Exit time asymptotics for small noise stochastic delay differential equations

Dynamical system models with delayed dynamics and small noise arise in a variety of applications in science and engineering. In many applications, stable equilibrium or periodic behavior is critical to a well functioning system. Sufficient conditions for the stability of equilibrium points or periodic orbits of certain deterministic dynamical systems with delayed dynamics are known and it is of interest to understand the sample path behavior of such systems under the addition of small noise. We consider a small noise stochastic delay differential equation (SDDE) with coefficients that depend on the history of the process over a finite delay interval. We obtain asymptotic estimates, as the noise vanishes, on the time it takes a solution of the stochastic equation to exit a bounded domain that is attracted to a stable equilibrium point or periodic orbit of the corresponding deterministic equation. To obtain these asymptotics, we prove a sample path large deviation principle (LDP) for the SDDE that is uniform over initial conditions in bounded sets. The proof of the uniform sample path LDP uses a variational representation for exponential functionals of strong solutions of the SDDE. We anticipate that the overall approach may be useful in proving uniform sample path LDPs for a broad class of infinite-dimensional small noise stochastic equations.Comment: 39 page

Highly efficient methods for the one-pot synthesis of b-substituted enones

A mild and practically-convenient one-pot procedure for the direct b-substitution of enones has been developed using a conjugate addition–oxidation strategy with a full range of copper-based reagents and N-tert-butylphenylsulfinimidoyl chloride; alkyl- and aryl-substituted enones are delivered in good to excellent yields

Micellar Nanoreactors

As clearly described in the series of illustrative examples reported above, the use of micellar environments in catalysis is not just a soapy version of homogeneous catalysis.71 Micelles behave much more as nanoreactors characterized by unique features with all the extra advantages intrinsic in the use of water as solvent. Micellar catalysis has been demonstrated to be suitable to almost all classes of chemical transformations, in particular for a wide range of reactions promoted by metal complexes or organometallic species, also with impressive examples in asymmetric catalysis. The great advantage of using catalysts already developed for use in organic media without the need of ligand modifications to make the catalyst compatible with water, together with the self-assembling nature of surfactants, is the key factor for the success of micellar catalysis with metal species. The surfactant is not just a spectator as usually the solvent is believed to be, rather it directs the overall system. A critical balance between catalyst, substrate, and surfactant properties must be analyzed in detail in order to ensure high yield, selectivity, and recyclability. It can be predicted that, thanks to their generally low cost, surfactants will soon find some applications in large-scale synthetic methods suitable for industrial applications

ppm Pd-catalyzed, Cu-free Sonogashira couplings in water using commercially available catalyst precursors.

A new catalyst that derives from commercially available precursors for copper-free, Pd-catalyzed Sonogashira reactions at the sustainable ppm level of precious metal palladium under mild aqueous micellar conditions has been developed. Both the palladium pre-catalyst and ligand are commercially available, bench stable, and highly cost-effective. The catalyst is applicable to both aryl- and heteroaryl-bromides as educts. A wide range of functional groups are tolerated and the aqueous reaction medium can be recycled. An application to a key intermediate associated with an active pharmaceutical ingredient (ponatinib) is discussed

Behavioral mechanisms of reproductive isolation in avian hybrid zones

Sexual signals and mating behaviors influence whether sympatric species interbreed, and can therefore promote or impede behavioral reproductive isolation between species in secondary contact. Traditionally, research on sexual selection and hybridization has focused on the importance of interspecific mate choice and species discrimination from the perspective of choosy females, and competition from the lens of aggressive and indiscriminate males. I examined two different avian systems to compare the role of male and female competition on hybridization: white-crowned sparrows on the west coast of the US, and sex-role reversed jacanas in Panama. Using genomics and experimental field techniques, I tested morphological, behavioral, and historical factors that influence patterns of gene flow between lineages. I found that contrary to traditional expectations, divergence in male competitive signals can promote reproductive isolation, and female competition can facilitate hybridization

Once To Every Man

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