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In this paper, based on the R-functions theory, methods have been developed and equations have been constructed for the 3D printing of hex-head screws with Bristol, Pentalobe, Polydrive and other types of screw slots. Such screws are used both in personal computers and other high-end equipment. The Bristol slot has four or six radial grooved beams. The advantage of the design of this slot is the correct perpendicular, rather than tangential, vector of force application when the slot is rotated by a tool, which minimizes the risk of stripping out the slot. For this reason, the Bristol slot is used in soft metal screws. Compared to the internal hex, the Bristol slot allows a noticeably higher torque, only slightly higher than that of the Torx slot. This type of slot is used in aviation, high-end telecommunications equipment, cameras, air brakes, agricultural equipment, astronomical equipment, and foreign military equipment. Variations with a pin in the center are found in game consoles to prevent the use of a flat-blade screwdriver as an improvised key. The Pentalobe slot is a five-point slot designed by Apple and used in its products to limit unauthorized disassembly. It was first used in mid 2009 to mount MacBook Pro batteries. Its miniature version was used in the iPhone 4 and later models, in the MacBook Air (available since late 2010 models), and the MacBook Pro with Retina screens. The Polydrive slot is a starlike slot with rounded star points, used in the automotive industry for applications requiring high tightening torque. The Torq-set slot is a cross slot for fasteners requiring high tightening torque. The grooves are slightly offset, not intersecting at one point. Fasteners with this type of slot are used in military aviation, for example, in E-3, P-3, F-16, Airbus, Embraer, and Bombardier Inc. The Phillips Screw Company owns the trademark and manufactures fasteners with this type of slot. The slot design standards are National Aerospace Standard NASM 3781 and NASM 4191 for the ribbed version. The resulting equations for the surfaces of screws were checked during the modeling of the screws before 3D printing. The 3D printing technology allows us to reduce the cost and labor intensity of manufacturing products, including complex slot screws. The analytical recording of designed objects makes it possible to use alphabetic geometric parameters, complex superposition of functions, which, in turn, allows us to quickly change their design elements. The positivity property of the constructed functions at the internal points of an object is very convenient for the implementation of 3D printing.

