Hopf algebra actions

Finite groups acting on rings by automorphisms, and group-graded rings are instances of Hopf algebras H acting on H-module algebras A. We study such actions. Let A^H = {a ε A¦h · A = (h) a, all h ε H}, the ring of H-invariants, and form the smash product A # H. We study the ring extensions A^H A A # H. We prove a Maschke-type theorem for A # H-modules. We form an associated Morita context [A^H, A, A, A # H] and use these to get connections between the various rings.     

Thermal helium clusters at 3.2 Kelvin in classical and semiclassical simulations

The thermodynamic stability of⁴He_4–13 at 3.2 K is investigated with the classical Monte Carlo method, with the semiclassical path-integral Monte Carlo (PIMC) method, and with the semiclassical all-order many-body method. In the all-order many-body simulation the dipole-dipole approximation including short-range correction is used. The resulting stability plots are discussed and related to recent TOF experiments by Stephens and King. It is found that with classical Monte Carlo of course the characteristics of the measured mass spectrum cannot be resolved. With PIMC, switching on more and more quantum mechanics. by raising the number of virtual time steps results in more structure in the stability plot, but this did not lead to sufficient agreement with the TOF experiment. Only the all-order many-body method resolved the characteristic structures of the measured mass spectrum, including magic numbers. The result shows the influence of quantum statistics and quantum mechanics on the stability of small neutral helium clusters.     

Optical spectra and laser-induced dissociation of supported Na particles

This paper reports new results on the optical spectra of Na particles and on laser-induced photodissociation of Na atoms from the surface of these particles. In continuation of our earlier studies we have performed experiments to elucidate the mechanism of thenonthermal dissociation process. Furthermore, theoretical calculations have been carried out with the goal to correlate the wavelength dependence of the photodissociation yield with the optical absorption spectra of the metal particles. In addition, manipulation of the size distribution of metal particles on supports is outlined as an application of the effect. This allows for the preparation of very special surfaces with novel physical and chemical properties.     

Regular polytopes from twisted Coxeter groups

Dedicated to Professor L. Danzer on the occasion of his 60th birthday     

Reflection of light by a slab containing electrically small dielectric spheres

Theoriginal and theenhanced Maxwell-Garnett estimates for the permittivity of a particulate medium are applied to the reflection of light by a composite dielectric slab. The reflection coefficients for incident s and p polarizations are calculated and some curves are plotted and discussed.     

Forward-backward multiplicity correlations in σ+ p,K + p andpp collisions at 250 GeV/c

Forward-backward multiplicity correlations in σ⁺,K ⁺ p andpp collisions at 250 GeV/c ( \(\sqrt s \) =22 GeV) are given for all charges and for the different charge combinations. The correlations are found to be caused predominantly by centrally produced particles. It is demonstrated that this result is an agreement with observations at the ISR and the CERNp \(\bar p\) -Collider. The results are compared to expectations from LUND, DPM and FRITIOF Monte Carlo models and a geometrical picture relating correlations in hadron-hadron collisions toe ⁺ e ^? data in terms of impact parameters is tested.     

Application of preparative high-speed counter-current chromatography for the separation of flavonoids from the leaves of Byrsonima crassa Niedenzu (IK)

The methanolic extract of the leaves of the medicinal plant Byrsonima crassa (Malpighiaceae) contain flavonoids with antioxidant activity. They were separated in a preparative scale using high-speed counter-current chromatography. The optimum solvent system used was composed of a mixture of ethyl acetate-n-propanol-water (140:8:80 (v/v/v)) and led to a successful separation between monoglucosilated flavonoids (quercetin-3-O-alpha-L-arabinoside, quercetin-3-O-beta-D-galactoside) and the biflavonoid amentoflavone in only 3.5 h. The purities of quercetin-3-O-alpha-L-arabinoside (95 mg), quercetin-3-O-beta-D-galactoside (16 mg) and the biflavonoid amentoflavone (114 mg) were all isolated at purity over 95%. Identification was performed by 1H NMR, 13C NMR and UV analyses.     

Sequestration within biomolecular condensates inhibits Aβ-42 amyloid formation

Biomolecular condensates are emerging as an efficient strategy developed by cells to control biochemical reactions in space and time by locally modifying composition and environment. Yet, local increase in protein concentration within these compartments could promote aberrant aggregation events, including the nucleation and growth of amyloid fibrils. Understanding protein stability within the crowded and heterogeneous environment of biological condensates is therefore crucial, not only when the aggregation-prone protein is the scaffold element of the condensates but also when proteins are recruited as client molecules within the compartments. Here, we investigate the partitioning and aggregation kinetics of the amyloidogenic peptide Abeta42 (Aβ-42), the peptide strongly associated with Alzheimer''s disease, recruited into condensates based on low complexity domains (LCDs) derived from the DEAD-box proteins Laf1, Dbp1 and Ddx4, which are associated with biological membraneless organelles. We show that interactions between Aβ-42 and the scaffold proteins promote sequestration and local increase of the peptide concentration within the condensates. Yet, heterotypic interactions within the condensates inhibit the formation of amyloid fibrils. These results demonstrate that biomolecular condensates could sequester aggregation-prone proteins and prevent aberrant aggregation events, despite the local increase in their concentration. Biomolecular condensates could therefore work not only as hot-spots of protein aggregation but also as protective reservoirs, since the heterogenous composition of the condensates could prevent the formation of ordered fibrillar aggregates.

Biomolecular condensates sequester an aggregation-prone peptide and prevent its aggregation, showing that heterotypic interactions within the condensates can prevent the formation of amyloid fibrils, despite the local increase in concentration.