Totally skew embeddings of manifolds

We study a version of Whitney’s embedding problem in projective geometry: What is the smallest dimension of an affine space that can contain an n-dimensional submanifold without any pairs of parallel or intersecting tangent lines at distinct points? This problem is related to the generalized vector field problem, existence of non-singular bilinear maps, and the immersion problem for real projective spaces. We use these connections and other methods to obtain several specific and general bounds for the desired dimension.     

Time domain study of the Drude–Born–Fedorov model for a class of heterogeneous chiral materials

We deal with the well‐posedness of the transient Maxwell equations in a particular class of heterogeneous isotropic chiral material modeled by the Drude–Born–Fedorov constitutive relations with different boundary conditions. A new formulation of the underlying evolution problems allows us to establish existence and uniqueness results. The selfadjointness of the curl operator multiplied by a piecewise smooth function in an appropriated Hilbert space is also proved. Copyright © 2012 John Wiley & Sons, Ltd.     

Über ein geometrisches Theorem und seine Anwendung auf die partiellen Differentialgleichungen vom elliptischen Typus

Ohne ZusammenfassungDie vorliegende Note ist die Übersetzung des bereits im Jahre 1914 in den Mitteilungen der Mathematischen Gesellschaft in Charkow erschienenen Aufsatzes Sur un théorème de géométrie et son application aux equations aux dérivées partielles du type elliptique. Für die freundliche Übersetzung sind die Schriftleitung und der Verfasser Herrn Tibor Radó in Szeged zu Dank verpflichtet.     

The steady Navier–Stokes/energy system with temperature‐dependent viscosity—Part 1: Analysis of the continuous problem

In this first part we propose and analyse a model for the study of two‐dimensional incompressible Navier–Stokes equations with a temperature‐dependent viscosity. The flow is supposed in a mixed convection regime and considers an outflow region, leading to a strongly coupled problem between the Navier–Stokes and energy equations, which will be justified theoretically. The coupling in the continuous problem is treated by an outer temperature fixed point strategy. Existence results for a particular variational formulation follows from this study. Further, a particular uniqueness result for small data is also obtained. Copyright © 2007 John Wiley & Sons, Ltd.     

Production of large quantities of “Janus” nanoparticles using wax-in-water emulsions

For the first time, large amount of Janus silica particles as small as 100 nm in diameter were prepared through a simple method based on the elaboration of Pickering emulsions of wax-in-water. Controlling the kinetic stabilization of wax droplets allows the fabrication of gram-sized quantities of regular asymmetric inorganic particles with high yield. In fact, our method is based on a limited coalescence process, which allows one to predict the quantity of interface which is produced when working with a known mass of wax, and thus to be sure that all introduced silica particles are adsorbed on the wax surface. To this end, the hydrophilic surface of the silica particles was made partially hydrophobic by adsorbing a known amount of surfactant: cetyltrimethylammonium bromide (CTAB). Varying the concentration in surfactant results in tuning the penetration rate of the particles in the wax droplets, leading to various dimension of the modified area. The broken spherical symmetry of the particle surface was thereafter revealed by the selective adsorption of gold nanoparticles on the amino-modified surface.     

Sur l'extension du théoréme limite du calcul des probabilités aux sommes de quantités dépendantes

Sans résumé