Borel-Cantelli sequences

A sequence $\{x_{n}\}_1^\infty$ in $[0,1)$ is called Borel-Cantelli (BC) if for all non-increasing sequences of positive real numbers $\{a_n\}$ with $\underset{i=1}{\overset{\infty}{\sum}}a_i=\infty$ the set $$\underset{k=1}{\overset{\infty}{\cap}} \underset{n=k}{\overset{\infty}{\cup}} B(x_n, a_n))=\{x\in[0,1)\mid |x_n-x|<a_n \text{for} \infty \text{many}n\geq1\}$$ has full Lebesgue measure. (To put it informally, BC sequences are sequences for which a natural converse to the Borel-Cantelli Theorem holds). The notion of BC sequences is motivated by the Monotone Shrinking Target Property for dynamical systems, but our approach is from a geometric rather than dynamical perspective. A sufficient condition, a necessary condition and a necessary and sufficient condition for a sequence to be BC are established. A number of examples of BC and not BC sequences are presented. The property of a sequence to be BC is a delicate diophantine property. For example, the orbits of a pseudo-Anosoff IET (interval exchange transformation) are BC while the orbits of a "generic" IET are not. The notion of BC sequences is extended to more general spaces.Comment: 20 pages. Some proofs clarifie

Influence of the autonomic nervous system on the clinical course of overactive bladder

Overactive bladder (OB) is a disease which is very easily diagnosed, but presents considerable difficulties in the choice of treatment mode. At present the specialists turn their attention to this syndrome due to a wide spread of the disease, its negative impact on quality of life, social and economic importance. Pathogenesis of OB is complex. Thus, under conditions of urothelium atrophy which takes place because of estrogen deficiency in postmenopausal women, in violation of its GAG protective layer, barrier function of urothelium are violated, which leads to its damage. The appearence of urination disorder symptoms are associated with the fact that atrophic mucosa of urethra and triangle of bladder are hypersensitive to even minimal portions of urine. Aging process also play a role in OB development including lowering ability of tissues to repair, their elasticity reduction, increased apoptosis and cell atrophy, degeneration of nerve endings, smooth muscle tone change, deterioration of urothelium and its GAG protective layer. It can be a result of manifestation of bladder outlet obstruction that causes OB symptoms in men suffering from benign hyperplasia, prostate cancer and chronic prostatitis

Effects of divalent dopants on the microstructure and conversion efficiency of Cr4+ ions in Cr,Me:YAG (Me – Ca, Mg, Ca/Mg) transparent ceramics

The efficiency of Cr4+:YAG is directly proportional to the transparency and concentration of Cr4+ which can be tuned by changing the divalent dopant. The aim of this study was to investigate the influence of different kinds of divalent dopants on the properties of Cr,Me:YAG (Me = Ca, Mg or Ca/Mg) ceramics made by solid-state sintering in vacuum. Pure YAG phases with an in-line transmittance of 80% at 1064nm were prepared. It was revealed that the Cr4+ concentration is directly proportional to the concentration of divalent dopants and it does not depend on the type of dopant. Our experiment proves that the efficiency of high optical quality Cr4+:YAG ceramics preparedby sintering does not change when different kinds of divalent additives are used

Application of Mock-Court as an Interdisciplinary Model for Consolidation of Professional Training of Law Students

This study deals with solving the current problem of pedagogy of high school – consolidation of theoretical and practical approaches to ensure the quality of professional training of law students. According to the author, the introduction of simulation modelling technologies in training courses allows enhancing interdisciplinarity in teaching, which is an important way of meeting the dynamic needs of students in close connection of theoretical and practical blocks of professional training of future specialists. The experience of the American Bar Association on the future of legal education has suggested the idea of applying mock-court as interdisciplinary models. Experimental application of mock-court was tested in the courses “Criminal Law” and “Civil Law”, which are part of the block of special disciplines of the educational and professional training program in specialty 081 “Law”. Mathematical data processing and STATA software were used to analyse the results obtained and to objectively consider the dynamics of changes in personality-organizational, operational-activity, cognitive-competence, personality-motivational, information-technological, linguistic-communicative components. The study showed the effectiveness of the use of mock-court on the development of all components of the readiness of law students for professional socialization. The authors concluded that the application of mock-court in the professional training of future lawyers contributes to feedback increasing students’ educational motivation and allows monitoring of changes in student development. This model can be applied to enhance interdisciplinarity in the teaching of other courses of the block of special subjects of professional training of lawyers

