Euler characteristic and related measures for random geometric sets

By an elementary calculation we obtain the exact mean values of Minkowksi functionals for a standard model of percolating sets. In particular, a recurrence theorem for the mean Euler characteristic recently put forward is shown to be incorrect. Related previous mathematical work is mentioned. We also conjecture bounds for the threshold density of continuum percolation, which are associated with the Euler characteristic.     

Congresses,conferences, symposia,meetings, and seminars in the field of chemical sciences held in 1995–1996

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Congresses, conferences, symposia, meetings, and seminars in the field of chemical sciences held in 1995–1996     

Congresses,Conferences, Symposia,Meetings, and Seminars in the Field of Chemical Sciences held in 1995–1996

Information

Congresses, Conferences, Symposia, Meetings, and Seminars in the Field of Chemical Sciences held in 1995–1996     

Lipid bilayer disruption by polycationic polymers: the roles of size and chemical functional group

Polycationic polymers are used extensively in biology to disrupt cell membranes and thus enhance the transport of materials into the cell. The highly polydisperse nature of many of these materials makes obtaining a mechanistic understanding of the disruption processes difficult. To design an effective mechanistic study, a monodisperse class of polycationic polymers, poly(amidoamine) (PAMAM) dendrimers, has been studied in the context of supported dimyristoylphosphatidylcholine (DMPC) lipid bilayers using atomic force microscopy (AFM). Aqueous solutions of amine-terminated generation 7 (G7) PAMAM dendrimers caused the formation of 15-40-nm-diameter holes in lipid bilayers. This effect was significantly reduced for smaller G5 dendrimers. For G3, no hole formation was observed. In addition to dendrimer size, surface chemistry had a strong influence on dendrimer-lipid bilayer interactions. In particular, acetamide-terminated G5 did not cause hole formation in bilayers. In all instances, the edges of bilayer defects proved to be points of highest dendrimer activity. A proposed mechanism for the removal of lipids by dendrimers involves the formation of dendrimer-filled lipid vesicles. By considering the thermodynamics, interaction free energy, and geometry of these self-assembled vesicles, a model that explains the influence of polymer particle size and surface chemistry on the interactions with lipid membranes was developed. These results are of general significance for understanding the physical and chemical properties of polycationic polymer interactions with membranes that lead to the transport of materials across cell membranes.     

Joint distribution of direction and length of typical I-segment in a homogeneous random planar tessellation stable under iteration

The paper deals with homogeneous random planar tessellations stable under iteration (random STIT tessellations). The length distribution of the typical I-segment is already known in the isotropic case [8]. In the present paper, the anisotropic case is treated. Then also the direction of the typical I-segment is of interest. The joint distribution of direction and length of the typical I-segment is evaluated. As a first step, the corresponding joint distribution for the so-called typical remaining I-segment is derived. Dedicated to the 80th birthday of Klaus Krickeberg     

Extremal properties of some geometric processes

In this paper some isoperimetric inequalities for stationary random tessellations are discussed. At first, classical results on deterministic tessellations in the Euclidean plane are extended to the case of random tessellations. An isoperimetric inequality for the random Poisson polygon is derived as a consequence of a theorem of Davidson concerning an extremal property of tessellations generated by random lines inR ². We mention extremal properties of stationary hyperplane tessellations inR ^d related to Davidson's result in cased=2. Finally, similar problems for random arrangements ofr-flats inR ^d are considered (r).This work was done while the author was visiting the University of Strathclyde in Glasgow.