The defocusing mechanism of isochronous resonances

We present a numerical study concerning the defocusing mechanism of isochronous resonance island chains in the presence of two permanent robust tori. The process is initialized and concluded through bifurcations of fixed points located on the robust tori. Our approach is based on a Hamiltonian system derived from the resonant normal form. Choosing a convenient parameter in this system, we are able to depict a comprehensive analysis of the dynamics of the problem.     

Projected Chvátal–Gomory cuts for mixed integer linear programs

Recent experiments by Fischetti and Lodi show that the first Chvátal closure of a pure integer linear program (ILP) often gives a surprisingly tight approximation of the integer hull. They optimize over the first Chvátal closure by modeling the Chvátal–Gomory (CG) separation problem as a mixed integer linear program (MILP) which is then solved by a general- purpose MILP solver. Unfortunately, this approach does not extend immediately to the Gomory mixed integer (GMI) closure of an MILP, since the GMI separation problem involves the solution of a nonlinear mixed integer program or a parametric MILP. In this paper we introduce a projected version of the CG cuts, and study their practical effectiveness for MILP problems. The idea is to project first the linear programming relaxation of the MILP at hand onto the space of the integer variables, and then to derive Chvátal–Gomory cuts for the projected polyhedron. Though theoretically dominated by GMI cuts, projected CG cuts have the advantage of producing a separation model very similar to the one introduced by Fischetti and Lodi, which can typically be solved in a reasonable amount of computing time. Gérard Cornuéjols was supported in part by NSF grant DMI-0352885, ONR grant N00014-03-1-0188, and ANR grant BLAN 06-1-138894. Matteo Fischetti was supported in part by the EU projects ADONET (contract n. MRTN-CT-2003-504438) and ARRIVAL (contract n. FP6-021235-2). Andrea Lodi was supported in part by the EU projects ADONET (contract n. MRTN-CT-2003-504438) and ARRIVAL (contract n. FP6-021235-2).     

A novel approach to consolidation of historical limestone: the calcium alkoxides

Potential utilization of calcium alkoxides as stone consolidants was considered. Reaction of Ca(OCH₃)₂, Ca(OCH₂CH₃)₂(CH₃CH₂OH)₄ and Ca[OCH(CH₃)₂]₂ with the atmosphere in different experimental conditions was studied. The reaction produced CaCO₃ and two different pathways seem to be involved, the first taking place through CO₂ insertion into the Ca–O bond of Ca(OR)₂ species with formation of an alkylcarbonate derivative, subsequently transformed into CaCO₃ through ROH elimination; the second takes place through hydrolysis of Ca(OR)₂ to Ca(OH)₂, which is then carbonated to CaCO₃. The vaterite/calcite ratios found in the final CaCO₃ vary considerably with the experimental conditions adopted. Investigations demonstrated the potentiality of Ca(OCH₃)₂ to act as a stone consolidant. In fact, impregnation of a porous substrate, simulating the deteriorated stone, with a methanol solution of Ca(OCH₃)₂, produced a crystalline vaterite film, which gradually filled all the pores and cavities of substrate and seems to fulfil the necessary requirements for a consolidant. Copyright © 2008 John Wiley & Sons, Ltd.     

An additive bounding procedure for the asymmetric travelling salesman problem

In this paper, new lower bounds for the asymmetric travelling salesman problem are presented, based on spanning arborescences. The new bounds are combined in an additive procedure whose theoretical performance is compared with that of the Balas and Christofides procedure (1981). Both procedures have been imbedded in a simple branch and bound algorithm and experimentally evaluated on hard test problems.     

Assessment of daily dietary intake of Hg and some essential elements in diets of children from the Amazon region

Summary Daily dietary intake of Hg and some essential elements in diets of children from communities in the Jaú National Park, Amazon region, were assessed. Diet samples were analyzed for total Hg content using cold vapor atomic absorption spectrometry and Ca, Fe, K, Na, Se and Zn contents by instrumental neutron activation analysis. The weekly tolerable provisional intake for Hg in the communities studied varied from 13 to 57 mg of Hg per kg of body weight, exceeding the limit of 5 mg ^. kg^-1 set by the WHO. Comparison of the daily dietary intake values to the new Dietary Reference Intakes (4-8 years), showed prevalence of inadequacy.     

{0, 1/2}-Chvátal-Gomory cuts

Given the integer polyhedronP _t := conv{x ∈ℤ ⁿ :Ax⩽b}, whereA ∈ℤ ^{m × n} andb ∈ℤ ^m , aChvátal-Gomory (CG)cut is a valid inequality forP ₁ of the type λτAx⩽⌊λτb⌋ for some λ∈ℝ ₊ ^m such that λτA∈ℤ ⁿ . In this paper we study {0, 1/2}-CG cuts, arising for λ∈{0, 1/2} ^m . We show that the associated separation problem, {0, 1/2}-SEP, is equivalent to finding a minimum-weight member of a binary clutter. This implies that {0, 1/2}-SEP is NP-complete in the general case, but polynomially solvable whenA is related to the edge-path incidence matrix of a tree. We show that {0, 1/2}-SEP can be solved in polynomial time for a convenient relaxation of the systemAx<-b. This leads to an efficient separation algorithm for a subclass of {0, 1/2}-CG cuts, which often contains wide families of strong inequalities forP ₁. Applications to the clique partitioning, asymmetric traveling salesman, plant location, acyclic subgraph and linear ordering polytopes are briefly discussed.     

Functionalized azabicycloalkane amino acids by nitrone 1,3-dipolar intramolecular cycloaddition

[reaction: see text] An efficient and operationally simple method for the synthesis of functionalized azaoxobicyclo[X.3.0]alkane amino acids has been devised. The key step is an intramolecular nitrone cycloaddition on 5-allyl- or 5-homoallylproline that was found to be completely regio- and stereoselective.     

Synthesis of α-trifluoromethyl-α-amino-β-sulfone hydroxamates: novel nanomolar inhibitors of matrix metalloproteinases

The racemic α-trifluoromethyl-α-amino-β-sulfone hydroxamates 1 were synthesized by means of a nucleophilic addition of sulfur-stabilized carbanions to a N-Cbz imine of trifluoropyruvate (4). The free amino derivative 1a was the most potent inhibitor of both MMP-3 (stromelysin-1) and MMP-9 (gelatinase-B), showing an IC₅₀ = 14 nM and 1 nM, respectively, and excellent selectivity versus MMP-1 (>5000-fold difference in inhibitory capacity). The N-Me derivative 1b was the most selective for MMP-3 with respect to MMP-9 (62-fold difference).