Features of microbiological diagnosis and choice of selective antibiotic therapy in patients with acute cholecystitis

The objective: to improve the results of destructive forms of acute cholecystitis (AC) surgery by the development of antibiotic therapy algorithm and taking into account the severity of the disease according to Tokyo guidelines (2013). Materials and methods: 266 patients having been operated on for AC made up a treatment group and 203 patients - the control one. In 234 treatment group patients microflora’s bacteriological study was carried out and its selective sensitivity to antibiotics was determined. Results and discussion. The AC treatment group patients (n=266) were arranged according to Tokyo guidelines (2013) into 3 grades. Mild course (grade I) consisted of 29 patients (11%), microbiological studies were not conducted. Antibiotic prophylaxis with beta-lactam antibiotics was used. At moderately severe AC (grade II, n = 200, 75%) escalation antibiotic therapy was carried out. At severe disease (grade III, n = 37, 14%) de-escalation antibiotic therapy was performed. Bacteriological studies were conducted in 237 patients with destructive forms of AC, at that 531 microflora isolates were cultured. Intestinal group microorganisms were the most frequently cultured. Beta-lactam antibiotics’ sensitivity was prevailing and constituted 83.3%. The number of suppurations in the treatment group decreased from 9.8% to 4.3%, and mortality rate decreased from 1.48% to 0.75% (

Echinococcosis at urology. Pelvic parasitic cyst. Case report

Introduction. Echinococcosis is a serious chronic parasitic disease. Early diagnostics and patients` treatment with echinococcal lesions is an up-to-date problem. Objective. The aim of the article is to present the clinical case of diagnostics and treatment of the patient with urological complications caused by parasitic echinococcal pelvic cyst. Clinical case. The article highlights the features of diagnostics and treatment of urological complications of pelvic echinococcal lesions. The patient was operated in volume: "Laparotomy. Resection of parasitic cyst of small pelvic cavity. Echinococcectomy of the liver, abdominal cavity, retroperitoneal space." The peculiarities of operation was highlighted. The postoperative period lasted without complications. Conclusions. The demonstrated clinical case points out the necessity of the dispanserisation, early diagnostics and special helminth treatment of the patients living in the endemic regions. It allows to prevent the appearance of the echonococcosis advanced cases that lead to the reoperations and frequent patients` disability

CERN as an international scientific collaboration

It's not a secret that scientific development has been much faster recently, first of all because of booming information technologies, as they dictate the world what it should be in the next moment. Everything changes, including approaches to scientific research. That is why nowadays such phenomenon as scientific collaborations have become very popular. In this article, the authors derive the definition of a scientific collaboration compiled on the basis of various approaches applicable to collaborations. The example of the major scientific collaboration of CERN (European Center for Nuclear Research) emphasizes the importance of each aspect in the derived definition and concludes that the unambiguous definition of the scientific collaboration is further applicable in further fundamental studies of this phenomenon

Перспективи створення нового лікарського засобу для корекції метаболічного синдрому на основі БАР мучниці звичайної листя

