On Sushchansky p-groups

We study Sushchansky p-groups. We recall the original definition and translate it into the language of automata groups. The original actions of Sushchansky groups on p-ary tree are not level-transitive and we describe their orbit trees. This allows us to simplify the definition and prove that these groups admit faithful level-transitive actions on the same tree. Certain branch structures in their self-similar closures are established. We provide the connection with, so-called, G groups that shows that all Sushchansky groups have intermediate growth and allows to obtain an upper bound on their period growth functions.Comment: 14 pages, 3 figure

Dynamics of Morbidity and Prevalence of Stroke of Population of the Volyn Area.

У статті розглянуто динаміку захворюваності та поширеності інсульту у Волинській області, яка свідчить про зростання захворюваності. Інсульт – друга за частотою причина смертності у світі. In the article the dynamics of morbidity and prevalence of stroke is considered in the Volyn area which testifies to growth of morbidity and prevalence. A stroke is the second on frequency reason of death rate in the world

Assessment of coal quality on the site “Uspenivska No 2” in Western Donbas based on the statistical analysis of its chemical and technological properties

Purpose. To conduct a comprehensive assessment of the coal seams’ quality on the site “Uspenivska No 2” in Lozivskyi coal-bearing area of the Western Donbas industrial district; establish their grade composition according to current standards, and find the main directions of their rational use. Methods. The research is based on the methods of analysis, synthesis, and statistical treatment of indices followed by the prognosis and refining of coal quality characteristics. Findings. We analyzed the reserves of fuel and energy resources of Ukraine and evaluated chemical and technological characteristics of coal seams for the site “Uspenivska No 2”. Statistical treatment of the data allowed to reveal the relationships between the quality indices and establish lateral and stratigraphic patterns. The grade composition has been specified and the ways of coal rational use have been considered. Originality. The distribution patterns of coal quality parameters have been established for the site “Uspenivska No 2” in Lozivskyi coal-bearing area of the Western Donbas by statistical analysis. In particular, statistical significance of the reduction in the vitrinite reflectance index and combustion heat, as well as the increase in volatiles output with increasing depth has been confirmed. Practical implications. Detailed statistical analysis of coal quality allowed giving recommendations on rational use and implementation of clean technologies of coal processing at the stage of geological exploration.Цель. Всесторонняя оценка качества основных промышленных угольных пластов участка “Успеновский №2” Лозовского угленосного района Западного Донбасса, установление их марочного состава по действующим стандартам и определение основных направлений их рационального использования. Методика. Методической основой исследований является анализ, обобщение и статистическая обработка показателей с последующим прогнозом и выявлением особенностей качества угля. Результаты. Выполнен анализ запасов топливно-энергетических ресурсов Украины, дана химико-технологическая характеристика углей пластов участка “Успеновский №2”. Проведенная статистическая обработка данных позволила выявить зависимости между показателями качества, а также установить латеральные и стратиграфические закономерности. Уточен марочный состав и пути рационального использования угля. Научная новизна. Путем статистического анализа установлены закономерности распределения показателей качества углей для пластов участка “Успеновский №” Лозовского угленосного района Западного Донбасса, в частности, подтверждена статистическая значимость уменьшения показателя отражения витринита и теплоты сгорания, а также увеличения выхода летучих веществ с увеличением глубины. Практическая значимость. Детальный статистический анализ данных качества угля позволяет дать рекомендации по рациональному использованию и внедрению чистых технологий переработки угля еще на стадии геологоразведочных работ.Мета. Оцінка якості основних промислових вугільних пластів ділянки “Успенівська №2” Лозівського вугленосного району Західного Донбасу, встановлення їх марочного складу за діючими стандартами та визначення основних напрямків раціонального використання. Методика. Методичною основою дослідження є проведення аналізу, узагальнення та статистичної обробки показників із подальшим прогнозом та виявленням особливостей якості вугілля. Результати. Виконано аналіз запасів паливно-енергетичних ресурсів України, надано хіміко-технологічну характеристику вугілля пластів ділянки “Успенівська №2”. Проведена статистична обробка даних, яка дозволила виявити залежності між показниками якості й встановити латеральні та стратиграфічні закономірності. Уточнено марочний склад і шляхи раціонального використання вугілля. Наукова новизна. Шляхом статистичного аналізу встановлено закономірності розподілу показників якості вугілля для пластів ділянки “Успенівська №2” Лозівського вугленосного району Західного Донбасу, зокрема, підтверджена статистична значимість зменшення показника відбиття вітриніту та теплоти згорання, а також збільшення виходу летючих речовин зі збільшенням глибини. Практична значимість. Детальний статистичний аналіз даних якості вугілля дозволяє надати рекомендації щодо раціонального використання та впровадження чистих технологій переробки вугілля ще на стадії геологорозвідувальних робіт.Авторы выражают благодарность в содействии и консультациях генеральному директору ГРГП “Донецкгеология”, д.э.н, к.геол.н. Н.В. Жикаляку

The Influence of Combined Pharmacotherapy with the Use of Trimetazidine and Potassium and Magnesium Salts of Gluconic Acid in Patients with Chronic Heart Failure of Ischemic Origin

