Chemoenzymatic synthesis of both enantiomers of 3-hydroxy- and 3-amino-3-phenylpropanoic acid

Ethyl (S)-3-hydroxy-3-phenylpropionate (S)-2 was obtained by the asymmetric reduction of ethyl 3-phenyl-3-oxopropionate 1 with the yeast Saccharomyces cerevisiae (ATCC 9080). The kinetic resolution of racemic ethyl 2-acetoxy-3-phenyl-propionate rac-3 with the same microorganism, gave after hydrolysis ethyl (R)- and (S)-3-hydroxy-3-phenylpropionates (R)-2 and (S)-2 which were converted by a straightforward series of reactions to the enantiomers of 3-amino-3-phenyl-propionic acids (S)-6 and (R)-6. The asymmetric reduction and hydrolytic kinetic resolution were also tested with several other whole cell systems under a variety of conditions.     

A support for the identification of non-tryptic peptides based on low resolution tandem and sequential mass spectrometry data: The INSPIRE software

A simple software, to be used as an aid in the identification of non-tryptic peptides based on low resolution (3D-ion trap) tandem (MS/MS) and sequential (MS³) mass spectrometry data, is presented.     

Optofluidic droplet router

This contribution presents an optofluidic droplet router which is able to route and steer microdroplets using optically induced forces created solely by the bulk photovoltaic effect on a nonlinear substrate. The combination of microfluidic tools with the properties of a photorefractive crystal allows for the generation of dielectrophoretic forces that can be either repulsive, leading to virtual barriers, or attractive, creating virtual rails. The sign of these forces is solely determined by the electrical properties of the liquid medium under investigation. Moreover, the induced structures on the bottom of the microfluidic channel are optically reconfigurable, so that the same device can easily be adopted for different purposes. Appropriate droplet‐generating devices are fabricated by UV illumination of SU‐8 and polydimethylsiloxane replica molding of the master structures. The bottom of the channels is formed by an iron‐doped lithium niobate crystal, whose internal electric fields are induced by structured illumination patterns and exert dielectrophoretic forces on droplets in the microfluidic section.

     

Dynamic equilibrium formulation of the oligopolistic market problem

The aim of this paper is to generalize the oligopolistic market equilibrium problems when the data depend on time. We present results regarding the existence of solutions to such problems. Moreover, we show that continuity regularity results hold, and we use them in order to numerically solve the dynamic equilibrium problem.     

Highly reduced iron-doped lithium niobate for optoelectronic tweezers

We investigate the applicability of highly reduced lithium niobate samples doped with iron for the use as optoelectronic tweezers. Increasing the reduction degree of Fe-doped lithium niobate is well known to increase the photoconductivity and reduce the writing time of internal space-charge fields. Based on our measurements of the photorefractive properties, we determine the optimal conditions for dielectrophoretic trapping and present the application of Fe-doped lithium niobate as optoelectronic tweezers. For higher reduction degrees, an unexpected decrease in the photovoltaic current density and the saturation space-charge field is reported.     

Simultaneous near field imaging of electric and magnetic field in photonic crystal nanocavities

The insertion of a metal-coated tip on the surface of a photonic crystal microcavity is used for simultaneous near field imaging of electric and magnetic fields in photonic crystal nanocavities, via the radiative emission of embedded semiconductor quantum dots (QD). The photoluminescence intensity map directly gives the electric field distribution, to which the electric dipole of the QD is coupled. The magnetic field generates, via Faraday's law, a circular current in the apex of the metallized probe that can be schematized as a ring. The resulting magnetic perturbation of the photonic modes induces a blue shift, which can be used to map the magnetic field, within a single near-field scan.     

Ideal homoatomic and heteroatomic photonic crystal molecules

A local tuning of the modes of photonic crystal systems both to blue and to red sides of the resonance is implemented by nano-infiltration/evaporation of water and laser micro-oxidation. This technology is used to completely control coupled photonic nanocavities (photonic crystal molecules). Beside the standard condition of zero detuning between identical modes of the two cavities (homoatomic molecule), we are also able to produce coupling between two modes of different polarization and spatial distribution (heteroatomic molecule).     

Generalized Jacobi Identities and Ball-Box Theorem for Horizontally Regular Vector Fields

Consider a family $\mathcal{H}:= \{X_{j} =: f_{j}\cdot\nabla: j=1,\ldots , m\}$ of C ¹ vector fields in ? ⁿ and let s∈?. We assume that for all p∈{1,…,s} and j ₁,…,j _p ∈{1,…,m} the horizontal derivatives $X_{j_{1}}X_{j_{2}}\cdots X_{j_{p-1}}f_{j_{p}}$ exist and are Lipschitz continuous with respect to the control distance defined by  $\mathcal{H}$ . Then we show that different notions of commutator agree. This involves an accurate analysis of some algebraic identities involving nested commutators which seem to have an independent interest. Our principal applications are a ball-box theorem, the doubling property, and the Poincaré inequality for Hörmander vector fields under an intrinsic “horizontal regularity” assumption on their coefficients.     

Graphs with prescribed Levi form trace

Abstract We prove existence and uniqueness of a viscosity solution of the Dirichlet problem related to the prescribed Levi mean curvature equation, under suitable assumptions on the boundary data and on the Levi curvature of the domain. We also show that such a solution is Lipschitz continuous by proving that it is the uniform limit of a sequence of classical solutions of elliptic problems and by building Lipschitz continuous barriers. Keywords: Levi mean curvature, Quasilinear degenerate elliptic PDE’s, Viscosity solutions, Comparison principle, Global Lipschitz estimates