Irrationalité de Valeurs Associées a l'Exponentielle de Carlitz

Lete and be the Carlitz-module analogues of their usual counterparts. We have proved in [4]-that these elements of are algebraically independent over whenq3. We study here the remaining caseq=2 and prove among other things that 1,e, are linearly independent over .

     

Facets for the cut cone I

We study facets of the cut coneC _n , i.e., the cone of dimension 1/2n(n – 1) generated by the cuts of the complete graph onn vertices. Actually, the study of the facets of the cut cone is equivalent in some sense to the study of the facets of the cut polytope. We present several operations on facets and, in particular, a lifting procedure for constructing facets ofC _n+1 from given facets of the lower dimensional coneC _n . After reviewing hypermetric valid inequalities, we describe the new class of cycle inequalities and prove the facet property for several subclasses. The new class of parachute facets is developed and other known facets and valid inequalities are presented.     

Dearomatization of 3-Nitroindoles with Highly γ-Functionalized Allenoates in Formal (3+2) Cycloadditions

3-Nitroindoles are easily reacted with highly substituted γ-allenoates in the presence of a commercially available phosphine catalyst. For instance, allenoates derived from biomolecules such as amino and deoxycholic acids are combined for the first time with 3-nitroindole. The corresponding dearomatized (3+2) tricyclic cycloadducts are obtained as α-regioisomers exclusively. DFT computations shed light on this multi-step reaction mechanism and on the selectivities observed in the sequence.     

CS2 Reductive Coupling to Acetylenedithiolate by a Dinuclear Ytterbium(II) Complex

The activation of CS₂ is of interest in a broad range of fields and, more particularly, in the context of creating new C−C bonds. The reaction of the dinuclear ytterbium(II) complex [Yb₂L₄], 1 , [L=(OtBu)₃SiO⁻] with carbon disulfide led to the isolation of unprecedented reduction products. In particular, the crystallographic characterization of complex [Yb₂L₄(μ-C₂S₂)], 2 , provided the first example of an acetylenedithiolate ligand formed from metal reduction of CS₂. Computational studies indicated that this unprecedented reactivity can be ascribed to the unusual binding mode of CS₂²⁻ in the isolated “key intermediate” [Yb₂L₄(μ-CS₂)], 3 , which results from the dinuclear nature of 1 .     

Analysis of several subcycling schemes in partitioned simulations of a strongly coupled fluid-structure interaction

Fluid-structure interaction (FSI) simulations are used extensively to calculate the vibration of structures subjected to an internal or external flow. In the case of partitioned FSI simulations, separate flow and structure solvers are used, which requires some kind of coupling between both. The time step in both solvers is typically taken the same, but this unnecessarily leads to long calculation times when the time step is small due to stability reasons in one of the two solvers. Subcycling, the procedure where the time step of one solver is chosen smaller than the time step used in the other solver, may reduce the computational cost of the FSI simulation. The subcycling procedure can be either explicit or implicit, the latter implying the use of coupling iterations in each time step. Contrary to explicit subcycling, no stability analyses of implicit subcycling schemes are found in the literature. In this paper, the temporal stability of the implicit subcycling procedure is investigated. The one-dimensional flow in an elastic cylindrical tube is studied analytically. The results of this analysis are subsequently compared to a partitioned two-dimensional axisymmetric FSI calculation with implicit coupling between the flow and structure solvers.     

An analysis of over-relaxation in a kinetic approximation of systems of conservation laws

The over-relaxation approach is an alternative to the Jin–Xin relaxation method in order to apply the equilibrium source term in a more precise way. This is also a key ingredient of the lattice Boltzmann method for achieving second-order accuracy. In this work, we provide an analysis of the over-relaxation kinetic scheme. We compute its equivalent equation, which is particularly useful for devising stable boundary conditions for the hidden kinetic variables.