Green's relations, regularity and abundancy for semigroups of quasi-onto transformations

Let V be an infinite-dimensional vector space and for every infinite cardinal n such that n≤dimV, let AE(V,n) denote the semigroup of all linear transformations of V whose defect is less than n. In 2009, Mendes-Gonçalves and Sullivan studied the ideal structure of AE(V,n). Here, we consider a similarly-defined semigroup AE(X,q) of transformations defined on an infinite set X. Quite surprisingly, the results obtained for sets differ substantially from the results obtained in the linear setting.

Structural and enzymatic characterization of ABgp46, a novel phage endolysin with broad anti-Gram-negative bacterial activity

The present study demonstrates the antibacterial potential of a phage endolysin against Gram-negative pathogens, particularly against multidrug resistant strains of Acinetobacter baumannii. We have cloned, heterologously expressed and characterized a novel endolysin (ABgp46) from Acinetobacter phage vb_AbaP_CEB1 and tested its antibacterial activity against several multidrug-resistant A. baumannii strains. LC-MS revealed that ABgp46 is an N-acetylmuramidase, that is also active over a broad pH range (4.0-10.0) and temperatures up to 50°C. Interestingly, ABgp46 has intrinsic and specific anti-A. baumannii activity, reducing multidrug resistant strains by up to 2 logs within 2 hours. By combining ABgp46 with several organic acids that act as outer membrane permeabilizing agents, it is possible to increase and broaden antibacterial activity to include other Gram-negative bacterial pathogens. In the presence of citric and malic acid, ABgp46 reduces A. baumannii below the detection limit (> 5 log) and more than 4 logs P. aeruginosa and Salmonella Typhimurium strains. Overall, this globular endolysin exhibits a broad and high activity against Gram-negative pathogens, that can be enhanced in presence of citric and malic acid, and be used in human and veterinary medicine.