Synthesis and Stereochemistry of Novel Dibrominated 1,5-Dioxaspiro[5.5]undecane Derivatives

 The synthesis and stereochemistry of new dibrominated spiro-1,3-dioxane derivatives are reported. Investigations by means of NMR methods and single crystal X-ray diffraction for two compounds revealed the high regio- and diastereoselectivity of the bromination reaction of some new spiro-1,3-dioxanes and the asymmetric induction of the chiral carbon atom located in the spiro skeleton.     

Heuristics for multi-attribute vehicle routing problems: A survey and synthesis

The attributes of vehicle routing problems are additional characteristics or constraints that aim to better take into account the specificities of real applications. The variants thus formed are supported by a well-developed literature, including a large variety of heuristics. This article first reviews the main classes of attributes, providing a survey of heuristics and meta-heuristics for Multi-Attribute Vehicle Routing Problems (MAVRP). It then takes a closer look at the concepts of 64 remarkable meta-heuristics, selected objectively for their outstanding performance on 15 classic MAVRP with different attributes. This cross-analysis leads to the identification of “winning strategies” in designing effective heuristics for MAVRP. This is an important step in the development of general and efficient solution methods for dealing with the large range of vehicle routing variants.     

Ueber das Verh?ltniss zwischen Glycerin und Alkohol im Wein

Ohne Zusammenfassung     

Optimal shape of a strongest inverted column

By using Pontryagin's maximum principle we determine the shape of the strongest column positioned in a constant gravity field, simply supported at the lower end and clamped at upper end (with the possibility of axial sliding). It is shown that the cross-sectional area function is determined from the solution of a nonlinear boundary value problem. A variational principle for this boundary value problem is formulated and two first integrals are constructed. These integrals lead to an a priori estimate of the value of one the missing initial condition and to the reduction of the order of the system. The optimal shape of a column is determined by numerical integration.     

Exact controllability for the magnetohydrodynamic equations

We study the local exact controllability of the steady state solutions of the magnetohydrodynamic equations. The main result of the paper asserts that the steady state solutions of these equations are locally controllable if they are smooth enough. We reduce the local exact controllability of the steady state solutions of the magnetohydrodynamic equations to the global exact controllability of the null solution of the linearized magnetohydrodynamic system via a fixed‐point argument. The treatment of the reduced problem relies on two Carleman‐type inequalities for the backward adjoint system. © 2003 Wiley Periodicals, Inc.     

Heron triangles with two fixed sides

In this paper, we study the function H(a,b), which associates to every pair of positive integers a and b the number of positive integers c such that the triangle of sides a, b and c is Heron, i.e., it has integral area. In particular, we prove that H(p,q)?5 if p and q are primes, and that H(a,b)=0 for a random choice of positive integers a and b.     

Path Relinking, Cycle-Based Neighbourhoods and Capacitated Multicommodity Network Design

In this paper, we propose a path relinking procedure for the fixed-charge capacitated multicommodity network design problem. Cycle-based neighbourhoods are used both to move along paths between elite solutions and to generate the elite candidate set by a tabu-like local search procedure. Several variants of the method are implemented and compared. Extensive computational experiments indicate that the path relinking procedure offers excellent results. It systematically outperforms the cycle-based tabu search method in both solution quality and computational effort and offers the best current meta-heuristic for this difficult class of problems.     

Über den Oxydationsverlauf bei Arylschwefelaryliden

Ohne Zusammenfassung