Massey products in symplectic manifolds

The paper is devoted to study of Massey products in symplectic manifolds. Theory of generalized and classical Massey products and a general construction of symplectic manifolds with nontrivial Massey products of arbitrary large order are exposed. The construction uses the symplectic blow-up and is based on the author results, which describe conditions under which the blow-up of a symplectic manifold X along its submanifold Y inherits nontrivial Massey products from X ot Y. This gives a general construction of nonformal symplectic manifolds.Comment: LaTeX, 48 pages, 2 figure

On Question about Actual Problems of Study of Genre Synthesis Origins in Poetics of Russian Literature of 20th-21st Centuries

The article identifies key problems of modern genology, such as the lack of unified criteria for the definition of the genre as an aesthetic category, subjectivity of genre relatedness in new concepts of the genre, the lack of a widely acceptable genre classifications and genre systems. Relevance of the study of a unified genre model of literature of 20th-21st centuries dramaturgy is proved with categorical position of dramatic genres transformation, synthesis / syncretism of homogeneous and heterogeneous form-and-content units in the whole structure of the dramatic text. Prospective directions of this study are designated. The definition of the category “meta-genre” is given. New principle of construction of genre models in latest domestic dramaturgy built on the basis of transgressive compounds-mates is demonstrated. There is an increase in the proportion of subjective principle in the artistic modeling of the present. The newest Russian dramaturgy is primarily considered as a dialogical zone of aesthetic experimentation and sustained literary traditions. At this, the integrity of the ontogeny of dramatic text in Russia, the continuity of stages of development and typological intersection of the “new drama,” “new wave,” “new new drama” with the dramaturgic heritage of the 19th century are emphasized. All marked characteristic features of the considered dramatic material are based on the realities of the complex socio-cultural construction and paradoxes of the metaphysical existence of 20th-21st centuries

Formulation of the uncertainty relations in terms of the Renyi entropies

Quantum mechanical uncertainty relations for position and momentum are expressed in the form of inequalities involving the Renyi entropies. The proof of these inequalities requires the use of the exact expression for the (p,q)-norm of the Fourier transformation derived by Babenko and Beckner. Analogous uncertainty relations are derived for angle and angular momentum and also for a pair of complementary observables in N-level systems. All these uncertainty relations become more attractive when expressed in terms of the symmetrized Renyi entropies

The Hilbert-Schmidt Theorem Formulation of the R-Matrix Theory

Using the Hilbert-Schmidt theorem, we reformulate the R-matrix theory in terms of a uniformly and absolutely convergent expansion. Term by term differentiation is possible with this expansion in the neighborhood of the surface. Methods for improving the convergence are discussed when the R-function series is truncated for practical applications.Comment: 16 pages, Late

Effect of Different Methods of Abdominal Decompression on the Dynamics of Intra-Abdominal Pressure in the Early Postoperative Period in Patients with Secondary Diffuse Peritonitis: Observational Study

Background. Intra-abdominal hypertension complicates the course of secondary diffuse peritonitis in at least 60–70% of cases. Abdominal decompression is an essential component in the complex of therapeutic measures in patients with secondary diffuse peritonitis. However, no clear criteria for choosing the method and timing of abdominal decompression have been developed so far. The effectiveness of its use in various forms of peritonitis remains controversial.Objectives — to study the dynamics of intra-abdominal pressure in the early postoperative period when using various methods of abdominal decompression in patients with secondary diffuse peritonitis.Methods. The work was performed on the basis of an observational clinical study under the auspices of Regional Clinical Emergency Hospital over a period from January 2021 to December 2022. The authors studied intra-abdominal pressure in 74 patients with secondary diffuse peritonitis in the early postoperative period. In 39 (52.7%) patients (group 1), decompression was carried out in the form of prolonged nasogastric intubation. 15 (20.3%) patients (group 2) underwent nasointestinal intubation. Group 3 was represented by 10 patients (13.5%) which were affected by open abdomen technology and vacuum assisted closure (VAC). Group 4 included patients with vacuum-assisted laparostoma who underwent nasointestinal intubation. The severity of peritonitis was assessed using WSES cIAIs Score and Mannheim Peritonitis Index. The dynamics of intra-abdominal pressure was determined through the urinary catheter using the Uno Meter Abdo Pressure® Kit (Unomedical, Russia) before surgery and within 5 days of the postoperative period. Statistical analysis was based on non-parametric Wilcoxon test for comparing the values of the same group at different periods of observation. Mann-Whitney U-test was used to compare absolute values in different groups.Results. Nasogastric tube did not provide an acceptable reduction in intra-abdominal pressure, especially in patients with severe forms of peritonitis. Prolonged nasointestinal intubation contributed to a steady decrease in intra-abdominal pressure throughout the postoperative period, while simultaneous intubation resulted in an increase in intra-abdominal hypertension after a decline in values one day after surgery. The best results of intra-abdominal pressure dynamics were observed in case of vacuum-assisted laparostomy and its combination with nasointestinal intubation. Throughout the postoperative period, the intra-abdominal pressure did not exceed 15–17 mmHg. This method can be used only in treatment of the most severe forms of peritonitis, with indications for sanitation relaparotomy and in case of threatened abdominal compression syndrome.Conclusion. The data obtained enable the process of choosing surgical tactics and method of abdominal decompression to be optimized with respect to the severity of peritonitis and intra-abdominal hypertension

