Analytic stratifications and the cut locus of a class of distance functions

We study the analytic singularities of viscosity solutions of equations of eikonal type and obtain that the analytic singular support of these functions has an analytic stratification. The singular support can be identified with the cut locus of the distance to the boundary of an open set, when the interior is equipped with a degenerate Riemannian metric. We apply the result to elliptic equations as well as to model operators of Grušin type.     

Mixed Norm and Multidimensional Lorentz Spaces

In the last decade, the problem of characterizing the normability of the weighted Lorentz spaces has been completely solved ([16], [7]). However, the question for multidimensional Lorentz spaces is still open. In this paper, we consider weights of product type, and give necessary and sufficient conditions for the Lorentz spaces, defined with respect to the two-dimensional decreasing rearrangement, to be normable. To this end, it is also useful to study the mixed norm Lorentz spaces. Finally, we prove embeddings between all the classical, multidimensional, and mixed norm Lorentz spaces. Research partially supported by KAW 2000.0048 and STINT KU 2002-4025. Research partially supported by Grants MTM2004-02299, 2005SGR00556 and The Swedish Research Council no. 624-2003-571.     

The formation of a liquid crystalline main chain polymer by means of photopolymerization

A nematic liquid crystal material containing a mercapto group and an olefinic group was synthesized. Photopolymerization of this compound in the liquid crystalline state resulted in a liquid crystalline main chain polymer which showed a relatively high birefringence. Due to scattering, the material had a low transmission at ambient temperatures.     

Enantioselective Alternating Olefin-Carbon Monoxide Copolymerization: A new concept for activity and stereoselectivity

Cationic Pd-complexes modified by dicyclohexyl{(R)-1-[(S)-2-(diphenylphosphino)ferrocenyl]ethyl}phosphine ( 1a ) give very active catalytic systems for the regioregular isotactic specific copolymerization of propene with CO. Other alk-1-enes also give stereoregular and regioregular copolymers, even if with lower productivity. The copolymers are isolated as poly(4-alkyl-tetrahydrofuran-2,2,5,5-tetrayl-2-oxy-2-methylenes) B in the solid state and give the isomeric poly(2-alkyl-1-oxopropane-1,3-diyls) A by dissolution in (CF₃)₂CHOH. Solid polymer A (R = Et) is formed back at least partially when the dissolved material is reprecipitated from MeOH. The use of the related (ferrocenyl)diphosphine ligands 1b ? e and 2 as the catalyst modifier shows that the presence of both elements of chirality and of large substituents on the P-atoms of the ligand is necessary to achieve good stereocontrol, and that the large difference in basicity between the two P-atoms is probably the reason for the good catalytic activity.     

Perfect MV-algebras and their Logic

In this paper, after recounting the basic properties of perfect MV-algebras, we explore the role of such algebras in localization issues. Further, we analyze some logics that are based on Łukasiewicz connectives and are complete with respect to linearly ordered perfect MV-algebras.      

Spironolactone and its Complexes with β-cyclodextrin: Modern NMR Characterization and Structural DFTB-SCC Calculations

In the present work, inclusion complexes of spironolactone (SP) with β-cyclodextrin (β-CD) in solid phase and aqueous solution were studied by solubility methods, NMR spectroscopy and thermal analysis. The results showed different kinds of complexations when freeze-drying and kneading methods were used. The freeze-drying product (1:1, SP:β-CD) showed lower degree of complexation and stability than the (1:2, SP:β-CD) compound obtained by kneading method. The spironolactone molecule was also studied by NMR spectroscopy at 400 MHz. The chemical shifts of all spironolactone atoms and their inclusion compounds were assigned. Extensive use of 1D and 2D NMR techniques, including ROESY experiment, allowed verifying the position of the spironolactone molecule inside the cyclodextrin cavity in both situations. In addition, DFTB-SCC quantum mechanical calculations of the inclusion compounds were performed. The predicted structural properties are in good agreement with ROESY NMR results.