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the most effective types of control over competitive activities is expert evaluation. Purpose of the study is to develop a methodology for expert assessment of competitive activities of highly qualified field hockey players. Material and methods. The study involved 16 highly qualified field hockey players, aged from 19 to 37 years. The average age of the players is 27.3±5.06 years. Sports Qualification: Master of sports of Ukraine. All players were given informed consent to participate in the study. The study was conducted in 2024 during the 2024 Olympic field hockey qualification competition (the city of Valencia, Spain). The research was carried out on the basis of the following methods: theoretical analysis and generalization of scientific and methodological literature; pedagogical observation; video recording of competitive activities; method of expert assessments; methods of Mathematical Statistics. Results. The author's methodology for expert assessment of competitive activity of field hockey players has been developed based on a 10-point scale, consisting of 5 criteria in the ball ownership phase and 5 criteria in the ball picking up phase. Each of the criteria is rated from 1 to 10 points. The fluctuation of the average values of the expert assessment of players of the national team of Ukraine in the matches of the Olympic qualification 2024 is in the range from 4.2±0.45 to 6.6±0.49 points. Conclusions. The developed methodology of expert assessment of competitive activity of highly qualified field hockey players is appropriate for effective management influences in the process of competitive activity of club and national teams in the Olympic sport – field hockey.

We propose an adaptive method for building a multivariate regression given by a weighted linear convolution of known scalar functions of deterministic input variables with unknown coefficients. As, for example, when multivariate regression is given by a multivariate polynomial. In contrast to the general procedure of the least squares method that minimizes only a single scalar quantitative measure, the adaptive method uses six different quantitative measures and represents a systemically connected set of different algorithms which allow each applied problem to be solved on their basis by an individual adaptive algorithm that, in the case of an active experiment, even for a relatively small volume of experimental data, implements a strategy of a statistically justified solving. The small amount of data of the active experiment we use in the sense that, for such an amount, the variances of estimates of unknown coefficients obtained by the general procedure of the least squares method do not allow to guarantee the accuracy acceptable for practice. We also proposed to significantly increase the efficiency of the proposed by O. A. Pavlov. and M. M. Holovchenko modified group method of data handling for building a multivariate regression which is linear with respect to unknown coefficients and given by a redundant representation. We improve it by including some criteria and algorithms of the adaptive method for building a multivariate regression. For the multivariate polynomial regression problem, the inclusion of a partial case of the new version of the modified group method of data handling in the synthetic method proposed by O. A. Pavlov, M. M. Golovchenko, and V. V. Drozd, for building a multivariate polynomial regression given by a redundant representation, also significantly increases its efficiency.

In this paper, we address the stabilization problem for nonlinear systems in a critical case. Namely, we study the class of canonical nonlinear systems. Canonical nonlinear systems or chain of power integrators is an important subject of research. Studying such systems is complicated by the fact that they cannot be mapped onto linear systems. Moreover, they have the uncontrollable first approximation. Previous results on smooth stabilization of such systems were obtained under the assumption that the powers in the right-hand side are strictly decreasing. In this work, we consider a case of non-increasing powers in the right-hand side for a three-dimensional system. A popular approach for studying such systems is the backstepping method, which is a method of step-wise stabilization. This method requires a sequential investigation of lower-dimensional subsystems. Backstepping enables the study of a wide range of nonlinear triangular systems but requires technically complex and cumbersome computations. Therefore, a natural question arises about constructing stabilizing controls of a simple form. Polynomial controls can serve as an example of such controls. In the paper, we demonstrate that linear controls can be considered as stabilizing controls. We derive sufficient conditions for the coefficients of the linear control that ensure the asymptotic stability of the zero equilibrium point of the corresponding closed-loop system. The asymptotic stability is proven using the Lyapunov function method, which is found as the sum of squares. The negative definiteness of the Lyapunov function derivative in a neighborhood of the origin guarantees asymptotic stability. In contrast to the case of strictly decreasing powers, additional conditions on the control coefficients, apart from their negativity, emerge. The obtained result extends to a broader class of nonlinear systems through stabilization by nonlinear approximation. This allows the consideration of systems with higher-order terms in the right-hand side. The effectiveness of the applied approach is illustrated by several model examples. The method used in this work to investigate the case of non-increasing powers can be applied to systems of higher dimensions.

Стаття присвячена формуванню нових наукових рішень щодо пошуку шляхів трансформації процесів планування та управління фінансами на підприємствах України як реакції на економічні виклики у країні. Доведено, що українські підприємства потребують трансформації процесів планування та управління фінансами і внесення змін у системні елементи планової та управлінської діяльності (мета, завдання, суб’єкти, об’єкти, предмет, умови, принципи, методи). Метою статті є розкриття напрямів трансформації процесів планування та управління фінансами на підприємствах України як реакції на економічні виклики у країні. Методологія: використано комплекс загальних та спеціальних методів на емпіричному і теоретичному рівнях, таких як: метод абстрагування для визначення системних елементів планової та управлінської діяльності підприємств України, що потребують трансформації; метод літературного аналізу для дослідження наукових розробок у сфері планування та управління фінансами на підприємствах; метод порівняння для деталізації трансформації системних елементів планової та управлінської діяльності підприємств України; методи систематизації, групування і логічного узагальнення для систематизації інформації, формування висновків і наукових пропозицій статті. У статті використано системно-функціональний, історичний та системний підходи у розкритті і вирішенні проблематики пошуку напрямів трансформації процесів планування та управління фінансами на підприємствах України як реакції на економічні виклики у країні. Результати: виявлено та запропоновано напрями трансформації процесів планування та управління фінансами на підприємствах України як реакції на економічні виклики у країні з акцентом на внесення змін у системні елементи планової та управлінської діяльності (мета, завдання, суб’єкти, об’єкти, предмет, умови, принципи, методи).

Стаття присвячена формуванню нових наукових рішень щодо пошуку шляхів удосконалення антикризового управління на підприємствах України з врахуванням розвитку галузевих ринків на яких суб’єкти підприємництва здійснюють фінансово-господарську та операційну діяльність. Доведено, що в сучасних умовах кризового розвитку економічної системи країни важливим є розробка та запровадження на вітчизняних підприємствах антикризового управління. Метою статті є формування сукупності заходів щодо оптимізації розробки та запровадження антикризового управління підприємствами України з врахуванням особливостей галузевих ринків (ринків товарів і ресурсів) на яких суб’єкти підприємництва здійснюють фінансово-господарську та операційну діяльність. Методологія: використано комплекс загальних та спеціальних методів на емпіричному і теоретичному рівнях, таких як: метод абстрагування для формування визначень термінів «антикризове управління на підприємстві» та «галузевий ринок (ринок товарів та ресурсів)»; методи аналізу та синтезу для формування сукупності заходів щодо оптимізації розробки та запровадження антикризового управління підприємствами України; метод порівняння для деталізації заходів антикризового управління для різних груп підприємств (галузевий лідер, галузевий переслідувач/переслідувачі, галузеві послідовники, «нішеві» підприємства); методи систематизації, групування і логічного узагальнення для систематизації інформації, формування висновків і наукових пропозицій статті. У статті використано системно-функціональний, історичний та системний підходи у розкритті і вирішенні проблематики удосконалення антикризового управління на підприємствах України з врахуванням розвитку галузевих ринків (ринків товарів та ресурсів). Результати: виявлено напрями оптимізації антикризового управління на підприємствах України з врахуванням розвитку галузевих ринків на яких суб’єкти підприємництва здійснюють фінансово-господарську та операційну діяльність.

Due to the importance of innovations as a factor for economic growth and competitiveness, ensuring their sustainable development is a universal task for the country. The most intense race for innovation is observed among countries striving for global dominance. This article is dedicated to the study of the specific features of innovation development in the United States, where innovative potential has become one of the cornerstones of their economic strategy and a key driver of their success. The United States has significant distinctions from other countries in terms of culture, institutions, economic organizations, economic regulation, etc., which together create the basic conditions for innovation and require consideration. The focus on innovation development in the United States is driven by intensified competition with other global players, particularly from China. The main goal of the research is to summarize and characterize the systemic features of innovation development in the United States, as well as to identify the key factors intensifying innovation productivity in the country. The study of the systemic features of innovation development in the United States covered the analysis of 1) civilizational factors; 2) institutional system; 3) economic system; 4) innovation system; 5) state innovation policy. The main factors intensifying innovation productivity in the United States were identified as the combination of entrepreneurial and large-scale capitalism, venture capital investment, and territorial agglomerations of innovative structures. The need to consider the peculiarities of innovation generation in the military sector, universities, and non-profit organizations has been justified. The strength of the United States innovation system has been statistically demonstrated, however, the increasing competition in science and innovation from China has been confirmed. This has led to the intensification and change in the type of state innovation policy in the United States, with a focus on targeted support for innovation in industry in the context of the green transition.

