On the analyticity of functions approximated by their q-Bernstein polynomials when q > 1

Since in the case q > 1 the q-Bernstein polynomials Bn,q are not positive linear operators on C[0, 1], the investigation of their convergence properties for q > 1 turns out to be much harder than the one for 0 < q < 1. What is more, the fast increase of the norms ∥Bn,q∥ as n → ∞, along with the sign oscillations of the q-Bernstein basic polynomials when q > 1, create a serious obstacle for the numerical experiments with the q-Bernstein polynomials. Despite the intensive research conducted in the area lately, the class of functions which are uniformly approximated by their q-Bernstein polynomials on [0, 1] is yet to be described. In this paper, we prove that if f:[0,1]→C is analytic at 0 and can be uniformly approximated by its q-Bernstein polynomials (q > 1) on [0, 1], then f admits an analytic continuation from [0, 1] into {z: z < 1}. © 2010 Elsevier Inc. All rights reserved

A scale of degrees of independence of random variables

A scale of degrees of independence of two random variables is studied. The lowest point of the scale is the lack of correlation and the highest one being the usual independence. The "middle" point is so-called convolutional independence which is defined by the condition that the distribution function of the sum of random variables is the convolution of the distribution functions of the summands. The scale consists of two parts. The first one is a linearly ordered set, the second one is a partially ordered set

BIOLOGICAL ASPECTS OF ASSOCIATION BETWEEN CARDIOVASCULAR DISEASES AND PERIODONTITIS

Paradontitis is associated with the risk of developing cardiovascular diseases as a pathogenic factor. The onset and spread of periodontitis occurs as a result of dysbacteriosis of commensal oral microbiota, that is further interacts with the hosts immune system, being the cause of development of low rank systemic inflammation and the most frequent cause of cardiovascular diseases. An important virulence factor of gram-negative bacteria that dominate in the oral microbiota in periodontitis is lipopolysaccharides, which are part of their cell membranes and being endotoxins. In humans, lipopolysaccharides play a central role in host immune responses, which is characterized by cytokine synthesis, activation of the immune system and provokes the risk of atherosclerotic changes and thromboembolic processes. At the same time, serum lipopolysaccharide activity correlates with serum IgG levels against P. gingivalis, the main causative agent of periodontitis. Lipopolysaccharides are the molecular association between oral dysbacteriosis and cardiometabolic disorders. Saliva lipopolysaccharides correlate with serum lipopolysaccharide activity and this association is enhanced in the presence of periodontitis. The oral microbiota is stably associated with such cardiovascular diseases as acute coronary syndrome and atherosclerosis. Certain types of microflora associated with cardiovascular diseases are identified. Some types associated with periodontitis, such as Porphyromonas gingivalis, are able to invade epithelial cells and multiply in them. Inflammation associated with endotoxemia in periodontitis explains the association with the clinical manifestations of cardiovascular diseases. All bacterial structural components and virulence factors are recognized in the host organism as antigens. They lead to the formation of antibodies, however, the mechanisms of their participation in the pathogenesis of periodontitis and other chronic diseases associated with paradontium are not yet clear. The contribution of cross-reactive antibodies obtained against host antigens is investigated as a response to the similarity of their epitopes with the antigens of bacteria, which is called molecular mimicry and which promotes inflammation. One of the most frequently studied epitopes is present in heat shock proteins (HSP), therewith eight members of the HSP family are associated with the development of cardiovascular diseases and mortality from them. Proteins of the HSP60 family are identified as major antigens in a number of bacterial species associated with periodontitis. The levels of antibodies to A. actinomycetemcomitans and P. gingivalis, which dominate in the oral microbiota in periodontitis are being studied. Serum positivity of IgA to these species is a predictor of recurrent stroke, myocardial infarction and other cardiovascular diseases. The high combined IgG response to A. actinomycetemcomitans and P. gingivalis is combined with calcification of the coronary artery. The combined effect of some oral pathogens causes a more significant impact on the development of cardiovascular diseases than the effect of a single microbe. Thus, both direct and indirect mechanisms are involved in the development of cardiovascular diseases that are associated with periodontitis, while patients are constantly exposed to dysbiotic bacteria and their virulence, which causes and maintains systemic low rank inflammation. Endotoxemia and antibody response are mediators that connect oral dysbacteriosis with an increased risk of cardiovascular diseases

Microbiome of the oral cavity and human health

Наводяться дані про мікробіом ротової порожнини людини, що необхідні для розуміння здоров’я і хвороб людини в цілому. За допомогою молекулярних методів було ідентифіковано близько 280 бактеріальних видів з ротової порожнини, визначені численні синтетичні гени, зв’язані з мікробіомом людини. Виявлено основні метаболічні класи пептидних малих молекул (РSM), вплив яких на здоров’я людини сьогодні інтенсивно досліджується; Приводятся данные о микробиоме ротовой полости человека, необходимые для понимания здоровья и болезней человека в целом. С помощью молекулярных методов было идентифицировано около 280 бактериальных видов из ротовой полости, определены многочисленные синтетические гены, связанные с микробиомом человека. Выявлены основные метаболические классы пептидных малых молекул (РSM), влияние которых на здоровье людей в настоящее время интенсивно исследуется; The above review of the literature cites the results of the study on the microbiome of the human oral cavity. The term “microbiome” was proposed by D. Lederberg “to designate the ecological community of commensal, symbiotic and pathogenic microorganisms that simply permeate the surrounding space. Understanding of human health and diseases is impossible without full identification of the collective microbiome of the human body as a whole, including identification and description of the phylogeny of the most common oral taxons. It is recognized that caries, periodontitis, otitis as well as many systemic diseases are caused by symbiosis of organisms in the biofilm, and not by one pathogen. These data are consistent with the provisions of the project «Human Microbiome» which considers that it is necessary to identify all the basic organisms that make up the human microbiome and that there must be tools for this identification. Each human oral cavity has a unique bacterial diversity, on average consisting of about 150 bacterial taxons. Approximately 280 bacterial species of the oral cavity were identified by molecular methods, mainly using cloning studies based on 16S rRNA genes. It was shown that in each community of microorganisms there can be both competition and interconnection, therefore research on microbiome should include a deeper knowledge of the molecular mechanisms supporting its complex network of functions. The «language of interactions» host-microbiome must be identified quantitatively and, ultimately, characterized functionally. There have been identified numerous biosynthetic genes linked, inter alia, with human oral microbiome, which encode the main metabolic classes of peptide small molecules (PSM). The obtained results show the complex expression of PSM, whose role in human health and in the development of the disease is as yet unknown and is currently being intensively studied. Several PSMs such as mutanobactins, salivaricines and proteases that mediate antagonistic interactions between bacteria in the oral cavity are isolated and structurally identified. However, the mechanisms that initiate the biosynthesis of these PSMs in the complex host-microbiome in vivo interactions are unknown yet and are currently being intensively studied