Creation of mathematical models of objects to be 3D printed is of considerable interest, which is associated with the active introduction of 3D printing in various industries. The advantages of using modern 3D printers are: lower production costs and shorter periods of time for their appearance on the market, modeling objects of any shape and complexity, speed and high precision of manufacturing, their ability to use various materials. One of the methods for solving the problem of creating a mathematical and computer model of the object being designed is the application of the R-functions theory, with the help of which it is possible to describe geometric objects of complex shapes in a single analytical expression. The use of alphabetic parameters, when one specifies geometric information in analytical form, allows one to quickly change the size and shape of the object being designed, which helps to spend less time on building computational models. The proposed method can significantly reduce the complexity of work in CAD systems in those cases when one needs to view a large number of design options in search of an optimal solution. This gives a great effect on reducing labor intensity in the construction of computational models to determine aero-gas-dynamic and strength characteristics. Characterization is also often associated with the need to account for changes in aircraft shape. This leads to the fact that the determination of aerodynamic characteristics only due to the need to build a large number of computational models increases the duration of work by months. With parametric assignments, computational regions change almost instantly. In this paper, on the basis of the basic apparatus of the theory of R-functions as well as cylindrical, spherical, ellipsoidal, and conusoidal support functions, a multiparametric equation for the surface of a Soyuz-Apollo spacecraft model is constructed. A number of support functions were normalized according to a general formula, which made it possible to illustrate a new approach to constructing three-dimensional equations for surfaces of a given thickness., Создание математических моделей объектов для 3D-печати представляет значительный интерес, который связан с активным внедрением 3D-печати в различные отрасли промышленности. Преимущества использования современных 3D-принтеров: снижение себестоимости изготовления продукции и сокращение сроков ее появления на рынке, моделирование объектов любой формы и сложности, быстрота и высокая точность изготовления, возможность использования различных материалов. Одним из методов решения проблемы создания математической и компьютерной модели проектируемого объекта является применение теории R-функций, при помощи которой можно описывать геометрические объекты сложной формы единым аналитическим выражением. Использование буквенных параметров при задании геометрической информации в аналитическом виде позволяет оперативно изменять размеры и форму проектируемых объектов, что помогает сократить затраты времени при построении расчетных моделей. Предложенный метод может существенно сократить трудоемкость работ в CAD-системах в тех случаях, когда требуется просмотреть большое количество вариантов конструкции в поисках оптимального решения. Это дает большой эффект по снижению трудоемкости при построении расчетных моделей для определения аэрогазодинамических и прочностных характеристик. Определение характеристик также часто связано с необходимостью учета изменения формы летательного аппарата. Это приводит к тому, что определение аэродинамических характеристик только за счет необходимости построения большого числа расчетных моделей увеличивает длительность работ на месяцы. При параметрическом задании изменение расчетных областей производится практически мгновенно. В работе на основе базового инструментария теории R-функций и цилиндрических, сферических, эллипсоидальных, конусоидальных опорных функций построено многопараметрическое уравнение поверхности макета космического корабля типа «Союз-Аполлон». Ряд опорных функций был нормализован по общей формуле, что дало возможность проиллюстрировать новый подход к построению трехмерных уравнений поверхностей заданной толщины., Створення математичних моделей об’єктів для 3D-друку становить значний інтерес, який пов'язаний з активним впровадженням 3D-друку в різні галузі промисловості. Переваги використання сучасних 3D-принтерів: зниження собівартості виготовлення продукції і скорочення термінів її появи на ринку, моделювання об'єктів будь-якої форми і складності, швидкість і висока точність виготовлення, можливість використання різних матеріалів. Одним з методів вирішення проблеми створення математичної та комп'ютерної моделі проектованого об'єкта є застосування теорії R-функцій, яка дозволяє описувати геометричні об'єкти складної форми єдиним аналітичним виразом. Використання буквених параметрів під час задання геометричної інформації в аналітичному вигляді дозволяє оперативно змінювати розміри і форму проектованих об'єктів, що допомагає скоротити витрати часу під час побудови розрахункових моделей. Запропонований метод може істотно скоротити трудомісткість робіт в CAD-системах в тих випадках, коли потрібно переглянути велику кількість варіантів конструкції в пошуках оптимального рішення. Це може зумовити значний ефект щодо зниження трудомісткості під час побудови розрахункових моделей для визначення аерогазодинамічних і міцнісних характеристик. Визначення характеристик також часто пов'язано з необхідністю врахування зміни форми літального апарата. Це призводить до того, що визначення аеродинамічних характеристик тільки за рахунок необхідності побудови великого числа розрахункових моделей для врахування цього фактора збільшує тривалість робіт на місяці. За параметричного задання зміна розрахункових областей проводиться практично миттєво. У роботі на основі базового інструментарію теорії R-функцій і циліндричних, сферичних, еліпсоїдальних, конусоїдальних опорних функцій побудовано багатопараметричне рівняння поверхні макета космічного корабля типу «Союз-Аполлон». Ряд опорних функцій був нормалізований за загальною формулою, що дало можливість проілюструвати новий підхід до побудови тривимірних рівнянь поверхонь заданої товщини.

Global experience related to increased pork production shows that breeding work has become an integral part of the technology, since it is impossible to further improve breeding and performance traits of animals without it and therefore the greater production of better quality pork. The paper presents the results of the breeding process arrangement for creation of F1 parental pig. Substantiation of breeding techniques when creating the final parental groups of sows (F1) with a high adaptive ability was based on complex methods to evaluate breeding animals, including traditional methods of domestic breeding and breeding indices. Evaluation of combination compatibility of breed-linear hybrids with the use of breeding indices during mating of parent initial forms allows to determine efficiency of using Yorkshire sows with Landrace boars, and Landrace sows with Yorkshire boars (final parental sows (F1)), which had significantly better reproductive indicators in comparison with BLW х BM genotype sows. Particularly efficient compatibility was recorded when selecting Yorkshire sows and Landrace boars. It was determined that in modern conditions an increase in the efficiency of breeding and pedigree work in pig breeding was based on the use of genetic methods, including: individual assessment of pedigree species according to the main breeding traits, evaluation of genome of each breeding animal, and use of breeding indices allowing to identify the true genetic potential of animals and predict performance traits of their offspring. The research relevance lies in using the innovative methodology for comprehensive assessment of combination compatibility of parental pairs, unified for pig husbandries and pig farms, which will make it possible to 10% accelerate the breeding process of forming the final parental forms of sows, ensure obtaining offspring with predictable reproductive, fattening and meat traits, and good adaptive ability.