Протягом останніх років автори в своїх публікаціях паралельно розвивали два різних підходи до побудови багатовимірних поліноміальних, зокрема, лінійних регресій, заданих надлишковим описом. Перший підхід дозволяв знаходження оцінок коефіцієнтів при нелінійних членах багатовимірної поліноміальної регресії зводити до побудови послідовності одновимірних поліноміальних регресій та розв’язання відповідних невироджених систем лінійних рівнянь. Другий підхід був реалізований на прикладі багатовимірної лінійної регресії, заданої надлишковим описом, і привів до створення методу, названого авторами модифікованим методом групового урахування аргументів (МГУА), так як він є модифікацією широко відомого методу евристичної самоорганізації МГУА (автор МГУА – академік НАН України О. Г. Івахненко). Модифікація полягає в тому, що завдання багатовимірної лінійної регресії надлишковим описом дозволяє для побудови множини часткових описів, один з яких має структуру шуканої регресії, використовувати не багаторівневий селекційний алгоритм, а ефективний алгоритм розбиття коефіцієнтів багатовимірної лінійної регресії на два класи. Як і в класичному МГУА, розв’язок знаходиться за допомогою перевірочної послідовності даних. Цей метод легко поширюється на випадок багатовимірної поліноміальної регресії, так як невідомі коефіцієнти в багатовимірну поліноміальну регресію входять лінійно. Кожен з двох підходів має свої переваги і недоліки. Очевидним наступним кроком є поєднання обох підходів в один. Це призвело до створення синтетичного методу, який реалізує переваги обох підходів, частково компенсуючи їх недоліки. В цій роботі наведена агрегована алгоритмічна структура синтетичного методу, теоретичні властивості часткових випадків і, як наслідок, обґрунтування його ефективності в цілому.

Any surgical intervention is associated with the possible development of complications. Surgical complications are traditionally an unpopular topic for discussion, but in recent decades they have received increased attention, due to both medical and economic factors. This review discusses the general concepts that characterize the negative consequences of surgical interventions in spinal neurosurgery: complications, adverse events, sentinel events, never events, collateral adverse outcomes. Classifications are given that allow systematizing these negative phenomena. Surgical treatment of the lumbar disk herniation is the most frequently performed spinal surgery. The true number of lumbar discectomies is difficult to estimate because this procedure is often not an isolated surgical intervention, but a step in a larger one. Being a routine surgical procedure, discectomy, performed in one or another way depending on the preferences of the surgeon and available equipment, is characterized by a rather low relative frequency of adverse events and complications compared to other types of spinal surgery. However, due to the significant number of interventions, the absolute figures may present a medical and economic problem. Most authors refer to the classic triad of “wrong level, wrong side, wrong patient” and foreign bodies in the area of surgical intervention as obvious medical errors. Damage to the intestine or peritoneum, trauma to the great vessels and trauma to the nerve roots are considered serious complications, but not always medical errors. The other most commonly reported adverse events of lumbar discectomy are durotomy, neurological complications, surgical wound complications, recurrent disc herniation, and reoperation. Until now, no clear classification of the negative consequences of lumbar discectomy, which would allow to verify the relationship between intraoperative adverse events (both surgical and anesthetic) and postoperative complications has been developed. In addition, it is extremely difficult, based on the criteria available in the literature, to identify a medical error in a number of iatrogenic complications, which requires further comprehensive study of the problem, since it has not only medical, but also legal consequences.

Стаття присвячена формуванню нових наукових рішень щодо пошуку шляхів підвищення ефективності, результативності та інклюзивності соціальної та економічної допомоги для військових та членів їх родин у воєнний та пост воєнний період. Доведено, що ключовою проблемою та викликом, що буде супроводжувати розвиток національної соціально-економічної системи у найближчі десятиріччя є економічна адаптація та соціальна допомога військовим і членам їх родин. Метою статті є розробка сукупності заходів та інструментів соціально-економічної підтримки і адаптації військових та членів їх родин під час війни України проти росії і після її закінчення. Методологія: використано комплекс загальних та спеціальних методів на емпіричному і теоретичному рівнях, таких як: метод абстрагування для відбору напрямів надання допомоги військовим та членам їх родин; методи аналізу та синтезу для побудови матриці забезпечення соціальною та економічною допомогою різних категорій військових і членів їх сімей; метод порівняння для визначення суб’єктів, яких можливо залучити до надання соціальної і/або економічної допомоги військовим та члени їх сімей; методи систематизації, групування і логічного узагальнення для систематизації інформації, формування висновків і наукових пропозицій статті. У статті використано системно-функціональний, історичний та системний підходи у розкритті і вирішенні проблематики надання допомоги військовим та членам їх родин у воєнний і поствоєнний час в Україні. Результати: виявлено ключові можливості забезпечення соціальної та економічної допомоги військовим і членам їх родин у воєнний та післявоєнний час з врахуванням об’єктивних складнощів держави і місцевих органів влади надавати таку допомогу.

Asigurarea masei probatorii este o provocare permanentă a organului de urmărire penală în procesul penal. Această provocare este materializată prin dorința făptuitorului/criminalului de a distruge probele care dovedesc vinovăția acestuia. În cadrul investigării infracțiunilor de criminalitate organizată acest pericol este mai iminent datorită modalităților de acționare a grupărilor şi organizațiilor criminale şi anume violența, cruzimea şi teroarea. De secole declarațiile persoanelor în privința cărora au fost îndreptate acțiunile criminale sau cei care au fost martori a aplicării acestor acțiuni au constituit cele mai viabile probe într-un proces penal. Reieșind din importanța și greutatea probelor date, acțiunile organizațiilor criminale în permanență au fost îndreptate în privința influențării şi distrugerii acestora. Anume acest fapt a determinat legislatorul să vină cu o poziție fermă în acest sens pentru asigurarea protecției de stat a persoanelor ce conlucrează cu organul de urmărire penală în vederea tragerii la răspundere penală a vinovaților.

Стаття присвячена формуванню нових наукових рішень щодо ідентифікації ключових соціально-економічних викликів для України у воєнний та пост воєнний період. Доведено, що російська військова агресія та терористичні атаки проти цивільного населення України з боку російської армії породжують нові, переважно негативні, виклики соціально-економічні системі країни, які будуть мати вплив на систему і у пост воєнний час. Метою статті є виявлення та характеристика викликів соціально-економічній системі України на макро-, мезо-, мікрорівнях у воєнний і післявоєнний час, а також розробка рекомендацій щодо усунення або зменшення впливу негативних викликів на економіку та соціальну сферу країни. Методологія: використано комплекс загальних та спеціальних методів на емпіричному і теоретичному рівнях, таких як: метод абстрагування для відбору рівнів проведення оцінки; методи аналізу та синтезу для виявлення ключових соціально-економічних викликів для України у воєнний та пост воєнний період; порівняння для визначення негативного впливу соціально-економічних викликів та розробки рекомендацій щодо його усунення на макро-, мезо, мікрорівнях в країні; методи систематизації, групування і логічного узагальнення для систематизації інформації, формування висновків і наукових пропозицій статті. У статті використано системно-функціональний, історичний та системний підходи у розкритті та вирішенні проблематики виявлення соціально-економічних викликів України у воєнний та поствоєнний час. Результати: виявлено ключові соціально-економічні виклики України у воєнний та поствоєнний час, а також їх негативний вплив на економіку та соціальну сферу країни на макро-, мезо-, мікрорівнях і сформована сукупність рекомендацій зі зменшення або усунення негативного впливу виявлених викликів.

Mixing processes are found in the chemical, pharmaceutical and food industries. Fluid mixing is one of the fundamental scientific problems associated with modern concepts of regular and chaotic dynamics. The paper considers the problem of mathematical modeling of the quasi-stationary process of mixing a viscous mixture. This problem consists of two sub-problems: determination of the velocity field in the flow region (Eulerian formalism) and investigation of the trajectories of individual fluid particles (Lagrange formalism). To solve the first subproblem, it is proposed to jointly use the principle of superposition, the structural method (method of R-functions) and the Ritz variational method. The methods of nonlinear dynamics and qualitative theory of differential equations are used to solve the second subproblem. A plane quasi-steady flow is considered in a rectangular region and it is assumed that the side walls are at rest, and the upper and lower walls move alternately according to the given laws. According to the method of R-functions, the structures of the solutions were built and the use of the Ritz variational method for the approximation of the uncertain components of the structures was justified. The operation of the proposed method is illustrated by the results of a computational experiment, which was conducted for different modes of wall motion. The practical interest of the considered regimes is due to the fact that they lead to the emergence of chaotic behavior when mixing occurs most efficiently. Using the methods of nonlinear dynamics, the location of periodic (hyperbolic and elliptical) points was investigated and the Poincaré section was constructed. Further research with the help of the method proposed in the work can be related to the consideration of flows in more geometrically complex regions and more complex mixing regimes, as well as in the application to the calculation of industrial problems.

