Fagnano Orbits of Polygonal Dual Billiards

Given a convex n-gon P, a Fagnano periodic orbit of the respective dual billiard map is an n-gon Q whose sides are bisected by the vertices of P. For which polygons P does the ratio Area Q/Area P have the minimal value? The answer is shown to be: for affine-regular polygons.     

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.     

Electrogenerated chemiluminescence of poly[(2,2′-bipyridyl)(4-(2-pyrrol-1-ylethyl)-4′-methyl-2,2′-bipyridyl)2]ruthenium (II) film

Elelctrogenerated chemiluminescence (ECL) of electropolymerized films based on [(2,2′-bipyridyl)(4-(2-pyrrol-1-ylethyl)-4′-methyl-2,2′-bipyridyl)₂]ruthenium (II) was firstly investigated in both organic and aqueous solution. The ECL behaviors have been explained by two typical mechanisms, namely, redox-cycling type and oxidative-reduction type. For the former, no co-reactant was required and for the latter, tripropylamine (TPA) and (NH₄)₂C₂O₄ were selected as co-reactants in the organic and aqueous system, respectively.     

A short and efficient synthesis of the NMDA glycine site antagonist: (3R,4R)-3-amino-1-hydroxy-4-methyl pyrrolidin-2-one (L-687,414)

A short and efficient synthesis of the NMDA glycine site antagonist: (3R,4R)-3-amino-1-hydroxy-4-methyl pyrrolidin-2-one (L-687,414) is described.     

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.     

Modélisation de l’impédance de transfert des câbles coaxiaux à blindages multiples

The shielding effectiveness of multishielded coaxial cables is determinated through the concept of the equivalent transfer impedance. The transfer impedance is computed from the main parameters of the coaxial structure. We describe in this paper the theoretical formulation to evaluate the amplitude of the disturbing voltage at the end of the cable flowed by the disturbing current. This result is used for the computation of the equivalent transfer impedance when the cable is made of various shields for exemple: homogeneous screens or braids. A comparison with the experimental results is also described.     

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.