Unmanned aerial vehicles (UAVs) are becoming increasingly demanded worldwide. The scope of their use is very extensive. They are used for military purposes, delivery of goods, environmental monitoring, border patrolling, aerial reconnaissance and mapping, traffic control, etc. UAVs have a number of important advantages over manned aircraft. These advantages include relatively low costs of UAVs at their long flight durations and ranges, their low operating costs, and the ability to perform maneuvers with overloads that exceed the physical capabilities of a human being, making their development more active. One cannot imagine the designing of UAVs and control systems without mathematical modeling. To build mathematical models, high-speed computers and modern software tools have been created, Solid Works, Ansys CFX, POLYE software systems being among them. There arises a problem of specifying and quickly changing geometric information to create a mathematical and computer model of the UAV being designed. At the design stage, there can be solved a lot of tasks that are put before researchers as regards the use of UAVs. At the same time, insufficient attention is paid to the parametric representation of aircraft surfaces. Expanding the scope of using the apparatus of the theory of R-functions for modeling UAV surfaces is an urgent scientific and technical task. In this paper, for the first time, using the theory of R-functions, we build up the equation of the surface of a flying wing UAV in the form of a single analytical expression with alphabetic parameters. This equation can be used in solving various practical problems as well as developing and manufacturing the product itself, for example, on a 3D printer. The proposed method for specifying the shapes of products by using a limited number of parameters can significantly reduce the complexity of work in CAD systems in cases where it is required to view a large number of design options in search of an optimal solution. In this paper, we build a 14-parameter family of flying wing UAV surfaces. By changing the values of alphabetic parameters, we can quickly explore its various forms.

В статті подано детальний поетапний аналіз всього циклу створення та функціонування фотоелектричних станцій в Україні з прив’язкою його до вимог щодо дотримання та забезпечення екології та охорони навколишнього природного середовища. Проаналізовано всі основні етапи, починаючи з того, на яких землях можна розміщувати фотоелектричні станції, яке обладнання необхідно переважно використовувати, як доцільно експлуатувати ці станції та закінчуючи виведенням їх з експлуатації та утилізацією складових частин станцій і рекультивацією території. Тут також досконально опрацьовано нормативно-правову та рекомендаційну документацію, що є та діє в Україні за екологічною та природоохоронною направленістю. При цьому враховано також і прогнозування екологічних ризиків, проведення державного моніторингу навколишнього природного середовища, врахування віддалених екологічних наслідків, щоб вплив діяльності людини на довкілля, технологічне навантаження на природне середовище були мінімальними. На основі проведеного аналізу нормативно-правової та рекомендаційної документації з екологічної та природоохоронної проблематики та її дотримання з прив’язкою до фотоелектричних станцій, що є обов’язковим за умови проектування, будівництва та експлуатації ФЕС, розроблено методичні рекомендації «Комплексні заходи та рекомендації зі зменшення впливу фотоелектричних станцій на довкілля». Бібл. 4, табл. 1.

Мета: провести огляд наукової літератури, присвяченої впливу йоги на організм людини як у стані здоров’я, так і у пацієнтів з хронічними хворобами. Матеріали і методи. Проведено огляд літератури з обраної теми в наукометричних базах даних Web of Science, PubMed, Google Scholar. Результати. Серцево-судинні захворювання є основною причиною захворюваності та смертності в країнах, що розвиваються. Фізичні вправи та йога сприяють зменшенню рівня серцево-судинних захворювань і можливих ускладнень, що виникають через них. Доведено, що йога сприяє фізичному і психічному здоров’ю шляхом виконання пози («асан»), регульованого дихання («пранаяма») і медитації («дх’яна»). Численні дослідження показали, що йога має швидкий регулюючий вплив на нервову систему та стрес. Також доведено, що коротка релаксаційна підготовка на основі йоги нормалізує функцію автономної нервової системи шляхом нормалізації як симпатичних, так і парасимпатичних впливів до більш фізіологічного середнього діапазону контрольних значень. Відповідно до літературних даних, під впливом курсів йоги відбувалась нормалізація або зниження артеріального тиску, рівня глюкози в крові, зникала тривожність, покращувався психоемоційний стан онкохворих та вагітних, оптимізувались показники роботи шлунково-кишкового тракту та опорно-рухової системи. Висновки. Згідно з проведеним оглядом літератури, йога має значний позитивний вплив на різні системи органів людини та може використовуватись як допоміжна ланка лікування більшості основних захворювань, зокрема артеріальної гіпертензії. У зв’язку з позитивним впливом йоги на психоемоційний стан людини, її можна рекомендувати з метою профілактики виникнення хронічних стресзалежних станів, починаючи з дитячого віку.

