Arithmetic groups, base change, and representation growth

Consider an arithmetic group $\mathbf{G}(O_S)$, where $\mathbf{G}$ is an affine group scheme with connected, simply connected absolutely almost simple generic fiber, defined over the ring of $S$-integers $O_S$ of a number field $K$ with respect to a finite set of places $S$. For each $n \in \mathbb{N}$, let $R_n(\mathbf{G}(O_S))$ denote the number of irreducible complex representations of $\mathbf{G}(O_S)$ of dimension at most $n$. The degree of representation growth $\alpha(\mathbf{G}(O_S)) = \lim_{n \rightarrow \infty} \log R_n(\mathbf{G}(O_S)) / \log n$ is finite if and only if $\mathbf{G}(O_S)$ has the weak Congruence Subgroup Property. We establish that for every $\mathbf{G}(O_S)$ with the weak Congruence Subgroup Property the invariant $\alpha(\mathbf{G}(O_S))$ is already determined by the absolute root system of $\mathbf{G}$. To show this we demonstrate that the abscissae of convergence of the representation zeta functions of such groups are invariant under base extensions $K \subset L$. We deduce from our result a variant of a conjecture of Larsen and Lubotzky regarding the representation growth of irreducible lattices in higher rank semi-simple groups. In particular, this reduces Larsen and Lubotzky's conjecture to Serre's conjecture on the weak Congruence Subgroup Property, which it refines.Comment: v1 Preliminary version. Comments are very welcome. v2 numerous corrections. v3 substantial revision. v4 final version, to appear in GAF

Similarity Classes of 3×33\times 3 Matrices over a Local Principal Ideal Ring

In this paper similarity classes of three by three matrices over a local principal ideal commutative ring are analyzed. When the residue field is finite, a generating function for the number of similarity classes for all finite quotients of the ring is computed explicitly.Mathematic

Applications of Chemically Modified Clay Minerals and Clays to Water Purification and Slow Release Formulations of Herbicides

42 páginas.- 6 figuras.- 9 talas.- 140 referencias.- © 2020 by the authors.This review deals with modification of montmorillonite and other clay-minerals and clays by interacting them with organic cations, for producing slow release formulations of herbicides, and efficient removal of pollutants from water by filtration. Elaboration is on incorporating initially the organic cations in micelles and liposomes, then producing complexes denoted micelle- or liposome-clay nano-particles. The material characteristics (XRD, Freeze-fracture electron microscopy, adsorption) of the micelle– or liposome–clay complexes are different from those of a complex of the same composition (organo-clay), which is formed by interaction of monomers of the surfactant with the clay-mineral, or clay. The resulting complexes have a large surface area per weight; they include large hydrophobic parts and (in many cases) have excess of a positive charge. The organo-clays formed by preadsorbing organic cations with long alkyl chains were also addressed for adsorption and slow release of herbicides. Another examined approach includes “adsorptive” clays modified by small quaternary cations, in which the adsorbed organic cation may open the clay layers, and consequently yield a high exposure of the siloxane surface for adsorption of organic compounds. Small scale and field experiments demonstrated that slow release formulations of herbicides prepared by the new complexes enabled reduced contamination of ground water due to leaching, and exhibited enhanced herbicidal activity. Pollutants removed efficiently from water by the new complexes include (i) hydrophobic and anionic organic molecules, such as herbicides, dissolved organic matter; pharmaceuticals, such as antibiotics and non-steroidal drugs; (ii) inorganic anions, e.g., perchlorate and (iii) microorganisms, such as bacteria, including cyanobacteria (and their toxins). Model calculations of adsorption and kinetics of filtration, and estimation of capacities accompany the survey of results and their discussion.T. Undabeytia acknowledges financial support by the Spanish Ministry of Science and Innovation (project CTM2016-77168–R; this project received funding by the European Social Fund). S. Nir acknowledges financial support by the Ministry of Science & Technology, Israel & The Ministry of Science and Technology of the People’s Republic of China (grant No. 3-15707).Peer reviewe

The environmental footprint of Holocene societies: a multi-temporal study of trails in the Judean Desert, Israel

The global distribution of footpaths and their inferred antiquity implies that they are widespread spatial and temporal anthropogenic landscape units. Arid environments are of special interest for investigating historically used footpaths, as older routes may preserve better due to minimal modern impact and slower pedogenic processes. Here we examine footpaths in the Judean Desert of the southern Levant, a human hotspot throughout the Holocene. We studied one modern and two archaeological footpaths (one attributed to the Early Bronze Age and one to the Roman period) using micromorphology, bulk samples laboratory analysis, and remote sensing. Field observations and color analysis indicate that footpaths in the studied arid limestone environment can result in brighter surface color than their non-path surroundings. Similar color changes are reflected using both laboratory analysis and high-resolution remote sensing, where the difference is also significant. Microscopically, the footpaths studied tend to be less porous and with fewer biogenic activities when compared to their non-path controls. However, the two ancient footpaths studied do exhibit minimal indicators of biogenic activities that are not detectable in the modern footpath sample. Our study shows that high-resolution remote sensing coupled with micromorphology, while using appropriate local modern analogies, can help to locate and assess both the environmental effect and the antiquity of footpaths

Metabolic-network-driven analysis of bacterial ecological strategies

Bacterial ecological strategies revealed by metabolic network analysis show that ecological diversity correlates with metabolic flexibility, faster growth rate and intense co-habitation