Variational inequalities with varying obstacles: The general form of the limit problem

When minimizing a functional of the calculus of variations with varying constraints of obstacle type, it may happen that, in the limit problem (when it exists), the constraint is no longer of obstacle type; it may take a “relaxed” form. This situation is analysed in this paper. Following De Giorgi's Γ-convergence approach, a class of functionals is constructed which is compact and which contains the obstacle constraint functionals. In this sense, this class of problems has been closed.     

On the integer-valued variables in the linear vertex packing problem

Given a graph with weights on vertices, the vertex packing problem consists of finding a vertex packing (i.e. a set of vertices, no two of them being adjacent) of maximum weight. A linear relaxation of one binary programming formulation of this problem has these two well-known properties: (i) every basic solution is (0, 1/2, 1)-valued, (ii) in an optimum linear solution, an integer-valued variable keeps the same value in an optimum binary solution.As an answer to an open problem from Nemhauser and Trotter, it is shown that there is a unique maximal set of variables which are integral in optimal (VLP) solutions.This research was supported by National Research Council of Canada GRANT A8528 and RD 804.     

Zur Existenz des Wellenoperators bei Anfangsrandwertproblemen von Maxwell-Typ

Ohne Zusammenfassung     

Donor‐Embedded Polybinaphthalenes for Nonlinear Optical Applications: Influence of the Incorporation of a Double Bond

Summary: In this paper two new donor‐embedded polybinaphthalenes prepared by the Heck reaction are presented. By introducing a double bond in the polymer backbone, the supramolecular structure was altered in comparison with polymers without the double bond. Comparison between the CD/UV‐Vis spectra of polymers, with and without the double bond (previously synthesized in our laboratory) proved this change in a supramolecular structure. The double bonds also allow crosslinking upon heat treatment. NLO experiments demonstrated a more stable nonlinearity over time depending on the degree of crosslinking.

     

Electrogenerated Base-Promoted Synthesis of Dithiocarbamate Acid Esters and 3-(N-Substituted-amino)-2-cyanodithiocrotonates from Primary or Secondary Amines and Carbon Disulfide

Electrogenerated cyanomethyl anion promotes the reaction between primary or secondary amines, carbon disulfide, and alkyl or benzyl halide. Secondary amines are converted to alkyl or benzyl dithiocarbamates, whereas primary amines give N-substituted alkyl or benzyl 3-amino-2-cyanodithiocrotonates. The mechanisms are discussed.     

Determination of the Avogadro constant by counting the atoms in a 28Si crystal

The Avogadro constant links the atomic and the macroscopic properties of matter. Since the molar Planck constant is well known via the measurement of the Rydberg constant, it is also closely related to the Planck constant. In addition, its accurate determination is of paramount importance for a definition of the kilogram in terms of a fundamental constant. We describe a new approach for its determination by counting the atoms in 1 kg single-crystal spheres, which are highly enriched with the 28Si isotope. It enabled isotope dilution mass spectroscopy to determine the molar mass of the silicon crystal with unprecedented accuracy. The value obtained, NA = 6.022,140,78(18) × 10(23) mol(-1), is the most accurate input datum for a new definition of the kilogram.     

Ultra-fast cyclosporin A quantitation in whole blood by Laser Diode Thermal Desorption – Tandem Mass Spectrometry; comparison with High Performance Liquid Chromatography–Tandem Mass Spectrometry

In the last decade the quantitation of immunosuppressive drugs has seen vast improvements in analytical methods, optimizing time, accuracy of analysis and cost. Laser Diode Thermal Desorption (LDTD) coupled to Atmospheric Pressure Chemical ionization–tandem mass spectrometry (APCI-MS/MS) represents a technological breakthrough that removes the chromatographic separation step and thereby significantly increases the analytical throughput for the quantitation of cyclosporin A (CsA) in whole blood for therapeutic drug monitoring (TDM).