Визначення варіабельності серцевого ритму на сьогодні вважають доступним, неінвазивним, достатньо простим і відносно дешевим методом оцінки автономної нервової системи. Більшість дослідників розглядає його як інтегральний маркер, який відображає стан усіх регуляторних систем організму. Зміни вегетативного балансу у вигляді активації симпатичної ланки розглядають як неспецифічний компонент адаптаційної реакції у відповідь на різні стресорні дії. За останні роки збільшилася кількість осіб зі зниженими пристосувальними можливостями організму – з дизадаптацією регуляції функціональних систем, що призводить до зриву відповідних механізмів. Мета дослідження – оцінити стан автономної нервової системи у студентів-іноземців жіночої статі молодших курсів медичного факультету. Матеріали і методи. У дослідження було залучено 20 студентів-іноземців жіночої статі ІІ–ІІІ курcів медичного факультету віком 18–22 роки. Реєстрацію варіабельності серцевого ритму проводили в умовах фізіологічного спокою, після 10-хвилинного відпочинку, та в умовах активної ортостатичної проби за загальновідомою методикою зa допомогою комп’ютерного діагностичного комплексу “КардіоЛаб” (“ХАІ-Медіка”, Україна). Результати досліджень та їх обговорення. Результати аналізу варіабельності серцевого ритму в стані фізіологічного спокою свідчать про те, що обстежувані характеризуються належними для здорових осіб показниками варіабельності серцевого ритму, а у відповідь на ортостатичну пробу демонструють вірогідне зростання активності симпатичної ланки автономної нервової системи LF на (261±187) мс, LF % на (12,6±0,6) % (p

Синдром автономних дисфункцій – це поліетіологічний синдром, що характеризується дисфункцією автономної нервової системи і функціональними порушеннями всіх систем організму. Поширеність САД, за даними деяких авторів, складає від 20 до 56 % всіх захворювань у осіб молодого віку, поступаючись лише ГРВІ. Мета – виявити студентів з автономними дисфункціями та оцінити функціональний стан їх організму кількісно за допомогою показника активності регуляторних систем (ПАРС). Матеріал і методи. До дослідження було залучено 100 студентів іноземців 2–3 курcів медичного факультету (1 група), та 100 студентів-українців молодших курсів інших факультетів (2 група) обох статей віком 17–23 роки. Для скринінгу автономних дисфункцій здійснювали анкетування за стандартним опитувальником А. М. Вейна. Для об’єктивної характеристики функціонального стану автономної нервової системи використовували показники варіабельності серцевого ритму, отримані шляхом 5-хвилинної реєстрації ІІ відведення зa допомогою комп’ютерного діагностичного комплексу «КардіоЛаб» («ХАІ-Медіка»,Україна). Зниження пристосувальних можливостей організму визначали за допомогою показника активності регуляторних систем (ПАРС). Результати. За даними опитувальника А. М. Вейна, серед студентів-іноземців ознаки вегетативних змін мали 32 студенти (32 %), а серед українців – 21 (21 %). Однак об’єктивно автономні дисфункції, підтверджені показниками варіабельності серцевого ритму, серед іноземців мали лише 18 осіб (18 %), а серед українців – 11 осіб (11 %) відповідно до загальної кількості опитаних студентів. Зокрема, 50 % студентів-іноземців та 54,5 % студентів-українців мали помірну функціональну напругу, тобто донозологічні стани, ПАРС 2–4; 22,2 % студентів-іноземців та 27,3 % студентів-українців мали виражену функціональну напругу, тобто преморбідний стан, ПАРС 5–6; 11,1 % студентів-іноземців та 9,1 % студентів-українців мали різко виражену функціональну напругу, стан незадовільної адаптації, ПАРС 7-8; 16,7 % студентів-іноземців та 9,1 % студентів-українців мали астенізацію (виснаження) регуляторних систем, ПАРС 9–10. Висновки. Опитувальник А. М. Вейна може бути використаний для скринінгу синдрому автономних дисфункцій, однак необхідним є об’єктивне підтвердження за допомогою вимірювання показників варіабельності серцевого ритму.

We consider conjugate boundary-value problems of heat exchange for the cases where a viscous incompressible liquid moves through channels with noncanonical cross section flowing around a bundle of rods. The influence of the type of packing on the velocity and temperature distributions is investigated. For the solution, we use the R-functions method in combination with the Ritz variational method. We consider the cases of cyclic, staggered, and rectangular packing of fuel elements.

