Ba-catalyzed direct Mannich-type reactions of a beta,gamma-unsaturated ester providing beta-methyl aza-Morita-Baylis-Hillman-type products

Barium-catalyzed direct Mannich-type reactions of a beta,gamma-unsaturated ester are described. The Ba-catalyst not only promoted the Mannich-type reactions, but also isomerized Mannich adducts to afford beta-methyl aza-Morita-Baylis-Hillman-type products in 61-88% yield from various aryl, heteroaryl, and alkyl imines. Preliminary trials on enantioselective variants with a chiral biaryldiol ligand gave products in up to 80% ee.     

Sulfur-bridged early-late heterobimetallics synthesized by incorporation of titanium,vanadium, and molybdenum into bis(hydrosulfido) templates of group 9 metals

Reactions of the bis(hydrosulfido) complexes [Cp*Rh(SH)(2)(PMe(3))] (1a; Cp* = eta(5)-C(5)Me(5)) with [CpTiCl(3)] (Cp = eta(5)-C(5)H(5)) and [TiCl(4)(thf)(2)] in the presence of triethylamine led to the formation of the sulfido-bridged titanium-rhodium complexes [Cp*Rh(PMe(3))(micro(2)-S)(2)TiClCp] (2a) and [Cp*Rh(PMe(3))(micro2-S)(2)TiCl(2)] (3a), respectively. Complex 3a and its iridium analogue 3b were further converted into the bis(acetylacetonato) complexes [Cp*M(PMe(3))(micro(2)-S)(2)Ti(acac)(2)] (4a, M = Rh; 4b, M = Ir) upon treatment with acetylacetone. The hydrosulfido complexes 1a and [Cp*Ir(SH)(2)(PMe(3))] (1b) also reacted with [VCl(3)(thf)(3)] and [Mo(CO)(4)(nbd)] (nbd = 2,5-norbornadiene) to afford the cationic sulfido-bridged VM2 complexes [(Cp*M(PMe(3))(micro2-S)(2))2V](+) (5a(+), M = Rh; 5b(+), M = Ir) and the hydrosulfido-bridged MoM complexes [Cp*M(PMe(3))(micro2-SH)(2)Mo(CO)(4)] (6a, M = Rh; 6b, M = Ir), respectively.     

Poincarésupergravity as broken superconformal gravity

We present a locally superconformal invariant theory of supergravity which is gauge equivalent to the usual, Poincaré, supergravity. This is achieved by means of a compensating scalar supermultiplet. This shows that local superconformal symmetry can be made compatible with gravitational phenomenology.     

syn-selective direct catalytic asymmetric Mannich-type reactions of hydroxyketones using Y{N(SiMe3)2}3/linked-BINOL complexes

[reaction, structure: see text] Chiral Y{N(SiMe3)2}3/linked-BINOL catalyst generated Y-enolate in situ from various hydroxyketones (R2 = aryl, heteroaryl). Beta-amino-alpha-hydroxy ketones (R1 = aryl, heteroaryl, alkenyl) were obtained syn-selectively (up to 96/4) in high ee (up to 98%) and good yield (up to 98% yield).     

On the connectedness of self-affine attractors

Let T = T(A, D) be a self-affine attractor in defined by an integral expanding matrix A and a digit set D. In the first part of this paper, in connection with canonical number systems, we study connectedness of T when D corresponds to the set of consecutive integers . It is shown that in and , for any integral expanding matrix A, T(A, D) is connected. In the second part, we study connectedness of Pisot dual tiles, which play an important role in the study of -expansions, substitutions and symbolic dynamical systems. It is shown that each tile of the dual tiling generated by a Pisot unit of degree 3 is arcwise connected. This is naturally expected since the digit set consists of consecutive integers as above. However surprisingly, we found families of disconnected Pisot dual tiles of degree 4. We even give a simple necessary and sufficient condition of connectedness of the Pisot dual tiles of degree 4. Detailed proofs will be given in [4]. Received: 2 March 2003     

A Survey on Topological Properties of Tiles Related to Number Systems

In the present paper we give an overview of topological properties of self-affine tiles. After reviewing some basic results on self-affine tiles and their boundary we give criteria for their local connectivity and connectivity. Furthermore, we study the connectivity of the interior of a family of tiles associated to quadratic number systems and give results on their fundamental group. If a self-affine tile tessellates the space the structure of the set of its ‘neighbors’ is discussed.