Dynamic stark effect in strongly coupled microcavity exciton polaritons

We present experimental observations of a nonresonant dynamic Stark shift in strongly coupled microcavity quantum well exciton polaritons-a system which provides a rich variety of solid-state collective phenomena. The Stark effect is demonstrated in a GaAs/AlGaAs system at 10?K by femtosecond pump-probe measurements, with the blueshift approaching the meV scale for a pump fluence of 2 mJ?cm^{-2} and 50?meV red detuning, in good agreement with theory. The energy level structure of the strongly coupled polariton Rabi?doublet remains unaffected by the blueshift. The demonstrated effect should allow generation of ultrafast density-independent potentials and imprinting well-defined phase profiles on polariton condensates, providing a powerful tool for manipulation of these condensates, similar to dipole potentials in cold-atom systems.     

Content of phenolic compounds in aerial parts of Chamomilla suaveolens from Estonia

The content of total polyphenols, flavonoids and coumarins in the aerial parts of pineapple weed (Chamomilla suaveolens (Pursh) Rydb.), growing wild in Estonia, was determined chromato-spectrophotometrically, and individual polyphenols were quantified using HPLC-DAD-MS/MS. The total content of polyphenols was rather similar in flowers (9.1-11.5%) and in whole aerial parts (8.4-10.9%) of pineapple weed. The upper one-third (1/3) and upper two-thirds (2/3) of the aerial parts contained more flavonoids (0.15 - 0.20%) than the flowers (0.12%). The content of coumarins showed no significant difference between the flowers and the upper 1/3 and 2/3 of the aerial parts. The main polyphenols in the flowers were dicaffeoylquinic acids (202-380 mkg/mL), chlorogenic acids (75-185 mkg/mL), and ferulic acid glycoside (61-124 mkg/mL). Also found were quercetin galactoside, apigenin acetylglucoside, malonylapigenin glucoside, as well as luteolin, quercetin and apigenin glycosides.     

Cd(1-x)Zn(x)O [0.05 ≤x≤ 0.26] synthesized by vapor-diffusion induced hydrolysis and co-nucleation from aqueous metal salt solutions

Nanoparticulate Cd(1-x)Zn(x)O (x = 0, 0.05-0.26, 1) is synthesized in a simple two-step synthesis approach. Vapor-diffusion induced catalytic hydrolysis of two molecular precursors at low temperature induces co-nucleation and polycondensation to produce bimetallic layered hydroxide salts (M = Cd, Zn) as precursor materials which are subsequently converted to Cd(1-x)Zn(x)O at 400 °C. Unlike ternary materials prepared by standard co-precipitation procedures, all products presented here containing < 30 mol% Zn(2+) ions are homogeneous in elemental composition on the micrometre scale. This measured compositional homogeneity within the samples, as determined by energy dispersive spectroscopy and inductively coupled plasma spectroscopy, is a testimony to the kinetic control achieved by employing slow hydrolysis conditions. In agreement with this observation, the optical properties of the materials obey Vegard's Law for a homogeneous solid solution of Cd(1-x)Zn(x)O, where x corresponds to the values determined by inductively coupled plasma analysis, even though powder X-ray diffraction shows phase separation into a cubic mixed metal oxide phase and a hexagonal ZnO phase at all doping levels.     

Permutahedra and generalized associahedra

Given a finite Coxeter system (W,S) and a Coxeter element c, or equivalently an orientation of the Coxeter graph of W, we construct a simple polytope whose outer normal fan is N. Reading's Cambrian fan Fc, settling a conjecture of Reading that this is possible. We call this polytope the c-generalized associahedron. Our approach generalizes Loday's realization of the associahedron (a type A c-generalized associahedron whose outer normal fan is not the cluster fan but a coarsening of the Coxeter fan arising from the Tamari lattice) to any finite Coxeter group. A crucial role in the construction is played by the c-singleton cones, the cones in the c-Cambrian fan which consist of a single maximal cone from the Coxeter fan.Moreover, if W is a Weyl group and the vertices of the permutahedron are chosen in a lattice associated to W, then we show that our realizations have integer coordinates in this lattice.     

An interpretation of E n -homology as functor homology

We prove that E _n -homology of non-unital commutative algebras can be described as functor homology when one considers functors from a certain category of planar trees with n levels. For different n these homology theories are connected by natural maps, ranging from Hochschild homology and its higher order versions to Gamma homology.     

