New chiral phosphine-phosphite ligands in the enantioselective palladium-catalyzed allylic alkylation

A series of chiral phosphine-phosphite ligands 1-6 have been synthesized and used in the enantioselective palladium-catalyzed reaction of rac-1,3-diphenyl-2-propenyl acetate with dimethyl malonate as nucleophile. Ligands 1a, 2, 3, 5a, 6a, and 6b have been synthesized starting from racemic tert-butylphenylphosphinoborane. The use of dynamically resolved Li phosphide (-)-sparteine provided the optically pure ligands. Crystals of the allylpalladium (6a) complex were obtained, suitable for X-ray crystal structure determination. The X-ray crystal structure of the allylpalladium (6a) complex revealed a longer palladium-carbon bond distance trans to the phosphine moiety indicating that the attack of the nucleophile takes place at the carbon trans to the phosphine moiety. This was confirmed by the fact that the phosphine moiety did not affect the enantioselectivity directly. Under mild reaction conditions, enantioselectivities up to 83% were obtained (25 degrees C) with ligand 1e. Systematic variation of the ligand bridge and the phosphite moiety showed that the configuration of the product is controlled by the atropisomerism of the biphenyl substituent at the phosphite moiety. The conformation of the biphenyl group, in turn, is controlled by the substituent at the chiral carbon in the bridge. Ligands with large bite angles yielded higher enantioselectivities.     

Intercalation of Benzamide into Kaolinite

Well-crystallized kaolinite (K) was initially reacted at 60 degrees C with a water/dimethylsulfoxide (DMSO) mixture and the resulting intercalation derivative (K-DMSO) was characterized by powder X-ray diffractometry (PXRD), thermal analysis (simultaneous TG and DSC), and Fourier-transformed infrared spectroscopy (FTIR). Benzamide crystals were then melted with the K-DMSO derivative at 140 degrees C for 4 days, when a gradual displacement of DMSO by benzamide was observed within the interlayer spacing of the modified kaolinite. The resulting material, after extensive washing with acetone, was characterized and compared to the results obtained previously for the K-DMSO composite. Benzamide intercalation proceeded by gradual displacement of DMSO molecules until completion. The structural stabilization of the K-BZ derivative was explained through the establishment of hydrogen bonds between the carbonyl oxygen atoms of the intercalated benzamide and aluminol groups present at the surface of the kaolinite layer. The interlamellar spacing of K-BZ was shown to be possibly occupied by benzamide molecules that were located at a 68 degrees orientation in relation to the layer surface. Unlike most intercalation molecules such as DMSO, variations in the interplanar spacing of kaolinite were consistent with the nonkeying of any other part of the molecule between the aluminosilicate interlayers. Copyright 2000 Academic Press.     

Parabolic problems in highly oscillating thin domains

Annali di Matematica Pura ed Applicata (1923 -) - In this work, we consider the asymptotic behavior of the nonlinear semigroup defined by a semilinear parabolic problem with homogeneous Neumann...     

Fine Analysis of the Quasi-Orderings on the Power Set

We pursue the fine analysis of the quasi-orderings and on the power set of a quasi-ordering (Q,). We set X Y if every xX is majorized in by some yY, and X Y if every yY is minorized in by some xX. We show that both these quasi-orderings are -wqo if and only if the original quasi-ordering is ( )-wqo. For this holds also restricted to finite subsets, thus providing an example of a finitary operation on quasi-orderings which does not preserve wqo but preserves bqo.     

Reverse mathematics and initial intervals

In this paper we study the reverse mathematics of two theorems by Bonnet about partial orders. These results concern the structure and cardinality of the collection of initial intervals. The first theorem states that a partial order has no infinite antichains if and only if its initial intervals are finite unions of ideals. The second one asserts that a countable partial order is scattered and does not contain infinite antichains if and only if it has countably many initial intervals. We show that the left to right directions of these theorems are equivalent to _ACA0${\mathsf{ACA}}_0$ and _ATR0${\mathsf{ATR}}_0$, respectively. On the other hand, the opposite directions are both provable in _WKL0${\mathsf{WKL}}_0$, but not in _RCA0${\mathsf{RCA}}_0$. We also prove the equivalence with _ACA0${\mathsf{ACA}}_0$ of the following result of Erdös and Tarski: a partial order with no infinite strong antichains has no arbitrarily large finite strong antichains.     

The Set of Better Quasi Orderings is ∏

In this paper we give a proof of the II¹₂-completeness of the set of countable better quasi orderings (viewed as a subset of the Cantor space). This result was conjectured by Clote in [2] and proved by the author in his Ph.d. thesis [6] (see also [7]). Here we prove it using Simpson's definition of better quasi ordering ([15]) and as little bqo theory as possible.     

Semilinear parabolic problems in thin domains with a highly oscillatory boundary

In this paper, we study the behavior of the solutions of nonlinear parabolic problems posed in a domain that degenerates into a line segment (thin domain) which has an oscillating boundary. We combine methods from linear homogenization theory for reticulated structures and from the theory on nonlinear dynamics of dissipative systems to obtain the limit problem for the elliptic and parabolic problems and analyze the convergence properties of the solutions and attractors of the evolutionary equations.