Topicality. The metabolic syndrome is pathogenetically interrelated metabolic disorders in the condition of a sick person. A large set of factors is involved in its occurrence. Risk factors include genetic predisposition, overeating, insulin resistance, obesity, bad habits, hypodynamics, stress and unfavorable environmental conditions. First of all, defects of the lipid and carbohydrate metabolism provoke a cascade of genetic, metabolic, hormonal, nervous, inflammatory and other reactions and disorders in cells, tissues and organs, causing the metabolic syndrome and associated diseases, such as diabetes, kidney and gallstone disease, hypertension, platelet hyperaggregation, etc. Therefore, the rational use of synthetic and herbal medicines in the complex correction of these disorders can slow down the development of the metabolic syndrome. Aim. To develop the method for obtaining a dry modified extract from bearberry, study its chemical composition, hypoglycemic and hypolipidemic activity in order to determine the prospects of its use for the correction of the metabolic syndrome. Materials and methods. The study object was a dry extract of bearberry leaves modified with cysteine. HPLC and spectrophotometry were used to analyze the extract obtained. The hypoglycemic and hypolipidemic activity of dry extracts of bearberry was studied in rats with insulin resistance. Results and discussion. The method for obtaining a dry modified extract from bearberry leaves was developed by adding cysteine. Phenologlycoside (arbutin), 2 phenolic acids (gallic and ellagic), 6 flavonoids, 8 saponins were identified in the extract, and their quantitative content was determined. Hyperoside and catechin were dominant among flavonoids, and ursolic acid, uvaol, and lupeol prevailed among saponins. The content of the main groups of phenolic compounds was determined in the extract by spectrophotometry. The introduction of the dry extract from bearberry leaves modified with cysteine has a normalizing effect on metabolic disorders on the background of a high-fructose diet; therefore, it can be a promising agent for the correction of the metabolic syndrome. Conclusions. As a result of the research conducted, a new dry extract from bearberry leaves modified with cysteine has been created. The phytochemical composition, hypoglycemic and hypolipidemic activities of the extract have been studied, indicating the prospects for its use to correct the metabolic syndrome.Актуальность. Метаболический синдром – это патогенетически взаимосвязанные метаболические нарушения в состоянии больного человека. Значительный комплекс факторов участвует в его возникновении. К факторам риска относятся: генетическая предрасположенность, избыточное питание, инсулинорезистентность, ожирение, вредные привычки, гиподинамия, стрессовые воздействия и неблагоприятные экологические условия окружающей среды. В первую очередь дефекты липидного и углеводного обменов провоцируют каскад генетических, метаболических, гормональных, нервных, воспалительных и других реакций и нарушений в клетках, тканях и органах, вызывает метаболический синдром и ассоциированные с ним заболевания, такие, как сахарный диабет, почечно- и желчнокаменная болезни, артериальная гипертензия, гиперагрегация тромбоцитов и тому подобное. Рациональное использование синтетических и растительных лекарственных средств в комплексной коррекции этих нарушений позволяет приостановить развитие метаболического синдрома. Цель исследования. Разработать способ получения сухого модифицированного экстракта толокнянки обыкновенной листьев, изучить его химический состав, гипогликемическую и гиполипидемическую активность с целью установления перспективы его использования для коррекции метаболического синдрома. Материалы и методы. Объектом исследования был сухой экстракт толокнянки обыкновенной листьев, модифицированный цистеином. Для анализа полученного экстракта использовали метод ВЭЖХ и спектрофотометрию. Гипогликемическую и гиполипидемическую активность сухих экстрактов толокнянки обыкновенной листьев изучали на крысах с инсулинорезистентностью. Результаты и обсуждение. Разработан способ получения сухого модифицированного экстракта с добавлением цистеина с толокнянки обыкновенной листьев. В экстракте идентифицированы фенологликозид (арбутин), 2 фенолкарбоновые кислоты (галловая и элаговая), 6 флавоноидов, 8 сапонинов, а также установлено их количественное содержание. Среди флавоноидов доминирующими были гиперозид и катехины, среди сапонинов – урсоловая кислота, уваол и лупеол. В экстракте методом спектрофотометрии установлено содержание основных групп фенольных соединений. Введение сухого экстракта толокнянки обыкновенной листьев, модифицированного цистеином, проявляет нормализующее действие на метаболические нарушения на фоне высокофруктозной диеты, поэтому он может быть перспективным агентом для коррекции метаболического синдрома. Выводы. В результате проведенных исследований был создан новый сухой экстракт толокнянки обыкновенной листьев, модифицированный цистеином, изучен его фитохимический состав, гипогликемическая и гиполипидемическая активность. Результаты исследований свидетельствуют о перспективности использования данного экстракта для коррекции метаболического синдрома.Актуальність. Метаболічний синдром – це патогенетично взаємозв’язані метаболічні порушення у стані хворої людини. Великий комплекс чинників зумовлює його виникнення. До факторів ризику належать: генетична схильність, надмірне харчування, інсулінорезистентність, ожиріння, шкідливі звички, гіподинамія, стресові впливи та несприятливі екологічні умови довкілля. Насамперед дефекти ліпідного і вуглеводного обмінів провокують каскад генетичних, метаболічних, гормональних, нервових, запальних та інших реакцій і порушень у клітинах, тканинах і органах, що спричиняє метаболічний синдром і асоційовані з ним захворювання, як-от: цукровий діабет; нирково- та жовчнокам’яна хвороби; артеріальна гіпертензія, гіперагрегація тромбоцитів тощо. Раціональне використання синтетичних і рослинних лікарських засобів у комплексній корекції цих порушень дозволяє призупинити розвиток метаболічного синдрому. Мета дослідження. Розробити спосіб одержання сухого модифікованого екстракту мучниці звичайної листя, вивчити його хімічний склад, гіпоглікемічну і гіполіпідемічну активність з метою визначення перспективи його використання для корекції метаболічного синдрому. Матеріали та методи. Об’єктом дослідження був сухий екстракт мучниці звичайної листя, модифікований цистеїном. Для аналізу одержаного екстракту використовували метод ВЕРХ і спектрофотометрію. Гіпоглікемічну й гіполіпідемічну активність сухих екстрактів мучниці звичайної листя вивчали на щурах з інсулінорезистентністю. Результати та їх обговорення. Розроблено спосіб одержання сухого модифікованого екстракту з мучниці звичайної листя з додаванням цистеїну. В екстракті ідентифіковано фенологлікозид (арбутин), 2 фенолкарбонові кислоти (галову та елагову), 6 флавоноїдів, 8 сапонінів і визначено їх кількісний вміст. Серед флавоноїдів переважали гіперозид і катехін, серед сапонінів – урсолова кислота, уваол і лупеол. В екстракті методом спектрофотометрії виявлено вміст основних груп фенольних сполук. Введення сухого екстракту мучниці звичайної листя, модифікованого цистеїном, проявляє нормалізувальну дію на метаболічні порушення на тлі високофруктозної дієти, і тому він може бути перспективним агентом для корекції метаболічного синдрому. Висновки. У результаті проведених досліджень було створено новий сухий екстракт мучниці звичайної листя, модифікований цистеїном, проведено дослідження його фітохімічного складу, гіпоглікемічної та гіполіпідемічної активності, що засвідчило перспективність його використання для корекції метаболічного синдрому

