Re-entrant and induced mesophases: Mixed systems showing re-entrant TGBA and re-entrant cholesteric phases

We have investigated the behaviour of chiral carbohydrate-based trioxadecalines with a cyano group in mixed systems. The mixture of a trioxadecaline having a Ch phase and a trioxadecaline having a Ch, S_A and a S*_Cphase sequence induces a re-entrant TGB_A and Ch phase. Below the stabilized S*_C phase, a re-entrant Ch phase is observed. In the mixture of the cholesteric trioxadecaline with CCH7, itself only showing a nematic phase, a TGB_A phase and a broad range S_A phase are induced from two non-smectic compounds. Both mixtures show a blue phase with a pitch ranging from the UV to red depending on the molar fraction.     

Der Einflu? der Eigendotierung des HgSe auf den Reaktionsmechanismus der doppelten Umsetzung zwischen PbTe und HgSe

Ohne Zusammenfassung     

Zur Thermodynamik quasitern?rer Mischphasen. 2. Mitt. Vollst?ndiges und partielles Gleichgewicht an Grenzfl?chen

Ohne Zusammenfassung     

Zur Thermodynamik quasitern?rer Mischphasen. 1. Mitt. Mittlere freie Enthalpie und Spinodale

Ohne Zusammenfassung     

The Betti polynomials of powers of an ideal

For an ideal I in a regular local ring or a graded ideal I in the polynomial ring we study the limiting behavior of as k goes to infinity. By Kodiyalam’s result it is known that β_i(S/I^k) is a polynomial for large k. We call these polynomials the Kodiyalam polynomials and encode the limiting behavior in their generating polynomial. It is shown that the limiting behavior depends only on the coefficients on the Kodiyalam polynomials in the highest possible degree. For these we exhibit lower bounds in special cases and conjecture that the bounds are valid in general. We also show that the Kodiyalam polynomials have weakly descending degrees and identify a situation where the polynomials all have the highest possible degree.     

Colloidal synthesis and structural control of PtSn bimetallic nanoparticles

PtSn bimetallic nanoparticles with different particle sizes (1-9 nm), metal compositions (Sn content of 10-80 mol %), and organic capping agents (e.g., amine, thiol, carboxylic acid and polymer) were synthesized by colloidal chemistry methods. Transmission electron microscopy (TEM) measurements show that, depending on the particle size, the as-prepared bimetallic nanocrystals have quasi-spherical or faceted shapes. Energy-dispersive X-ray (EDX) analyses indicate that for all samples the signals of both Pt and Sn can be detected from single nanoparticles, confirming that the products are actually bimetallic but not only a physical mixture of pure Pt and Sn metal nanoparticles. X-ray diffraction (XRD) measurements were also conducted on the bimetallic particle systems. When compared with the diffraction patterns of monometallic Pt nanoparticles, the bimetallic samples show distinct shifts of the Bragg reflections to lower degrees, which gives clear proof of the alloying of Pt with Sn. However, a quantitative analysis of the lattice parameter shifts indicates that only part of the Sn atoms are incorporated into the alloy nanocrystals. This is consistent with X-ray photoelectron spectroscopy (XPS) measurements that reveal the segregation of Sn at the surfaces of the nanocrystals. Moreover, short PtSn bimetallic nanowires were synthesized by a seed-mediated growth method with amine-capped bimetallic particles as precursors. The resulting nanowires have an average width of 2.3 nm and lengths ranging from 5 to 20 nm.     

Chain Blockers and Convoluted Catalan Numbers

We give new interpretations of Catalan and convoluted Catalan numbers in terms of trees and chain blockers. For a poset P we say that a subset A ? P is a chain blocker if it is an inclusionwise minimal subset of P that contains at least one element from every maximal chain. In particular, we study the set of chain blockers for the class of posets P = C _a × C _b where C _i is the chain 1 < ? < i. We show that subclasses of these chain blockers are counted by Catalan and convoluted Catalan numbers.     

Imaging biomolecular interactions by fast three-dimensional tracking of laser-confined carrier particles

The quantitative study of the near-equilibrium structural behavior of individual biomolecules requires high-resolution experimental approaches with longtime stability. We present a new technique to explore the dynamics of weak intramolecular interactions. It is based on the analysis of the 3D Brownian fluctuations of a laser-confined glass bead that is tethered to a flat surface by the biomolecule of interest. A continuous autofocusing mechanism allows us to maintain or adjust the height of the optical trap with nanometer accuracy over long periods of time. The resulting remarkably stable trapping potential adds a well-defined femto-to-piconewton force bias to the energy landscape of molecular configurations. A combination of optical interferometry and advanced pattern-tracking algorithms provides the 3D bead positions with nanometer spatial and >120 Hz temporal resolution. The analysis of accumulated 3D positions has allowed us not only to identify small single biomolecules but also to characterize their nanomechanical behavior, for example, the force-extension relations of short oligonucleotides and the unfolding/refolding transitions of small protein tethers.