Periodic,multiplicative number-theoretical functions

D. Leitmann andD. Wolke [3] proved that multiplicative functions, which are restrictions of continuous, periodic functionsF: with irrational period, are constant equal to 0 or 1. In this note a simpler proof for this result is given.     

Cationic molybdenum oxo alkylidenes stabilized by N-heterocyclic carbenes: from molecular systems to efficient supported metathesis catalysts

Cationic d⁰ group 6 olefin metathesis catalysts have been recently shown to display in most instances superior activity in comparison to their neutral congeners. Furthermore, their catalytic performance is greatly improved upon immobilization on silica. In this context, we have developed the new family of molecular cationic molybdenum oxo alkylidene complexes stabilized by N-heterocyclic carbenes of the general formula [Mo(O)(CHCMe₃)(IMes)(OR)[X⁻]] (IMes = 1,3-dimesitylimidazol-2-ylidene; R = 1,3-dimesityl-C₆H₃, C₆F₅; X⁻ = B(3,5-(CF₃)₂C₆H₃)₄⁻, B(Ar^F)₄, tetrakis(perfluoro-t-butoxy)aluminate (PFTA)). Immobilization of [Mo(O)(CHCMe₃)(IMes)(O-1,3-dimesityl-C₆H₃)⁺B(Ar^F)₄⁻] on silica via surface organometallic chemistry yields an active alkene metathesis catalyst that shows the highest productivity towards terminal olefins amongst all existing molybdenum oxo alkylidene catalysts.

The first cationic molybdenum oxo complexes were synthesized and immobilized on partially dehydroxylated silica. Vastly enhanced catalytic activity for terminal olefins was found compared to their neutral congeners.     

Enzyme-Catalyzed Synthesis of O-Glycopeptide Building Blocks

Abstract

In 1988, MOSBACH et aL¹ reported the synthesis of a-D-mannopyranosy1-L-serine and Q -D-N-acetylgalactosamino-L-serine by reversing the hydrolytic activity of a -mannosidase from jack beans and a -N-acetylgalactosaminidase from beef liver, respectively. The yields in these equilibrium-controlled syntheses² using high concentrations of monosaccharide and serine were highly dependent on the enzyme concentration and ranged from 5 to 10 percent in both cases.     

Eigenvalues of a statistical mechanics matrix

We consider the problem of finding the spectrum of an n × n matrix which arises in the study of a certain model of long-range interactions in a one-dimensional statistical mechanics system. Our analysis exhibits a curious resemblance of the suitably normalized distribution of eigenvalues to the Marčenko–Pastur law in the limit n → ∞.     

Proliferative reactive gliosis is compatible with glial metabolic support and neuronal function

Background

Trail-making tests, such as the Concept Shifting Task (CST), can be used to test the effects of treatment on cognitive performance over time in various neuropsychological disorders. However, cognitive performance in such experimental designs might improve as a result of the practice obtained during repeated testing rather than the treatment itself. The current study investigated if practice affects the accuracy and duration of performance on the repeatedly administered Concept Shifting Task modified to make it resistant to practice (mCST). The mCST was administered to 54 healthy participants twice a day, before and after a short break, for eight days. Results. The ANOVA and meta-analysis showed that there was no improvement in the mCST accuracy on the last vs. the first trial (Hedges' g = .14, p = .221) or within the session (after vs. before the break on all days; g = .01, p = .922). However, the participants performed the task faster on the last vs. the first trial (g = -.75, p < .001) and after vs. before the break on all days (g = -.12, p = .002). Conclusions. Repeated administration of the mCST does not affect the accuracy of performance on the test. However, practice might contribute to faster performance on the mCST over time and within each session.     

The Cellular Interactions of PEGylated Gold Nanoparticles: Effect of PEGylation on Cellular Uptake and Cytotoxicity

Poly(ethylene glycol) (PEG) is frequently used to coat various medical nanoparticles (NPs). As PEG is known to minimize NP interactions with biological specimens, the question remains whether PEGylated NPs are intrinsically less toxic or whether this is caused by reduced NP uptake. In the present work, the effect of gold NP PEGylation on uptake by three cell types is compared and evaluated the effect on cell viability, oxidative stress, cell morphology, and functionality using a multiparametric methodology. The data reveal that PEGylation affects cellular NP uptake in a cell‐type‐dependent manner and influences toxicity by different mechanisms. At similar intracellular NP numbers, PEGylated NPs are found to yield higher levels of cell death, mostly by induction of oxidative stress. These findings reveal that PEGylation significantly reduces NP uptake, but that at similar functional (= cell‐associated) NP levels, non‐PEGylated NPs are better tolerated by the cells.