Global heat kernel bounds via desingularizing weights

We obtain global heat kernel bounds for semigroups which need not be ultracontractive by transferring them to appropriately chosen weighted spaces where they become ultracontractive. Our construction depends upon two assumptions: the classical Sobolev imbedding and a “desingularizing” (L¹,L¹) bound on the weighted semigroup.     

The first encapsulation of hydroxynitrile lyase from Hevea brasiliensis in a sol-gel matrix

A straightforward process for the encapsulation of HbHNL under low methanol conditions has been developed. By adding a sol, prepared by hydrolysis of TMOS/MTMS at pH 2.8 with continuous removal of methanol, to a stirred solution of the enzyme in a buffer at pH 6.5, at least 65% of the activity of the free enzyme could be recovered after the encapsulation. The aquagels were successfully used in the synthesis of (S)-cyanohydrins.     

Time-Reversed Dynamical Entropy and Irreversibility in Markovian Random Processes

A concept of time-reversed entropy per unit time is introduced in analogy with the entropy per unit time by Shannon, Kolmogorov, and Sinai. This time-reversed entropy per unit time characterizes the dynamical randomness of a stochastic process backward in time, while the standard entropy per unit time characterizes the dynamical randomness forward in time. The difference between the time-reversed and standard entropies per unit time is shown to give the entropy production of Markovian processes in nonequilibrium steady states.     

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.     

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.     

Coherent backscattering of electromagnetic waves in a magnetised plasma

Summary A microwave coherent backscattering experiment has been carried out on Mirabelle, a weakly ionised plasma device, with the objective of measuring the electron density fluctuation level. The experiment is a preliminary step in order to prepare the detection system for a microwave stimulated backscattering experiment. The incident electromagnetic wave is focused in front of a plane grid which excites ion acoustic or electron Bernstein waves inducing fluctuations in the plasma. The backscattering signal is collected by the launching circuit and detected by homodyne mixing. The typical ratio of the scattered power to the incident power is about 10⁻¹² and the relative density fluctuations are of the order of δn _e/n _e=10⁻³ against a background electron density ofn _e=1–5·10⁹ cm⁻³. The backscattering measurement is compared with Langmuir probe measurements. The spectral width of the backscattered signal has also been studied, by taking into account effects due to the incident wave focusing and plasma wave damping. The authors of this paper have agreed to not receive the proofs for correction