Complexity indices for the traveling salesman problem based on short edge subgraphs

Central European Journal of Operations Research - We present the extension of our previous work on complexity indices for the traveling salesman problem (TSP). Since we study the symmetric...     

Fundamental solutions for the wave operator on static Lorentzian manifolds with timelike boundary

Letters in Mathematical Physics - We consider the wave operator on static, Lorentzian manifolds with timelike boundary, and we discuss the existence of advanced and retarded fundamental solutions...     

On the adiabatic limit of Hadamard states

We consider the adiabatic limit of Hadamard states for free quantum Klein–Gordon fields, when the background metric and the field mass are slowly varied from their initial to final values. If the Klein–Gordon field stays massive, we prove that the adiabatic limit of the initial vacuum state is the (final) vacuum state, by extending to the symplectic framework the adiabatic theorem of Avron–Seiler–Yaffe. In cases when only the field mass is varied, using an abstract version of the mode decomposition method we can also consider the case when the initial or final mass vanishes, and the initial state is either a thermal state or a more general Hadamard state.     

Analytical investigations of adornment pieces from Susani (Timiş County,Romania)

Journal of Thermal Analysis and Calorimetry - The samples originate from the funerary cache of a cremation burial mound dating from the Late Bronze Age (according to the Reinecke chronological...     

Synthesis of benzylidenecycloalkan-1-ones and 1,5-diketones under Claisen–Schmidt reaction: Influence of the temperature and electronic nature of arylaldehydes

Herein, we present the results of the influence of reaction temperature and the electronic nature of arylaldehydes in the reactions of benzocycloalkan-1-ones and arylaldehydes under classical Claisen–Schmidt condensation conditions. The products obtained, 2-arylidene derivatives of benzocycloalkan-1-ones and/or spiropolycyclic-1,5-diketones through multicomponent reactions, depended on the electronic nature of arylaldehyde and the reaction temperature. Besides, under identical conditions, 2-arylideneindan-1-ones afforded bis-indane-1,5-diketones through a process that involves Michael addition reaction, which is also dependent on the temperature. Theoretical studies using density-functional theory allowed understanding the chemical reactivity and the site selectivity of α,β-enones used in this work through the calculation of global and local electrophilicity on C–β. Both the electrophilicity of C-β and the temperature led the course of reaction toward the formation of aldol condensation, aldol condensation/Michael addition, and aldol condensation/dimerization products. This work is the first to perform the structural and configurational assignments of bis-indane-1,5-diketones.     

Remarques sur la limite α→0 pour les fluides de grade 2Global existence and uniqueness of solutions to the equations of third grade fluids

We consider the limit α→0 for the equation of the second grade fluids. We prove that weak convergence of the solutions to a weak solution of the Navier–Stokes equation holds under the assumption that the initial data weakly converges in L². To cite this article: D. Iftimie, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 83–86     

Constructing Hadamard States via an Extended Møller Operator

We consider real scalar field theories, whose dynamics is ruled by normally hyperbolic operators differing only by a smooth potential V. By means of an extension of the standard definition of Møller operator, we construct an isomorphism between the associated spaces of smooth solutions and between the associated algebras of observables. On the one hand, such isomorphism is non-canonical, since it depends on the choice of a smooth time-dependant cut-off function \({\chi}\). On the other hand, given any quasi-free Hadamard state for a theory with a given V, such isomorphism allows for the construction of another quasi-free Hadamard state for a different potential. The resulting state preserves also the invariance under the action of any isometry, whose associated Killing field \({\xi}\) is complete and fulfilling both \({\mathcal{L}_\xi V=0 \,\, {\rm and} \,\, \mathcal{L}_\xi\chi=0}\). Eventually, we discuss a sufficient condition to remove on static spacetimes, the dependence on the cutoff via a suitable adiabatic limit.