Generators and relations for wreath products

Generators and defining relations for wreath products of groups are given. Under some condition (conormality of the generators) they are minimal. In particular, it is just the case for the Sylow subgroups of the symmetric groups.Comment: 4 page

A characterization of admissible algebras with formal two-ray modules

In the paper we characterize, in terms of quivers and relations, the admissible algebras with formal two-ray modules introduced by G. Bobi\'nski and A. Skowro\'nski [Cent. Eur. J.Math.1 (2003), 457--476].Comment: Mainly correcting typos. Also a new abstract and minor changes in the introduction and subsection 3.

On Gelfand-Zetlin modules

summary:[For the entire collection see Zbl 0742.00067.]\par Let {\germ g}\sb k be the Lie algebra {\germ gl}(k,\mathcal{C}), and let U\sb k be the universal enveloping algebra for {\germ g}\sb k. Let Z\sb k be the center of U\sb k. The authors consider the chain of Lie algebras {\germ g}\sb n\supset {\germ g}\sb{n-1}\supset\dots\supset {\germ g}\sb 1. Then Z=\langle Z\sb k\mid k=1,2,\dots n\rangle is an associative algebra which is called the Gel'fand-Zetlin subalgebra of U\sb n. A {\germ g}\sb n module $V$ is called a $GZ$-module if V=\sum\sb x\oplus V(x), where the summation is over the space of characters of $Z$ and V(x)=\{v\in V\mid(a-x(a))\sp mv=0, m\in\mathcal{Z}\sb +, $a\in\mathcal{Z}\}$. The authors describe several properties of $GZ$- modules. For example, they prove that if $V(x)=0$ for some $x$ and the module $V$ is simple, then $V$ is a $GZ$-module. Indecomposable $GZ$- modules are also described. The authors give three conjectures on $GZ$- modules and

The International Algebraic Conference dedicated to the 100th anniversary of L.A. Kaluzhnin

The International Algebraic Conference dedicated to the 100th anniversary of an outstanding mathematician and teacher, the founder of Algebra and Mathematical Logic Department of Taras Shevchenko National University of Kyiv Professor L.A. Kaluzhnin was held on 7–12 July 2014 in Kyiv

Igor Rostislavovich Shafarevich (03.06.1923 -- 19.02.2017)

The great Russian mathematician Igor Rostislavovich Shafarevich died on February 19, 2017. This news grieved the whole mathematical society, since his name was inseparably linked to so many outstanding achievements and ideas of the modern mathematics, especially number theory and algebraic geometry

Patterns in the development of collective immunity to SARS-CoV-2 during the COVID-19 pandemic

The ongoing coronavirus disease (COVID-19) pandemic over the past three years has caused close attention to the problem of herd immunity, which is understood as: "resistance to the spread of a contagious disease within a population or herd". Collective immunity is formed both as a result of infection (natural spread of the pathogen in a population of susceptible individuals) and as a result of the use of specific vaccines. During the COVID-19 pandemic, both mechanisms for the formation of collective immunity were realized. In the first wave, there was a natural formation of collective immunity to the virus following recoveries from COVID-19 caused by pandemic spread of SARS-CoV-2. Starting from December 2020, the widespread use of specific vaccines against SARS-CoV-2 began in the USA, Great Britain, China, Russia, and a number of other countries. This launched the process of post-vaccination collective immunity formation; its features have depended on the vaccine types implemented. Currently, in those countries where vaccination and revaccination of recovered patients is widely carried out, immunity is "hybrid" in nature. Several commonalities should be noted in the pandemic experience: a somewhat regular, periodic (wavelike) nature of the COVID-19 epidemic process; changes in pathogen genetics in variants in all countries; and expansive mass vaccination programs in many populations. From these, we can draw some conclusions about the general trend for all countries in the formation of collective immunity during the pandemic: At the beginning of the pandemic in 2020, overall population seroprevalence did not exceed 20%. Other findings were: the highest seroprevalence rates were noted in the children's age group; pronounced regional differences were revealed; and the highest indicators were noted among medical workers. Collective immunity developed as a result of infection or illness, and in the majority of seropositive volunteers, it was represented by antibodies to both antigens. At the height of the pandemic in the summer of 2021, population seroprevalence reached 50%. This was due to both a significant number of convalescents and the start of mass vaccination campaigns. In all countries, specific differences in seroprevalence (by age, region, profession) leveled out, leading to more uniformity. During this period, the formation of "hybrid" immunity is clearly prominent, and the proportion of individuals with antibodies to RBD alone increased (due to vaccination with vector vaccines).  Later, mass vaccination, as well as involvement of most of the population in the epidemic process due to the emergence of the highly contagious Omicron strain, raised the level of collective immunity to 80-90%. This led to a sharp decrease in COVID-19 incidence in the second half of 2022 in all countries participating in the study. In the later stages of the pandemic (2022-2023), almost 90% of seropositive volunteers had hybrid immunity, reflected as antibodies to both antigens (Nc, RBD)