Toxicity bioassay of waste cooking oil-based biodiesel on marine microalgae

The world biodiesel production is increasing at a rapid rate. Despite its perceived safety for the environment, more detailed toxicity studies are mandatory, especially in the field of aquatic toxicology. While considerable attention has been paid to biodiesel combustion emissions, the toxicity of biodiesel in the aquatic environment has been poorly understood. In our study, we used an algae culture growth-inhibition test (OECD 201) for the comparison of the toxicity of B100 (pure biodiesel), produced by methanol transesterification of waste cooking oil (yellow grease), B0 (petroleum diesel fuel) and B20 (diesel-biodiesel blended of 20% biodiesel and 80% petroleum diesel fuel by volume). Two marine diatoms Attheya ussuriensis and Chaetoceros muelleri, the red algae Porphyridium purpureum and Raphidophyte Heterosigma akashiwo were employed as the aquatic test organisms. A sample of biodiesel from waste cooking oil without dilution with petroleum diesel (B100) showed the highest level of toxicity for the microalgae A. ussuriensis, C. muelleri and H. akashiwo, compared to hexane, methanol, petroleum diesel (B0) and diluted sample (B20). The acute EC50 in the growth-inhibition test (96 h exposure) of B100 for the four species was in the range of 3.75–23.95 g/L whereas the chronic toxicity EC50 (7d exposure) was in the range of 0.42–16.09 g/L