Correlations of the Moebius and Liouville functions and the twin prime conjecture

In this note we describe weight functions that exhibit a transitional behavior between weak and strong correlation with the Liouville function. We also describe a binary problem which may be considered as an interpolation between Chowla's conjecture for two-point correlations of the M\"obius function and the twin prime conjecture, in view of recent parity breaking results of K. Matom\"aki, M. Radziwi{\l}{\l} and T. Tao

100% of the zeros of the Riemann zeta-function are on the critical line

We consider a specific family of analytic functions $g_{\alpha,T}(s)$, satisfying certain functional equations and approximating to linear combinations of the Riemann zeta-function and its derivatives of the form $c_0\zeta(s)+c_1\frac{\zeta'(s)}{\log T}+c_2\frac{\zeta''(s)}{(\log T)^2}+\dots+c_{K}\frac{\zeta^{(K)}(s)}{(\log T)^{K}}$. We also consider specific mollifiers of the form $M(s)D(s)$ for these linear combinations, where $M(s)$ is the classical mollifier, that is, a short Dirichlet polynomial for $1/\zeta(s)$, and the Dirichlet polynomial $D(s)$ is also short but with large and irregular Dirichlet coefficients, and arises from substitution for $w$, in Runge's complex approximation polynomial for $f(w)=\frac1{c_0+w}$, of the Selberg approximation for $\frac{c_1}{\log T}\frac{\zeta'}{\zeta}(s)+\frac{c_2}{(\log T)^2}\frac{\zeta''}{\zeta}(s)+\dots+\frac{c_{K}}{(\log T)^{K}}\frac{\zeta^{(K)}}{\zeta}(s)$ (analogous to Selberg's classical approximation for $\frac{\zeta'}{\zeta}(s)$). Exploiting the functional equations previously mentioned (concerning translation of the variable $s$), together with the mean-square asymptotics of the Levinson-Conrey method and the Selberg approximation theory (with some additional results) we show that almost all of the zeros of the Riemann zeta-function are on the critical line.Comment: 33 pages, 1 figur

Antiproliferative activity of glycosaminoglycan-like polysaccharides derived from marine molluscs

Despite the increasing availability of new classes of cancer treatment, such as immuneand targeted therapies, there remains a need for the development of new antiproliferative/cytotoxic drugs with improved pharmacological profiles that can also overcome drug resistant forms of cancer. In this study, we have identified, and characterised, a novel marine polysaccharide with the potential to be developed as an anticancer agent. Sulphated polysaccharides isolated from the common cockle (Cerastoderma edule) were shown to have antiproliferative activity on chronic myelogenous leukaemia and relapsed acute lymphoblastic leukaemia cell lines. Disaccharide and monosaccharide analysis of these marine polysaccharides confirmed the presence of glycosaminoglycan-like structures that were enriched in ion-exchange purified fractions containing antiproliferative activity. The antiproliferative activity of these glycosaminoglycan-like marine polysaccharides was shown to be susceptible to heparinase but not chondrotinase ABC digestion. This pattern of enzymatic and antiproliferative activity has not previously been seen, with either marine or mammalian glycosaminoglycans. As such, our findings suggest we have identified a new type of marine derived heparan sulphate/heparin-like polysaccharide with potent anticancer properties

Problems of Power Point presentations on music lessons in the preschool educational institutions

This article considers the problems of Power Point presentations on music lessons in the preschool educational institutions

Sleep disorders and their significance in the development of cognitive impairments

The review of literature considers the possible mechanisms responsible for the development of sleep disorders in patients with varying degrees of cognitive impairments. It assesses the association of the severity of cognitive impairments (CI) with the degree of sleep disorders. The treatment of sleep disorders in patients with cognitive disorders, the benefits and risks of current hypnotic drugs are discussed in detail. Recommendations are given to manage patients with sleep disorders concurrent with cognitive dysfunctions. Melatonin preparations are noted to be effective in treating insomnia in patients with CI

European Education: Phenomenon, Myth, or Project?