Цитологические эффекты в лимфатических узлах зоны абдоминальной лимфодиссекции после интраоперационной фотодинамической терапии при злокачественных новообразованиях желудочно-кишечного тракта

Cytological studies on lymph nodes of abdominal lymphodissection zone after local intraoperative photodynamic therapy (IOPDT) of gastrointestinal cancers were carried out. As a result of the PDT, the metastatic cells are destroyed, their cytoplasmic membranes and the cytoplasm disappears, leaving behind interphase nuclei ("naked nuclei") (p<0,0001). Cytological confrmation of apoptosis (the presence of apoptotic bodies) in metastatic lymph nodes after IOPDT sessions on the lymph nodes of the abdominal lymphodissection zone is also presented.Проведены цитологические исследования материала лимфатических узлов зоны абдомининальной лимфодиссекции после интраоперационной фотодинамической терапии (ИОФДТ) при злокачественных новообразованиях желудочно‑кишечного тракта. Установлено, что в результате проведения ФДТ клетки метастатических опухолей разрушаются с исчезновением цитоплазматической мембраны и цитоплазмы, при этом остаются только интерфазные ядра («голые ядра») (р<0,0001). Также представлено цитологическое подтверждение апоптоза (наличие апоптотических телец) в лимфатических узлах с метастазами после курсов ИОФДТ в лимфатических узлах зоны абдоминальной лимфодиссекции

Challenges in QCD matter physics - The Compressed Baryonic Matter experiment at FAIR

Substantial experimental and theoretical efforts worldwide are devoted to explore the phase diagram of strongly interacting matter. At LHC and top RHIC energies, QCD matter is studied at very high temperatures and nearly vanishing net-baryon densities. There is evidence that a Quark-Gluon-Plasma (QGP) was created at experiments at RHIC and LHC. The transition from the QGP back to the hadron gas is found to be a smooth cross over. For larger net-baryon densities and lower temperatures, it is expected that the QCD phase diagram exhibits a rich structure, such as a first-order phase transition between hadronic and partonic matter which terminates in a critical point, or exotic phases like quarkyonic matter. The discovery of these landmarks would be a breakthrough in our understanding of the strong interaction and is therefore in the focus of various high-energy heavy-ion research programs. The Compressed Baryonic Matter (CBM) experiment at FAIR will play a unique role in the exploration of the QCD phase diagram in the region of high net-baryon densities, because it is designed to run at unprecedented interaction rates. High-rate operation is the key prerequisite for high-precision measurements of multi-differential observables and of rare diagnostic probes which are sensitive to the dense phase of the nuclear fireball. The goal of the CBM experiment at SIS100 (sqrt(s_NN) = 2.7 - 4.9 GeV) is to discover fundamental properties of QCD matter: the phase structure at large baryon-chemical potentials (mu_B > 500 MeV), effects of chiral symmetry, and the equation-of-state at high density as it is expected to occur in the core of neutron stars. In this article, we review the motivation for and the physics programme of CBM, including activities before the start of data taking in 2022, in the context of the worldwide efforts to explore high-density QCD matter.Comment: 15 pages, 11 figures. Published in European Physical Journal

