On adjacency operators of locally finite graphs

A graph $\Gamma$ is called locally finite if, for each vertex $v$ of $\Gamma$, the set $\Gamma(v)$ of all neighbors of $v$ in $\Gamma$ is finite. For any locally finite graph $\Gamma$ with vertex set $V(\Gamma)$ and for any field $F$, let $F^{V(\Gamma)}$ be the vector space over $F$ of all functions $V(\Gamma) \to F$ (with natural componentwise operations) and let $A^{({\rm alg})}_{\Gamma,F}$ be the linear operator $F^{V(\Gamma)} \to F^{V(\Gamma)}$ defined by $(A^{({\rm alg})}_{\Gamma,F}(f))(v) = \sum_{u \in \Gamma(v)}f(u)$ for all $f \in F^{V(\Gamma)}$, $v \in V(\Gamma)$. In the case of finite graph $\Gamma$ the mapping $A^{({\rm alg})}_{\Gamma,F}$ is the well known operator defined by the adjacency matrix of $\Gamma$ (over $F$), and the theory of eigenvalues and eigenfunctions of such operator is a well-developed (at least in the case $F = \mathbb{C}$) part of the theory of finite graphs. In this paper we develope a theory of eigenvalues and eigenfunctions of $A^{({\rm alg})}_{\Gamma,F}$ for arbitrary infinite locally finite graphs $\Gamma$ (although a few results may be of interest for finite graphs) and fields $F$ with a special emphasis on the case when $\Gamma$ is connected with uniformly bounded vertex degrees and $F = \mathbb{C}$. By the author opinion, previous attempts in this direction were not quite satisfactory since were limited by consideration of rather special eigenfunctions and corresponding eigenvalues.Comment: in Russia

Возможности и риски кооперации компаний производственной сферы и сферы услуг в России в соответствии с концепцией Индустрия 4.0

Between 2015 and 2016, an international study was conducted to determine just what Industry 4.0 meant to companies from various countries, how vital cooperation in the area among companies from various countries was, and how this cooperation could be best organized. The survey featured no companies from Russia. Between 2018 and 2019, a similar study was carried out by the authors of this work among Russian companies, its purpose being to identify some of the key common and specific traits in existing approaches to cooperation in Industry 4.0 among Russian and foreign companies. To obtain comparable results, the study relied on a research methodology developed by the National Academy of Science and Engineering (Germany), which employed it in its survey engaging 150 company executives from six different countries. In Russia, a total of 50 interviews were conducted of executives of Russian companies of varying size and sector, with data gathered via in-depth interviews, one-on-one questionnaire-based interviews, and online surveys. Based on the survey results, many Russian companies, just like their foreign counterparts, are perfectly aware of the opportunities and risks of Industry 4.0 and of the need to adopt common standards and address issues related to fostering cooperation, but their assessments are rather polarized, with some highly excited about the potential it offers, and others somewhat wary of the risks it may be fraught with – which may be due to differences in the level of their technological development. Prior research did not produce comparative assessments based on a single methodology on senior management’s take on the opportunities and risks of the cooperation of Russian and foreign companies in Industry 4.0. The findings could be utilized in developing appropriate measures for bolstering the cooperation, which could be mutually beneficial for companies representing various countries and sectors.En 2015-2016 Se realizó un estudio internacional para averiguar qué significa para las compañías de diferentes países, Industria 4.0, cuánta cooperación se necesita de las compañías de diferentes países en esta área y cómo está mejor organizada esta cooperación. Entre los participantes de la encuesta no hubo empresas de Rusia. En 2018-2019 se realizó el mismo estudio; los autores del artículo realizado entre las compañías rusas, el propósito del estudio es identificar características comunes y específicas en los enfoques de cooperación en la Industria 4.0 de compañías rusas y extranjeras. Para obtener resultados comparables, nuestro estudio se basa en la metodología de investigación de la Academia Nacional de Ciencias e Ingeniería de Alemania, en la que se entrevistó a 150 ejecutivos de empresas en seis países. En Rusia, se realizaron 50 entrevistas con gerentes de empresas rusas de diversos tamaños y de diferentes industrias, la recolección de datos se realizó mediante entrevistas en profundidad, entrevistas personales en el cuestionario y encuesta en línea. Las empresas rusas, así como las extranjeras, evalúan las oportunidades y los riesgos de la Industria 4.0, la necesidad de estándares comunes y los problemas para desarrollar la cooperación, pero sus evaluaciones están más polarizadas: algunas aprecian más las capacidades de la Industria 4.0, otras consideran los riesgos debido a las diferencias en Su desarrollo tecnológico. En estudios anteriores, no se realizó una evaluación comparativa utilizando la misma metodología de los cargos de alta dirección en relación con las oportunidades y los riesgos de la cooperación entre empresas rusas y extranjeras dentro de la Industria 4.0. Los resultados obtenidos nos permiten desarrollar medidas para fortalecer la cooperación, mutuamente beneficiosas para empresas de diferentes industrias y países.В 2015-2016 гг. проведено международное исследование с тем, чтобы выяснить, что означает для компаний из разных стран Индустрия 4,0, насколько необходимо сотрудничество компаний из разных стран в этой области и как это сотрудничество лучше организовать. Среди участников опроса не было компаний из России. В 2018-2019 гг. проведено такое же исследование авторы статьи провели среди российских компаний, цель исследования – выявить общие и специфические черты в подходах к сотрудничеству в Индустрии 4,0 российских и зарубежных компаний. Для получения сравнимых результатов наше исследование опирается на исследовательскую методологию Национальной академии наук и инжиниринга Германии, в рамках которого были опрошены 150 руководителей компаний в шести странах. В России проведено 50 интервью с руководителями российских предприятий разного размера и из разных отраслей, сбор данных проводился с помощью глубоких интервью, личного интервью по анкете и онлайн опроса. Российские компании так же, как и зарубежные, оценивают возможности и риски Индустрии 4,0, необходимость общих стандартов и проблемы развития сотрудничества, но их оценки более поляризованы: одни более высоко оценивают возможности Индустрии 4,0, другие – риски в силу различий в уровне свое технологического развития. В предыдущих исследованиях не проводилась сравнительная оценка по одной методологии позиций топ-менеджмента относительно возможностей и рисков сотрудничества российских и зарубежных компаний в рамках Индустрии 4,0. Полученные результаты позволяют разработать меры по укреплению сотрудничества, взаимовыгодные для компаний из разных отраслей и стран

