Abstract involutions of algebraic groups and of Kac-Moody groups

Based on the second author's thesis in this article we provide a uniform treatment of abstract involutions of algebraic groups and of Kac-Moody groups using twin buildings, RGD systems, and twisted involutions of Coxeter groups. Notably we simultaneously generalize the double coset decompositions established by Springer and by Helminck-Wang for algebraic groups and by Kac-Wang for certain Kac-Moody groups, we analyze the filtration studied by Devillers-Muhlherr in the context of arbitrary involutions, and we answer a structural question on the combinatorics of involutions of twin buildings raised by Bennett-Gramlich-Hoffman-Shpectorov

On the distortion of twin building lattices

We show that twin building lattices are undistorted in their ambient group; equivalently, the orbit map of the lattice to the product of the associated twin buildings is a quasi-isometric embedding. As a consequence, we provide an estimate of the quasi-flat rank of these lattices, which implies that there are infinitely many quasi-isometry classes of finitely presented simple groups. In an appendix, we describe how non-distortion of lattices is related to the integrability of the structural cocycle

Supersensitive Multifluorophore RNA‐FISH for Early Virus Detection and Flow‐FISH by Using Click Chemistry

The reliable detection of transcription events through the quantification of the corresponding mRNA is of paramount importance for the diagnostics of infections and diseases. The quantification and localization analysis of the transcripts of a particular gene allows disease states to be characterized more directly compared to an analysis on the transcriptome wide level. This is particularly needed for the early detection of virus infections as now required for emergent viral diseases, e. g. Covid‐19. In situ mRNA analysis, however, is a formidable challenge and currently performed with sets of single‐fluorophore‐containing oligonucleotide probes that hybridize to the mRNA in question. Often a large number of probe strands (>30) are required to get a reliable signal. The more oligonucleotide probes are used, however, the higher the potential off‐target binding effects that create background noise. Here, we used click chemistry and alkyne‐modified DNA oligonucleotides to prepare multiple‐fluorophore‐containing probes. We found that these multiple‐dye probes allow reliable detection and direct visualization of mRNA with only a very small number (5–10) of probe strands. The new method enabled the in situ detection of viral transcripts as early as 4 hours after infection

Quotients of incidence geometries

We develop a theory for quotients of geometries and obtain sufficient conditions for the quotient of a geometry to be a geometry. These conditions are compared with earlier work on quotients, in particular by Pasini and Tits. We also explore geometric properties such as connectivity, firmness and transitivity conditions to determine when they are preserved under the quotienting operation. We show that the class of coset pregeometries, which contains all flag-transitive geometries, is closed under an appropriate quotienting operation.Comment: 26 pages, 5 figure

LiFtEr: Language to Encode Induction Heuristics for Isabelle/HOL

Proof assistants, such as Isabelle/HOL, offer tools to facilitate inductive theorem proving. Isabelle experts know how to use these tools effectively; however, there is a little tool support for transferring this expert knowledge to a wider user audience. To address this problem, we present our domain-specific language, LiFtEr. LiFtEr allows experienced Isabelle users to encode their induction heuristics in a style independent of any problem domain. LiFtEr's interpreter mechanically checks if a given application of induction tool matches the heuristics, thus automating the knowledge transfer loop.Comment: This is the pre-print of our paper of the same title accepted at APLAS2019 (https://doi.org/10.1007/978-3-030-34175-6_14). We updated the draft after fixing the errata found by Kenji Miyamot

Организация электроснабжения электрохимической защиты магистральных трубопроводов

В процессе эксплуатации магистральные газопроводы (МГ), как и большинство других металлических подземных коммуникаций, подвергаются воздействию процессов коррозии. Интенсивность этих процессов, а, следовательно, и состояние МГ зависит от целого ряда факторов, к числу которых следует отнести: коррозионную активность и характеристики грунтов в местах прокладки газопровода, глубину залегания участков газопровода, пересечениями с ЛЭП высокого напряжения или с электрифицированной железной дорогой – источниками блуждающих токов, качеством изоляционного покрытия, наличием и эффективностью настройки средств электрохимической защитыIn the process of exploitation of magistral gas pipelines (MG), like most other metal pose of communication, are exposed to corrosion processes. The intensity of these processes, and, consequently, the condition of the person MG depends on a number of factors, among which include: corrosiveness and the characteristics of the grunts in the field strip, the gazebo, the depth of the selenium sites gazebo leading from Lap high voltage electrician or from the sale of honey for the presence of wandering well, the quality of the insulation coating, lithium and effective tuning of electrochemical protectio

The Distributional Impact of Statewide Property Tax Relief: the Michigan Case

This study uses data from a random survey of 2001 Michigan households to analyze the extent to which the Michigan ctreuit-breaker has been successful in reducing the income regressivity of the property tax and in changing relative property tax burdens. Because of its relatively extensive coverage, including renters as well as homeowners and the nonaged as well as the aged, the circuit-breaker has yielded a more equal distribution of income within Michigan. Its potential to change the distribution of income depends on the particular formula utilized, but redistributional effects have thus far been lamited because program participation has been positively correlated with income. To the extent that reductions in the price ofpublic services created by the circuit-breaker are perceived by households, the biggest stimulus appears to be in high property tax/high-income countiesPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/68848/2/10.1177_109114218301100201.pd