Monitoring of coronavirus infection in the kyrgyz population

Purpose of the study: to study the dynamics of developing herd immunity against SARS-CoV-2 in the population of the Republic of Kyrgyzstan during COVID-19. Materials and methods. The work was carried out using the methodology for assessing population immunity developed by Rospotrebnadzor (Russia) as well as the Ministry of Health (Kypgyzstan) and the St. Petersburg Pasteur Institute. The selection of participants was carried out by questionnaire using a cloud (Internet server) service. To monitor population immunity, a cohort of 2421 subjects was formed, who participated in all stages of seromonitoring. Volunteers were randomized according to age groups (1–17, 18–29, 30–39, 40–49, 50–59, 60–69, 70+ years), regional and professional factors. Antibodies (Abs) against SARS-CoV-2 nucleocapsid (Nc) and the receptor binding domain (RBD) of S-glycoprotein were determined by qualitative and quantitative methods. The study was carried out in 3 stages according to a single scheme: 1st stage — 06/28–07/03/2021, 2nd — 21–25/02/2022 and 3rd — 31/10–04/11/2022. Since 2021, Kyrgyzstan has been vaccinating the population against SARS-CoV-2 mainly using inactivated whole-virion vaccines. Results. Population immunity against SARS-CoV-2 was predominantly accounted for by both Ab types (Nc+RBD+). By the 3rd stage, the percentage of such persons reached 99.2%, Nc–RBD– volunteers — up to 0.8%. At the 1st stage, middle-aged people dominated, but age differences were leveled out by the 2nd stage. The greatest impact on seroprevalence was found among medical workers, the smallest — among businessmen and industrial workers. Populational vaccination significantly impacted on the state of herd immunity that reached 25% by the 3rd stage. The refusals of the population in Kyrgyz Republic from vaccination noted at the 2nd and especially 3rd stages did not significantly affect level of herd immunity, which could probably be associated with asymptomatic cases of COVID-19, against which primary vaccination had a booster effect. Conclusion. The dynamics of population humoral immunity against SARS-CoV-2 included a number of changes in the level of circulating antibodies (Nc, RBD), caused by both primary infection and vaccination. The herd immunity formed in population of Kyrgyzstan allowed to reduce the incidence of COVID-19 to almost sporadic level

Achievement of maximal SARS-CoV-2 collective immunity among the Tajik population by March 2022

Despite all efforts of the world community, the COVID-19 pandemic remains one of the main epidemiological challenges of our time. Even with its widespread distribution, the infection may have certain local features due to social, geographic, and climatic factors. Objective: to study collective immunity to SARS-CoV-2 in the population of the Republic of Tajikistan.A cross-sectional, randomized study of herd immunity was carried out according to a program developed by Rospotrebnadzor and the St. Petersburg Pasteur Institute, taking into account WHO recommendations. The ethics committees of the corresponding entities approved the study: Tajik Ministry of Health and Social Protection; and the St. Petersburg Pasteur Institute (Russia). Based on questionnaire results, 4,022 people were selected, representing 0.15% (95% CI: 0.14-0.15) of the total population randomized by age and region. In subsequent laboratory analysis, 3682 people took part. The distribution and quantitative content of antibodies (Abs) to viral nucleocapsid (N Ag) and receptor binding domain (RBD Ag) were determined by ELISA. When questioned, a history of SARS-CoV-2 vaccination was indicated by 69.7% (95% CI: 68.2-71.2) of the volunteer cohort. Vector vaccines were most frequently used (50.6%; 95% CI: 48.7-52.5), with whole-virion inactivated preparations in second place (23.0%: 95% CI: 21.4-26.6) and mRNA vaccines in third place (21.0%; 95% CI:19.4-22.6).The cohort (n = 3682) featured 27.5% men and 72.5% women. The overall seroprevalence was 98.5% (95% CI: 97.7-99.2) in men and 99.4% (95% CI: 99.0-99.6) in women (differences statistically insignificant). Overall seroprevalence in the cohort was 99.2% (95% CI: 98.8-99.4) and ranged from 97.2 to 100% in certain subgroups. Asymptomatic seropositivity in the whole cohort was 98.4% (95% CI: 97.6-99.1). As a result of a mandatory vaccination program introduced in Tajikistan under a COVID-19 Emergency Project, the level of herd immunity among vaccinated individuals reached 99.5% (95% CI: 99.1-99.7), which is similar to the level reached in the cohort as a whole.The epidemic situation that developed in Tajikistan by mid-March 2022 was characterized by an almost absolute level of herd immunity, as evidenced by an absence of detected overt COVID-19 cases since the end of February (2022)