A number of scientific works of Prof. O. A. Pavlov and his disciples is devoted to the development of an original method of efficient estimation of coefficients at nonlinear terms of multivariate polynomial regression given by a redundant description under the conditions of an active experiment. The solution of the formulated problem is reduced to the sequential construction of univariate polynomial regressions (finding efficient estimates for the coefficients at nonlinear terms) and solving the corresponding systems of linear nondegenerate equations, the variables of which are the estimates for coefficients at nonlinear terms of the multivariate polynomial regression given by the redundant description. Thus, the problem was reduced to the estimation of the coefficients at linear terms of a multivariate linear regression given by a redundant description in the conditions of an active experiment. We have proposed an original method of its solution that uses a cluster analysis algorithm. The algorithm’s implementation significantly reduces the enumeration of partial descriptions of multivariate linear regression followed by the finding of the residual sum of squares for each of them. This allows using the chi-squared criterion to build a linguistic variable which value gives a qualitative assessment (high reliability, acceptable reliability, low reliability, unreliability) to the obtained result. The analysis of the computational experiments made it possible to modify the proposed method, which significantly increased its efficiency, first of all, of finding a reliable structure of the sought multivariate linear regression given by the redundant description. The method modification, in particular, has reduced the enumeration of partial descriptions and has led to a more efficient use of the general procedure of the least squares method.

the problem of tibial bone non-unions after fractures is an actual and not finally solved problem. The use of ring spoke-rod devices is the leading method of treatment. Improvement of this technology is a generally accepted direction to improve the results of treatment. The aim of the work was to improve the results of the treatment of non-unions of the lower leg bones based on the improvement of the fixation technology of ring retainers. In order to fulfill the task of the research, the problematic issues of fixation of non-unions of lower leg bones after fractures with spoke-rod ring devices were studied; the formulated concept of solving the existing shortcomings of the method in the experiment; clinical applications and analysis of the obtained results. The influence of the spatial fixation of the rod in the ring fixator of the spoke-rod type was determined experimentally. The subject of the study was a Sawbones® synthetic bone with a fracture model, which was fixed with a ring fixator of the spoke-rod type by 2 models. In our "apparatus-bone" fixation experiment, all the main parameters of both models (number of rings, spokes, angles of intersection of spokes and fracture planes) were similar. The difference between the two models was only in the presence or absence of a stiffener for fixing the rod. 60 victims met the criteria for inclusion in the study. 31 patients were operated on with the use of ring devices with increased rigidity of rod fixation according to the proposed method; they formed the main group. 29 patients - the comparison group, the treatment was carried out according to the generally accepted method using fixation of the rod without a rib of "stiffness". Clinical evaluation of the results was carried out using the anatomic-functional scale of the Modified Functional Evaluation System by Karlstrom-Olerud. The obtained experimental data indicated an improvement in the stiffness parameters of the spoke-rod system when using rod fixation with a stiffening rib. The greatest effect was obtained during the bending test - the indicator increased from 0.91 to 1.19 H/mm (by 23.53%). The results of clinical effectiveness obtained by us (good and excellent 77.8%; unsatisfactory in 2.8%) can be compared with the data of most researchers. Anatomic-functional results in the main group with a high probability (95%) exceeded the results in the comparison group. Experimental data were confirmed by clinical results. The anatomic-functional results in the main group according to the values of the estimated anatomic-functional scale of the Modified Functional Evaluation System by Karlstrom-Olerud with a high probability (>95%) exceeded the results in the comparison group. Bearing in mind the severity of the lesion, we consider the obtained clinical results to be encouraging. Application of the proposed improvements and further investigation of their effectiveness should be recommended.

The purpose of this article is to consider the cosmopolitan aspect of Yuri Kuznetsov’s early works. Kuznetsov was the Russian poet of the 2nd half of the 20th century. The main method of research for us is the method of ontological poetics, and elements of interdisciplinary and comparative analysis. It allows us to consider an artistic text in the context of consciousness and subconsciousness, archetypes and phenomena of the surrounding being. They, in turn, form a personal author’s myth. Yuri Kuznetsov creates his own poetic myth based on the real events of his own biography. In particular, the phenomenon of war has a key influence on it. The author is a “children of war” generation representative (born in 1941). His father died at the front in 1944. This fact determines Yuri Kuznetsov’s further outlook and path in literature. The article examines a number of the poet’s early poems. The opposition of Nature and War concepts can already be traced to each other at this stage. The latter is portrayed as an unnatural phenomenon that hinders the development of personality. Nature symbolizes life and natural dynamics, and War symbolizes halt and death, lack of dynamics. It comes into direct conflict with the laws of Nature. The leitmotif of the poet’s early work is the idea of man and nature’s unity. Such unity, in the end, allows us to build a progressive cosmopolitan model of the Home-Universe. It consists of three parts: Family-Home, Motherland-Home, and Planet-Home. The cosmopolitan orientation of Yuri Kuznetsov’s poems is manifested in his craving for the idea of “world citizenship”. At the same time, the fundamentally important fact is not the rejection of the Motherland and one’s own cultural identity, but their inclusion in a common threefold ontological model. The article also attempts to compare Yuri Kuznetsov’s work with the ideas of Russian symbolism representatives of the early 20th century. Conclusion. Based on the interdisciplinary analysis of the literary text, here are the following research results: 1. In poet Yuri Kuznetsov’s early works there is a process of upward movement along the vertical axis: from the personal myth and the lyrical “I/me” to the universal human experience. The latter, at the same time, is a unifying factor leading to the formation of an anti-war position. 2. The poet’s early works use cosmopolitan motives in the context of the verb “to create” which is semantically equivalent to the verbs “to generate” and “to build”, as well as connotatively close to the ontological processes of dynamics and movement. The verb “to create” is also opposed to the concept of War and is considered as part of the author`s anti-war position. Creativity acts both as an anti-destructive manifesto and as a means of uniting elements of the artistic world scattered by war. We should note that the author’s artistic world is closely connected with his biography and personal family history. 3. Through creativity Yuri Kuznetsov attempts to comprehend the phenomenon of War in three interdependent contexts: family, country and planet (“all people”). This approach allows us to come to the conclusion that war is incompatible with the natural course of things, that is, in fact, with the laws of Nature. 4. The sphere of the unconscious plays a key role in the formation of the author’s anti-war position and the stepped three-part model of the House. One more important connotation of the verb “to create” is connected with it. This connotation can be defined as the process of integrating the personal author’s unconscious into the collective unconscious (“great”). At the same time, a prerequisite for successful integration is a “storm”, a certain dynamic involving vertical ascent. The conclusions of such integration lead the author to the idea of “world citizenship” and universal interconnection. This, in turn, forms an anti-war position based on the similarity of the two sides in the “friend-foe” opposition.

Стаття присвячена формуванню нових наукових рішень щодо удосконалення управління конкурентоспроможністю суб’єктів господарювання в Україні під впливом змін у зовнішньому та внутрішньому середовищі, які викликані військовими діями на території країни. Доведено, що українські підприємства потребують внесення суттєвих змін в управління конкурентоспроможністю задля забезпечення відповідного рівня супротиву конкурентам на внутрішніх та зовнішніх ринках збуту продукції (робіт, послуг). Метою статті є формування сукупності шляхів трансформації управління конкурентоспроможністю на підприємствах України в умовах російської військової агресії з врахуванням наявності негативних та позитивних внутрішніх і зовнішніх фактори впливу на великі, середні, малі та мікро вітчизняні підприємства. Методологія: використано комплекс загальних та спеціальних методів на емпіричному і теоретичному рівнях, таких як: метод абстрагування для відбору груп підприємств для проведення дослідження; методи аналізу та синтезу для виявлення ключових зовнішніх і внутрішніх факторів позитивного та негативного впливу на управління конкурентоспроможністю підприємствами України; порівняння для визначення особливостей управління конкурентоспроможністю на підприємствах різних груп в країні (великі, середні, малі, мікро); методи систематизації, групування і логічного узагальнення для систематизації інформації, формування висновків і наукових пропозицій статті. У статті використано системно-функціональний, історичний та системний підходи у розкритті та вирішенні проблематики управління конкурентоспроможністю на підприємствах України в умовах російської військової агресії. Результати: розроблена сукупність шляхів трансформації управління конкурентоспроможністю на українських суб’єктах підприємницької діяльності в умовах російської військової агресії з врахуванням поділу підприємств на великі, середні, малі та мікропідприємства, яка дозволить вітчизняним суб’єктам господарювання вигравати конкурентну боротьбу на внутрішніх та зовнішніх ринках збуту продукції (робіт, послуг).

