A Tate cohomology sequence for generalized Burnside rings

We generalize the fundamental theorem for Burnside rings to the mark morphism of plus constructions defined by Boltje. The main observation is the following: If D is a restriction functor for a finite group G, then the mark morphism φ:D₊→D⁺ is the same as the norm map of the Tate cohomology sequence (over conjugation algebra for G) after composing with a suitable isomorphism of D⁺. As a consequence, we obtain an exact sequence of Mackey functors

     

Visualizing macromolecular complexes with in situ liquid scanning transmission electron microscopy

A central focus of biological research is understanding the structure/function relationship of macromolecular protein complexes. Yet conventional transmission electron microscopy techniques are limited to static observations. Here we present the first direct images of purified macromolecular protein complexes using in situ liquid scanning transmission electron microscopy. Our results establish the capability of this technique for visualizing the interface between biology and nanotechnology with high fidelity while also probing the interactions of biomolecules within solution. This method represents an important advancement towards allowing future high-resolution observations of biological processes and conformational dynamics in real-time.     

Generalized Rotation Surfaces in {\mathbb E^4}

In the present study we consider generalized rotation surfaces imbedded in an Euclidean space of four dimensions. We also give some special examples of these surfaces in ${\mathbb E^4}$ . Further, the curvature properties of these surfaces are investigated. We give necessary and sufficient conditions for generalized rotation surfaces to become pseudo-umbilical. We also show that every general rotation surface is Chen surface in ${\mathbb E^4}$ . Finally we give some examples of generalized rotation surfaces in ${\mathbb E^4}$ .     

Catalytic activity of Ru/tetrahydropyrimidinium salts system for transfer hydrogenation reactions

New 1,3‐dialkyltetrahydropyrimidinium salts as NHC precursors have been synthesized and characterized. The in situ prepared three‐component 1,3‐dialkyltetrahydropyrimidinium salts/[RuCl₂(p‐cymene)]₂ and KOH catalyzes quantitatively the transfer hydrogenation of ketones under mild reaction conditions in 2‐propanol. Also, the molecular structure of 1,3‐bis(2‐methylbenzyl)‐3,4,5,6‐tetrahydropyrimidinium was determined using single‐crystal X‐ray diffraction. Ions of the title compound are linked by C? H…Cl and O? H…Cl hydrogen bonding interactions. The N? C? N bond angle (124.3(2)°) and C? N bond lengths (1.316(3) and 1.314(3) Å) confirm the existence of strong resonance in this part of the molecule. Copyright © 2015 John Wiley & Sons, Ltd.     

Star polymers by photoinduced copper‐catalyzed azide–alkyne cycloaddition click chemistry

Well‐defined star polymers consisting of tri‐, tetra‐, or octa‐arms have been prepared via coupling‐onto strategy using photoinduced copper(I)‐catalyzed 1,3‐dipolar cycloaddition click reaction. An azide end‐functionalized polystyrene and poly(methyl methacrylate), and an alkyne end‐functionalized poly(ε‐caprolactone) as the integrating arms of the star polymers are prepared by the combination of controlled polymerization and nucleophilic substitution reactions; whereas, multifunctional cores containing either azide or alkyne functionalities were synthesized in quantitatively via etherification and ring‐opening reactions. By using photoinduced copper‐catalyzed azide–alkyne cycloaddition (CuAAC) click reaction, reactive linear polymers are simply attached onto multifunctional cores to form corresponding star polymers via coupling‐onto methodology. The chromatographic, spectroscopic, and thermal analyses have clearly demonstrated that successful star formations can be obtained via photoinduced CuAAC click reaction. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 1687–1695