Effects of Al concentration and resulting long-period superstructures on the plastic properties at room temperature of Al-rich TiAl single crystals

The role of Al₅Ti₃ and h-Al₂Ti long-period superstructures on the plastic properties of TiAl at room temperature is investigated on five single crystals with aluminium content comprised between 54.7 at.%, and 62.5 at.%. After annealing at 1200°C for 1?h, the Al₅Ti₃ superstructure develops in the L1₀ (γ) matrix upon increasing Al concentration except for Ti–62.5 at.%Al where h-Al₂Ti substitutes for Al₅Ti₃. The CRSS for <110]{111} first increases abruptly with the development of the Al₅Ti₃-type ordering. Then, the CRSS reaches a plateau at which dislocations assemble in groups of four to prevent extra anti-phase boundary (APB) from being engendered during glide throughout the Al₅Ti₃ phase. In Ti–62.5 at.%Al, the CRSS for ordinary slip further increases upon the precipitation of h-Al₂Ti in the L1₀ phase, whereas it decreases when the crystal is fully transformed into single-phased Al₅Ti₃. <101] superlattice dislocations are primarily activated under both the [210] and [1?1?8.6] load orientations irrespective of the Al concentration, but the dislocation microstructure strongly depends on orientation as well as on the degree of Al₅Ti₃ ordering. In the [210] orientation, the frequency of the decomposition of <101] dislocations into 1/2<110] and 1/2<112] dislocations decreases abruptly with the development of Al₅Ti₃. This is interpreted in terms of the increased difficulty to move ordinary dislocations. Under the [1?1?8.6] orientation, the density of faulted dipoles diminishes remarkably with the development of Al₅Ti₃. This is consistent with the transformation of the low energy extrinsic stacking fault of the L1₀ phase into a higher energy complex extrinsic stacking fault.     

Low generation PEGylated phosphorus-containing dendrons with phosphonate anchors

We present a simple strategy to obtain non-symmetrical polyethylene glycols equipped with telechelic phosphorus-containing dendrimeric moieties having adhesive phosphonate surface functions. The dendronized PEG tails were characterized by means of multi-nucleus NMR. The grafting abilities of model symmetrical PEG compounds equipped with telechelic amino-bis(methylene-dimethylphosphonates) and amino-bis(methylenephosphonic acids) were rapidly screened on plasma treated silicon wafers and activated silica.     

Preparation of Chiral Amino Esters by Asymmetric Phase‐Transfer Catalyzed Alkylations of Schiff Bases in a Ball Mill

The asymmetric alkylation of Schiff bases under basic conditions in a ball mill was performed. The starting Schiff bases of glycine were prepared beforehand by milling protected glycine hydrochloride and benzophenone imine, in the absence of solvent. The Schiff base was then reacted with a halogenated derivative in a ball mill in the presence of KOH. By adding a chiral ammonium salt derived from cinchonidine, the reaction proceeded asymmetrically under phase‐transfer catalysis conditions, giving excellent yields and enantiomeric excesses up to 75 %. Because an equimolar amount of starting material was used, purification was greatly simplified.     

Electronic structure of IPR and non-IPR endohedral metallofullerenes: Connecting orbital and topological rules

The electronic structure of endohedral metallofullerenes is rationalized by connecting the apparently independent orbital and topological rules that explain the stability of this family of fullerenes. The separation of the 12 pentagons of the fullerene, which is maximized in order to minimize the Coulomb repulsion, is found to be correlated with the orbital energies of the cage that accepts the electron transfer from the internal cluster. An explanation for the absence of non-IPR cages in large-size EMFs is also provided.     

A Lie symmetry approach for the solution of the inverse kinematics problem

In this paper, it is considered the inverse kinematics problem, which is faced from a differential point of view. In particular, it is shown that an asymptotic inverse kinematics can be interpreted as a Lie symmetry of the direct kinematics. A parameterization of all Lie symmetries of the direct kinematics is proposed, and the classical Newton and gradient method are obtained as particular cases.     

Extremal Values of L-Functions Associated with Newforms in the Half-Plane of Absolute Convergence

We prove estimates for extremal values of L-functions associated with newforms f in the half-plane of absolute convergence of their Dirichlet series expansion. The proof is based on an effective version of Kronecker's approximation theorem and estimates for the Fourier coefficients of the newform f.     

Weak density of smooth maps for the Dirichlet energy between manifolds

We prove that given a simply connected compact manifold M and a closed manifold N, any map in the Sobolev space W ^1,2(M,N) can be approximated weakly by smooth maps between M and N. Submitted: September 2002, Final version: November 2002.     

Functional Quantization and Small Ball Probabilities for Gaussian Processes

Quantization consists in studying the L ^r -error induced by the approximation of a random vector X by a vector (quantized version) taking a finite number n of values. We investigate this problem for Gaussian random vectors in an infinite dimensional Banach space and in particular, for Gaussian processes. A precise link proved by Fehringer⁽⁴⁾ and Dereich et al. ⁽³⁾ relates lower and upper bounds for small ball probabilities with upper and lower bounds for the quantization error, respectively. We establish a complete relationship by showing that the same holds for the direction from the quantization error to small ball probabilities. This allows us to compute the exact rate of convergence to zero of the minimal L ^r -quantization error from logarithmic small ball asymptotics and vice versa.