Introduction. A rapid increase in the number of objects that simultaneously take part in combat operations in the air requires improvement of systems for recognizing military objects both in terms of qualitative and quantitative indicators. This requires the development of appropriate algorithms for identifying new-generation "friend-foe" objects. Such algorithms can be based on various methods of information security, in particular symmetric and asymmetric cryptographic algorithms and other methods of cryptography. The purpose of the article is to survey modern systems of state recognition of objects (SSRO), identify their shortcomings and provide recommendations for their elimination. Results. The requirements for SSRO as a system for processing, transmitting, securing information and identifying objects based on cryptography and computer security methods are defined. Common and distinctive features for civil and military identification systems are highlighted. The advantages and disadvantages of the existing SSRO are shown. Recommendations are formulated to address the shortcomings of the existing SSRO. An example of a stand and a hardware and software basis for studying SSRO algorithms with backup channels is given. Conclusions. Eliminating the shortcomings of the SSRO and improving the level of its reliability will require the implementation of the following organizational and technical measures. 1. Replacing the current state recognition system with a more modern one, which will support more modern cryptographic algorithms and a larger number of recognition objects. Adding support for radio tag recognition (RF tags). 2. Support for recognition lines in various directions, including "ground – UAV", "plane – tank", "plane – UAV" and others. Adding support for the NATO standard – STANAG 4579, adopted in 2001, and others. 3. Using of broad-spectrum signals to reduce the probability of detection and interception, as well as a number of signal-code structures and a working frequency grid.

The increasing importance of innovation as a factor in the effectiveness and competitiveness of companies makes them pay special attention to the processes of obtaining and using knowledge that require special management. International companies, being innovatively active for expansion, are a special subject of knowledge management (KM). In such companies, KM has significant specific features related to their structure, which includes foreign subsidiaries, and the nature of their activities, covering different national markets. Due to the specifics of such companies, they widely use information technology in management and, in particular, use special information tools for KM. The research is aimed to characterize the specific features of KM in international companies and to provide the rationale behind using new information tools for KM, which can be used to improve the effectiveness of innovation. The main focus of the paper is on the specific features of KM in international companies, taking into account their structure and nature of activities, namely: 1) specific features related to the content of the KM, taking into account the number of subsidiaries, the scale of activities, the complexity of tasks, etc.; comparison of the models of internalization and externalization in obtaining new knowledge by companies; 2) specific features related to the internal environment (involvement of all levels of management, multicultural environment, creation of communities of intensive knowledge); 3) specific features related to the external environment, covering interaction with consumers, partners and authorities of different countries; 4) specific features related to the innovative activity (distribution of powers between the parent company and subsidiaries, coordination of research and development (R&D), organization of innovation processes). The global approach of international companies to the development of innovations is substantiated, which determines the content of KM, as well as the need to create a KM system, part of which is information tools. Their improvement allows for enhancing the quality of KM and the effectiveness of innovation. In terms of KM in an international company, the purpose of such information tools as an R&D management information system, a single innovation management platform, a tool for formalizing knowledge, and a corporate knowledge base, is determined. In the future, it is expected to study the effects of the proposed tools, highlight the problems of their introduction and operation, as well as a set of measures to overcome these problems.

We present the methods for constructing a multivariate polynomial given by a redundant representation based on the results of a limited active experiment. We solve the problem in two formulations. The first is the problem of constructing a multivariate polynomial regression given by a redundant representation based on the results of a limited active experiment. The solution method is based on the previous results of Professor A. A. Pavlov and his students showing the fundamental possibility of reducing this problem to the sequential construction of univariate polynomial regressions and solving the corresponding nondegenerate systems of linear equations. There are two modifications of this method. The second modification is based on proving for an arbitrary limited active experiment the possibility of using only one set of normalized orthogonal polynomials of Forsythe. The second formulation refers to the solution of this problem for a particular but sufficient from the practical point of view case when an unknown implementation of a random variable is not added to the initial measurement results during an active experiment. This method is a modification of the solution method for the multivariate polynomial regression problem. Also, we used the main results of the general theory (which reduces the multivariate polynomial regression problem solving to the sequential construction of univariate polynomial regressions and solution of corresponding nondegenerate systems of linear equations) to consider and strictly substantiate fairly wide from the practical point of view particular cases leading to estimating the coefficients at nonlinear terms of the multivariate polynomial regression as a solution of linear equations with a single variable.

In the study of the physicochemical properties of low molecular weight polybutadiene rubber with functional hydroxyl groups (Hydroxyl Terminated Poly Butadien – HTPB), which is a raw material for solid rocket fuel (SRP), an experimental batch of rubber was made and 3 synthesis of experimental batches of low molecular weight polybutadiene rubber with functional hydroxyl groups was carried out. The current work obtains a HTPB physical and chemical characteristics that meet the requirements of regulatory documentation (ND). During this work, the physical and chemical characteristics of HTPB rubber were determined to compliance with regulatory documentation. The readiness of the equipment for conducting the synthesis of HTPB rubber (collector, dispensers, reactor, separator, rotary evaporators, vessel, igniter) was checked. The sequence of execution of technological operations for the synthesis of rubber has been worked out. According to the results of the study, the compliance of the physical and chemical parameters of the obtained raw materials for SPR with the requirements of the ND was established and a conclusion was made about the admission to production. After checking the operability of the main and auxiliary technological equipment, no comments were found. Because of the preparation of technological equipment for the synthesis of HTPB rubber, no comments were found. According to the results of the operations of loading samples into the dispensers and collector, it was found that with a decrease in the volume of butadiene in the container, it is necessary to increase the argon pressure to load it into the collector. According to the results of the operations, filling the reactor with prepared samples of raw materials, no comments were found either. The results of the study of the physicochemical properties of the obtained raw materials for the manufacture of SPR showed almost complete compliance with the requirements of ND, except for the weight loss during drying. Subsequent studies are aimed at modifying the technology for obtaining low molecular weight polybutadiene rubber and studying the physicochemical properties of raw materials for solid rocket fuel.

Subject of study: technologies implemented in modern video coding algorithms to ensure the appropriate level of reliability in the conditions of their compact presentation. The goal is to develop a technology for transforming the alphabet of a video information based on a quantitative criterion while ensuring the required quality in networks. Objectives: to formulate requirements to video images in dynamic video surveillance systems; to analyze the existing factors leading to an imbalance between the compression and quality characteristics of existing video coding algorithms; to develop a technology for transforming the alphabet of a video information based on a quantitative criterion (attribute) for the best presentation of the encoded data; to develop a mathematical model for the formation of a quantitativeindicator for the transformation of the video images; to analyze the effectiveness of using the developed mathematical model for the formation of a quantitative indicator to provide the required trustworthiness of data for the video information resource; to assess the effectiveness of the developed technology for transforming the original message in terms of a quantitative indicator to ensure the best presentation of the encoded data; to investigate the dynamics of the probabilistic and statistical characteristics of the original message as a result of transformation according to the quantitative criterion of the significance of the elements. The research methods: compression coding methods implemented on the basis of the JPEG algorithms. The research results: a new approach has been proposed based on the transformation of the encoded alphabet of data by use of a quantitative criterion. A mathematical model has been developed for the formation of a quantitative attributethat determines the significance of the elements of the original message. Conclusions. A technology has been developed for transforming the alphabet of the original message, which allows creating conditions for a more profitable presentation of the encoded data due to a significant increase in the dynamic range of probabilistic and statistical characteristics for the transformed message while ensuring the required level of video image quality.

