A pyrimidine thiolate Rh(I) complex: structure, bonding and one-dimensional interactions in solid and in solution

The reaction of [Rh(micro-Cl)(COD)]2 with 4,6-dimethyl-pyrimidinethiolate (Me2-pymt) and subsequent substitution of COD by CO yields [Rh(Me2-pymt)(CO)2]. The stacking pattern found in this compound is in contradiction with previously studied comparable square-planar complexes of type d8-[M(chelate)(monodentate)2] in which each ligand has different pi-acidic character. A theoretical study of the intermolecular interactions and conformation of the title compound has been carried out, combining semi-empirical band calculations on the real chains and ab initio(MP2 level) calculations on a model dimer. The combination of electronic and steric effects determines the rotation of the successive monomers and the deviation from linearity of the one-dimensional stacks. Its behaviour in solution is also special, developing a blue colour and forming micelles, when adding water to acetone solutions.     

Réactions d'addition-élmination à partir d'hétérocycles germaniés du type . III. Cas des diéthyl-2,2-germa-2-oxazolidines-1,3 (R = et; X = O; Y = NH,NMe)

Addition-elimination reactions from germanium heterocycles . III. 2,2-Diethyl-2-germa-1,-3-oxazolidines (R = Et; X = O; Y = NH, NMe) . The reactions of 2,2-diethyl-2-germa-1,3-oxazolidines with heterocumulenes (PhNCO, PhNCS, CS₂, CO₂, CH₂?C?O) and carbonyl compounds (aldehydes and ketones) are studied. Generally, monoinsertion derivatives are formed by addition of one molecule of the unsaturated compound accross the Ge? N bond. This bond is always the most reactive center of the molecule. In the case of the carbonyl compounds used, diinsertion may occur in a second step by a further addition across a Ge? O bond. Generally, this latter reaction is reversible. By thermal eliminat on of (Et₂GeO)_n or (Et₂GeS)₃ the monoaddition derivatives yield the corresponding oxazolidines and thiooxazolidines. The mechanisms of these reactions are discussed.     

A new regularization of equilibrium problems on Hadamard manifolds: applications to theories of desires

In this paper, we introduce a new proximal algorithm for equilibrium problems on a genuine Hadamard manifold, using a new regularization term. We first extend recent existence results by considering pseudomonotone bifunctions and a weaker sufficient condition than the coercivity assumption. Then, we consider the convergence of this proximal-like algorithm which can be applied to genuinely Hadamard manifolds and not only to specific ones, as in the recent literature. A striking point is that our new regularization term have a clear interpretation in a recent “variational rationality” approach of human behavior. It represents the resistance to change aspects of such human dynamics driven by motivation to change aspects. This allows us to give an application to the theories of desires, showing how an agent must escape to a succession of temporary traps to be able to reach, at the end, his desires.

     

On Anosov energy levels of hamiltonians on twisted cotangent bundles

LetT ^* M denote the cotangent bundle of a manifoldM endowed with a twisted symplectic structure [1]. We consider the Hamiltonian flow generated (with respect to that symplectic structure) by a convex HamiltonianH: T ^* M, and we consider a compact regular energy level ofH, on which this flow admits a continuous invariant Lagrangian subbundleE. When dimM3, it is known [9] that such energy level projects onto the whole manifoldM, and thatE is transversal to the vertical subbundle. Here we study the case dimM=2, proving that the projection property still holds, while the transversality property may fail. However, we prove that in the case whenE is the stable or unstable subbundle of an Anosov flow, both properties hold.     

Self and mutual admittance of slot antennas on a dielectric half-space

In this paper, an efficient implementation of the spectral domain moment technique is presented for computing the self and mutual coupling between slot antennas on a dielectric half-space. It is demonstrated that by the proper selection of the weighting functions in the method of moments, the analytic evaluation or simplification of the transverse moment integrals is enabled. This results into a significant reduction of the required computational labor. The method is then utilized in order to provide design data for the self and mutual admittances between two slot antennas on a dielectric substrate lens in the case of fused quartz ( _r =3.80), crystal quartz ( _r =4.53), silicon ( _r =11.9) and GaAs ( _r =12.8). The presented technique and associated results are useful when designing twin slot quasi-optical receivers, imaging arrays, phased arrays or power-combining arrays of slot elements at millimeter-wave frequencies.     

On the Haar measure of the quantumSU(N) group

We prove that the Haar state associated to the compact matrix quantum groupSU (N) is faithful for ]–1,1[,0, and anyN2.