Zur Geometrie von Frühstückseiern

Zusammenfassung  Die euklidische Geometrie von Eifl?chen und Eik?rpern bietet eine gute Gelegenheit, geometrische Begriffsbildungen und Sachverhalte aus der Fl?chentheorie einem breiten Publikum anschaulich zu machen. In dieser Arbeit er?rtern wir die erstaunliche Stabilit?t von Eierschalen und dazu verwandte Probleme unter heuristisch-mathematischen Gesichtspunkten. Dem Andenken an Karl Peter Grotemeyer gewidmet Drittmittelangaben (partially supported): Lange: DFG-Forschergruppe 565 „Polyhedral Surfaces“, Polthier: DFG-Forschungszentrum MATHEON, Simon: DFG-PI-158/4-5 Mathematics subject classification (2000)  53C40, 53A04, 53A05     

Admissibility and Observability of Observation Operators for Semilinear Problems

This paper deals with semilinear evolution equations with unbounded observation operators. Sufficient conditions are given guaranteeing that the output function of a semilinear system is in L²_loc([0, ∞); Y). We prove that the Lebesgue extension of the observation operators are invariant under nonlinear globally Lipschitz continuous perturbations. Further, relations between the corresponding -extensions are studied. We show that exact observability of linear autonomous system is conserved under small Lipschitz perturbations. The obtained results are illustrated by several examples.      

Influence of N‐Alkyl Substituents and Counterions on the Structural and Mesomorphic Properties of Guanidinium Salts: Experiment and Quantum Chemical Calculations

A series of N‐4‐(4′‐alkoxybiphenyl)‐N′,N′,N”,N“‐tetramethylguanidinium salts was synthesized with varying alkoxy chain lengths and additional N‐alkyl substituents, each with a number of different counterions. X‐ray crystal‐structure analyses of 1b I , 1b PF₆ , 2a I , and 4a I reveal bilayer structures in the solid state and, for the 1b and 1b PF₆ salts, a hydrogen‐bond‐type connectivity between the guanidinium N‐H group and the anion is found. For the N‐alkyl homologues 2a I and 4a I the anion is still oriented close to the head group, although at a larger distance. Ion pairs are present also in solution, as demonstrated by ¹H NMR: the N‐H chemical shift shows a good linear correlation with the radius, and hence the hardness, of the anion. The intramolecular conformational flexibility of 1b I , 2b I , 3b I, and 4b I was studied by temperature‐dependent ¹H NMR spectroscopy and discrete activation barriers were determined for rotations about each of the three C? N partial double bonds of the guanidinium core. The relative heights of the individual barriers change between the N‐H and the N‐alkylguanidinium salts. A fourth barrier is observed for the rotation about the N? biphenyl bond. DFT calculations of charge densities show that the positive charge resides primarily on the central carbon atom. Rotational barriers were calculated for N′‐substituted 2‐amino‐1,3‐dimethylimidazolidinium cations as models, and are in qualitatively good agreement with the NMR data. Mesomorphic properties were studied by differential‐scanning calorimetry, polarizing optical microscopy, and X‐ray diffraction (WAXS/SAXS). All liquid‐crystalline guanidinium salts exhibit smectic A mesophases. Clearing temperatures show a linear correlation with the anionic radius. Substitution of the N‐H group with methyl, ethyl, or propyl results in decreasing mesophase widths and a concomitant shrinkage of the layer spacings.     

Profiling of mouse synaptosome proteome and phosphoproteome by IEF

Synapses play important roles in neurotransmission and neuroplasticity. For an in‐depth analysis of the synaptic proteome and phosphoproteome, synaptosomal proteins from whole mouse brain were analyzed by IEF and MS resulting in the largest synaptosome proteome described to date, with 2980 unique proteins identified with two or more peptides. At the same time, 118 synaptosomal phosphoproteins were identified, eight of which are reported for the first time as phosphorylated. Expression of selected proteins in synaptosomes was investigated by Western blot. We demonstrate that IEF is a powerful method to interrogate complex samples such as brain tissue both at the proteome and the phosphoproteome level without the need of additional enrichment for phosphoproteins. The detailed synaptoproteome data set reported here will help to elucidate the molecular complexity of the synapse and contribute to our understanding of synaptic systems biology in health and disease.