Despite the intense competition in business, for successful work, enterprises have to outstrip their competitors not only in terms of technology and indicators of core operating activities, but also in the quality of management systems that ensure a quick response of business entities to changes that occur. Now enterprises are interested in realistically presenting their financial situation not only today, but also in the near future. This is necessary in order to effectively develop its economic activity and timely fulfill its obligations to the state, business partners and other enterprises and organizations. In a market economy, which is characterized by the independence of business entities and the own responsibility of enterprises for the results of financial and economic activities, there is an objective need for constant monitoring, analysis, adjustment and forecasting of changes in the financial condition and assessment of the financial capabilities of the enterprise for the future. The use of budgeting contributes not only to the recovery of those firms where it is used, but also has a great impact on the global processes of strengthening and enriching the national economic system. Therefore, the main purpose of budgeting is to predict the receipts of the enterprise, determine costs, the effectiveness of each economic and financial situation, justify the likely direction of using the financial resources of the enterprise. This is what determines the relevance of our research. A significant contribution to the development and analysis of the methodological, theoretical and practical foundations of budgeting at the enterprise was made by the following domestic and foreign scientists: S. Beloblovsky, M.D. Bilyk, S. Kovtun, S.F. Golov, Z.M. Levchenko and P.V. Ivanyuta, A.A. Tereshchenko, Jailo G. Siegel and Jai K. Shim et al. Based on the relevance and degree of scientific development of the problem, the purpose of the work is to study financial planning at an enterprise, its features and principles of construction, as well as directions for increasing the efficiency of its application. The subject of the research is the financial budgeting of the activities of business entities. To solve all the tasks, such methods were used as analysis and synthesis, generalization to combine the thoughts of different scientists, comparison when considering various classifications of enterprise budgets, description of financial budgets. The informative basis of the research in the course of the study was textbooks and teaching aids, scientific works of leading domestic specialists in the field of theory and practice of financial planning and budgeting, in which a description of financial budgets is given in the most complete and accessible form, conference proceedings. The theoretical provisions, conclusions and proposals developed in the work for assessing the prospects for the development of an enterprise deepen the systemic approaches to their study, and also create the basis for predicting its future financial and economic state and substantiation of possible ways of developing budgeting in the financial planning system at the enterprise.

Over the past 20 years, dairy farms in Ukraine have been actively introducing the keeping of cows in easy-to-assemble premises. However, in a moderate climate (with four distinct year seasons), the issues of microclimate, energy losses of animals and their behavior during the cold period of the year for keeping in such premises have not been fully studied. The purpose of this work was to study the influence of the heat insulation elements use of side curtains in easy-to-assemble premises during the period of low temperatures on microclimate, energy outgoings for thermoregulation and behavior of cows. The research conducted in the central part of Ukraine (Kyiv region). The research was conducted during January-February (29-43 days of the year) 2021. This period characterized by low average daily temperatures of -12.2– -18.7°С, strong wind gusts and daily precipitation in the form of snow. Two easy-toassemble premises for 400 heads were used for research. Parameters of placements (LxWxH): 150х32х10.5 m. The first one was without the use of curtains heat insulation elements, and the second one was with these elements of heat insulation. It was found that the use of polycarbonate wall heat insulation elements had a positive effect on the microclimate in the placement during the period of low temperatures. Indicators of average daily air temperatures in the placement were 3.2 and 8.8°C higher compared to the temperature in the same premise without the use of heat insulation elements and the environment. The wind speed also differed by 0.18 and 11.04 m/s, respectively. In addition, the heat insulation of the walls affected the temperature under the lying cow (+1.8°C), energy outgoings for thermoregulation (-1.93 MJ) and the number of cows that lay in the period of the lowest temperatures (+3.23-9.83%) compared to the placement without heat insulation elements. The difference in temperature of rubber carpet in the compared premises was significant: +3.3°C in the premises with heat insulation elements compared to the premises without heat insulation

The article substantiates and proves the expediency of using economic-mathematical modeling for the formation of a forecast of economic trends and identification of probable ways of development of socio-economic phenomena and processes. These circumstances determine the relevance of in-depth research into the process of forecasting using mathematical methods and evaluation of the adopted decision. The purpose of the work is the use of modern tools of analytical and simulation economic-mathematical modeling for forecasting the development trends of economic entities in conditions of uncertainty. An analysis of methods and models for forecasting time series and determination of the most effective combinations of them for forecasting economic phenomena and processes was carried out, and the possibility of using them in practice for the analysis and planning of the activities of economic entities was investigated. The option of solving the problem of forecasting economic development trends was carried out on the basis of statistical data, using the example of hotel business enterprises. Methods and models of time series research and forecasting were used in the work: correlation analysis, autoregression and moving average methods, artificial neural network (ANN) models, and autoregressive moving average (ARIMA) model. The results showed that both the ARIMA model and the ANN model can be effectively used for forecasting tasks. It is proven that the ANN model has a higher prediction accuracy at time intervals that are close to the original data. At the same time, the ARIMA model is more appropriate for long-term forecasting. The obtained results allow us to put forward ideas about the simultaneous use of both models, which can compensate for the shortcomings of each of them. Also, the models can be used separately for more accurate forecasting of values ​​for the required time period. More effective is the method by which artificial neural networks can be applied to solve the problem of clustering. This will allow you to single out ranges for forecasting. And then apply ARIMA forecasting to the obtained data sets. The proposed algorithm can be used to determine trends in the development of the hotel industry, as its application reduces the risk of forecasting errors. The results of the work consist of practical recommendations regarding the features of the application of economic and mathematical modeling methods for the construction of forecast indicators and prospects for the development of economic entities. The built model uses the properties of basic forecasting models, which allows for an increase in the degree of reliability and validity of scientific research.

Purpose: to determine the degree of influence of special preparatory exercises on indicators of coordination abilities of basketball players of initial preparation groups. Material and methods: the study involved 40 athletes aged 9 - 11 years, that are part of initial training groups of the second year of study in the sports school № 7 in Kharkiv (control group 20 athletes, experimental group 20 athletes). To establish the indicators of coordination readiness of young basketball players, the standard test exercises proposed by L.P. Sergienko [13] were used. Results: in the training process of the experimental group of special - preparatory exercises were used: various jumps and acrobatic exercises, as well as sets of exercises on a trampoline. This technique had a positive effect on the coordination abilities of basketball players in the initial training group, and significant differences were found between the results before and after the pedagogical experiment (p0,05).

The article aims at clarifying the classification features of the forms and directions of technology transfer, and analyzing empirical data on technology transfer operations in Ukraine. The effectiveness, efficiency and immediacy of technology transfer depend on the choice of its rational forms and directions of technology transfer. The combined form of transfer is considered to be most promising, as it encompasses the advantages of both the vertical and horizontal transfer forms based on the open innovation business model. Ukraine has prerequisites for the implementation of this form of technology transfer, but it is necessary to increase the innovative activity of industrial enterprises and research organizations, and to increase funding for innovation. In the future the authors plan to suggest an organizational and economic mechanism to increase innovation activity at the enterprise level. In 2007-2019 research and development at industrial enterprises (R&D) accounted for about 15% in the total cost of innovation, in average. The lowest share of R&D in total expenditures on innovation was observed in 2011 (7.5%), and the highest share was observed in 2018, comprising 26.3%. The share of costs for vertical transfer is 69.6-89.5%, which is much higher than that for horizontal transfer, which is 10.5-30.4%. The main reason for the decrease in the level of technology transfer at Ukrainian enterprises is the limited funding from the state and the negative investment climate in the country. The share of non-commercial transfers has been lower than 1% since 2012. Combined transfer based on digital technology platforms is virtually absent.

In earlier papers we introduced a representation of isotopy classes of compact surfaces embedded in the three-sphere S3 by so called rectangular diagrams. The formalism proved useful for comparing Legendrian knots. The aim of this paper is to prove a Reidemeister type theorem for rectangular diagrams of surfaces.

In recent decades, there has been an intensification of international scientific and technological cooperation (ISTC), which takes place in various forms. The publication is aimed at generalizing the methodological bases of research and examining the main tendencies in the development of modern ISTC. The essence of ISTC and its objective predeterminence are defined, its importance as a factor of a world-wide development on the basis of the global spread of the achievements of science is specified. The peculiarities of ISTC progress at both macro- and micro-levels, which covers all stages of knowledge acquisition and takes place in an intensive manner in the field of both fundamental and applied research, are explained. The main elements of the methodology of the ISTC research are: principles, conditions of development, types, forms, directions, mechanisms and main effects. It is substantiated that the most important precondition for the development of ISTC is its institutionalization. International business became one of the leading forces in the ISTC. The main structural tendencies in the development of ISTC (increasing the degree of institutionalization, geographical diversification, diversification of the directions of cooperation, wide application of information and communication technologies (ICT), international scientific associations, etc.) are allocated. The peculiarities of participation in the ISCT of both developed and developing countries, as well as spatial changes (increasing the level of globalization, intensification of cooperation at the level of cities, universities, innovation zones; development of spatial and network structures of production, organization and use of knowledge; intensification of global mobility of highly qualified personnel, transfer of technologies) are explained. Attention is drawn to the formation of global innovation networks; development of intensive knowledge communities; expanding participation of universities in the ISTC; increasing the number of information platforms as the basis of ISTC; expanding the role of international scientometric databases, repositories, archives, libraries on the Internet. Measures are proposed to intensify and improve the ISTC system at both the global and the regional levels, especially the multilateral mechanisms to support developing countries. Attention is focused on the need to use a noosphere approach.

