Un modèle discret du couplage entre les fils dans une structure tisséeA discrete model for the coupling between the yarns in a woven fabric

The coupling between yarns in a piece of fabric has been analysed at the mesoscopic scale, in terms of its impact on the macroscopic unidirectional behaviour. Starting from a discrete model of a woven structure associated to a variational formulation of the equilibrium of the structure, the coupling between both yarns is introduced, the potential energy of which is calculated. The initial shape of the yarn, represented by a planar undulated beam supposed to be periodic, is described by a Fourier series. The coefficients of the series are expressed vs. the contact force exerted at the top of the undulations, and vs. the mechanical properties of the solicited yarn. The contact force is then expressed vs. the mechanical properties of the transverse yarn and vs. the vertical displacement of the contact point. The potential energy of the coupling is then built, assuming the continuity of the displacement at the contact points. The equilibrium shape of the yarn submitted to unidirectional traction is obtained numerically as the minimum of the total potential energy. The simulated traction curve reproduces in a satisfactorily manner the observed behaviour. The respective contributions of the flexional and extensional effects of the yarn are analysed. The consideration of the coupling enhances the rigidity of the response of the yarn; one demonstrates the effect of the geometrical and mechanical parameters of the transverse yarn. To cite this article: B. Ben Boubaker et al., C. R. Mecanique 331 (2003).     

Well‐Defined Single‐Site Monohydride Silica‐Supported Zirconium from Azazirconacyclopropane

The silica‐supported azazirconacyclopropane ?SiOZr(HNMe₂)(η²‐NMeCH₂)(NMe₂) ( 1 ) leads exclusively under hydrogenolysis conditions (H₂, 150 °C) to the single‐site monopodal monohydride silica‐supported zirconium species ?SiOZr(HNMe₂)(NMe₂)₂H ( 2 ). Reactivity studies by contacting compound 2 with ethylene, hydrogen/ethylene, propene, or hydrogen/propene, at a temperature of 200 °C revealed alkene hydrogenation.     

Consideration of the yarn–yarn interactions in meso/macro discrete model of fabric: Part II: Woven fabric under uniaxial and biaxial extension

A mesoscopic discrete model of fabric has been developed, accounting for the yarn–yarn interactions occurring at the yarn crossing points. The fabric yarns, described in their initial state by a Fourier series development, are discretized into elastic straight bars represented by stretching springs, and connected at frictionless hinges by rotational springs. In the first part of the paper, the behavior under uniaxial tension of a single yarn has been investigated, and the impact of the interactions of the transverse yarns has been quantitatively assessed. The consideration of the yarn interactions is extended in this second part at the scale of the whole network of interwoven yarns, under uniaxial and biaxial loading conditions. The effect of the transverse yarns properties under uniaxial tension is evidenced, as well as the impact of the biaxial loading ratio.     

Solid‐State NMR and DFT Studies on the Formation of Well‐Defined Silica‐Supported Tantallaaziridines: From Synthesis to Catalytic Application

Single‐site, well‐defined, silica‐supported tantallaaziridine intermediates [≡Si‐O‐Ta(η²‐NRCH₂)(NMe₂)₂] [R=Me ( 2 ), Ph ( 3 )] were prepared from silica‐supported tetrakis(dimethylamido)tantalum [≡Si‐O‐Ta(NMe₂)₄] ( 1 ) and fully characterized by FTIR spectroscopy, elemental analysis, and ¹H,¹³C HETCOR and DQ TQ solid‐state (SS) NMR spectroscopy. The formation mechanism, by β‐H abstraction, was investigated by SS NMR spectroscopy and supported by DFT calculations. The C?H activation of the dimethylamide ligand is favored for R=Ph. The results from catalytic testing in the hydroaminoalkylation of alkenes were consistent with the N‐alkyl aryl amine substrates being more efficient than N‐dialkyl amines.     

Recent advances in the enantioselective 1,3-dipolar cycloaddition of azomethine ylides and dipolarophiles

The synthesis of diastereo- and enantiopure heterocyclic molecules via catalytic asymmetric 1,3-dipolar cycloaddition reaction between azomethine ylides, generated in situ from α-amino acid-derived iminoesters and dipolarophiles is considered one of the most powerful and versatile techniques. In this review, we make a detailed overview of the latest developments in this area since 2014 and highlight the recent improvements in the structural scope of dipolarophiles, azomethine ylide precursors, and chiral ligands.     

On per-iteration complexity of high order Chebyshev methods for sparse functions with banded Hessians

Some algorithms for unconstrained and differentiable optimization problems involve the evaluation of quantities related to high order derivatives. The cost of these evaluations depends widely on the technique used to obtain the derivatives and on some characteristics of the objective function: its size, structure and complexity. Functions with banded Hessian are a special case that we study in this paper. Because of their partial separability, the cost of obtaining their high order derivatives, subtly computed by the technique of automatic differentiation, makes High order Chebyshev methods more interesting for banded systems than for dense functions. These methods have an attractive efficiency as we can improve their convergence order without increasing significantly their algorithmic costs. This paper provides an analysis of the per-iteration complexities of High order Chebyshev methods applied to sparse functions with banded Hessians. The main result can be summarized as: the per-iteration complexity of a High order Chebyshev method is of order of the objective function’s. This theoretical analysis is verified by numerical illustrations.     

Existence of Solutions of a Nonlinear Hammerstein Integral Equation

In this article, we are concerned with existence results for a nonlinear Hammerstein integral equation in L ¹ spaces. Making use of the De Blasi measure of weak noncompactness, we establish variants of some Krasnosel'skii type theorem involving the weak topology of Banach spaces.     

The Chebyshev–Shamanskii Method for Solving Systems of Nonlinear Equations

We present a method, based on the Chebyshev third-order algorithm and accelerated by a Shamanskii-like process, for solving nonlinear systems of equations. We show that this new method has a quintic convergence order. We will also focus on efficiency of high-order methods and more precisely on our new Chebyshev–Shamanskii method. We also identify the optimal use of the same Jacobian in the Shamanskii process applied to the Chebyshev method. Some numerical illustrations will confirm our theoretical analysis.     

Asymmetric synthesis of spirocyclohexanone-pyrrolidine via AgI-catalysed asymmetric 1,3-dipolar cycloaddition of azomethine ylides

Cinchonine was effectively used in an AgOAc-catalysed asymmetric 1,3-dipolar cycloaddition of azomethine ylides with 2,6-bis(arylmethylidene) cyclohexanones, affording spiropyrrolidine derivatives with excellent yields (up to 99%), diastereoselectivities (up to 96:04 dr), and enantioselectivities (up to 99% ee).