An exact algorithm for a vehicle routing problem with time windows and multiple use of vehicles

The vehicle routing problem with multiple use of vehicles is a variant of the classical vehicle routing problem. It arises when each vehicle performs several routes during the workday due to strict time limits on route duration (e.g., when perishable goods are transported). The routes are defined over customers with a revenue, a demand and a time window. Given a fixed-size fleet of vehicles, it might not be possible to serve all customers. Thus, the customers must be chosen based on their associated revenue minus the traveling cost to reach them. We introduce a branch-and-price approach to address this problem where lower bounds are computed by solving the linear programming relaxation of a set packing formulation, using column generation. The pricing subproblems are elementary shortest path problems with resource constraints. Computational results are reported on euclidean problems derived from well-known benchmark instances for the vehicle routing problem with time windows.     

A remark on the inviscid limit for two-dimensional incompressible fluids

In this article, we shall study the inviscid limit of two dimensional fluids with bounded voticity. We prove that the solution of incompressible Navier-Stokes system converges strongly in L² to the solution of the Euler incompressible system in the case of two-dimensional fluids in the whole space.     

Evolution d'une singularite ponctuelle dans un fluide compressible

In this work, we study the regularity of the solution of compressible Euler system when the Cauchy data is conormal to this origin. We prove that, outside the origin, the solution is conormal to the disjoint union of a smooth curve and a smooth hypersurface.     

Dispersion Characteristics of Arbitrary Periodic Structures with Rectangular Grooves

The dispersion characteristics of a circular cylindrical waveguide with periodic surface corrugations consisting of rectangular grooves with smoothing are examined using the Space Harmonic Method (SHM). The whole structure is divided into two regions, one describing the propagation volume and one inside the grooves. In the first region, the Floquet theorem is applicable and the field distribution is expressed as a summation of spatial Bloch components, whereas in the second one an appropriate Fourier expansion of standing waves is used. Applying the boundary conditions an infinite system of equations is obtained, which is solved numerically by truncation. Several cases are considered, including the limiting cases of a sinusoidal and a rectangular corrugation profile, to check the accuracy of the method proposed as well as its dependence on the corrugation profile. Numerical results are presented only for transverse magnetic modes, although the formalism can be easily extended to include all kinds of waves that can in principle propagate in such a structure.     

Intertwined Detection and Recognition Roles of Tetrazine in Synergistic Anion-π and H-bond Based Anion Receptor

The intrinsic properties of tetrazine as a π-anion receptor and as an on/off recognition probe merged with H-bond ability of an urea motif into a single architecture constitutes a new generation of well-defined anion receptors. Complexation properties directly benefit from the dual and synergistic contribution of tetrazine and urea. In this study, we report on the synthesis and assessment of binding properties to anions of diverse geometries. Association constants have been predicted by theoretical calculations and evaluated by multiple and complementary experimental techniques including electrospray-mass tandem spectroscopy, NMR, UV-visible, steady state fluorescence spectroscopies and time resolved fluorescence. These results provide the basis for a better understanding of both the complexation and the anion-dependent quenching mechanism.     

Interaction of Ca2+ with uracil and its thio derivatives in the gas phase

The structures and relative stabilities of the complexes formed by uracil and its sulfur derivatives, namely, 2-thio-, 4-thio, and 2,4-dithio-uracil when interacting with Ca(2+) in the gas phase have been analyzed by means of density functional theory (DFT) calculations carried out at the B3LYP/6-311++G(3df,2p)//B3LYP/6-31+G(d,p) level. For uracil and 2,4-dithiouracil, where the two basic sites are the same, Ca(2+) attachment to the heteroatom at position 4 is preferred. However, for the systems where both types of basic centers, a carbonyl or a thiocarbonyl group, are present, Ca(2+)-oxygen association is favored. The most stable complexes correspond to structures with Ca(2+) bridging between the heteroatom at position 2 of the 4-enol (or the 4-enethiol) tautomer and the dehydrogenated ring nitrogen, N3. The enhanced stability of these enolic forms is two-fold, on the one hand Ca(2+) interacts with two basic sites and on the other triggers a significant aromatization of the ring. Besides, Ca(2+) association has a clear catalytic effect on the tautomerization processes which connect the oxo-thione forms with the enol-enethiol tautomers. Hence, although the enol-enethiol tautomers of uracil and its thio derivatives should not be observed in the gas phase, the corresponding Ca(2+) complexes are the most stable species and should be accessible, because the tautomerization barriers are smaller than the Ca(2+) binding energies.     

Theoretical and electrochemical studies on organometallic symmetrical schiff base complexes of Zn(II), Cu(II), Ni(II) and Co(II)

The electronic communication between two redox centres through a Schiff base complex has been investigated in a series of ethylenediimine-bis(1-ferrocenyl-1,3-butanedionate) complexes of Zn(II) 1, Cu(II) 2, Ni(II) 3 and Co(II) 4. Cyclic voltammetry experiments of 1 and 2 exhibit a unique two-electron reversible oxidation wave, whereas in the case of 3 and 4 two and three one-electron oxidation processes are, respectively, observed. These results suggest some electronic interaction between the iron atoms of the ferrocenyl groups. DFT calculations carried out on model complexes show that for all the studied compounds the removal of the first two electrons corresponds to the oxidation processes of the iron centres in the weakly coupled ferrocenyl termini. The electronic communication between the two iron centres increases on going from 1 to 4. Finally, a re-indexation of the bands observed in the UV-Visible spectra has been carried out using TDDFT calculations.     

Catalytic Alkyne Semihydrogenation with Polyhydride Ni/Ga Clusters

The bimetallic, decanuclear Ni₃Ga₇-cluster of the formula [Ni₃(GaTMP)₃(μ²-GaTMP)₃(μ³-GaTMP)] ( 1 , TMP=2,2,6,6-tetramethylpiperidinyl) reacts reversibly with dihydrogen under the formation of a series of (poly-)hydride clusters 2 . Low-temperature 2D NMR experiments at −80 °C show that 2 consist of a mixture of a di- ( 2_Di ), tetra- ( 2_Tetra ) and hexahydride species ( 2_Hexa ). The structures of 2_Di and 2_Tetra are assessed by a combination of 2D NMR spectroscopy and DFT calculations. The cooperation of both metals is essential for the high hydrogen uptake of the cluster. Polyhydrides 2 are catalytically active in the semihydrogenation of 4-octyne to 4-octene with good selectivity. The example is the first of its kind and conceptually relates properties of molecular, atom-precise transition metal/main group metal clusters to the respective solid-state phase in catalysis.     

Computational study on the kinetics of the reaction between Ca and urea

A computational study, in the framework of statistical kinetic theories, of the reaction of Ca²⁺ with urea has been carried out. The kinetically preferred products are NH₃ + [CaOCNH]²⁺, which are the fifth products in order of stability. The second kinetically preferred products are , followed by [CaNH₃]²⁺+HNCO, whereas the most stable ones, and , appear only in residual quantities. These estimates are in agreement with the experimental evidence and provide a suitable mechanism to understand the competition between Coulomb explosion and neutral loss processes.