The peculiarity of the current development stage of the world economy is manifested in the growing level of internationalization in research and innovation, as well as in deepening international scientific and technological cooperation and exchange. This is especially true for Europe, where a holistic innovation system (IS) of the European Union (EU) has been formed. The integration in the EU IS is of strategic importance for Ukraine and requires appropriate scientific, practical and conceptual foundations. The article aims at presenting the strategic principles of Ukraine's integration into the EU innovation system. The peculiarities of the EU IS formation, its boundaries and main elements (participants; organizations supporting innovation; trans-European "chains" of knowledge generation and transformation, etc.) are considered. The necessity to choose the convergent vector of development for Ukraine’s national innovation system and the relevant advantages of this direction while reforming the R&D sector, supporting research and innovation are substantiated. The conceptual basis for including Ukraine’s science and technology complex in the EU IS is spelled out. It is determined that the main point here is the development of cooperation in science and technology between Ukraine and the EU in such a way that a number of principles are observed (taking into account the uniqueness of the EU IS, its advantages and disadvantages; the use of the European paradigm to support innovation, etc.). The preconditions for integration into the EU IS are identified, in particular, ensuring high-level protection of rights and intellectual property. It is also important to develop a mechanism for deepening international cooperation in science and technology between Ukraine and the EU, which should implement special measures of state support. The principle of cumulation, as well as differentiated approach, should become the grounds for stimulating cooperation. The necessity for Ukraine to participate in the EU programs is proven, and general preconditions for it are substantiated. The process of strengthening scientific and technological ties should be based on new information platforms. To stimulate international partnership, it is also advisable to create various infrastructure organizations (technology transfer centers, project expertise, training and research centers).

Основною метою статті є виявлення факторів, що вплинули на основи формування концепцій Н. Макіавеллі. Методологія була заснована на елементах структурного та функціонального аналізу. Використовуючи теорії Э. Дюркгейма, А. Редкліффа-Брауна, Мертона, автор розглядав систему, в якій усі частини служать для задоволення потреб системи в цілому, забезпечуючи її існування у зовнішньому середовищі концептуальних полів. У результаті було виявлено, що основи теоретичної бази Н. Макіавеллі знайшли своє відображення у пануванні історичного методу й опорі на античних авторів. Макіавеллі використовував цей історичний метод некритично. Його приклади абстраговані від історичного контексту і занадто грубо застосовані до його сучасників. Государ був першим політичним памфлетом, який відхилив трансценденталізм, у тому вигляді, в якому він існував до Канта. Під цим розуміється відмова від наявності будь-якого єдиного ціннісного орієнтиру. Іншим теоретичним методом став історичний. Через політичні причини Н. Макіавеллі не міг вказувати прямо на сучасників. Тому він вишуковав за допомогою античних авторів зручні метафоричні історії для пояснення своєї позиції. Основою методології Макіавеллі був постулат, що влада передує закону, звичаю і юстиції. Макіавеллі стверджував, що злість людської природи, нерозсудливість населення, і тенденція товариств вироджуватися може в якійсь мірі контролюватися або регулюватися законами, які, будучи встановленими, викликають у людях ініціативність і терпимість. Він вважав, що люди не роблять добро без необхідності. Тим самим простежується ставлення до законів як до надбудови звичаїв. За цих умов хороших законів не може бути там, де немає добре озброєної виконавчої влади. Макіавеллі вважав, що безпека всіх держав будується на основі військової дисципліни, яка в свою чергу ґрунтується на хороших законах. При цьому військова безпека є первинною, і без неї не може існувати щось законне. Це переказ ідей Полібія, який так само стверджував, що перед буквами закону повинна бути якась примусова сила, щоб змусити людей до виконання їх обов’язків.

У межах цієї статті було розглянуто підходи теорій політичного ринку до функціонування державного управління. Розглянуто різні погляди на теорію. Комплексний характер визначених дослідницьких цілей і завдань зумовлює застосування у статті комплексного методологічного підходу, заснованого на сучасних системних і дослідницьких проблемах, що стосуються функціонування сучасних партійних систем і політичного розвитку. Цим запропоновано цілісний розгляд теорії в єдності концептуальних і прикладних аспектів. Провідним методом дослідження обрано метод системного аналізу. Методологічним принципом, представленим у всіх підрозділах цієї статті, є принцип діалектики, що дав змогу дослідити погляди теоретиків з урахуванням їхньої внутрішньої суперечливості й мінливості. Важливо зазначити, що в частинах, присвячених розглядові проблематики політичної боротьби, було застосовано елементи структурно-функціонального аналізу. Однією із засад методології дослідження були положення теорії політичного реалізму, які вказують на те, що головним суб’єктом системи міжнародних відносин є національна держава. Нормативно-ціннісний метод було застосовано для з’ясування значення конкретних чинників впливу культури на процес зміни відносин усередині політологічних шкіл. Метод порівняльного аналізу був корисним для визначення спільного й особливого в політичних поглядах. Головним завданням теорії суспільного вибору було нормативно розв’язати такі проблеми демократії як тиранія більшості, масовізація культури й моралі, наявність неефективного уряду, демагогія і порожній простір демократії (наявність на посадах людей, більшість який являє собою змінну масу, використовувану задля представлення громадян загалом), але аж ніяк не створити пояснення для всього спектра політичного життя. Теорія суспільного вибору показує можливий варіант існування політичної системи, щоправда, з іншого боку.

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The specifics of the modern stage of development of the world-economy system, among other things, is manifested in the growth of the level of internationalization of research and innovation activities, which was naturally accompanied by the intensification of international scientific-technological exchange (ISTE). It is the main factor that characterizes the grade of integration of the country into the world economy. This exchange is identified with the spread (diffusion) of knowledge, covering almost all industries, sphere of services, economy sectors. The article examines the main elements of the theoretical base of the ISTE research (theories of diffusion of innovations, industry diffusion of innovations, S-shaped curve, value of transactions, strategic management, industrial organization, social exchange, theory of international trade and internationalization, theory of economic mechanisms, the authors’ own concepts and models). The concepts according to which the ISTE is described (diffusion, transfusion of knowledge; diffusion of innovations as embodied knowledge; international technology transfer) and its main channels (global, interregional, international, cross-border) are researched. The reasons for the development of the ISTE are analyzed and its importance is substantiated. The peculiarities of participation in the ISTE of both the developed and the developing countries are considered – the main motives, forms, prevailing channels, and basic limitations. The grounds that determine the country’s success in absorbing new knowledge are provided (universities, information infrastructure, human resources, perception of innovation). The important role of international organizations (UNCTAD, WTO, WHO, etc.) in the ISTE, which form international policy in the sphere of intellectual property protection and ensuring global cooperation, is underlined. It is emphasized that the main problems in the ISTE are related to the divergence of interests of the State and business. The main tasks for the governments of the countries on achieving the optimum of the ISTE (improvement of the national innovation system, formation of special infrastructure of ISTE, training of scientific personnel, organization of special work on the absorption of new knowledge and their adaptation, dissemination of advantages of the ISTE, formation of the State policy on development and regulation of participation in the ISTE) have been formulated.

В последние годы в области объяснения поведения избирателей произошел ренессанс, в значительной степени обусловленный неожиданными исходами выборов. За минувшие пять лет ученые многое узнали о том, как избиратели на самом деле принимают решения и что их поведение подразумевает для демократической ответственности и общественного благосостояния. Тем не менее, эти достижения в области знаний также породили больше открытых вопросов, чем ответов. Ретроспективное голосование – это концепция в американской политической науке, суть которой сводиться к тому, что общество может оценивает прошлую политическую деятельность правительства. Избиратели рассматривают деятельность правительства по таким критериям как эффективность экономики, системы уголовного правосудия, социальной стабильности, экологические и медицинские результаты в сроки, установленные выборами (2-4 года), а потом через голосование на выборах граждане формулируют более успешные правительства. В Украине данная тема практически никогда не была освещена. Цель этой статьи дать системную оценку теории ретроспективного голосования, как ведущей теории современных электоральных демократий. Цель статьи была достигнута с помощью метода системного анализа.

Рассматривается задача построения многомерной полиномиальной регрессии по заданному ее избыточному описанию на основе результатов активного эксперимента. Избыточное описание означает включение в него членов, возможно, отсутствующих в структуре исследуемой регрессии. Таким образом, возникает проблема по результатам активного эксперимента не только оценить значения неизвестных коэффициентов многомерной полиномиальной регрессии, но и исключить из ее избыточного описания лишние члены. Решение поставленной задачи базируется на: (а) получении новых свойств коэффициентов нормированных ортогональных полиномов Форсайта; (б) возможности сведения задачи оценки неизвестных коэффициентов нелинейных членов многомерной полиномиальной регрессии к задаче оценки коэффициентов множества одномерных полиномиальных регрессий и решения соответствующих систем линейных равенств; (в) использовании метода для исключения лишних членов многомерной нелинейной полиномиальной регрессии, который органически включает в себя как методологию кластерного анализа, так и основную идею метода группового учета аргументов – разбиение экспериментальных данных на два множества, одно из которых не используется для оценок неизвестных коэффициентов многомерной полиномиальной регрессии, заданной избыточным описанием.

