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.

     

Exact and inexact penalty methods for the generalized bilevel programming problem

We consider a hierarchical system where a leader incorporates into its strategy the reaction of the follower to its decision. The follower's reaction is quite generally represented as the solution set to a monotone variational inequality. For the solution of this nonconvex mathematical program a penalty approach is proposed, based on the formulation of the lower level variational inequality as a mathematical program. Under natural regularity conditions, we prove the exactness of a certain penalty function, and give strong necessary optimality conditions for a class of generalized bilevel programs.     

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.     

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.     

The crystal structure of 3′-methoxy-5-phenyl-5,10-dihydrophenarsazine,C19H16AsNO

The crystal structure of 3′-methoxy-5-phenyl-5,10-dihydrophenarsazine, C₁₉H₁₆AsNO has been determined by the single crystal x-ray diffraction method. The crystals are monoclinic with a = 15.305(6), b = 5.809(2), c = 17.595(6)Å, β = 92.92(2)°, V = 1562.3(1.0ų, space group P2,/n, Z = 4 and d_calc = 1.485g cm⁻³. An automatic diffractometer with graphite monochromatized MoKα radiation was used to obtain 1480 observed reflection with I > 3σ(I) at 2θ < 50°. Final R = 0.040 and wR = 0.032. The tricyclic ring is folded with the central ring in a flattened boat conformation. The folding angle between the least-squares planes of the two benzo rings is 164.6(2)°. The 3′-methoxyphenyl group is in a boat-axial conformation with respect to the central ring.     

Crystal structure determination of 10-trifluoroacetylphenothiazine

The structure of the title compound has been determined by single crystal X-ray methods. The crystals are monoclinic, space group P2₁/n with four molecules in a cell of dimensions a = 14.365(4), b = 5.942 (2), c = 17.359(3) Å, β = 119.88(2)° and V = 1298.0(6) Å. The structure has been refined by full-matrix least-squares to R = 0.043 using 1650 observed reflections. This study shows that the folding angle between the two benzo planes is 131.8(1)°, one of the smallest values observed in phenothiazine derivatives. Also, the trifluoroacetyl group is perpendicular to the plane bisecting the tricyclic ring, in contrast to most 10-aryl-substituted phenothiazines where the substituent is approximately parallel to the plane bisecting the tricyclic ring.