Housing environment and external migration as factors influencing population health

This article investigates the impact of housing quality and type on the health of migrants in developing countries, emphasizing factors such as overcrowding, sanitation, and access to healthcare. It further explores how specific aspects of housing quality, including structural integrity, ventilation, insulation, and access to utilities, influence population health. A comprehensive review of relevant literature is conducted, presenting evidence on the relationship between housing conditions and the prevalence of respiratory diseases, cardiovascular diseases, and mental disorders. The study focuses on Kyrgyzstan, aiming to elucidate how various living conditions affect the health of its population. The analysis utilizes secondary data from sociological studies and scientific research from various countries, offering recommendations applicable to Kyrgyzstan. Numerous contributing factors are identified, including the economic and social damage associated with inadequate housing, housing construction, and improvements in living conditions; air quality; indoor temperature and warmth; infestation by parasites and pests; and sanitary and hygienic conditions. The article concludes with practical recommendations for policy and intervention

Systems of Hess-Appel'rot Type and Zhukovskii Property

We start with a review of a class of systems with invariant relations, so called {\it systems of Hess--Appel'rot type} that generalizes the classical Hess--Appel'rot rigid body case. The systems of Hess-Appel'rot type carry an interesting combination of both integrable and non-integrable properties. Further, following integrable line, we study partial reductions and systems having what we call the {\it Zhukovskii property}: these are Hamiltonian systems with invariant relations, such that partially reduced systems are completely integrable. We prove that the Zhukovskii property is a quite general characteristic of systems of Hess-Appel'rote type. The partial reduction neglects the most interesting and challenging part of the dynamics of the systems of Hess-Appel'rot type - the non-integrable part, some analysis of which may be seen as a reconstruction problem. We show that an integrable system, the magnetic pendulum on the oriented Grassmannian $Gr^+(4,2)$ has natural interpretation within Zhukovskii property and it is equivalent to a partial reduction of certain system of Hess-Appel'rot type. We perform a classical and an algebro-geometric integration of the system, as an example of an isoholomorphic system. The paper presents a lot of examples of systems of Hess-Appel'rot type, giving an additional argument in favor of further study of this class of systems.Comment: 42 page

Systems of Hess-Appel'rot type

We construct higher-dimensional generalizations of the classical Hess-Appel'rot rigid body system. We give a Lax pair with a spectral parameter leading to an algebro-geometric integration of this new class of systems, which is closely related to the integration of the Lagrange bitop performed by us recently and uses Mumford relation for theta divisors of double unramified coverings. Based on the basic properties satisfied by such a class of systems related to bi-Poisson structure, quasi-homogeneity, and conditions on the Kowalevski exponents, we suggest an axiomatic approach leading to what we call the "class of systems of Hess-Appel'rot type".Comment: 40 pages. Comm. Math. Phys. (to appear

Magnetic and structural properties of barium hexaferrite BaFe12O19 from various growth techniques

