Summarising of the polyparametric functional sets according to own elements of the hybrid Fourier – legendre – eulerian operator in the polar axis segment [R0, R3]

Методом порівняння розв'язків, побудованих на трискладовому сегменті полярної осі для сепаратної системи із диференціальних рівнянь Фур'є, Лежандра та Ейлера другого порядку для модифікованих функцій методом функцій Коші та методом відповідного скінченного гібридного інтегрального перетворення підсумовано поліпараметричну сім'ю функціональних рядів.Efficient introduction of composites in modern technological processes requires to be aware of their physical-technological parameters, foremost in stationary operating regimes, in which they operate after sharp temperature or power load. It results in thermomechanic problems of the lump – homogenous media. In practice even in the simplest model problems the values, which characterise the stationary state, are expressed as polyparametric functional set, which can be adjacent conventionally in the condition, when it represents the analytical function. It follows, that the functional set is reasonable to be replaced by its adjacent result, which is of special importance for the engineering calculations. Solution of the separate system of the Fourier, Legendre and Eulerian differential equations is based on the three-component segment of the polar axis with the boundary conditions and conjugation conditions taking advantage of the Cauchy functions method. With this purpose at first the fundamental system of these equations solutions was obtained, and the boundary conditions the conjugation conditions result in heterogonous algebraic system, which consists of six equations, to find the values Aj, Bj, the determinant of which does not equal zero. The main solutions of the boundary problem, which are caused by the boundary conditions for the Green function and heterogeneity of the conjugation conditions, were found. The solution of this boundary problem is built by the method of the relative finite hybrid integral transformation. Polyparametric family of the functional sets has been summarised while comparing these solutions

Eikonal algebra on a graph of simple structure

An eikonal algebra ${\mathfrak E}(\Omega)$ is a C*-algebra related to a metric graph $\Omega$. It is determined by trajectories and reachable sets of a dynamical system associated with the graph. The system describes the waves, which are initiated by boundary sources (controls) and propagate into the graph with finite velocity. Motivation and interest to eikonal algebras comes from the inverse problem of reconstruction of the graph via its dynamical and/or spectral boundary data. Algebra ${\mathfrak E}(\Omega)$ is determined by these data. In the mean time, its structure and algebraic invariants (irreducible representations) are connected with topology of $\Omega$. We demonstrate such connections and study ${\mathfrak E}(\Omega)$ by the example of $\Omega$ of a simple structure. Hopefully, in future, these connections will provide an approach to reconstruction.Comment: 38 pages, 11 figure

Canonical form of C∗C^*-algebra of eikonals related to the metric graph

The eikonal algebra $\mathfrak E$ of the metric graph $\Omega$ is an operator $C^*$--algebra defined by the dynamical system which describes the propagation of waves generated by sources supported in the boundary vertices of $\Omega$. This paper describes the canonical block form of the algebra $\mathfrak E$ of an arbitrary compact connected metric graph. Passing to this form is equivalent to constructing a functional model which realizes $\mathfrak E$ as an algebra of continuous matrix-valued functions on its spectrum $\widehat{\mathfrak{E}}$. The results are intended to be used in the inverse problem of reconstruction of the graph by spectral and dynamical boundary data. Bibliography: 28 items

Equation level matching: An extension of the method of matched asymptotic expansion for problems of wave propagation

We introduce an alternative to the method of matched asymptotic expansions. In the "traditional" implementation, approximate solutions, valid in different (but overlapping) regions are matched by using "intermediate" variables. Here we propose to match at the level of the equations involved, via a "uniform expansion" whose equations enfold those of the approximations to be matched. This has the advantage that one does not need to explicitly solve the asymptotic equations to do the matching, which can be quite impossible for some problems. In addition, it allows matching to proceed in certain wave situations where the traditional approach fails because the time behaviors differ (e.g., one of the expansions does not include dissipation). On the other hand, this approach does not provide the fairly explicit approximations resulting from standard matching. In fact, this is not even its aim, which to produce the "simplest" set of equations that capture the behavior

