Some mathematical aspects of the scaling limit of critical two-dimensional systems

It has been observed long ago that many systems from statistical physics behave randomly on macroscopic level at their critical temperature. In two dimensions, these phenomena have been classified by theoretical physicists thanks to conformal field theory, that led to the derivation of the exact value of various critical exponents that describe their behavior near the critical temperature. In the last couple of years, combining ideas of complex analysis and probability theory, mathematicians have constructed and studied a family of random fractals (called ‘Schramm-Loewner evolutions’ or SLE) that describe the only possible conformally invariant limits of the interfaces for these models. This gives a concrete construction of these random systems, puts various predictions on a rigorous footing, and leads to further understanding of their behavior. The goal of this paper is to survey some of these recent mathematical developments, and to describe a couple of basic underlying ideas. We will also briefly describe some very recent and ongoing developments relating SLE, Brownian loop soups and conformal field theory.     

Flame synthesis of calcium carbonate nanoparticles

Calcium carbonate nanoparticles of 20-50 nm size were obtained from a flame spray process where combustion of specific calcium-containing precursors results in amorphous or crystalline calcium carbonate particles depending on the spray flow conditions.     

Zur projektiven Differentialgeometrie der Flächen,die von einer einparametrigen Schar von Kegelschnitten erzeugt werden

Ohne ZusammenfassungDie vorliegende Arbeit ist zusammen mit den noch folgenden Teilen II und III aus einer von der Naturwissenschaftlich-mathematischen Fakultät der Albert-Ludwigs-Universität in Freiburg i. Br. angenommenen Habilitationsschrift hervorgegangen.     

Über einander ein- und umbeschriebene Laplace-Ketten in mehrdimensionalen projektiven Räumen

Ohne ZusammenfassungMit 3 Textabbildungen     

Über sich schließende Figuren asymptotisch transformierter Kurven undW-transformierter Flächen

Ohne Zusammenfassung     

Magnetic silyl scaffold enables efficient recycling of protecting groups

A novel organic/inorganic hybrid material comprising carboncoated cobalt nanoparticles and a poly(benzylchloride)styrene shell is the first magnetic support that complies with important requirements for immobilized reagents and scavengers, that is, stability under harsh conditions (e.g., acids), sufficient loading (up to 2 mmol g(-1)), and satisfying magnetization. The durability of the scaffold was demonstrated by immobilization of a trialkylsilane reagent, which served as a "magnetic" protecting group for a number of primary and secondary alcohols. Importantly, the scaffold could be efficiently separated, recycled, and reused after alcohol cleavage (HF·pyridine) via regeneration of the silyl chloride moiety with BCl(3).