The group of isometries of a locally compact metric space with one end

In this note we study the dynamics of the natural evaluation action of the group of isometries G of a locally compact metric space (X,d) with one end. Using the notion of pseudo-components introduced by S. Gao and A.S. Kechris we show that X has only finitely many pseudo-components exactly one of which is not compact and G acts properly on this pseudo-component. The complement of the non-compact component is a compact subset of X and G may fail to act properly on it.     

Characterization of functions as radiation patterns in linear elasticity

In this paper a necessary and sufficient condition for a pair of vector functions to be radiation patterns is presented. More precisely, it is proved that two vector functions, the first in the radial direction and the second in the tangential one, are radiation patterns if and only if there are two entire harmonic vector functions whose radial and tangential projections, respectively, are identical with the previous functions on the unit sphere and whose L²-norm over a sphere of radius R is a function of exponential type in the variable R.     

A Liouville type theorem for the Schrödinger operator

In this paper we prove that the equation on a complete Riemannian manifold of dimension without boundary and with nonnegative Ricci curvature admits no positive solution provided that is a function satisfying and where , and are constants depending only on the dimension, thus generalizing similar results in P. Li and S. T. Yau (Acta Math. 156 (1986), 153-201), J. Li (J. Funct. Anal. 100 (1991), 233-256) and E. R. Negrin (J. Funct. Anal. 127 (1995), 198-203) in all of which is assumed to be subharmonic. We also give a generalization in case the Ricci curvature of is not necessarily positive but its negative part has quadratic decay under the additional assumption that is unbounded from above.

     

On embeddings of proper and equicontinuous actions in zero-dimensional compactifications

We provide a tool for studying properly discontinuous actions of non-compact groups on locally compact, connected and paracompact spaces, by embedding such an action in a suitable zero-dimensional compactification of the underlying space with pleasant properties. Precisely, given such an action we construct a zero-dimensional compactification of with the properties: (a) there exists an extension of the action on , (b) if is the set of the limit points of the orbits of the initial action in , then the restricted action remains properly discontinuous, is indivisible and equicontinuous with respect to the uniformity induced on by that of , and (c) is the maximal among the zero-dimensional compactifications of with these properties. Proper actions are usually embedded in the endpoint compactification of , in order to obtain topological invariants concerning the cardinality of the space of the ends of , provided that has an additional ``nice" property of rather local character (``property Z", i.e., every compact subset of is contained in a compact and connected one). If the considered space has this property, our new compactification coincides with the endpoint one. On the other hand, we give an example of a space not having the ``property Z" for which our compactification is different from the endpoint compactification. As an application, we show that the invariant concerning the cardinality of the ends of holds also for a class of actions strictly containing the properly discontinuous ones and for spaces not necessarily having ``property Z".

     

Identification of Polyphenol Derivatives as Novel SARS-CoV-2 and DENV Non-Nucleoside RdRp Inhibitors

The Coronavirus Disease 2019 (COVID-19) and dengue fever (DF) pandemics both remain to be significant public health concerns in the foreseeable future. Anti-SARS-CoV-2 drugs and vaccines are both indispensable to eliminate the epidemic situation. Here, two piperazine-based polyphenol derivatives DF-47 and DF-51 were identified as potential inhibitors directly blocking the active site of SARS-CoV-2 and DENV RdRp. Data through RdRp inhibition screening of an in-house library and in vitro antiviral study selected DF-47 and DF-51 as effective inhibitors of SARS-CoV-2/DENV polymerase. Moreover, in silico simulation revealed stable binding modes between the DF-47/DF-51 and SARS-CoV-2/DENV RdRp, respectively, including chelating with Mg²⁺ near polymerase active site. This work discovered the inhibitory effect of two polyphenols on distinct viral RdRp, which are expected to be developed into broad-spectrum, non-nucleoside RdRp inhibitors with new scaffold.     

One-Step Synthesis of Janus Fluorographene Derivatives

Fluorographene, a two-dimensional derivative of graphene, is an excellent starting material for the synthesis of graphene derivatives. In this work, a one-step, substrate-free method for the asymmetric functionalization of fluorographene layers with hydroxyl groups by a facile nucleophilic substitution reaction is reported. Such a chemical modification occurs in a biphasic aqueous–organic system under mild conditions, leading to Janus graphene nanosheets functionalized by hydroxyl groups on one side and retaining fluorine atoms on the other. The reported experimental route paves the way for two-dimensional bifacial graphene templates, thus broadening the application potential of graphene materials.     

Mushroom Polysaccharides and Lipids Synthesized in Liquid Agitated and Static Cultures. Part II: Study of Volvariella volvacea

Volvariella volvacea strains were studied in relation with their ability to produce biomass, lipids and polysaccharides. Firstly, screening of four strains (AMLR 188, 190, 191 and 192) was performed in agar cultures, where the mycelial growth rate of the strains was measured, and in static liquid cultures, where the production of biomass, the biosynthesis of total cellular lipids and the consumption of glucose were monitored. For all strains, biomass production was significant (13?C15?g?l^?1) and total lipid in dry weight (%, w/w) ranged from 3 to 12?%. Afterwards, a detailed kinetic analysis of mycelial biomass, extra- and intra- cellular polysaccharides (EPS, IPS, respectively) as well as lipid production by a V. volvacea selected strain was conducted in submerged static and agitated cultures. Maximum values of 15?g?l^?1 biomass, ??1.0?g?l^?1 EPS and 5.5?g?l^?1 IPS were recorded. Agitation did not have severe impact on biomass, EPS and IPS production, but it increased total lipid in dry weight quantities. EPS, IPS and lipid in dry weight values decreased with time. Glucose was the major cellular carbohydrate detected. Total fatty acid analysis of cellular lipids was performed for all V. volvacea strains and linoleic acid ^??9,12C18:2 was predominant. Neutral lipids constituted the major fraction of cellular lipids, but their quantity decreased as fermentation proceeded. Phospholipids were the most saturated lipid fraction.     

Formation and plasmonic response of self-assembled layers of colloidal gold nanorods and branched gold nanoparticles

The plasmonic properties of self-assembled layers of rod- and branched-shaped gold nanoparticles were investigated using optical techniques. Nanoparticles were synthesized by a surfactant-guided, seed-mediated growth method. The layers were obtained by gradual assembly of nanoparticles at the interface between a polar and a nonpolar solvent and were transferred to a glass slide. Polarization and angle-dependent extinction measurements showed that the layers made of gold nanorods were governed by an effective medium response. The response of the layers made by branched gold particles was characterized by random light scattering. Microscopic mapping of the spatial mode structure demonstrates a uniform optical response of the nanoparticle layers down to a submicrometer length scale.