Hardy type inequalities with exponential weights for a class of convolution operators

In this paper we consider operators of the form H=λ(-i∇), with λ analytic in a strip and with some specific growth conditions at infinity, and prove Hardy type estimates in L ²(ℝ ⁿ ) with exponential weights. In fact we extend our previous results [19] from bounded analytic functions on a strip to analytic functions with polynomial growth in that strip.     

Radiometric and fluorimetric determination of aminosilanes and protein covalently bound to thermally pretreated glass substrates

Derivatization of solid soda-lime glass spheres with aminosilanes and the stability of these groups near physiological pH in flow streams of aqueous buffered solutions are described. The presence of immobilized and adsorbed amines in the nanomolar range is confirmed by using two independent methods, one based on a radiotracer and the other on the fluorescent marker, fluorescamine. A method for covalently attaching bovine serum albumin to the beads is described.     

Plasticization of poly(lactide) with blends of tributyl citrate and low molecular weight poly(d,l-lactide)-b-poly(ethylene glycol) copolymers

Polylactide (PLA) is a potential candidate for the partial replacement of petrochemical polymers because it is biodegradable and produced from annually renewable resources. Characterized by its high tensile strength, unfortunately the brittleness and rigidity limit its applicability. For a great number of applications such as packaging, fibers, films, etc., it is of high interest to formulate new PLA grades with improved flexibility and better impact properties.In order to develop PLA-based biodegradable packaging, the physico-mechanical properties of commercially available PLA should be modified using biodegradable plasticizers. To this end, PLA was melt-mixed with blends of tributyl citrate and more thermally stable low molecular weight block copolymers based on poly(d,l-lactide) and poly(ethylene glycol) of different molecular weights and topologies. The copolymers have been synthesized using a potassium based catalyst which is expected to be non toxic and were characterized by utilization of TGA, GPC and NMR techniques.The effect of the addition of up to 25 wt% plasticizer on the thermo-mechanical properties of PLA was investigated and the results were correlated with particular attention to the relationship between properties and applications.To confirm the safety of the catalyst used for the preparation of the copolymers, in vitro cytotoxicity tests have been carried out using MTS assay and the results show their biocompatibility in the presence of the fibroblast cells.Compost biodegradation experiments carried out using neat and plasticized PLA have shown that the presence of plasticizers accelerates the degradation of the PLA matrix.     

Invariance for stochastic differential systems with time-dependent constraining sets

The first part of this article presents invariance criteria for a stochastic differential equation whose state evolution is constrained by time-dependent security tubes. The key results of this section are derived by considering an equivalent problem where the square of distance function represents a viscosity solution to an adequately defined partial differential equation. The second part of the paper analyzes the broader context when solutions are constrained by more general time-dependent convex domains. The approach relies on forward stochastic variational inequalities with oblique reflection, the generalized subgradients acting as a reacting process that operates only when the solution reaches the boundary of the domain.     

Adding Value in Production of Multifunctional Polylactide (PLA)–ZnO Nanocomposite Films through Alternative Manufacturing Methods

Due to the added value conferred by zinc oxide (ZnO) nanofiller, e.g., UV protection, antibacterial action, gas-barrier properties, poly(lactic acid) (PLA)–ZnO nanocomposites show increased interest for utilization as films, textile fibers, and injection molding items. The study highlights the beneficial effects of premixing ZnO in PLA under given conditions and its use as masterbatch (MB), a very promising alternative manufacturing technique. This approach allows reducing the residence time at high processing temperature of the thermo-sensitive PLA matrix in contact of ZnO nanoparticles known for their aptitude to promote degradation effects onto the polyester chains. Various PLA–ZnO MBs containing high contents of silane-treated ZnO nanoparticles (up to 40 wt.% nanofiller specifically treated with triethoxycaprylylsilane) were produced by melt-compounding using twin-screw extruders. Subsequently, the selected MBs were melt blended with pristine PLA to produce nanocomposite films containing 1–3 wt.% ZnO. By comparison to the more traditional multi-step process, the MB approach allowed the production of nanocomposites (films) having improved processing and enhanced properties: PLA chains displaying higher molecular weights, improved thermal stability, fine nanofiller distribution, and thermo-mechanical characteristic features, while the UV protection was confirmed by UV-vis spectroscopy measurements. The MB alternative is viewed as a promising flexible technique able to open new perspectives to produce more competitive multifunctional PLA–ZnO nanocomposites.     

