Markov semigroups, monoids, and groups

A group is Markov if it admits a prefix-closed regular language of unique representatives with respect to some generating set, and strongly Markov if it admits such a language of unique minimal-length representatives over every generating set. This paper considers the natural generalizations of these concepts to semigroups and monoids. Two distinct potential generalizations to monoids are shown to be equivalent. Various interesting examples are presented, including an example of a non-Markov monoid that nevertheless admits a regular language of unique representatives over any generating set. It is shown that all finitely generated commutative semigroups are strongly Markov, but that finitely generated subsemigroups of virtually abelian or polycyclic groups need not be. Potential connections with word-hyperbolic semigroups are investigated. A study is made of the interaction of the classes of Markov and strongly Markov semigroups with direct products, free products, and finite-index subsemigroups and extensions. Several questions are posed.Comment: 40 pages; 3 figure

Approximations from Anywhere and General Rough Sets

Not all approximations arise from information systems. The problem of fitting approximations, subjected to some rules (and related data), to information systems in a rough scheme of things is known as the \emph{inverse problem}. The inverse problem is more general than the duality (or abstract representation) problems and was introduced by the present author in her earlier papers. From the practical perspective, a few (as opposed to one) theoretical frameworks may be suitable for formulating the problem itself. \emph{Granular operator spaces} have been recently introduced and investigated by the present author in her recent work in the context of antichain based and dialectical semantics for general rough sets. The nature of the inverse problem is examined from number-theoretic and combinatorial perspectives in a higher order variant of granular operator spaces and some necessary conditions are proved. The results and the novel approach would be useful in a number of unsupervised and semi supervised learning contexts and algorithms.Comment: 20 Pages. Scheduled to appear in IJCRS'2017 LNCS Proceedings, Springe

Economical adjunction of square roots to groups

How large must an overgroup of a given group be in order to contain a square root of any element of the initial group? We give an almost exact answer to this question (the obtained estimate is at most twice worse than the best possible) and state several related open questions.Comment: 5 pages. A Russian version of this paper is at http://mech.math.msu.su/department/algebra/staff/klyachko/papers.htm V2: minor correction

The structure of quotients of the Onsager algebra by closed ideals

We study the Onsager algebra from the ideal theoretic point of view. A complete classification of closed ideals and the structure of quotient algebras are obtained. We also discuss the solvable algebra aspect of the Onsager algebra through the use of formal Lie algebras.Comment: 33 pages, Latex, small topos corrected-Journal versio

Detailed analysis of the continuum limit of a supersymmetric lattice model in 1D

We present a full identification of lattice model properties with their field theoretical counter parts in the continuum limit for a supersymmetric model for itinerant spinless fermions on a one dimensional chain. The continuum limit of this model is described by an $\mathcal{N}=(2,2)$ superconformal field theory (SCFT) with central charge c=1. We identify states and operators in the lattice model with fields in the SCFT and we relate boundary conditions on the lattice to sectors in the field theory. We use the dictionary we develop in this paper, to give a pedagogical explanation of a powerful tool to study supersymmetric models based on spectral flow. Finally, we employ the developed machinery to explain numerically observed properties of the particle density on the open chain presented in Beccaria et al. PRL 94:100401 (2005).Comment: 28 pages, 7 figures, 3 tables, 1 appendix, this work is based on chapter 4 of the authors PhD Thesis: L. Huijse, A supersymmetric model for lattice fermions, University of Amsterdam (2010

The Seven-sphere and its Kac-Moody Algebra

We investigate the seven-sphere as a group-like manifold and its extension to a Kac-Moody-like algebra. Covariance properties and tensorial composition of spinors under $S^7$ are defined. The relation to Malcev algebras is established. The consequences for octonionic projective spaces are examined. Current algebras are formulated and their anomalies are derived, and shown to be unique (even regarding numerical coefficients) up to redefinitions of the currents. Nilpotency of the BRST operator is consistent with one particular expression in the class of (field-dependent) anomalies. A Sugawara construction is given.Comment: 22 pages. Macropackages used: phyzzx, epsf. Three epsf figure files appende

КЛИНИЧЕСКОЕ НАБЛЮДЕНИЕ СМЕШАННОЙ ФОРМЫ ПСЕВДОТУБЕРКУЛЕЗА

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Analysis of critical incidents during the intrahospital transport of patients and prevention

The article deals with changes in the gas and biochemical composition of blood in patients during intrahospital transport. Changes registered in patients who were on artificial lung ventilation revealed violations of the homeostasis of the blood gas composition, in particular, a decrease in the partial oxygen tension in arterial blood during manual Ambu ventilation, which can lead to negative electrolyte shifts and clinical consequences in the form of critical incidents. Invasive monitoring of blood gas composition should reduce the risk of critical incidents during medical evacuation.В статье рассмотрены изменения газового и биохимического состава крови у пациентов при внутригоспитальной транспортировке. Изменения, зарегистрированные у пациентов, находившихся на искусственной вентиляции легких, выявили нарушения гомеостаза газового состава крови, в частности, снижение парциального напряжения кислорода в артериальной крови при ручной вентиляции мешком Амбу, что может приводить к негативным электролитным сдвигам и клиническим последствиям в виде развития критических инцидентов. Инвазивный мониторинг газового состава крови должен снизить риски развития критических инцидентов в процессе медицинской эвакуации