Objective Introduction: Heart rate variability is a highly informative non-invasive method of research not only for the functional state of the cardiovascular system and also for the integrative regulatory activity of the autonomic nervous system. The positive effect of diaphragmatic breathing is positive in the mode of biological feedback using portable devices, but there is little evidence of the use of yoga breathing gymnastics in order to influence the heart rate variability. The aim: To compare the possibilities of using courses of breathing gymnastics of yogis and diaphragmatic breathing sessions in the mode of biological feedback using a portable device. Patients and methods Materials and methods: The study involved 70 practically healthy foreigners, who were divided into 2 groups of 35 people. Participants of the 1st group daily engage in respiratory exercises pranayama for 15 minutes in 1 month. Participants in the 2nd group used the MyCalmBeat portable device. Heart rate variability was registered by using the computer diagnostic complex "CardioLab" ("KhAI-Medika", Ukraine). Results Results: In both groups there was similar dynamics of heart rate variability indices, but its severity was different. The common integral effect was a significant growth of heart rate variability both according to statistical and spectral indicators - total power increased, as well as high-frequency component. The power of the very-low frequency waves has probably decreased only in the group with the device. In the percentage structure of the cardiac rhythm spectrum, the specific weight of very-low frequency component and the percentage of high-frequency component increased. Conclusion Conclusions: Respiratory gymnastics yoga for 15 minutes daily contributes to the growth of heart rate variability through the suppression of the central link (very-low frequency component) of regulation of cardiac rhythm and increased activity of parasympathetic influences (high-frequency component), as well as the redistribution of regulatory activity of the central nervous system between the central and peripheral links of regulation of the cardiac rhythm in favor of the latter.

Local breeds can serve as an important source of genetic variability in domestic animal species. This study aimed to assess the genetic diversity and population structure of Belarusian Red cattle and their differentiation from other European cattle populations based on genome-wide SNP genotypes. Twenty pedigree-recorded non-closely related cows of Belarusian Red cattle were genotyped using the Illumina BovineHD BeadChip. Genotypes of 22 other European cattle breeds were included in the study for comparison. A total of 28 562 SNPs passed through the quality control checks and were selected for analysis. The Belarusian Red cattle displayed a moderate level of genetic variability (U HE = 0.341, HO = 0.368), and the highest heterozygote excess (U FIS = -0.066), among the studied breeds; this reflects the contribution of multiple breeds to their formation. The principal component analysis, FST -based Neighbor-Net tree and Admixture clustering, clearly distinguished the Belarusian Red cattle from the other European cattle breeds. Moreover, the presence of ancestral genomic components of Danish Red and Brown Swiss breeds were clearly visible, which agrees with the breed's history and its recent development. Our study highlights the importance of maintaining the specific genomic components, which makes a significant contribution to the global genetic diversity in the modern population of Belarusian Red cattle, allowing us to consider them a valuable national genetic resource. Our research results will be useful for the development of conservation programs for this local cattle breed.

This research studied the interrelationship between the immune and oxidative-antioxidant systems in a group of individuals who had lived for a long time in areas contaminated with radionuclides after the Chernobyl catastrophe and as a result experienced prolonged exposure to small doses of ionizing radiation. We have examined a group of 100 students aged 18–24, where 50 of them formed the control group and the remaining 50 belonged to the experimental group as they arrived from the territories of enhanced radioecological control (IV radiation zone, density of soil contamination by isotope 137Cs 3.7 x 104 – 18.5 x 104 Bq/m2). Here we determined the level of cortisol, leukocytes and their populations, the levels of lymphocyte subpopulations with phenotypes CD3+, CD5+, CD4+, CD8+, CD16+, CD72+, immunoregulatory index CD4+/CD8+, indicators of phagocytic activity of neutrophils and monocytes, IgG (H), IgM (H), IgA (H), malondialdehyde (MDA), ceruloplasmin (CP), transferrin (Tr), sulfhydryl (SH); and also calculated the oxidative stress index (OSI). We performed the analysis twice: in the absence/presence of additional emotional stress such as an examination session. The studies showed an increase in the oxidative stress index in the group examined from the experimental cluster, especially in terms of emotional stress. At the same time, the neutrophil level increased, but phagocytic activity of neutrophils and monocytes, the relative and absolute number of lymphocytes with phenotypes CD3+, CD5+, CD4+, CD4+/CD8+, and IgG levels decreased. Consequently we revealed the negative correlation between the indexes of oxidative stress in the group of examined (the oxidative stress index (ISO)/the level of malonic dialdehyde (MDA)) and the parameters of phagocytic activity of monocytes, the immunoregulatory index CD4+/CD8+, and the number of lymphocytes with the CD16+ phenotype. In this study we demonstrated the decrease in the participation of ceruloplasmin (CP) as an important antioxidant factor in maintaining the immune homeostasis of the group examined from radiation-contaminated areas compared with control group. The evidence of this is the lack of reliable correlation between ceruloplasmin level and immune system parameters. Moreover we found that radiation-induced intensification of oxidative processes in the experimental group grew in conditions of additional stresses of an emotional nature. Besides, it was accompanied by a significant correlation in the level of oxidative stress and phagocytic activity parameters. Reducing phagocytic activity and the CD4+/CD8+ index on the background of oxidative stress increase can be considered as a sign of immune system ageing, while a decrease in the number of lymphocytes with the CD16+ phenotype is a sign of antitumor defense inhibition. Thus, we draw the conclusion that the inhabitants of the territories of strengthened radioecological control, undergoing exposure to small doses of ionizing radiation from birth, show a significant imbalance of redox homeostasis, which creates the preconditions for immunoreactivity pathology development at the level of both innate and acquired immunity.