Relevance of tresearch topic. In the context of the transition of the national economy to the model of sustainable development, investment and innovation activities should be aimed at solving these problems. Investment and innovation should not only lead to economic growth, but also to sustainability. Therefore, the study of the problems of developing organizational and economic mechanisms to activate the financing of investment and innovation activity of industrial enterprises in the context of transition of the national economy to the model of sustainable development is relevant and significant. Formulation of the problem. The models and methods of stimulating the investment and innovation activity of industrial enterprises in the conditions of the so-called "systemic crisis", which is manifested not only in the system of economic indicators, but also in other elements of the functioning of the state, do not yet have adequate justification. It is necessary to develop scientific and practical recommendations on directions of stimulating financing of investment and innovative activity of industrial enterprises in the conditions of transition of national economy to the model of sustainable development. Analysis of recent research and publications. Some problems of formation and realization of organizational and economic mechanisms of activation of investment and innovative activity of industrial enterprises, as well as the transition of the national economy to the model of sustainable development are covered in scientific works. Some provisions of this problem are covered in scientific papers on structural modernization of the economy, support for economic growth, innovative society, technological modernization of the economy, etc. Selection of unexplored parts of the general problem. In the current context, it is necessary to carry out additional research on perspective mechanisms for financing investment and innovation activities in the context of the transition of the national economy to the sustainable development model. Setting the task, the purpose of the study. The purpose of the study is to develop scientifically sound recommendations for intensifying the financing of investment and innovation activities of industrial enterprises in the context of the transition of the national economy to the model of sustainable development. Method or methodology for conducting research. Methodological basis of the study were general scientific and special methods of knowledge of economic phenomena and processes. In formulating concepts and categories, the method of abstraction was used; methods of analysis, synthesis, induction, deduction; methods of retrospective analysis; logic-analytical method; statistical methods; method of system analysis; economic-statistical and forecast-analytical methods. Presentation of the main material (results of work). The organization of the national economy on the principles of sustainable development implies profound structural changes in management, implementation of innovative approaches in all spheres of economic, social and political life of society. For Ukraine the pressing issue of transition of the national economy to the model of sustainable development is to increase the efficiency of formation and implementation of the state investment and innovation policy. In Ukraine, the level of investment does not ensure the expanded reproduction of fixed assets. Innovation activity in the Ukrainian industry remains traditionally low. In Ukraine, the aging of fixed assets is constantly observed, now the level of deterioration of fixed assets on the average in the economy exceeds 50%. In today's economy, a key element in securing investment through the use of attracted sources is the financial market system. Creation of new and modernization of existing fixed assets is the main direction of investment activity of industrial enterprises. Therefore, the efficiency of the entire investment process is determined not only by the volume and structure of both the sources and the directions of investments, but also by their economic return, which is manifested only as a result of the use of the resulting investment projects. During the crisis in Ukraine, there was a radical change in the structure of the economy in favor of the low-tech and raw material industries, which still remains. In the world markets, Ukraine is represented mainly by raw materials and semi-finished products. The implementation of the sustainable development model is possible on the basis of effective implementation of the state policy of stimulating the financing of investment and innovation activity of industrial enterprises. The use of financial instruments to stimulate investment and innovation activities should provide assistance in solving macroeconomic problems: growth of gross domestic product; improving the competitiveness of the economy; supporting the development of high-tech industries; further formation of institutions of the national innovation system; promotion of high-tech exports; introduction of resource-saving technologies. The directions of further improvement of the state policy aimed at the development of mechanisms for financing the investment and innovation activity of industrial enterprises (including in terms of modernization of the financial system and financial markets) are proposed. It is advisable to take measures to optimize the fiscal (fiscal) policy, which in the conditions of post-crisis development will act as the main stimulator of investment and innovation activity of industrial enterprises. A list of appropriate measures is provided. In the context of the implementation of the strategy of transition of the national economy to the model of sustainable development, the state investment and innovation should provide an orientation to stimulate the so-called "social investment". Key directions of social investment realization: creation of social climate in the country, region; formation of balanced social infrastructure of the country, region, enterprise; support for public health and the level of environmental safety; raising the level of education of the population; promoting the spiritual development of the nation; forming a system of mentoring at the enterprise and ensuring the change of professional generations; development and effective functioning of the labor market. It is advisable to modernize the mechanism of public-private partnership organization. It is necessary to adapt to the best international experience of national IPR instruments. All government programs implemented within the framework of state investment and innovation activities should be cost-effective, and therefore their results should be subject to economic analysis. The field of application of results. The results obtained can be used in the process of formation and implementation of the state investment and innovation policy, as well as in the process of implementation of the strategy for support of sustainable development. Conclusions according to the article. For Ukraine the pressing issue of transition of the national economy to the model of sustainable development is to increase the efficiency of formation and implementation of the state policy of stimulating the financing of investment and innovation activities. This is especially relevant for the industrial sector, as the fixed assets of the industry have a high level of wear. Unfortunately, in Ukraine the efficiency of the implementation of the state investment and innovation policy is insufficient. It is possible to solve the problem of increasing the efficiency of formation and implementation of state support mechanisms for financing the investment and innovation activity of industrial enterprises by improving the appropriate organizational, economic and financial instruments. This task can be solved, in particular, by increasing the efficiency of the formation and implementation of relevant state target programs. The directions of improvement of the state policy aimed at development of mechanisms of financing of investment and innovative activity of industrial enterprises are highlighted, in particular: solving of strategic tasks of development of banking sector and strengthening of its orientation on long-term crediting of industrial enterprises; realization of investment and innovation requests of the national economy; - creation of the State Development Bank (State Investment Bank); support for further development of the stock market and its infrastructure; bringing investment legislation to international standards; expanding the range of financial instruments available to investors. The list of measures to optimize the fiscal policy, which in the conditions of post-crisis development will be the main stimulator of investment and innovation activity of industrial enterprises, is presented. All government programs implemented within the framework of state investment and innovation activities should be cost effective. In the context of the implementation of the strategy of transition of the national economy to the model of sustainable development, it is advisable to take measures to expand the so-called "social investment".

Introduction. Since the thyroid gland (TG), like the rest of the human body, is characterised by wide variety in shape and size, the evaluation of its linear and volumetric parameters by ultrasound images is one of the most important and objective ways of quantitative characteristics of the organ. There are scarce studies into TG morphometry by ultrasound in the Precarpathian region, which is one of the oldest endemic places in Europe. Objective. The aim of the current research study is to conduct the morphometric analysis of TG in adolescents of different sex and constitution who are indigenous inhabitants of the Precarpathian regionMaterials and methods. Therefore, the morphometric analysis of TG linear and morphometric parameters has been conducted in 179 adolescents inhabiting the territory. Ultrasonography has been carried out in Lviv Regional Infectious Clinical Hospital by means of “CHISON” sonograph. Three longitudinal and three anteroposterior dimensions of TG right and left lobes at different levels were measured based on the sonograms taken UDC: 611. 641 ̶ 018.1:6at the angle of 20 - 30° to the median plane. The volume of each TG lateral lobe was measured by the following formula: AxBxCx0.52, where A is the lobe length, B is the lobe width, C is the lobe thickness, and 0.52 is the coefficient of allowance. Results. The ratio between the linear parameters of the lobes has been revealed to be determined rather by constitutional than by sex peculiarities of those under study. It is statistically probable that longitudinal dimensions of both lobes in dolichomorphic people of both sexes exceed the analogous ones in mesomorphs and brachymorphs of both sexes. TG lobes in brachymorphs, in particular, are wider compared with those in both mesomorphs and dolichomorphs, irrespective of sex. The analysis of TG volumetric parameters in different body types of both sexes has indicated that TG volume in brachymorphs dominates in volume over mesomorphs and dolichomorphs, irrespective of sex. Moreover, the volume of the right lobe is larger than the volume of the left one by 0.5 -1.0 cm3 in all of the body types of both sexes. The difference is especially marked in males of the brachymorphic body type. Although there is no statistically probable difference in male and female TG volumes of mesomorphs and dolichomorphs. TG volumes in male brachymorphs are markedly larger than in female ones. As for volume variations they are quite extensive from a minimal male TG volume of 4.85 cm3 to a maximal one of 17.52 cm3, and from a minimal female TG volume of 3.09 cm3 to a maximal one of 14.51 cm3. Conclusions. Thuse the results of TG morphometry by ultrasound demonstrate that there is a direct correlation between TG linear, volumetric parameters and sex or body types, which should be taken into consideration while making a diagnosis in order to avoid incorrect positive diagnoses of TG hypo- or hyperplasia.

