Non-covalent synthesis in aqueous solution of discrete multi-porphyrin aggregates with programmable stoichiometry and sequence

This unprecedented calixarene templated, noncovalent synthesis of multi-porphyrin complexes in aqueous solution makes it possible to plan the nature, stoichiometry, and sequence of porphyrins. The proposed method presents the same accuracy of the covalent approach and a 100% yield, but it is not as time-consuming as the latter method.     

Compactly Supported Wavelets Through the Classical Umbral Calculus

We explore compactly supported scaling functions of wavelet theory by means of classical umbral calculus as reformulated by Rota and Taylor. We set a theory of orthonormal scaling umbra which leads to a very simple and elementary proof of Lawton's theorem for umbrae. When umbrae come from a wavelet setting, we recover the usual Lawton condition for the orthonormality of the integer translates of a scaling function.     

On the selection rules for spin-Lorentz cobordisms

A recent result of Gibbons and Hawking on the existence of spin-Lorentz cobordisms is applied to the class of 3-manifolds that can support a non-negative scalar curvature metric. We call such manifolds admissible. It is shown how in general the existence of a spin-Lorentz cobordism restricts the number-mod-2 of certain prime manifolds to occur in the prime decomposition, which are explicitly listed in the case of admissible manifolds.     

The Dirichlet energy of mappings from ${\bf B^3}$ into a manifold: density results and gap phenomenon

Weak limits of graphs of smooth maps with equibounded Dirichlet integral give rise to elements of the space . We assume that the 2-homology group of has no torsion and that the Hurewicz homomorphism is injective. Then, in dimension n = 3, we prove that every element T in , which has no singular vertical part, can be approximated weakly in the sense of currents by a sequence of smooth graphs {u _k } with Dirichlet energies converging to the energy of T. We also show that the injectivity hypothesis on the Hurewicz map cannot be removed. We finally show that a similar topological obstruction on the target manifold holds for the approximation problem of the area functional.Received: 9 May 2003, Accepted: 5 June 2003, Published online: 25 February 2004     

A characterization of the family of lines external to a hyperbolic quadric of PG (3, q)

In this paper we characterize the family of external lines to a hyperbolic quadric of PG (3, q).     

Index information algorithm with local tuning for solving multidimensional global optimization problems with multiextremal constraints

 Multidimensional optimization problems where the objective function and the constraints are multiextremal non-differentiable Lipschitz functions (with unknown Lipschitz constants) and the feasible region is a finite collection of robust nonconvex subregions are considered. Both the objective function and the constraints may be partially defined. To solve such problems an algorithm is proposed, that uses Peano space-filling curves and the index scheme to reduce the original problem to a H?lder one-dimensional one. Local tuning on the behaviour of the objective function and constraints is used during the work of the global optimization procedure in order to accelerate the search. The method neither uses penalty coefficients nor additional variables. Convergence conditions are established. Numerical experiments confirm the good performance of the technique. Received: April 2002 / Accepted: December 2002 Published online: March 21, 2003 RID="⋆" ID="⋆" This research was supported by the following grants: FIRB RBNE01WBBB, FIRB RBAU01JYPN, and RFBR 01–01–00587. Key Words. global optimization – multiextremal constraints – local tuning – index approach     

On the hypergroups with four proper pairs and two or three non-scalar elements

In this paper one continues the study of hypergroups with for proper pairs. In particular one considers the case when the scalars group is not empty and the set of non-scalar elements has size two or three. This work is produced by support of the Italian M.U.R.S.T. (quota 40%). No version of this paper will be published elsewhere.     

Mononuclear heterocyclic rearrangements 5. Kinetic Investigation of the behaviour of (e)- and (z)-phenylhydrazones of 3-benzoyl-5-phenyl-1,2,4-oxadiazole in benzene. Isomerization and rearrangement

The kinetic behaviour of the geometrical isomers I-E and I-Z of the title compound in the presence of piperidine in benzene has been investigated. The kinetic results suggest that I-Z rearranges directly into 2,5-diphenyl-4-benzoylamino-1,2,3-triazole (II), whereas I-E probably rearranges only through the intermediate I-Z formed by isomerization. All the reactions studied are piperidine-catalyzed.