von Neumann’s trace inequality for Hilbert–Schmidt operators

von Neumann’s inequality in matrix theory refers to the fact that the Frobenius scalar product of two matrices is less than or equal to the scalar product of the respective singular values. Moreover, equality can only happen if the two matrices share a joint set of singular vectors, and this latter part is hard to find in the literature. We extend these facts to the separable Hilbert space setting, and provide a self-contained proof of the “latter part”.     

Dynamics of Bacteriorhodopsin in the Dark-Adapted State from Solution Nuclear Magnetic Resonance Spectroscopy

To achieve efficient proton pumping in the light-driven proton pump bacteriorhodopsin (bR), the protein must be tightly coupled to the retinal to rapidly convert retinal isomerization into protein structural rearrangements. Methyl group dynamics of bR embedded in lipid nanodiscs were determined in the dark-adapted state, and were found to be mostly well ordered at the cytosolic side. Methyl groups in the M145A mutant of bR, which displays only 10 % residual proton pumping activity, are less well ordered, suggesting a link between side-chain dynamics on the cytosolic side of the bR cavity and proton pumping activity. In addition, slow conformational exchange, attributed to low frequency motions of aromatic rings, was indirectly observed for residues on the extracellular side of the bR cavity. This may be related to reorganization of the water network. These observations provide a detailed picture of previously undescribed equilibrium dynamics on different time scales for ground-state bR.     

PTML modeling for peptide discovery: in silico design of non-hemolytic peptides with antihypertensive activity

Molecular Diversity - Hypertension is a medical condition that affects millions of people worldwide. Despite the high efficacy of the current antihypertensive drugs, they are associated with...     

Fast and efficient preparation of Baylis-Hillman-derived (E)-allylic azides and related compounds in aqueous medium

A practical access to alkyl- and aryl-substituted (E)-2-(azidomethyl)alkenoates and related azido compounds from the corresponding allylic bromides in aqueous acetone is described. An alternative method to obtain the starting bromides based on heterogeneous catalysis under mild conditions was also investigated.     

Projektive Punktskalen und Summationsformeln für Tschebyscheff-Polynome

Zusammenfassung. Mit Hilfe der projektiven Geometrie werden neuartige Summationsformeln hergeleitet, die die Tschebyscheff-Polynome und modifizierte Polynome enthalten; z. B. gilt für alle : Daraus ergeben sich wiederum interessante Summationsformeln für die Hyperbelfunktionen; es gilt z. B. für positive reelle Zahlen t: Eingegangen am 28.02.96, revidierte Fassung am 25.08.97 / Angenommen am 09.10.97     

Bubble point pressure estimates from Gibbs ensemble simulations

Bubble pressure points of ethanol–1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea refrigerant) mixtures from the third Industrial Fluid Properties Simulation Challenge are computed using publicly available molecular simulation software. Several published force fields are compared against the known answers provided in the contest guidelines and the best force fields are used to make predictions for the unknown results.     

Synthese und Eigenschaften von Sr3Mo1.5Zn0.5O7‐δ, einer Phase mit perowskitverwandter Schichtstruktur

Synthesis and Properties of the Layered Perovskite Phase Sr₃Mo_1.5Zn_0.5O_7‐δ The new layered perovskite phase Sr₃Mo_1.5Zn_0.5O_7‐δ was synthesized by solid state reaction using a Zn/ZnO oxygen buffer. The crystal structure was refined from X‐ray powder pattern by the Rietveld method. The compound crystallizes tetragonal in the space group I4/mmm (no. 139) with the lattice parameters a = 3.9631(3) Å, c = 20.583(1) Å. An oxygen deficiency corresponding to δ ≈ 0.25 was determinated, indicating the presence of molybdenum in mixed valence (Mo⁴⁺ and Mo⁶⁺).