Barium hexaferrite powder samples with grains in the m-range were obtained from solid-state sintering, and crystals with sizes up to 5 mm grown from PbO, Na2CO3, and BaB2O4 fluxes, respectively. Carbonate and borate fluxes provide the largest and structurally best crystals at significantly lower growth temperatures of 1533 K compared to flux-free synthesis (1623 K). The maximum synthesis temperature can be further reduced by the application of PbO-containing fluxes (down to 1223 K upon use of 80 at % PbO), however, Pb-substituted crystals Ba1-xPbxFe12O19 with Pb contents in the range of 0.23(2) x 0.80(2) form, depending on growth temperature and flux PbO content. The degree of Pb-substitution has only a minor influence on unit cell and magnetic parameters, although the values for Curie temperature, saturation magnetization, as well as the coercivity of these samples are significantly reduced in comparison with those from samples obtained from the other fluxes. Due to the lowest level of impurities, the samples from carbonate flux show superior quality compared to materials obtained using other methods

Measurement of nuclear modification factors of gamma(1S)), gamma(2S), and gamma(3S) mesons in PbPb collisions at root s(NN)=5.02 TeV

The cross sections for ϒ(1S), ϒ(2S), and ϒ(3S) production in lead-lead (PbPb) and proton-proton (pp) collisions at √sNN = 5.02 TeV have been measured using the CMS detector at the LHC. The nuclear modification factors, RAA, derived from the PbPb-to-pp ratio of yields for each state, are studied as functions of meson rapidity and transverse momentum, as well as PbPb collision centrality. The yields of all three states are found to be significantly suppressed, and compatible with a sequential ordering of the suppression, RAA(ϒ(1S)) > RAA(ϒ(2S)) > RAA(ϒ(3S)). The suppression of ϒ(1S) is larger than that seen at √sNN = 2.76 TeV, although the two are compatible within uncertainties. The upper limit on the RAA of ϒ(3S) integrated over pT, rapidity and centrality is 0.096 at 95% confidence level, which is the strongest suppression observed for a quarkonium state in heavy ion collisions to date. © 2019 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3.Peer reviewe

Azimuthal separation in nearly back-to-back jet topologies in inclusive 2-and 3-jet events in pp collisions at root s=13TeV

A measurement for inclusive 2- and 3-jet events of the azimuthal correlation between the two jets with the largest transverse momenta, Delta phi(12), is presented. The measurement considers events where the two leading jets are nearly collinear ("back-to-back") in the transverse plane and is performed for several ranges of the leading jet transverse momentum. Proton-proton collision data collected with the CMS experiment at a center-of-mass energy of 13 TeV and corresponding to an integrated luminosity of 35.9 fb(-1) are used. Predictions based on calculations using matrix elements at leading-order and next-to-leading-order accuracy in perturbative quantum chromodynamics supplemented with leading-log parton showers and hadronization are generally in agreement with themeasurements. Discrepancies between the measurement and theoretical predictions are as large as 15%, mainly in the region 177 degrees <Delta phi(12) <180 degrees. The 2- and 3-jet measurements are not simultaneously described by any of models.Peer reviewe

MUSiC : a model-unspecific search for new physics in proton-proton collisions at root s=13TeV

Results of the Model Unspecific Search in CMS (MUSiC), using proton-proton collision data recorded at the LHC at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 35.9 fb(-1), are presented. The MUSiC analysis searches for anomalies that could be signatures of physics beyond the standard model. The analysis is based on the comparison of observed data with the standard model prediction, as determined from simulation, in several hundred final states and multiple kinematic distributions. Events containing at least one electron or muon are classified based on their final state topology, and an automated search algorithm surveys the observed data for deviations from the prediction. The sensitivity of the search is validated using multiple methods. No significant deviations from the predictions have been observed. For a wide range of final state topologies, agreement is found between the data and the standard model simulation. This analysis complements dedicated search analyses by significantly expanding the range of final states covered using a model independent approach with the largest data set to date to probe phase space regions beyond the reach of previous general searches.Peer reviewe

Development and validation of HERWIG 7 tunes from CMS underlying-event measurements

This paper presents new sets of parameters (“tunes”) for the underlying-event model of the HERWIG7 event generator. These parameters control the description of multiple-parton interactions (MPI) and colour reconnection in HERWIG7, and are obtained from a fit to minimum-bias data collected by the CMS experiment at s=0.9, 7, and 13Te. The tunes are based on the NNPDF 3.1 next-to-next-to-leading-order parton distribution function (PDF) set for the parton shower, and either a leading-order or next-to-next-to-leading-order PDF set for the simulation of MPI and the beam remnants. Predictions utilizing the tunes are produced for event shape observables in electron-positron collisions, and for minimum-bias, inclusive jet, top quark pair, and Z and W boson events in proton-proton collisions, and are compared with data. Each of the new tunes describes the data at a reasonable level, and the tunes using a leading-order PDF for the simulation of MPI provide the best description of the dat