Stochastic Arithmetic: s-spaces and Some Applications

It has been recently shown that computation with stochastic numbers as regard to addition and multiplication by scalars can be reduced to computation in familiar vector spaces. In this work we show how this can be used for the algebraic solution of linear systems of equations with stochastic right-hand sides. On several examples we compare the algebraic solution with the simulated solution using the CADNA package.     

Gray code for derangements

We give a Gray code and constant average time generating algorithm for derangements, i.e., permutations with no fixed points. In our Gray code, each derangement is transformed into its successor either via one or two transpositions or a rotation of three elements. We generalize these results to permutations with number of fixed points bounded between two constants.     

Turnpike Property in Optimal Microbial Metabolite Production

Journal of Optimization Theory and Applications - We consider the problem of maximization of metabolite production in bacterial cells formulated as a dynamical optimal control problem (DOCP)....     

Nonlinear oscillations beyond caustics

This paper studies the focusing of high-frequency solutions of semilinear hyperbolic equations. In previous papers, we studied two opposite phenomena. First, the focusing of nonlinear waves can force the solutions to blow up, even before reaching the caustics. Second, for strongly dissipative equations, nonlinear oscillations can be completely absorbed when they reach the caustic set. In this paper, we study the intermediate case of equations with globally Lipschitz nonlinearities. The nonlinear oscillations persist after crossing the caustic set. The solutions are described using oscillatory integrals, which are associated with Lagrangian manifolds in the cotangent bundle. The equations of nonlinear geometric optics lift to these manifolds. In contrast to the linear case, the transport equations for amplitudes living above the same points of spacetime are coupled. © 1996 John Wiley & Sons, Inc.     

Calcul de la fonction correlation de phonon pour la diffraction d'une particule par un solide

A method of calculating expressions of the type $\text{<T exp[?i}\text{k}{}_1\text{u}{}_{\ln }\text{(t}{}_1\text{)] ... exp [?i}\text{k}{}_{\mathrm{n}}\text{u}{}_{\ln }\text{(t}{}_{\mathrm{n}}\text{>}$ which is simpler than that based on Wick's theorem is proposed. Expressions of the above type are widely used in studying the effects of temperature in electron and neutron diffraction.     

Dynamical selection of the primordial density fluctuation amplitude

In inflationary models, the predicted amplitude of primordial density perturbations Q is much larger than the observed value (～10(-5)) for natural choices of parameters. To explain the requisite exponential fine-tuning, anthropic selection is often invoked, especially in cases where microphysics is expected to produce a complex energy landscape. By contrast, we find examples of ekpyrotic models based on heterotic M theory for which dynamical selection naturally favors the observed value of Q.     

New stereoselective reaction of methylglyoxal with 2-aminopyridine and adenine derivatives: formation of imino acid-nucleic base derivatives in water under mild conditions

A remarkable stereoselective reaction of methylglyoxal with 2-aminopyridine, the nucleic base adenine and adenine nucleosides leads in good yield to heterocycles of a new family in water under mild conditions and should be of interest in the understanding of the biological effects of methylglyoxal which is toxic, mutagenic and involved in diabetic complications.     

Palladium-catalyzed hydrophosphinylation of alkenes and alkynes

Various palladium catalysts promote the addition of hypophosphorous derivatives ROP(O)H(2) to alkenes and alkynes in good yields and under mild conditions. Particularly, Cl(2)Pd(PPh(3))(2)/2 MeLi, and Pd(2)dba(3)/xantphos allow for phosphorus-carbon bond formation instead of transfer hydrogenation. Commercial aqueous solutions of hypophosphorous acid can be employed successfully at ambient temperature. With styrene and terminal alkynes, the regioselectivity (linear versus branched products) can be controlled to some extent with the catalytic system employed. The methodology considerably extends upon previous routes for the preparation of H-phosphinic acids and other organophosphorus compounds.