УСУНЕННЯ ПОХИБКИ КОНТУРУ РЕГУЛЮВАННЯ СТРУМУ БАГАТОФУНКЦІОНАЛЬНОГО ОДНОФАЗНОГО МЕРЕЖЕВОГО ІНВЕРТОРА

Purpose. Elimination of the error of the inverter current control loop by improving its structure and justifying the parameters, which will ensure compliance with the current quality standard at the common coupling to the distribution grid of the load and the multi-functional grid inverter at the output of the renewable source of electrical energy. Methodology. Synthesis of structure of current control loop based on analysis of processes in electrical circuits and computer simulation. Results. Relationships for determining the input voltage of the inverter, reactor inductance and modulation frequency in accordance with the grid voltage, the maximum values of the inverter current and the amplitude of its ripple when combining the function of the active power filter. Dependencies of the amplitude of the pulsations of the output current of the inverter and the errors in the fundamental harmonic in accordance with the voltage at the input of the inverter, the modulation frequency and inductance of the output reactor are obtained. Originality. The structure of the inverter current control loop has been improved with a combination of proportional, integrating and differentiating links, and their parameters have been determined to ensure compensation of the disturbing action on input of the reference and compensation of the error of current from the disturbing action of the grid voltage regardless of its value. Practical value. The obtained solutions are the basis for the design of converters of electric power systems with renewable sources of electricity with improved energy efficiency. Мета. Усунення похибки контуру регулювання струму інвертора шляхом удосконалення його структури та обґрунтування параметрів, що сприятиме відповідності стандарту якості струму в точці підключення до розподільчої мережі навантаження і багатофункціонального мережевого інвертора на виході поновлювального джерела електроенергії. Методика. Синтез структури контуру регулювання струму на базі аналізу процесів у електричних колах з використанням комп’ютерного моделювання. Результати. Одержані залежності амплітуди пульсацій вихідного струму інвертора і похибки за основною гармонікою від напруги на вході інвертора, частоти ШІМ і індуктивності реактора. Співвідношення для визначення значень вхідної напруги інвертора, індуктивності реактору та частоти ШІМ згідно напрузі мережі, максимальних значень струму інвертора та амплітуди його пульсацій за суміщенням функції силового активного фільтра. Наукова новизна. Удосконалено структуру контуру регулювання струму зі сполученням пропорційної, інтегруючої та диференціючої ланок і визначені їх параметри для забезпечення компенсації збурюючої дії за завданням і компенсації похибки струму від збурюючої дії напруги мережі незалежно від її значення. Практичне значення. Отримані рішення є основою для проектування перетворювачів для систем з поновлювальними джерелами електроенергії з покращеною енергоефективністю

Simulation of epoxicomposites structures optical characteristics with operator transformations parameters

Розглянуто науково-практичну проблему створення композитних матеріалів і покриттів на їх основі з підвищеними експлуатаційними характеристиками шляхом дослідження структур зон міжфазної взаємодії в процесі тверднення епоксикомпозитів. Встановлено закономірності кінетики формування зовнішніх поверхневих шарів як прояву таких зон залежно від умісту, дисперсності й фізико-хімічної природи введеного у зв’язувач наповнювача та видано рекомендації щодо прогнозованого регулювання властивостями cформованих матеріалів. Обгрутовано вплив структурних характеристик і геометричних параметрів зовнішніх поверхневих шарів у матриці навколо частинок наповнювача на фізико-механічні характеристики композитного матеріалу.The theoretical and practical problem of composite materials and coatings creating with improved performance by studying the band structure of the interphase interactions during the curing epoxycomposites was considered. There were established the regularities of formation cinetics of the outer surface layers, as a manifestation of such zones. They depend on the content, dispersion and physico- chemical nature of the introduction in the filler and the type of recommendations for management of the predicted properties of generated materials. There was investigated and substantiated the influence of structural characteristics and geometric parameters of the outer surface layers of the matrix around the filler particles and fibers on the dynamics of physical and mechanical char-acteristics of cross-linking of the composite material. A mathematical model of resource in the process of curing epoxycomposites based was builed on the methodology defined boundaries and visualization of spatial clusters of external potentials of the surface layers of dispersed filler. It made the possibility to assess the characteristics of the main stages of the dynamics around dispersed particles microstructures in the volume of the filler matrix composite. It has been hypothesized about the decisive influence of the areas geometric parameters of interfacial interaction on changes in physical and mechanical properties of the filled epoxy composites was . This approach is based on well-developed views, including academician Lipatov Y. S., influence of the solid surface on the kinetics of the formation, morphology, intra - and intermolecular bonds, on the topology of the nets, etc. and, in the end, on the final properties of the polymer matrix. The results of these studies will be used in the development of technology of formation materials and coatings based on them

Simulation of epoxicomposites structures optical characteristics with operator transformations parameters

Розглянуто науково-практичну проблему створення композитних матеріалів і покриттів на їх основі з підвищеними експлуатаційними характеристиками шляхом дослідження структур зон міжфазної взаємодії в процесі тверднення епоксикомпозитів. Встановлено закономірності кінетики формування зовнішніх поверхневих шарів як прояву таких зон залежно від умісту, дисперсності й фізико-хімічної природи введеного у зв’язувач наповнювача та видано рекомендації щодо прогнозованого регулювання властивостями cформованих матеріалів. Обгрутовано вплив структурних характеристик і геометричних параметрів зовнішніх поверхневих шарів у матриці навколо частинок наповнювача на фізико-механічні характеристики композитного матеріалу.The theoretical and practical problem of composite materials and coatings creating with improved performance by studying the band structure of the interphase interactions during the curing epoxycomposites was considered. There were established the regularities of formation cinetics of the outer surface layers, as a manifestation of such zones. They depend on the content, dispersion and physico- chemical nature of the introduction in the filler and the type of recommendations for management of the predicted properties of generated materials. There was investigated and substantiated the influence of structural characteristics and geometric parameters of the outer surface layers of the matrix around the filler particles and fibers on the dynamics of physical and mechanical char-acteristics of cross-linking of the composite material. A mathematical model of resource in the process of curing epoxycomposites based was builed on the methodology defined boundaries and visualization of spatial clusters of external potentials of the surface layers of dispersed filler. It made the possibility to assess the characteristics of the main stages of the dynamics around dispersed particles microstructures in the volume of the filler matrix composite. It has been hypothesized about the decisive influence of the areas geometric parameters of interfacial interaction on changes in physical and mechanical properties of the filled epoxy composites was . This approach is based on well-developed views, including academician Lipatov Y. S., influence of the solid surface on the kinetics of the formation, morphology, intra - and intermolecular bonds, on the topology of the nets, etc. and, in the end, on the final properties of the polymer matrix. The results of these studies will be used in the development of technology of formation materials and coatings based on them

