Generalized Ces\`aro operators on Dirichlet-type spaces

In this note, we introduce and study a new kind of generalized Ces\`aro operators $\mathcal{C}_{\mu}$, induced by a positive Borel measure $\mu$ on $[0, 1)$, between the Dirichlet-type spaces. We characterize the measures $\mu$ for which $\mathcal{C}_{\mu}$ is bounded (compact) from one Dirichlet-type space $\mathcal{D}_{\alpha}$ into another one $\mathcal{D}_{\beta}$.Comment: Accepted by Acta Mathematica Scienti

Functional comparison of anti-restriction and anti-methylation activities of ArdA, KlcA, and KlcAHS from Klebsiella pneumoniae

Anti-restriction proteins are typically encoded by plasmids, conjugative transposons, or phages to improve their chances of entering a new bacterial host with a type I DNA restriction and modification (RM) system. The invading DNA is normally destroyed by the RM system. The anti-restriction proteins ArdA, KlcA, and their homologues are usually encoded on plasmid of carbapenemase-resistant Klebsiella pneumoniae. We found that the plasmid sequence and restriction proteins affected horizontal gene transfer, and confirmed the anti-restriction and anti-methylation activities of ArdA and KlcA during transformation and transduction. Among the three anti-restriction proteins, ArdA shows stronger anti-restriction and anti-methylation effects, and KlcAHS was weaker. KlcA shows anti-methylation only during transformation. Understanding the molecular mechanism underlying the clinical dissemination of K. pneumoniae and other clinically resistant strains from the perspective of restrictive and anti-restrictive systems will provide basic theoretical support for the prevention and control of multidrug-resistant bacteria, and new strategies for delaying or even controlling the clinical dissemination of resistant strains in the future

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals <1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data

Composition Operator, Boundedness, Compactness, Hyperbolic Bloch-Type Space βμ∗, Hyperbolic-Type Space

In this paper, we obtain some characterizations of composition operators Cφ, which are induced by an analytic self-map φ of the unit disk Δ, from hyperbolic Bloch type space βμ∗ into hyperbolic type space QK,p,q∗

Generalized Hilbert operators acting between weighted Fock spaces

In this paper we introduce and study several new generalized Hilbert operators acting between the weighted Fock spaces. We provide some sufficient and necessary conditions for the boundedness and compactness of the generalized Hilbert operators from one weighted Fock space to another