Introduction: Heart rate variability is a highly informative non-invasive method of research not only for the functional state of the cardiovascular system and also for the integrative regulatory activity of the autonomic nervous system. The positive effect of diaphragmatic breathing is positive in the mode of biological feedback using portable devices, but there is little evidence of the use of yoga breathing gymnastics in order to influence the heart rate variability. The aim: To compare the possibilities of using courses of breathing gymnastics of yogis and diaphragmatic breathing sessions in the mode of biological feedback using a portable device.Materials and methods: The study involved 70 practically healthy foreigners, who were divided into 2 groups of 35 people. Participants of the 1st group daily engage in respiratory exercises pranayama for 15 minutes in 1 month. Participants in the 2nd group used the MyCalmBeat portable device. Heart rate variability was registered by using the computer diagnostic complex "CardioLab" ("KhAI-Medika", Ukraine).Results: In both groups there was similar dynamics of heart rate variability indices, but its severity was different. The common integral effect was a significant growth of heart rate variability both according to statistical and spectral indicators - total power increased, as well as high-frequency component. The power of the very-low frequency waves has probably decreased only in the group with the device. In the percentage structure of the cardiac rhythm spectrum, the specific weight of very-low frequency component and the percentage of high-frequency component increased.Conclusions: Respiratory gymnastics yoga for 15 minutes daily contributes to the growth of heart rate variability through the suppression of the central link (very-low frequency component) of regulation of cardiac rhythm and increased activity of parasympathetic influences (high-frequency component), as well as the redistribution of regulatory activity of the central nervous system between the central and peripheral links of regulation of the cardiac rhythm in favor of the latter.

Aim. Intravital video microscopy of cells is a highly informative approach to the study of cell cultures. Often, this method allows refining and complementing the data obtained by researchers at the visual study of living cultures or fixed preparations. The main problem of the long intravital video microscopy is the maintenance of cell activity. To solve this problem, video-computer "Tsitomir" has been developed. Methods. During cultivation the images of the cell culture areas (from one to several hundred) specified by researcher are captured at regular intervals (time-lapse method of photography). A motorized sample stage allows moving the culture vessel with the joystick, as well as to scan the specified cell culture sites automatically. Results. In our investigations, we studied such processes as cell division, death, differentiation, motility and massive changes of cell cultures associated with cancerous transformation, including abnormal morphological changes and cell aggregation. The effectiveness of the intravital cell microscopy use to test the anti-cancer drugs is shown as well. Conclusions. Opportunities of video-complex enable its use in biomedical research, in the development of cell technologies, the study of the action of pharmacological agents and sanitary-hygienic regulation of chemicals in the cell assay systems. Obtained through "Tsitomir" photos and videos can also be used as educational material for students of biological, medical and agricultural universities.Keywords: cell culture, intravital videomicroscopy, differentiation, proliferation, anti-cancer protection.

Reliable testing of effects of various natural and synthetic substances on cells is critical in searching for effective inhibitory or stimulating agents. Such work is essential in the discovery of anticancer drugs and testing toxicity of newly synthesized compounds. We use the TSITOMIR (“World of Cells”) computer video complex developed in cooperation with the Planar Corporation (Minsk). This complex is intended for time-lapse video microscopy of living cells (mouse and human fibroblasts, cells from human hair follicle and urine, cancer cultures). We elaborated a method for counting cells in low-density cell cultures to calculate the number of cells in the same growth substrate areas during cultivation, and to build cell genealogy trees. We also developed a non-invasive technology for receiving and analysing cells from human hair follicle and urine. It was shown that the cells obtained aged after a two-week cultivation, and therefore were not prone to immortalization, i.e., suitable for use in research for regenerative medicine. The method allows to obtain cell numbers in dynamics and makes it possible to get statistically valid quantitative data by using a minimal number of culture flasks. This approach can be exploited for testing antiproliferative and apoptosis-inducing effects, as well as the action of various substances and their combinations.