Phenolic compounds in plants: biogenesis and functions

Phenolic compounds (PCs) in plants play an important role in growth control and have antioxidant, structural, attractant, signaling and protective functions. Information on the discovery, study and identification of phenolic compounds in plants, their role in the complex system of secondary metabolites has been analyzed and summarized. The functions of PCs at the macromolecular, cellular as well as organism and population levels are described. The pathways of PCs formation, enzymes responsible for their synthesis and the plasticity of the synthesis in a plant cell are highlighted. The involvement of PCs in the plant breathing, photosynthesis, oxidation-reduction processes and regulation of the plants physiological state are discussed

Entropic Uncertainty Relations in Quantum Physics

Uncertainty relations have become the trademark of quantum theory since they were formulated by Bohr and Heisenberg. This review covers various generalizations and extensions of the uncertainty relations in quantum theory that involve the R\'enyi and the Shannon entropies. The advantages of these entropic uncertainty relations are pointed out and their more direct connection to the observed phenomena is emphasized. Several remaining open problems are mentionedComment: 35 pages, review pape

Exotic smooth structures and symplectic forms on closed manifolds

We give a short proof of the (known) result that there are no Kaehler structures on exotic tori. This yields a negative solution to a problem posed by Benson and Gordon. W discuss the symplectic version of the problem and analyze results which yield an evidence for the conjecture that there are no symplectic structures on exotic tori.Comment: AMSLaTeX, 16 pages, a new version. A survey of the symplectic version of the problem is adde

Mетод реструктуризації відеоданих в системах компресійного кодування для підвищення достовірності

The subject of research in the article is the processing of video images using orthogonal transformation for data exchange in information and communication networks. The analysis of known algorithms for encoding video information with the active use of a statistical approach in data cod\-ing has been presented. The aim of the study is to develop a method for restructuring video information resource data in the compression coding systems for increasing information reliability. This will allow you to ensure the neutralizaon of the errors and avoid the destruction of video data during its reconstruction while maintaining the structural-statistical regularity and controlled loss of quality. The task of the article is to develop a method for restructuring information resource data using structural regularity in a binary sequence that specifies video information resource data; to analyze the effectiveness of the application of the developed method for restructuring video data by a quantitative attribute from the standpoint of creating conditions for additional reduction of the structural redundancy of code representation as well as to analyze the effectiveness of the application of the developed method of restructuring the information space from the standpoint of increasing reliability. The article presents a solution to the scientific problem that is aimed to develop methods for increasing reliability of compact video images in information and telecommunication networks of aero segment systems. As a result, the use of the developed method of restructuring video data based on the number of series of units makes it possible to create conditions for additional reduction in the structural redundancy of the code representation of information due to significant reduction of the power of the information space within which the data is encoded; the conditions are provided for localizing the effect of errors in the process of reconstructing video information resources; the conditions are created for reducing the time of data processing due to the fact that the developed method of data restructuring does not require transformations on message elements.Предметом досліджень в статті є процеси обробки відеозображення з застосуванням ортогонального перетворення для передачі даних у інформаційно-телекомунікаційних мережах. Виконаний аналіз відомих алгоритмів кодування відеоінформації, що активно використовують статистичний підхід для компактного представлення кодованих даних. Метою є розробка методу реструктуризації даних відеоінформаційного ресурсу в системах компресійного кодування для підвищення достовірності інформації. Що дозволить при збереженні стpyктypно–стaтистичної зaкономipностi та контрольованої втрати якості, забезпечити локалізацію впливу помилок та запобігти руйнування відеоданих при реконструкції відеоданих. Завдання: розробити метод реструктуризації даних інформаційного ресурсу з використанням структурних закономірностей в двійковій послідовності, якою задаються дані відеоінформаційного ресурсу; провести аналіз ефективності застосування розробленого методу реструктуризації відеоданих за кількісною ознакою з позиції створення умов для додаткового скорочення структурної надмірності кодового подання; провести аналіз ефективності застосування розробленого методу реструктуризації інформаційного простору з позиції підвищення рівня достовірності. Представлено рішення наукової задачі, спрямованої на розробку методів підвищення достовірності компактно представлених відеозображень в інформаційно-телекомунікаційних мережах для систем аеросегменту. Отримані наступні результати: використання розробленого методу реструктуризації відеоданих за ознакою кількості серій одиниць дозволяє створити умови додаткового скорочення структурної надмірності кодового представлення інформації за рахунок суттєвого скорочення потужності інформаційного простору, в межах якого кодуються дані; забезпечуються умови для локалізації дії помилок в процесі реконструкції відеоінформаційних ресурсів; створюються умови для скорочення часу на обробку даних, в зв'язку з тим, що розроблений метод реструктуризації даних не вимагає проведення перетворень над елементами повідомлення

Layered material platform for surface plasmon resonance biosensing

Plasmonic biosensing has emerged as the most sensitive label-free technique to detect various molecular species in solutions and has already proved crucial in drug discovery, food safety and studies of bio-reactions. This technique relies on surface plasmon resonances in ~50 nm metallic films and the possibility to functionalize the surface of the metal in order to achieve selectivity. At the same time, most metals corrode in bio-solutions, which reduces the quality factor and darkness of plasmonic resonances and thus the sensitivity. Furthermore, functionalization itself might have a detrimental effect on the quality of the surface, also reducing sensitivity. Here we demonstrate that the use of graphene and other layered materials for passivation and functionalization broadens the range of metals which can be used for plasmonic biosensing and increases the sensitivity by 3-4 orders of magnitude, as it guarantees stability of a metal in liquid and preserves the plasmonic resonances under biofunctionalization. We use this approach to detect low molecular weight HT-2 toxins (crucial for food safety), achieving phase sensitivity~0.5 fg/mL, three orders of magnitude higher than previously reported. This proves that layered materials provide a new platform for surface plasmon resonance biosensing, paving the way for compact biosensors for point of care testing