuss other kinds of theoretical and empirical statistical tests, and give a bibliographic survey of recent papers on the subject.     

Range reliability in random walks

This paper introduces a definition of reliability based on a process range. Thus, process failure is defined when the range of a process first reaches a given and unacceptable level. The Mean Time To Failure (MTTF) which is denned as the mean of the first time for a range to attain a given amplitude is then calculated for an asymmetric random walk process. The probability distribution of the range is then given and the process reliability over long periods of system operations are then calculated. Applications such as the control of wings movements, stock price and exchange rates volatility (defined in terms of reliability) are also used to motivate the usefulness of range processes in reliability studies. Finally, we point out that there is necessarily a relationship between the range reliability and the propensity of a series to become chaotic.     

Encapsulation of ZnS:Mn2+ nanocrystals with diblock copolymers

The encapsulation of the nanocrystalline manganese‐doped zinc sulfide (ZnS:Mn) in poly(styrene‐b‐2vinylpyridine) (PS‐PVP) diblock copolymers is reported. Below the critical micelle concentration in the absence of nanocrystals (NCs), inverse micelles of PS‐PVP were induced by adding ZnS:Mn NCs, the presence of which was confirmed by scanning force microscope and dynamic light scattering. In toluene, a PS‐selective solvent, the less‐soluble PVP blocks preferentially surround the ligand‐coated ZnS:Mn NCs. For PS‐PVP encapsulated ZnS:Mn NCs, the ratio of blue emission to orange emission of ZnS:Mn NCs is dependent on both the concentration of PS‐PVP and the solvent quality. The pyridine of PVP blocks form complexes with the Zn atoms via the nitrogen lone pair and thus the sulfur vacancies are passivated. As a result, the defect‐related blue emission is selectively quenched even when the micelles are not formed. As the concentration of PS‐PVP encapsulating the ZnS:Mn NCs increases, the intensity of blue emission decreases. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3227–3233, 2006     

Convergent Star Product Algebras on ‘ax+b’

We define nontempered (exponential growth) function spaces on the Lie group ax+b which are stable under some left-invariant (convergent) star product. The techniques used to achieved the latter come from symmetric spaces geometry and star representation theory.     

Reactions de photoaddition de benzo[b]selenophenes avec l'acetylene dicarboxylate de methyle et avec le dichloro-1,2 ethylene

Photoirradiated in presence of acetophenone, benzo[b]selenophene and its 3-methyl derivative add to dimethyl acetylenedicarboxylate. In each ease, the primary reaction product is unstable and has not been isolated. Photoexeited in its triplet state (the energy of which is in the neighbourhood of 69 $\text{kcal}\text{mole}$) benzo[b]selenophene and its 2- and 3-methyl, 2,3 dimethyl, 3 acetoxy and 2-methyl-3-acetoxy derivatives add to 1,2 dichloroethylene leading to cyclobutanes. Neither cyclo-addition occurs in absence of photosensitiser. Single-crystal X-ray analysis gave the structures of the two adducts of 3-acetoxybenzo[b]selenophene with trans-1,2-dichloroethylene. In both compounds the chlorine atoms are trans.