Understanding singularities in Cartan's and NSF geometric structures

In this work we establish a relationship between Cartan's geometric approach to third order ODEs and the 3-dim Null Surface Formulation (NSF). We then generalize both constructions to allow for caustics and singularities that necessarily arise in these formalisms.Comment: 22 pages, 2 figure

IgM-producing tumors in the BALB/c mouse: a model for B-cell maturation

Five adjuvant induced BALB/c tumors producing IgM—McPc 1748, W 3469, TEPC 183, McPc 774, and Y 5781—were characterized morphologically by electron microscopy, analysis of the distribution of surface-bound and intracytoplasmic IgM using immunofluorescence, and by biochemical study of IgM synthesis, turnover, and secretion. The cells of different tumors appear to represent different stages in B-cell maturation when compared to normal, lipopolysaccharide-stimulated B cells. Thus, McPc 1748 tumor cells resemble 10–25-h stimulated normal B cells, 3469 cells resemble 20–35-h stimulated B cells, TEPC 183 cells resemble 45–65-h stimulated B cells, Y 5781 cells resemble 80–110-h stimulated B cells, and McPc 774 cells resemble 100–130-h stimulated B cells

Synthesis and characterization of a tetrathia[7]helicenebased rhenium(I) complex

Tetrathia[7]helicenes (7-TH), formed by thiophene and benzene rings ortho-fused in an alternating fashion, are emerging as one of the most popular class of chiral helical-shaped molecules, thanks to their peculiar electronic and chiroptical properties suitable for manifold applications in different areas of science.1 In particular, transition metal-based 7-TH systems are an extremely appealing class of complexes, in which the coordination of metals with the \uf070-helical ligand, bearing appropriate coordinating functionalities, provides original chiral architectures. Indeed, the effective functionalization of the \uf061-position(s) of the terminal thiophene ring(s) of the 7-TH scaffold allows the introduction of a variety of substituents, including those with efficient coordinating ability (e.g. cyano2, phosphane3, phosphine oxide4). For example, Rh(I)5 and Au(I)6 complexes based on 7-TH phosphanes have been successfully used in the homogenous transition metal catalysis. In our ongoing studies on 7-TH-based organometallic complexes, we have focused on a novel field of investigation concerning the development of rhenium-based polynuclear complexes containing 7-TH phosphine oxide ligands. In this communication, we describe the synthesis and the characterization of a novel dinuclear rhenium(I) complex (Figure 1), along with the elucidation of its tridimensional structure by single crystal X-ray diffraction studies