The paper discusses issues of reforming the system of higher professional education in Russia. The authors state that the main goals of organizing the European zone of higher education were alien to the Russian educational tradition and were not implemented in Russia over the past two decades. Moreover, these efforts have led to the destruction of the unified educational space of the country, a decline in the quality and accessibility of education, and the loss of value-based worldviews. Analyzing the situation, the authors of the article reveal the underlying causes of failure in the fundamental incompatibility of the socio-cultural paradigms of European and Russian education. A comparative analysis of the activities of European and Russian universities formed the basis for the statement about the necessary and reasonable formation of a national education system capable of a productive dialogue with the Euro-American civilization. The authors speak in favor of the approach would meet the Russian national features and ensure the sustainable development of the Russian educational system

Авторские изменения в библейском тексте: цитаты в проповедях Симеона Полоцкого

The article is devoted to a linguistic analysis of biblical quotations from the collection of sermons “Obied dushevnyi” (1681), compiled by the first court preacher Simeon of Polotsk (1629–1680). More than one third of all the identified quotations can be characterized as inexact quotations: they demonstrate the author’s interference with grammar, word order, and lexis of the biblical text. Such changes in biblical texts, introduced by Simeon, can be conditioned by several causes, among which are the influence of the revision of liturgical books, the influence of textual models in other languages, and the rhetorics and pragmatics of a sermon as a literary genre. The article focuses on the most significant linguistic changes to the biblical text introduced by Simeon: changes made in the context of the revision of liturgical books, and changes that continue and develop the revision, and apply it in a more consistent way. In addition, changes connected to the rhetorics and pragmatics of a sermon as a literary genre are briefly listed. The linguistic analysis of biblical texts in “Obied” provided in the article forms a base for further complex linguistic and philological research on the language of Simeon’s sermons.Статья посвящена лингвистическому анализу библейских цитат из сборника проповедей “Обед душевный” (1681), составленного первым придворным проповедником Симеоном Полоцким (1629–1680). Более трети из всех выявленных цитат представляют собой неточные цитаты и демонстрируют вмешательство автора в библейский текст на уровне грамматических категорий, порядка слов и лексики. Подобные изменения, внесенные Симеоном, могут быть обусловлены целым рядом причин, среди которых влияние книжной справы XѴII века, ориентация на иноязычные текстовые модели, а также риторика и прагматика проповеди как литературного жанра. В фокусе статьи находятся наиболее значительные лингвистические изменения библейского текста, сделанные Симеоном в контексте книжной справы и продолжающие ее. Также кратко перечисляются изменения, связанные с риторикой и прагматикой проповеди. Предлагаемый в данной статье анализ “чужого” библейского текста в поучительных словах Симеона формирует базу для дальнейшего комплексного лингвистического и филологического исследования языка его поучительных слов

Dementia: epidemiology, clinical picture, diagnosis, approaches to therapy

The review of literature discusses in detail the clinical signs of non-dementia cognitive impairments (CIs) and differences between subclinical, mild, and moderate CIs. It considers in detail the manifestations of dementia, the typical clinical picture of the most common forms of dementia, such as Alzheimer’s disease, Lewy body dementia, and vascular dementia. The paper outlines basic approaches to the pathogenetic therapy for dementia and the efficiency and safety of using NMDA receptor antagonists in patients with this pathology

FRANCE: SOCIAL CLEAVAGES IN THE FACE OF POLITICAL PROCESSES

The article examines the social schisms existing in French society and the impact that these divisions had on the social climate and political processes in the country. The factors contributing to the formation of these imbalances are analyzed. It is shown that although the ruling circles have smoothed out the social consequences of numerous extraordinary events that took place during Macron’s rule, they have not been able to mitigate the fundamental social divisions. The author comes to the conclusion that the abundance of deep social divisions in society leads to social instability, fragmentation of the political space and a significant increase in the influence of populist movements. Special attention is paid to the problems of increasing the degree of radicalism in the political arena and the degree of aggression and violence in society