Mathematical models of heat exchange in the motion of an incompressible viscous liquid through channels with a helical type of symmetry, including polyzonal finning of fuel elements, in curvilinear nonorthogonal coordinates are proposed. For a laminar flow in the domain of thermal stabilization, we reduce the three-dimensional problem to the two-dimensional problem and investigate the influence of a twist parameter on the distribution of a temperature field. Numerical solutions of model multiparameter problems of calculation of stationary temperature fields by the R-function method (RFM) are considered, which enables us to choose appropriate structural means of the RFM for the subsequent solution of real problems.

Normalized equations for regular no-gons translated nd times in a regular nb-gon are set up based on coordinate transformations that allow translating geometric objects on segments. Such approaches are especially important in solving automation problems in solid modeling, geometric design, and boundary-value problems of mathematical physics.

Based on R-functions, a general algorithm is proposed for automatic construction of predicate and analytical functions of a geometrical object consisting of a given list of standard primitives. Normalized functions of standard primitives with alphabetic parameters are constructed that determine the position, sizes, and orientation of the primitives. The capabilities of automation of constructing equations of geometrical objects from standard primitives are illustrated with the help of the system POLYE.

The causes of the indefinite propagation of immortalized cell populations remain insufficiently understood, that hinders the research of such fundamental processes as ageing and cancer. In this study the interrelations between clonal proliferation and abnormalities of mitotic divisions in the immortalized cell line established from the mouse embryo were investigated with the aid of computerized microscopy of living cells. 3 mitoses with three daughter cells and 7 asymmetric mitoses which generated two daughter cells of conspicuously different sizes were registered among 71 mitotic divisions in the individual cell genealogy. Abnormal mitotic divisions either did not slow the proliferation in cell clones compared with progenies of cells that divided by means of normal mitoses or were followed by the acceleration of divisions in consecutive cell generations. These data suggest that abnormal mitotic divisions may contribute to the maintenance of the immortalized state of cell populations by means of generating chromosomal instability.

In a general setting, the transfinite interpolation problem requires constructing a single function f(x) that takes on the prescribed values and/or derivatives on some collection of point sets. The sets of points may contain isolated points, bounded or unbounded curves, as well as surfaces and regions of arbitrary topology. All such closed semi-analytic sets may be represented implicitly by real valued functions with guaranteed differential properties. Furthermore, such functions may be constructed automatically using the theory of R-functions. We show that such implicit representations may be used to solve the general transfinite interpolation problem using a generalization of the classical inverse distance weighting interpolation for scattered data. The constructed interpolants may be used to approximate boundary value and smoothing problems in a meshfree manner.

The R-Function Method (RFM) solution structure is a functional expression that satisfies all given boundary conditions exactly and contains some undetermined functional components. It is complete if there exists a choice of undetermined component that transform the solution structure into an exact solution. Such a structure was used by Kantorovich (Kantorovich and Krylov, 1958) and his students to solve boundary value problems with homogeneous boundary conditions on geometrically simple domains. RFM is based on the theory of R-functions (Rvachev, 1982) that allows construction of a set of functions vanishing on the boundary and can be applied to problems with arbitrarily complex domains and boundary conditions. The resulting solution method is essentially meshfree, in the sense that the spatial discretization no longer needs to conform to the geometry of the domain, and can be completely automated. This paper summarizes the main principles of RFM, proves its completeness, and presents numerical results for several simple test problems.

This paper is devoted to developing constructive methods of the theory of R-functions. It gives the first discussion of methods of constructing the equations of loci with symmetry of translation type for duplicated domains not separated by lines and with point symmetry of cyclic type for regions both possessing and lacking axial symmetry. The possible applications are illustrated by numerous examples carried out using the POLE system, including solutions of boundary-value problems involving the influence of cyclically located circular and star-shaped insulators on an electric field.

We present a computational model of the process of solidification of metal in molds of complicated configuration. The model is based on the theory of R-functions, which makes it possible to construct the normal equations of drawings and introduce additional parameters into these equations, by means of which one can assure the required behavior of the solution corresponding to the technological implementation of the process. Computational experiments were carried out using thePOLE system.

