New water-soluble calix[4]arene-bis(benzocrown-6) for caesium-sodium separation by nanofiltration-complexation

Calix-bis(benzocrown-6) 6 and 7 were converted into the water-soluble receptors 9, 10, 12 and 15 by introducing hydroxy, carboxy, sulfato or diethanolamino groups at the para position of the phenolic ring and/or on the benzo-ether moieties. The complexation properties of these ionophores were studied for all alkali cations in methanolic and aqueous media. Stability constants were calculated by UV-Vis spectroscopy. All ligands showed a more or less affinity for the larger cations, depending on the nature and the position of the substituents grafted on the benzo-ether chain only or both on the calixarene ring and the benzo-ether loop. For selective Cs⁺/Na⁺ separation, the efficiency of the ligands was evaluated by means of a nanofiltration system. In comparison with the known tetrahydroxylated bis-crown-6 calix[4]arene 1, compounds 9, 12 and 15 represent the most selective ligands for the Cs⁺ cation in a moderate salted medium ([NaNO₃]=85 g/L).     

Stereoselective adduct formation of α-acylcamphorato-copper(II) chelates with some chiral Lewis bases

The formation constants of the mono-adducts of α-acylcamphorato-copper(II) chelates such as (+)-Cu(facam)₂, (?)-Cu(facam)₂, (+)-Cu(hfbc)₂ and (?)-Cu(hfbc)₂ with some chiral Lewis bases were determined spectrophotometrically in benzene. In order to compare the adduct formation constants obtained with the (+)- and (?)-forms, some pairs of chiral Lewis bases such as 1-amino-2-propanol [(R)(?), (S)(+)], 1-(α-naphthyl)ethylamine [(R)(+), (S)(?)], α-phenyl ethylamine [(R)(+), (S)(?)] and also quinine and quinidine were examined as neutral ligands. Although not very pronounced, the effects of combinations obtained for (+)- or (?)-Cu(II) chelates and (+)- or (?)-ligands indicate that formation constants obtained by the formation of adducts with the ligands having different directions of the optical rotation seems to be superior to those with the same direction.     

Catalytic and Atom‐Economic C −C Bond Formation: Alkyl Tantalum Ureates for Hydroaminoalkylation

Atom‐economic and regioselective C ?C bond formation has been achieved by rapid C?H alkylation of unprotected secondary arylamines with unactivated alkenes. The combination of Ta(CH₂SiMe₃)₃Cl₂, and a ureate N,O‐chelating‐ligand salt gives catalytic systems prepared in situ that can realize high yields of β‐alkylated aniline derivatives from either terminal or internal alkene substrates. These new catalyst systems realize C?H alkylation in as little as one hour and for the first time a 1:1 stoichiometry of alkene and amine substrates results in high yielding syntheses of isolated amine products by simple filtration and concentration.     

Recovery of Immersions from Their Metric Tensors and Nonlinear Korn Inequalities: A Brief Survey

The authors discuss the existence and uniqueness up to isometries of Enof immersions φ : Ω  R~n→ E~n with prescribed metric tensor field(g ij) : Ω→ S~n, and discuss the continuity of the mapping(gij) →φ defined in this fashion with respect to various topologies. In particular, the case where the function spaces have little regularity is considered. How, in some cases, the continuity of the mapping(gij) →φ can be obtained by means of nonlinear Korn inequalities is shown.     

Géométries Lorentziennes de dimension 3 : classification et complétude

We classify three-dimensional Lorentz homogeneous spaces G/I having a compact manifold locally modeled on them. We prove a completeness result: any compact locally homogeneous Lorentz threefold M is isometric to a quotient of a Lorentz homogeneous space G/I by a discrete subgroup Γ of G acting properly and freely on G/I. Moreover, if I is noncompact, G/I is isometric to a Lie group L endowed with a left invariant Lorentz metric, where L is isomorphic to one of the following Lie groups:

Shape-preserving bivariate polynomial approximation inC([−1,1]×[−1,1])

In this paper we construct bivariate polynomials attached to a bivariate function, that approximate with Jackson-type rate involving a bivariate Ditzian-Totik ω2-modulus of smoothness and preserve some natural kinds of bivariate monotonicity and convexity of function.The result extends that in univariate case-of D. Leviatan in [5-6], improves that in bivariate case of the author in [3] and in some special cases, that in bivariate case of G. Anastassiou in [1].     

Approximation of Analytic Functions with an Arbitrary Order by Generalized Baskakov–Faber Operators in Compact Sets

By using a sequence \(\lambda _{n}>0\), \(n\in \mathbb {N}\) with the property that \(\lambda _{n}\rightarrow 0\) as fast we want, in this paper we obtain the approximation order \(O(\lambda _{n})\) for a generalized Baskakov–Faber operator attached to analytic functions of exponential growth in a continuum \(G\subset \mathbb {C}\). Several concrete examples of continuums G are given for which this operator can explicitly be constructed.     

An operator approach to zero-sum repeated games

We consider two person zero-sum stochastic games. The recursive formula for the valuesvλ (resp.v _n) of the discounted (resp. finitely repeated) version can be written in terms of a single basic operator Φ(α,f) where α is the weight on the present payoff andf the future payoff. We give sufficient conditions in terms of Φ(α,f) and its derivative at 0 for limv _n and limvλ to exist and to be equal. We apply these results to obtain such convergence properties for absorbing games with compact action spaces and incomplete information games.