Defining the Objectives of Testing for Correct Interpretation of Its Results

One of the most important stages of the test development - the goal-setting stage - is considered. As a research task the authors determined the evaluation of the study of the problem of goal-setting in the pedagogical literature and literature on testology. The authors prove that the quality of the test content depends on the results of the goal-setting stage. The idea that the purpose of testing is important for the correct interpretation of its results is also approved. Based on the analysis of the literature on testology, the authors conclude that, creating a test, the developer sets a task to display in its content the main thing that students should know as a result of training, and it is necessary to structure the objectives of the test control. The description of different types of learning objectives is given. The levels of assimilation of knowledge distinguished by different researchers are listed. Recommendations are given for the correct formulation of the test objectives. Attention is paid to the knowledge, skills and learned methods of activity that can be checked using tests. The authors of the article come to the conclusion that the definition of the goals of testing is necessary in order to clarify what students’ results will be evaluated using the test

Development of plastic areas in angle points zone under concentrated force

Отримано аналітичний розв’язок антиплоскої пружно-пластичної задачі про розвиток пластичних шарів для ідеально пружно-пластичної смуги з кутовими точками на її межі. Знайдено довжину пластичних шарів залежно від величини зосередженої сили, прикладеної на великій відстані від вершин кутів. Визначено критичне навантаження, за якого настає пластичне руйнування смуги.Investigations of plastic areas in the strain concentrators threshold is still the main problem of solid body mechanics and fracture mechanics. They are important because of wide introduction into engineering practice high-plastic materials with high fracture toughness in which while operating considerable plastic deformation can occur. Analytical solution of anti-plane elasto-plastic problem for the ideal elasto-plastic area with angular points on its edges was obtained. Plastic deformations are considered to be localized in the layers of zero thickness on the notch angles bisectrices. The length of plastic layers as the function of concentrated force applied in great distance from angle apexes was found. Maximum load value was found under which the layers coincide, developing from the opposite notch tips and the area loses its load resistance. The less is the angle on notch tips, the less is maximum load. When the notch angle equals zero (the notch changes into mathematical section) it is minimum and equals 78% of the critical load for smooth zone. When the angle value in notch tips approaches its maximum acceptable value 90°, under which angular points disappear and zone edges become smooth, plastic areas gradually disappear as well and stress-strained state gradually becomes homogeneous. Simple formulae for the plastic layer lengths dependence on loading according to the plastic area linear model (PALM) were reduced. Their analysis testified the high accuracy of this model. For steel 0,3X14H7B with shearing yield limit 688 mPa the PALM will provide accuracy not less than 5% until the average shearing load in the zone cross-section does not exceed 75,5 mPa. Carried out investigations consider the case of maximum possible interaction of stress concentrators – the distance between concentrators in infinitely small in comparison with their dimensions. As concentrators interaction decreases the plastic area linear model accuracy, it is reasonable to consider the obtained estimations of accuracy to be the highest and not to be decreased under weaker interactions

Clinician and carer moral concerns when caring for children who tube-feed.

Child healthcare can be vexed by moral concerns - this extends to the care of children who tube-feed. Children who tube-feed often receive care from family members and clinicians of various disciplines. Each brings expertise, experiences, values, and views to a situation, prioritising the child's needs while attending to those they deem important in potentially disparate ways. Their understanding of a situation is shaped by beliefs, feelings, and perceptions. How then are key decisions made about the care of a child who tube-feeds? This article explores clinicians' and carers' moral concerns when caring for children who tube-feed. Interviews with clinicians (n = 9) and carers (n = 9) clarified three findings: first, there are often disparate beliefs about the need for tube-feeding; second, tube-feeding can evoke strong emotions; and third, it can be difficult to normalise tube-feeding. This article demonstrates how challenges can emerge when relationships between clinicians and carers diverge. Furthermore, it establishes how an ethic of care can bring different interests together to bolster the relationships required to optimise feeding care and promote health outcomes among children who tube-feed and their carers. This requires improved dialogue between and among clinicians and carers to create shared understandings of what is, what should be, and how to benefit children who tube-feed