Solidification of metal castings can be modeled by an implicit real-valued function whose behavior is determined by physical parameters prescribed on the boundary of a casting. We show how to construct such functions using theory of R-functions for two-dimensional castings represented by their boundaries. The parameterized form of the constructed functions is convenient for studying, controlling, and optimizing their behavior in terms of the physical parameters specified on the boundary of the casting. The proposed approach can also be used for modeling multiple cavities in a same sand mold, generalizes to three-dimensional castings, and is applicable to other physical phenomena that may be suitable for analysis based on empirical knowledge.

Described are the concepts and applications of the R-functions theory in continuum mechanics boundary value problems which model fields of different physical natures. With R-functions there appears the possibility of creating a constructive mathematical tool which incorporates the capabilities of classical continuous analysis and logic algebra. This allows one to overcome the main obstacle which hinders the use of variational methods when solving boundary value problems in domains of complex shape with complex boundary conditions, this obstacle being connected with the construction of so-called coordinate sequences. In contrast to widely used methods of the network type (finite difference, finite and boundary elements), in the R-functions method all the geometric information present in the boundary value problem statement is reduced to analytical form, which allows one to search for a solution in the form of formulae called solution structures containing some indefinite functional components. A method of constructing solution structures satisfying the required conditions of completeness has been developed. The structural formulae include the left-hand sides of the normalized equations of the boundaries of the domains or their regions being considered, thus allowing one to change the solution structure expeditiously when changing the geometric shape. Given in the work is a definition of the basic class of R-functions, solution with their help of the inverse problem of analytical geometry (construction of equations of specified configurations); generalization of the Taylor-Hermite formulae for functional spaces in which points are represented by lines and surfaces; and construction of solution structures of some types of boundary value problems. Shown are the solutions of a number of concrete problems in these application fields with the use of the RL language and POLYE system.

A comparative analysis is conducted of solutions of two model problems in electrostatics obtained with the help of general and partial structures, i.e., satisfying or not satisfying natural boundary conditions. The problem is solved for composite piecewise-homogeneous media with natural boundary conditions, including large contrast of physical characteristics.

We consider the stationary flow in a cavity with a moving lid, and as a mathematical model we use a fourth-order partial differential equation in the current function with boundary conditions of Neumann and Dirichlet type. The solution is constructed using the apparatus of R-functions.

The effect of the ratio of characteristic diode base dimensions to its height for a constant volume is determined. The effect of the shape of the diode side surface on its resistance is investigated. Practical recommendations are proposed on the application of the obtained results to design optimization of solid state components used in radiometric devices.

The skin-effect resistance in Schottky-barrier diodes with a complex form of the boundaries is calculated using the theory of R functions and the Ritz variational method. The minimum resistance due to the skin effect is determined by the choice of the diode geometry. A numerical experiment and aphysical analysis enabled the proposed method of calculation to be recommended to designers of both individual solid-state components and radiometer systems.

Modern radio physics has in recent years been characterized by rapid development of theory and engineering practice in the millimeter and submillimeter wave ranges. The dimensions of the systems, which are usually quite arbitrary in shape, are commensurate with or substantially in excess of the wavelength. This necessitates determination of the eigenvalues and eigenfunctions of regions with boundaries of complex form (waveguides, microstrip structures, resonators, etc.). One important problem is to lay the electrodynamic foundation for computer-aided design of microwave devices over a broad wavelength range [i]. A procedure for analytic description of the complex geometric shapes of real objects is especially important for development of the appropriate algorithm and their numerical implementation in computers. The theory of R functions, which is utilized in solving interior and exterior electrodynamic boundary value problems [2-11], is promising for this purpose.

1. Cladding of high-strength steel with type 08KhN2GMTA deposited metal aids in increasing the resistance to failure of plate metal under repeated static biaxial bending in a 3% sodium chloride solution. 2. With an amplitude of operating stresses of 70% of the yield strength of the high-strength steel the cladding layer at first experiences plastic deformation, which leads to the formation of residual stresses and a change in the degree of asymmetry of the subsequent load cycles of the external layers in a favorable direction. 3. The appearance in the cladding layer of residual compressive stresses and the decrease on the sample surface of the maximum tensile stresses aids in increasing the resistance to the origin and initial growth of a corrosion-fatigue crack.

6-Carbonyl-substituted lepidines and their quaternary salts were synthesized. Quino-4-cyanines were obtained from them. The introduction of carbonyl-containing substituents substantially deepens the color of the dyes obtained.

6-Carbonyl-substituted lepidines and their quaternary salts were synthesized. Quino-4-cyanines were obtained from them. The introduction of carbonyl-containing substituents substantially deepens the color of the dyes obtained.