The Stationary Navier-Stokes System in Nonsmooth Manifolds: The Poisson Problem in Lipschitz and <Emphasis Type="Italic">C</Emphasis><Superscript>1</Superscript> Domains

We consider the linearized version of the stationary Navier-Stokes equations on a subdomain of a smooth, compact Riemannian manifold M. The emphasis is on regularity: the boundary of is assumed to be only C¹ and even Lipschitz, and the data are selected from appropriate Sobolev-Besov scales. Our approach relies on the method of boundary integral equations, suitably adapted to the variable-coefficient setting we are considering here. Applications to the stationary, nonlinear Navier-Stokes equations in this context are also discussed.     

Transmission problems and spectral theory for singular integral operators on Lipschitz domains

We prove the well-posedness of the transmission problem for the Laplacian across a Lipschitz interface, with optimal non-tangential maximal function estimates, for data in Lebesgue and Hardy spaces on the boundary. As a corollary, we show that the spectral radius of the (adjoint) harmonic double layer potential K∗ in is less than , whenever is a bounded convex domain and 1<p?2.     

Efficient single-photon counting at 1.55 microm by means of frequency upconversion

We demonstrate efficient single-photon detection at 1.55 microm by means of sum-frequency mixing with a strong pump at 1.064 microm in periodically poled lithium niobate followed by photon counting in the visible region. This scheme offers significant advantages over existing InGaAs photon counters: continuous-wave operation, higher detection efficiency, higher counting rates, and no afterpulsing. We achieved single-photon upconversion efficiency of 90% at 21.6 W of circulating power in a resonant pump cavity with a 400-mW Nd:YAG laser. We observed high background counts at strong circulating pump powers due to efficient upconversion of pump-induced fluorescence photons.     

The Banach envelopes of Besov and Triebel-Lizorkin spaces and applications to partial differential equations

With “hat” denoting the Banach envelope (of a quasi-Banach space) we prove that if 0<p<1, 0<q<1, ℝ, while if 0<p<1, 1≤q<+∞, ∝, and if 1≤p<+∞, 0<q<1, ℝ. Applications to questions regarding the global interior regularity of solutions to Poisson type problems for the three-dimensional Lamé system in Lipschitz domains are presented.     

Synthesis and Pd-catalyzed coupling of1-C-stannylated glycals

Abstract

1-Tributylstannyl glycals were applied as versatile tools in the Pd(0)-mediated synthesis of glycal phthalonitrile conjugates. Likewise, selective homo-coupling of 1-tributylstannyl glycals furnishing C1-C1’ linked glycal dimers was investigated by using Pd(II)-species. For both Stille type couplings the rate-accelerating effect of copper(I) thiophene-2-carboxylate (CuTC) was exploited. The synthesis of stannylated glycal precursors was significantly improved by establishing a one-pot two-step procedure via glycosyl sulfoxides.     

New trends in polylactide (PLA)-based materials: “Green” PLA-Calcium sulfate (nano)composites tailored with flame retardant properties

Starting from gypsum, a by-product of lactic acid fabrication process, novel “green” composites have been produced by melt-blending polylactide (PLA) and this filler after a previous specific dehydration to obtain anhydrite II (AII). Such a material is potentially interesting in biodegradable/rigid packaging and in technical applications requiring rigidity, heat resistance and dimensional stability. In order to obtain PLA-AII composites characterized by specific end-use flame retardant properties, the addition of selected organo-modified layered silicates (OMLS) was considered. Co-addition of AII and OMLS leads to PLA (nano)composites characterized by good (nano)filler dispersion, thermal stability and adequate mechanical resistance. The flame retardant properties as shown by cone calorimetry showed significant increase in the ignition time compared to neat PLA and a substantial decrease, i.e., ca. 40%, of the maximum rate of heat release, whereas the UL94 HB test was successfully passed revealing non-dripping effect and extensive char formation. The study represents a new approach in formulating novel PLA grades with improved characteristic features.     

Embedding polynomial matrices of one variable

A non square matrix with coefficients in K[z] can (if a condition on its minors is satisfied) be embedded into a square matrix with determinant 1. Finding theoretically and in an algorithmic way an embedding of small degree is solved by a construction with vector bundles on the projective line over K.     

Combined Routeing and Scheduling for the Transportation of Containerized Cargo

A tractor-trailer problem, with full load, from the class of combined routeing and scheduling problems is described. Distinctive features of the problem are: movements must be carried out within certain time windows; subsets of movements are linked in the sense that they must be executed in a certain order; and different priorities are attached to different movements. A new bidirectional sequential constructive heuristic is developed for the solution of this problem. The method constructs routes and schedules for the available tractor fleet. The algorithm attempts to minimize the total time for all the movements by minimizing the time taken up by unproductive movements (so-called deadhead) and waiting time between movements. Some practical aspects of the implementation of the approach are discussed.