On theorems of Brauer-Nesbitt and Brandt for characterizations of small block algebras

Let A be a finite group acting on a finite group G via automorphisms. Assume that $$(|A|,|G|)=1$$ . We prove that if $$C_G(A)$$ is a Hall $$\pi $$ -subgroup of G, then G has a normal $$\pi $$ -complement.     

碳化镍钼催化剂的制备及其甲烷干气重整活性(英文)

Nickel molybdenum carbide catalysts were prepared and their activities in the CO2 reforming of methane at a low CO2/CH4 reactant ratio were investigated using a microreactor at atmospheric pressure and at 973 K.The effect of the catalyst preparation method and the Ni/Mo ratio on the increase in catalyst life and the promotion of catalytic activity were investigated using N2 adsorption,X-ray diffraction, temperature-programmed carburization,temperature-programmed reaction,and a reforming reaction.The 25Ni75Mo catalyst that was carburized at 813 K exhibited the highest hydrogen formation ability and gave the least carbon deposition.The incomplete carburization of the Mo oxide species in the catalyst that was carburized at a lower temperature gradually gave a more active carburized species.The NiMoOxCy in the catalyst was more active in hydrogen formation during the dry reforming of methane whileβ-Mo2C andη-Mo3C2 were less active.     

Quiver W-algebras

For a quiver with weighted arrows, we define gauge-theory K-theoretic W-algebra generalizing the definition of Shiraishi et al. and Frenkel and Reshetikhin. In particular, we show that the qq-character construction of gauge theory presented by Nekrasov is isomorphic to the definition of the W-algebra in the operator formalism as a commutant of screening charges in the free field representation. Besides, we allow arbitrary quiver and expect interesting applications to representation theory of generalized Borcherds–Kac–Moody Lie algebras, their quantum affinizations and associated W-algebras.     

Quiver elliptic W-algebras

We define elliptic generalization of W-algebras associated with arbitrary quiver using our construction (Kimura and Pestun in Quiver W-algebras, 2015. arXiv:1512.08533 [hep-th]) with six-dimensional gauge theory.     

Development of a Versatile Protein Labeling Tool for Live-Cell Imaging Using Fluorescent β-Lactamase Inhibitors

To understand the function of protein in live cells, real-time monitoring of protein dynamics and sensing of their surrounding environment are important methods. Fluorescent labeling tools are thus needed that possess fast labeling kinetics, high efficiency, and long-term stability. We developed a versatile chemical protein-labeling tool based on fluorophore-conjugated diazabicyclooctane β-lactamase inhibitors (BLIs) and wild-type TEM-1 β-lactamase protein tag. The fluorescent probes efficiently formed a stable carbamoylated complex with β-lactamase, and the labeled proteins were visualized over a long period of time in live cells. Moreover, use of an α-fluorinated carboxylate ester-based BLI prodrug enabled the probe to permeate cell membranes and stably label intracellular proteins after unexpected spontaneous ester hydrolysis. Lastly, combining the labeling tool with a pH-activatable fluorescent probe allowed visual monitoring of lysosomal protein translocation during autophagy.