On the choice of explicit stabilizing terms in column generation

Column generation algorithms are instrumental in many areas of applied optimization, where linear programs with an enormous number of columns need to be solved. Although successfully employed in many applications, these approaches suffer from well-known instability issues that somewhat limit their efficiency. Building on the theory developed for nondifferentiable optimization algorithms, a large class of stabilized column generation algorithms can be defined which avoid the instability issues by using an explicit stabilizing term in the dual; this amounts at considering a (generalized) augmented Lagrangian of the primal master problem. Since the theory allows for a great degree of flexibility in the choice and in the management of the stabilizing term, one can use piecewise-linear or quadratic functions that can be efficiently dealt with using off-the-shelf solvers. The practical effectiveness of this approach is demonstrated by extensive computational experiments on large-scale Vehicle and Crew Scheduling problems. Also, the results of a detailed computational study on the impact of the different choices in the stabilization term (shape of the function, parameters), and their relationships with the quality of the initial dual estimates, on the overall effectiveness of the approach are reported, providing practical guidelines for selecting the most appropriate variant in different situations.     

Estimation and tests of independence in copula models via divergences

We introduce new estimates and tests of independence in copula models with unknown margins using ?-divergences and the duality technique. The asymptotic laws of the estimates and the test statistics are established both when the parameter is an interior point or not. To cite this article: S. Bouzebda, A. Keziou, C. R. Acad. Sci. Paris, Ser. I 347 (2009).     

Vector subspaces and operators with the Stone condition

We introduce the notion of an operating function on a subset of a F{\Phi} -algebra E. Then we use this notion to generalize results from Huijsmans and de Pagter (Proc. Lond. Math. Soc. 48:161–174, 1984) about the connection between vector subspaces and subalgebras of E. In the second part we investigate the analogous problem for operators.     

Essential oils of Daucus carota subsp. carota of Tunisia obtained by supercritical carbon dioxide extraction

The essential oils and supercritical CO2 extracts of wild Daucus carota L. subsp. carota from two different sites in Tunisia were investigated. The main components of the essential oil of the flowering and mature umbels with seeds from Sejnane were eudesm-7(11)-en-4-ol (8.2 - 8.5%), carotol (3.5 - 5.2%), sabinene (12.0 -14.5%), a-selinene (7.4 - 8.6) and 11-alpha-(H)-himachal-4-en-1-beta-ol (12.7 - 17.4%), whereas the oils from Tunis were predominantly composed of elemicin (31.5 - 35.3%) and carotol (48.0 - 55.7%). The antimicrobial activity of the essential oils were assayed by using the broth dilution method on Escherichia coli ATCC 35218 and Staphylococcus aureus ATCC 43300, and clinical strains of Candida albicans and C. tropicalis 1011 RM. The MIC values obtained were all > 2.5% (v/v).     

Hierarchical porous carbon with designed pore architecture and study of its adsorptive properties

Ordered mesoporous carbon nanoparticles have been synthesized by a nanocasting procedure from furfuryl alcohol impregnation into alumino–silica UVM-7 material. By a proper adjustment of the synthesis parameters, furfuryl alcohol volume vs. template pore volume, it was possible to obtain a carbonaceous templated material which keeps the hierarchical bimodal porosity of the silica together with its high surface area (>1000 m²/g), as it was confirmed by means of electron transmission microscopy and N₂ adsorption isotherms. This carbon material was evaluated by testing it as a sorbent for several pesticides in aqueous solutions. Its absorption efficiency was compared with typical commercial solid phase extraction materials such as silica C₁₈ and graphitized carbon black GCB.     

Crystal structure,thermal analysis,and IR spectroscopic investigation of bis(2-amino-6-methyl) pyridinium sulfate

Synthesis, crystal structure refinement, phase transitions studied by thermal analysis, and IR spectroscopic investigation of 2C₆H₉N₂ < eqid2 > ⋅SO₄²⁻ are reported. The title compound crystallizes in the monoclinic space group C2/c (no. 15) with a = 10.5068(4) Å, b = 10.2225(5) Å, c = 14.0422(7) Å, and β = 104.489(3)^∘. A crystal packing diagram shows layers built by all the components of the structure and centered by planes z = 1/4 and 3/4. The pyridine substituents stack forming channels parallel to the c direction with dimensions of 4.163(1) Å and 5.148(4) Å. Thermal analysis shows that the anhydrous compound possesses an irreversible weak phase transition.     

Crystal structure and thermal analysis of 1,5-diammonium-2-methyl pentane sulfate monohydrate

Chemical preparation, x-ray single crystal, and thermal analysis of C₆H₁₈N₂SO₄·H₂O (denoted DMPS) are described. The compound crystallizes in the triclinic system with P space group. Its unit cell dimensions are a = 5.826(1) Å, b = 10.014(1) Å, c = 11.221(1) Å, = 66.716(1)°, = 84.395(1)°, = 83.759(1)°, V = 596.7(1) ų, and Z = 2. The DMPS structure is built up from inorganic chains parallel to the a axis and linked via O(W)-H···O hydrogen bonds. These chains are interconnected by organic groups. Thermal analysis reveals the presence of one water molecule in the structure and shows a reversible weak phase transition.