Practical aspects of (1)H transverse paramagnetic relaxation enhancement measurements on macromolecules

The use of (1)H transverse paramagnetic relaxation enhancement (PRE) has seen a resurgence in recent years as method for providing long-range distance information for structural studies and as a probe of large amplitude motions and lowly populated transient intermediates in macromolecular association. In this paper we discuss various practical aspects pertaining to accurate measurement of PRE (1)H transverse relaxation rates (Gamma(2)). We first show that accurate Gamma(2) rates can be obtained from a two time-point measurement without requiring any fitting procedures or complicated error estimations, and no additional accuracy is achieved from multiple time-point measurements recorded in the same experiment time. Optimal setting of the two time-points that minimize experimental errors is also discussed. Next we show that the simplistic single time-point measurement that has been commonly used in the literature, can substantially underestimate the true value of Gamma(2), unless a relatively long repetition delay is employed. We then examine the field dependence of Gamma(2), and show that Gamma(2) exhibits only a very weak field dependence at high magnetic fields typically employed in macromolecular studies. The theoretical basis for this observation is discussed. Finally, we investigate the impact of contamination of the paramagnetic sample by trace amounts (5%) of the corresponding diamagnetic species on the accuracy of Gamma(2) measurements. Errors in Gamma(2) introduced by such diamagnetic contamination are potentially sizeable, but can be significantly reduced by using a relatively short time interval for the two time-point Gamma(2) measurement.     

A fast method for solving fluid–structure interaction problems numerically

The paper presents a semi‐implicit algorithm for solving an unsteady fluid–structure interaction problem. The algorithm for solving numerically the fluid–structure interaction problems was obtained by combining the backward Euler scheme with a semi‐implicit treatment of the convection term for the Navier–Stokes equations and an implicit centered scheme for the structure equations. The structure is governed either by the linear elasticity or by the non‐linear St Venant–Kirchhoff elasticity models. At each time step, the position of the interface is predicted in an explicit way. Then, an optimization problem must be solved, such that the continuity of the velocity as well as the continuity of the stress hold at the interface. During the Broyden, Fletcher, Goldforb, Shano (BFGS) iterations for solving the optimization problem, the fluid mesh does not move, which reduces the computational effort. The term ‘semi‐implicit’ used for the fully algorithm means that the interface position is computed explicitly, while the displacement of the structure, velocity and the pressure of the fluid are computed implicitly. Numerical results are presented. Copyright © 2008 John Wiley & Sons, Ltd.     

Domain sensitivity analysis of the acoustic far‐field pattern

We consider acoustic scattering problems described by the mixed boundary value problem for the scalar Helmholtz equation in the exterior of a 2D bounded domain or in the exterior of a crack. The boundary of the domain is assumed to have a finite set of corner points where the scattered wave may have singular behaviour. The paper is concerned with the sensitivity of the far‐field pattern with respect to small perturbations of the shape of the scatterer. Using a modification of the method of adjoint problems, we obtain an integral representation for the Gâteaux derivative which contains only boundary values of functions easily computable by standard BEM and which depends explicitly on the perturbation of the boundary. In some cases, we show the direct influence of the singularities of the solution on the sensitivity of the far‐field pattern. In this way, we generalize the domain sensitivity analysis developed earlier for smooth domains by Hettlich, Kirsch, Kress, Potthast and others. Finally, we show that the same approach can be applied to scattering from 3D domains with smooth edges. Copyright © 2002 John Wiley & Sons, Ltd.