A bilevel programming approach to the travelling salesman problem

We show that the travelling salesman problem is polynomially reducible to a bilevel toll optimization program. Based on natural bilevel programming techniques, we recover the lifted Miller-Tucker-Zemlin constraints. Next, we derive an O(n²) multi-commodity extension whose LP relaxation is comparable to the exponential formulation of Dantzig, Fulkerson and Johnson.     

Fiber Bragg grating sensor demodulation technique by synthesis of grating parameters from its reflection spectrum

In this paper, we present a very reliable simulating algorithm to synthesize the physical parameters of a fiber Bragg grating structure from its reflection spectrum. The knowledge of the gratings parameters allows the determination of the maximum wavelength. The algorithm is then tested to monitor the shift of the central wavelength in response to a change of temperature. Our numerical program uses the transfer matrix method and the Nelder–Mead simplex algorithm. It can be easily implemented in the case of twin Bragg gratings. A twin grating is composed of two identical gratings separated by a short length of fiber. The demodulation technique has been tested experimentally with temperature sensors. It is very accurate and provides absolute measurements.     

Rotation numbers in the infinite annulus

Using the notion of free transverse triangulation we prove that the rotation number of a given probability measure invariant by a homeomorphism of the open annulus depends continuously on the homeomorphism under some boundedness conditions.

     

Planarity and Edge Poset Dimension

Different areas of discrete mathematics lead to instrinsically different characterizations of planar graphs. Planarity is expressed in terms of topology, combinatorics, algebra or search trees. More recently, Schnyder's work has related planarity to partial order theory. Acyclic orientations and associated edge partial orders lead to a new characterization of planar graphs, which also describes all of the possible planar embeddings. We prove here that there is a bijection between bipolar plane digraphs and 2-dimensionalN-free partial orders. We give also a characterization of planarity in terms of 2-colorability of a graph and provide a short proof of a previous result on planar lattices.     

Convergence Properties of Feasible Descent Methods for Solving Variational Inequalities in Banach Spaces

This work is concerned with the analysis of convergence properties of feasible descent methods for solving monotone variational inequalities in Banach spaces.     

Magnetism in amorphous Fe-Si alloys

Fe-Si alloys have been obtained by the vapor quenching technique. Resistance measurements, electron microscopy and diffraction results are typical of an amorphous system. The Mössbauer spectra of these amorphous alloys, fitted in terms of a distribution of hyperfine fields, show the existence of a local magnetic order with, however, a proportion of weakly or even no coupled Fe atoms which is temperature and Fe-concentration dependent.     

Reactions SRN1 en serie heterocyclique: IV: Reactivite des sels du dimethyl-2,2 nitro-5 dioxanne-1,3

2-Alkyl 2-nitro 1,3-propanediol, 2-alkylidene 1,3-propanediol and 2-dialkylidene 1,3-propanediol are prepared via S_RN1 reactions with salts of 2,2-dimethyl 5-nitro 1,3-dioxane and acid-catalyzed cleavage of the resulting acetals.     

Method for confirmation of synthetic corticosteroids in doping urine samples by liquid chromatography-electrospray ionisation mass spectrometry

In this study, we report on the development of a method to confirm simultaneously nine of the most commonly abused synthetic corticosteroids in urine based on liquid chromatography-electrospray ionisation mass spectrometry. A considerable simplified sample preparation procedure, including liquid-liquid phase extraction with Extrelut-NT3 columns, provided both excellent sample purification and high overall recoveries. Complete HPLC separations were obtained on a reversed-phase column with 1 mM ammonium acetate-acetonitrile (60:40, v/v) as mobile phase. Mass spectral acquisition was done in the negative ion, and selected ion monitoring modes to identify the drugs with at least three characteristic ions. Detection limits were determined at < or =1 ng/ml and the confirmation limits at 1 to 5 ng/ml.