The objective of the research was to improve the efficiency of treatment of patients with chronic heart failure (CHF) of ischemic genesis by adding potassium and magnesium salts of gluconic acid and trimetazidine to the background therapy (BT). Materials and methods. Registration of electrocardiogram (ECG) and ECG Holter Monitoring (ECG HM) was performed in order to achieve the aim. The study involved 84 patients with postinfarction cardiosclerosis with CHF. Patients were randomized into four groups depending on treatment characteristics. The first group included patients with heart failure of ischemic genesis treated with BT; the second group consisted of patients with CHF, who were treated with BT and potassium and magnesium salts of gluconic acid; the third group included patients with CHF who were prescribed trimetazidine on the background of BT; the fourth group consisted of patients treated with BT in combination with potassium and magnesium salts of gluconic acid and trimetazidine.Results of the research. The proposed treatment regimens were proved to be effective in reducing ischemic parameters after 6 and 12 months of treatment. Anti-ischemic treatment using a combination of potassium and magnesium salts of gluconic acid and trimetazidine on the background of BT led to the most significant change in the average number of myocardial ischemia episodes in examined patients. Indicator of the average daily number of ischemic episodes before the research in the first group decreased after treatment by 29.21 %. The average number of myocardial ischemia episodes during the day in the second group decreased by 38.50 % and constituted (2.78±0.10) after treatment. The addition of trimetazidine to BT in patients of III group was accompanied by significant anti-ischemic effect reducing the average daily number of ischemic episodes by 43.8 % (p<0.001). It should be noted that the anti-ischemic treatment of group IV patients using a combination of  BT, potassium and magnesium salts of gluconic acid and trimetazidine resulted in the most statistically significant change in this indicator in examined patients, namely by 48.90 % (p<0.001).Conclusions. Thus, a more significant anti-ischemic effect was observed when using combined treatment with potassium and magnesium salts of gluconic acid and trimetazidine compared with BT in a separate combination with each of these drugs

Dynamics of Heart Failure Markers in Patients after Past Myocardial Infarction with the Use of Potassium and Magnesium Salts of Gluconic Acid, Eplerenone and Rivaroxaban

The objective of the research was to increase the efficiency of treatment of patients with chronic heart failure (CHF) and post-infarction cardiosclerosis by adding potassium and magnesium salts of gluconic acid, eplerenone and rivaroxaban to the background therapy taking into account the indices of growth differentiation factor 15 (GDF-15), aldosterone and galectin-3. Materials and methods of the research. Emmunoenzymometric determination of the galectin-3, GDF-15 and aldosterone levels concentration in blood serum was conducted to achieve the stated objective. 42 patients with CHF and post-infarction cardiosclerosis after coronary artery stenting in the acute period of myocardial infarction (MI) were examined. The patients were randomized into four groups according to the peculiarities of treatment. Group I included patients with CHF and post-infarction cardiosclerosis treated with the background therapy (BT). Group II consisted of patients with CHF who were treated with BT and addition of potassium and magnesium salts of gluconic acid. Group III included patients with CHF who were prescribed eplerenone secondary to BT. Group IV consisted of patients who were treated with BT and rivaroxaban. Results. The proposed treatment regimens were proved to be effective in reduction of GDF-15, aldosterone and galectin-3 indices in 12 months of treatment. Conducted therapy with the use of rivaroxaban secondary to BT led to more intensive decrease in GDF-15 concentration in comparison with the use of potassium and magnesium salts of gluconic acid or eplerenone on the background of BT. This index constituted (2110.21±107.4) pg/ml before the treatment in these patients and significantly decreased to (1286.75±109.6) pg/ml being significantly before the therapy. The performed treatment with the use of eplerenone secondary to BT was proved to be more effective for normalization of aldosterone and galectin-3 levels in blood serum compared to other studied treatment regimens. The average value of aldosterone changed in the treatment process by 67.24%. Thus, the average level of this index constituted (139.8±7.63) pg/ml before the treatment and was equal to (45.8±5.52) pg/ml at the end of the treatment course. The average value of galectin-3 in patients with CHF and post-infarction cardiosclerosis was noted to be (34.69±1.67) ng/ml before the treatment. It constituted (22.53±0.98) ng/ml after the end of treatment being significantly lower compared to the value before the treatment. The average value of this index changed in the course of twelve-month treatment by 35.05%. Lower risk of sudden cardiac arrest (SCA), acute coronary syndrome (ACS) and stroke was observed in the patients with CHF and post-infarction cardiosclerosis with the use of rivaroxaban secondary to BT.Conclusions. Thus, the use of rivaroxaban combination therapy secondary to BT led to more intensive decrease in GDF-15 concentration in comparison with the use of potassium and magnesium salts of gluconic acid or eplerenone. Conducted therapy with the use of eplerenone on the background of BT was more effective for the normalization of galectin-3 and aldosterone levels in the blood compared to other studied treatment regimens

Resolvent convergence of Sturm-Liouville operators with singular potentials

In this paper we consider the Sturm-Liuoville operator in the Hilbert space $L_2$ with the singular complex potential of $W^{-1}_2$ and two-point boundary conditions. For this operator we give sufficient conditions for norm resolvent approximation by the operators of the same class.Comment: 6 pages, to appear in Math. Note