Hetarylpyrazoles. IV. Synthesis and reactions of 1,5′-bipyrazoles

A number of 1, 5′-bipyrazoles were obtained from the condensation of pyrazol-5-ylhydrazine and 1, 3-dicarbonyl compounds. Electrophilic substitution reactions of these 1, 5′-bipyrazoles occur at the four position of the pyrazole ring.     

“4,7-lactams”, intermediates for penems synthesis. I. skeletal conversion of penicillanic acid to (+)-2,2,5,5-tetramethyl-9-oxo-3-oxa-6-thia-azabicyclo[5,2,01,7]nonane

The synthesis of chiral “4,7-lactam“ $\text{5}$ has been accomplished starting from natural 6-aminopenicillanic acid.     

A nonlinear parabolic free boundary problem

Summary When two immiscible fluids in a porous medium are in contact with one another, an interface is formed and the movement of the fluids results in a free boundary problem for determining the location of the interface along with the pressure distribution throughout the medium. The pressure satisfies a nonlinear parabolic partial differential equation on each side of the interface while the pressure and the volumetric velocity are continuous across the interface. The movement of the interface is related to the pressure through Darcy’s law. Two kinds of boundary conditions are considered. In Part I the pressure is prescribed on the known boundary. A weak formulation of the classical problem is obtained and the existence of a weak solution is demonstrated as a limit of a sequence of classical solutions to certain parabolic boundary value problems. In Part II the same analysis is carried out when the flux is specified on the known boundary, employing special techniques to obtain the uniform parabolicity of the sequence of approximating problems. Entrata in Redazione il 29 novembre 1975. This research was supported in part by the National Science Foundation, the Senior Fellowship Program of the North Atlantic Treaty Organization, the Italian Consiglio Nazionale delle Ricerche, and the Texas Tech. University.     

Is diffusion limited aggregation scale invariant?

Recent work showing evidence for multiscaling in large two dimensional DLA clusters is reviewed. A connection between multiscaling and multifractality is also shown resulting in a weak localization of the growth sites (δ-sites) in shells around the cluster seed.     

Polycyclic hydroxyquinones-xix : Regiospecific synthesis of anthracyclinones via the diels-alder reaction with dichloronaphthazarins

A convenient route to the daunomycinone precursor 18via a succession of Diels-Alder reactions from 2,7-dichloronaphthazarin (9) is described. In a similar manner, starting from 2,6-dichloronaphthazarin (19) compound 20, a regioisomer of 18,is synthesized. This methodology constitutes a regiospecific approach to (±)-daunomycinone and related anthracyclinones.     

Strongly prime alternative pairs with minimal inner ideals

In this paper, we use the known classification of the finite capacity simple alternative pairs and the version of the Litoff Theorem for Jordan pairs to describe all the strongly prime alternative pairs with nonzero socle. We study the inheritance of some properties (primeness, nondegenerancy,…) when passing from the original alternative pair to the symmetrized pair. Thus, we can apply Jordan theoretical results to the alternative case. This work has been partially supported by 1) the “Plan Andaluz de Investigación y Desarrollo Tecnológico” with project no. 1027 and 2) the DGICYT with project no. PB93-0990     

On a problem on chamber systems

It is well known that a geometry belonging to a disconnected diagram is the direct sum of geometries corresponding to the connected components of the diagram. On the other hand, chamber systems with a disconnected diagram exist which do not split as direct products of components of smaller rank. Many finite examples of this kind are discussed in Groups of Lie Type and their Geometries (CUP, 1995, pp. 185–214), but none of them is simply connected. In this article, we construct a simply connected finite example.