Linearformen in Logarithmen vonU-Zahlen und Transzendenz von Potenzen

Ohne Zusammenfassung     

Phase coexistence during surface phase transitions

In contrast to standard thermodynamic models, we observe phase coexistence over an extended temperature range at a first-order surface phase transition. We have measured the domain evolution of the Si(111)-( 7x7) to ( 1x1) phase transition with temperature, using low-energy electron microscopy. Comparison with detailed, quantitative theoretical predictions shows that coexistence is due to long-range elastic and electrostatic domain interactions. Phase coexistence is predicted to be a universal feature of surface phase transitions.     

Polynomial interpolation on the unit sphere II

The problem of interpolation at (n+1)² points on the unit sphere by spherical polynomials of degree at most n is proved to have a unique solution for several sets of points. The points are located on a number of circles on the sphere with even number of points on each circle. The proof is based on a method of factorization of polynomials. Dedicated to Mariano Gasca on the occasion of his 60th birthday The second author was supported by the Graduate Program Applied Algorithmic Mathematics of the Munich University of Technology. The work of the third author was supported in part by the National Science Foundation under Grant DMS-0201669.     

Deorphaning Pyrrolopyrazines as Potent Multi‐Target Antimalarial Agents

The discovery of pyrrolopyrazines as potent antimalarial agents is presented, with the most effective compounds exhibiting EC₅₀ values in the low nanomolar range against asexual blood stages of Plasmodium falciparum in human red blood cells, and Plasmodium berghei liver schizonts, with negligible HepG2 cytotoxicity. Their potential mode of action is uncovered by predicting macromolecular targets through avant‐garde computer modeling. The consensus prediction method suggested a functional resemblance between ligand binding sites in non‐homologous target proteins, linking the observed parasite elimination to IspD, an enzyme from the non‐mevalonate pathway of isoprenoid biosynthesis, and multi‐kinase inhibition. Further computational analysis suggested essential P. falciparum kinases as likely targets of our lead compound. The results obtained validate our methodology for ligand‐ and structure‐based target prediction, expand the bioinformatics toolbox for proteome mining, and provide unique access to deciphering polypharmacological effects of bioactive chemical agents.     

Discovery of Small‐Molecule Interleukin‐2 Inhibitors from a DNA‐Encoded Chemical Library

Libraries of chemical compounds individually coupled to encoding DNA tags (DNA‐encoded chemical libraries) hold promise to facilitate exceptionally efficient ligand discovery. We constructed a high‐quality DNA‐encoded chemical library comprising 30 000 drug‐like compounds; this was screened in 170 different affinity capture experiments. High‐throughput sequencing allowed the evaluation of 120 million DNA codes for a systematic analysis of selection strategies and statistically robust identification of binding molecules. Selections performed against the tumor‐associated antigen carbonic anhydrase IX (CA IX) and the pro‐inflammatory cytokine interleukin‐2 (IL‐2) yielded potent inhibitors with exquisite target specificity. The binding mode of the revealed pharmacophore against IL‐2 was confirmed by molecular docking. Our findings suggest that DNA‐encoded chemical libraries allow the facile identification of drug‐like ligands principally to any protein of choice, including molecules capable of disrupting high‐affinity protein–protein interactions.     

Novel Urea-Siloxane Polymers as Gelling Agents for Silicone Fluids: Influence of the Hard Segment

Summary. A series of polyureas were synthesized from amino terminated polydimethylsiloxane oligomers, diamine comonomers, and various diisocyanates. These polymers were characterized by nuclear magnetic resonance (NMR), infrared (IR) spectroscopy, and size exclusion chromatography (SEC). The gelation behavior in silicone fluids such as dimethylcyclosiloxanes was investigated. The influence of the structure of the hard segment on the gelation properties was evaluated.     

Determination of benzoylureas in ground water samples by fully automated on-line pre-concentration and liquid chromatography-fluorescence detection

An on-line pre-concentration method for the analysis of five benzoylureas (diflubenzuron, triflumuron, hexaflumuron, lufenuron and flufenoxuron) in ground water samples was evaluated using two C(18) columns, and fluorescence detection after photochemical induced fluorescence (PIF) post-column derivatization. The trace enrichment was carried out with 35 mL of ground water modified with 15 mL of MeOH on a 50 mm x 4.6 mm I.D. first enrichment column (C-1) packed with 5 microm Hypersil Elite C(18). Retention properties of pesticides and humic acids usually contained in ground water were studied on C-1 at concentration levels ranging between 0.04 and 14.00 microg/L in water samples. The results obtained in this study show that the pesticides are pre-concentrated in the first short column while the humic acids contained in the ground water samples are eluted to waste. Pesticides recoveries ranged between 92.3 and 109.5%. The methodology proposed was used to determine benzoylureas in ground water samples at levels lower than 0.1 microg/L (maximum levels established by the European Union).     

Cesàro means of Jacobi expansions on the parabolic biangle

We study Cesàro (C,δ) means for two-variable Jacobi polynomials on the parabolic biangle . Using the product formula derived by Koornwinder and Schwartz for this polynomial system, the Cesàro operator can be interpreted as a convolution operator. We then show that the Cesàro (C,δ) means of the orthogonal expansion on the biangle are uniformly bounded if δ>α+β+1, α≥β≥0. Furthermore, for the means define positive linear operators.     

Particle injection into a chain: decoherence versus relaxation for Hermitian and non‐Hermitian dynamics

A model system for the injection of fermionic particles from filled source sites into an empty chain is investigated. The ensuing dynamics for Hermitian as well as for non‐Hermitian time evolution, where the particles cannot return to the bath sites (quantum ratchet), is studied. A non‐homogeneous hybridization between bath and chain sites permits transient currents in the chain. Non‐interacting particles show decoherence in the thermodynamic limit: the average particle number and the average current density in the chain become stationary for long times, whereas the single‐particle density matrix displays large fluctuations around its mean value. Using the numerical time‐dependent density‐matrix renormalization group (t‐DMRG) method it is demonstrated, on the other hand, that sizable density‐density interactions between the particles introduce relaxation which is by orders of magnitudes faster than the decoherence processes.