The article is dedicated to the iconographic depictions of the hunt found on the Irish High crosses, in particular, the Banagher cross-shaft (Co. Offaly) and the Bealin High Cross (Co. Westmeath) involving a religious figure holding a crozier and a trapped stag. The author looks at further iconographic and literary evidence that can provide the basis of these scenes. Iconography and prosopography of the early Anatolian, Gallo-Roman and Celtic deities are also compared with the early Irish data from a typological religious perspective.

Розглянуто першу крайову задачу для одновимірного нелінійного рівняння теплопровідності, де коефіцієнт теплопровідності та функція потужності теплових джерел степенево залежать від температури. Для числового аналізу цієї задачі запропоновано використати метод двобічних наближень на основі методу функцій Гріна. Після заміни невідомої функції крайова задача зведена до інтегрального рівняння Гаммерштейна, яке розглянуто як нелінійне операторне рівняння у напівупорядкованому банаховому просторі. Отримано умови існування єдиного додатного розв’язку задачі та умови двобічної збіжності до нього послідовних наближень. Розроблений метод програмно реалізовано та досліджено під час розв’язання тестових задач. Результати обчислювального експерименту проілюстровано графічною та табличною інформаціями. Проведені експерименти підтвердили працездатність та ефективність розробленого методу і дозволяють рекомендувати його для використання на практиці для розв’язання задач системного аналізу та математичного моделювання нелінійних процесів.

Стаття присвячена актуальним питанням визначення ролі профспілок у підтриманні належного рівня життя населення. Проаналізовано діяльність профспілки, кошторис її витрат, наслідки діяльності профспілки для працівників і визначено фактори інноваційного розвитку. Досліджено стан профспілок на сьогоднішній день та запропоновано шляхи покращення ситуації. Визначено роль профспілок як на мікро-, так і на макро- рівнях, проаналізовано форму співпраці органів державної влади та профспілок. Розкрито теоретичні основи, практичні особливості ролі профспілок у підтриманні належного рівня життя працівників, здійснення співпраці державного сектору і профспілок. Визначено проблеми нагляду та контролю стосовно дотримання законодавчих норм і правил щодо організації праці громадян України та ролі профспілок у цих процесах. Проаналізовано тенденції соціально-економічних умов суспільно корисної праці.

Background. The aim of the study is to evaluate the quality and safety of the sedative effect of anesthesia in ambulant ophthalmic surgery by using continuous intravenous infu­sion of Dexmedetomidine. Materials and Methods. Patients were randomized into groups by age (people from 65 to 75 years old, old age 76 years, middle age, young people, children), by gender (men, women). The physical status of patients was assessed using the ASA scale and the dynamics of vegetatic activity by the Kerdo index. Sedation was assessed using the Richmond Sedation Scale RASS. Results. It was found that the difference in the frequency of adverse effects of the appointment of Dexmedetomidine clearly confirms the need to adjust the dose of Dexmede­tomidine, depending on the state of the autonomic nervous system. The use of Dexmedetomidine according to the rec­ommendations made it possible to achieve a safe level of sedation and eliminate side effects in ambulant ophthalmic surgery. Conclusions: Parenteral continuous infusion of Dexmedetomidine pro­vides an effective level of sedation for ambulant ophthalmic surgery and maintaining patient­surgeon contact. Safety is confirmed by a low level of critical incidents, no respiratory depression at the target sedation level. The patency of the upper airways was better compared to previous experience with propofol.

У статті розглянуто проблему людської гідності за доби Просвітництва (на прикладі філософії І. Канта) у контексті сучасного філософського дискурсу проблеми. Зазначено, що подальший розвиток суспільства формує запит на правову соціально-орієнтовану державу, де надаються та забезпечуються широкі права та свободи для усіх громадян (незалежно від національності, віросповідання, культури, матеріального стану), що зрештою стає важливою засадою осмислення та буття людської гідності. Йдеться про право громадянина висловлювати свою думку та громадянську позицію, а завдання влади забезпечувати широкий спектр прав та свобод, які визначаються І. Кантом як моральні (природні). Ось чому звернення сучасних філософів та дослідників до філософії І. Канта, його тлумачення природи людини, її прав та свобод, що зумовлене певною схожістю доби Просвітництва та сучасного етапу розвитку суспільства. Означена подібність втілилася у низці факторів, що створюють нову картину світу, а саме: кардинальні зміни політичного, соціального та економічного устрою; традиційного людського буття та життєвого світу; швидкість та глобалізм сучасних трансформацій не тільки у виробничих сферах, а й у соціально-побутових, морально-етичних та суспільно-політичних відносинах. Наголошено, що названі процеси втілюються у моральному (природному) та адміністративному праві і суттєво впливають на свободи та рівність усіх членів суспільства; самостійність дій кожного члена спільноти як громадянина; відсутність патерналізму на рівні взаємин громадянин-суспільство-влада. Таким чином, представлена І. Кантом етично-правова концепція людської гідності знаходить розуміння та застосування в концептах аргументативної та екологічної етики, етики відповідальності у прагненні до створення таких владних структур, за яких суспільний консенсус досягається через аргументований діалог усіх членів суспільства та колективну відповідальність за дії. Таким чином цілісна реконструкція роздумів І. Канта про людину, її гідність та свободу, засвідчує органічну приналежність української філософії до європейського інтелектуального та філософського контексту розуміння загальнолюдських морально-етичних норм, прав і свобод

The subject of this research is the image classification methods based on a set of key points descriptors. The goal is to increase the performance of classification methods, in particular, to improve the time characteristics of classification by introducing hashing tools for reference data representation. Methods used: ORB detector and descriptors, data hashing tools, search methods in data arrays, metrics-based apparatus for determining the relevance of vectors, software modeling. The obtained results: developed an effective method of image classification based on the introduction of high-speed search using hash structures, which speeds up the calculation dozens of times; the classification time for the considered experimental descriptions increases linearly with decreasing number of hashes; the minimum metric value limit choice on setting the class for object descriptors significantly affects the accuracy of classification; the choice of such limit can be optimized for fixed samples databases; the experimentally achieved accuracy of classification indicates the efficiency of the proposed method based on data hashing. The practical significance of the work is - the classification model’s synthesis in the hash data representations space, efficiency proof of the proposed classifiers modifications on image examples, development of applied software models implementing the proposed classification methods in computer vision systems.

The aim of the article is to explore the features of the foreign economic and foreign policy cooperation of the Republic of Tajikistan at the present stage. The role and place of Tajikistan in the system of interregional cooperation are analyzed. The features of foreign economic and military and political cooperation of Tajikistan are investigated. It is proved that the main regional partners and key players in the region are Russia, China and Iran. The main directions of bilateral cooperation of Tajikistan with the leading states of the region are considered. The specificity of relations between Tajikistan and Russia, China, and Iran, as the main foreign policy partners of Tajikistan, is shown. The influence of the foreign policy factor on the preservation of internal political stability in Tajikistan is revealed.

Вестибулярні ядра є першою ланкою опрацювання сигналів про рухи та зміну положення тіла в просторі. У птахів ці ядра досягли високого рівня розвитку, оскільки представники Aves опанували повітряний простір, що супроводжувалось ускладненням локомоції та орієнтації. Унаслідок адаптивної радіації всередині класу виокремемо ряд екологічних груп, представники яких відрізняються за місцем проживання, способом життя, трофічною спеціалізацією, а відтак і складністю локомоції. Усередині класу є як літаючі, плаваючі, бігаючі види, так і ті, що поєднують усі названі вище способи переміщення. Такі еволюційні пристосування повинні відобразитися на морфології відділів мозку, які контролюють положення тіла в просторі та напрямок його руху. Тому ми поставили за мету провести порівняльно-морфологічне дослідження дорсо-латерального, вентро-латерального та вентро-медіального вестибулярних ядер видів, що відрізняються як за способом польоту, так і за вправністю пересування твердим субстратом. Першим досліджуваним птахом обрано голуба сизого (Columba livia), який здатний до маневреного польоту в умовах міста й управно пересувається по землі. Другий досліджуваний вид – хвилястий папужка (Melopsittacus undulatus), котрий в умовах чагарників та щільної рослинності активно рухається твердим субстратом (у тому числі гілками дерев та кущів) і спритно маневрує в польоті. Також досліджено мозок канюка звичайного (Buteo buteo), який пересувається по землі не так вправно, як папужка чи голуб, і характеризується планеруючим та ширяючим польотом. У результаті дослідження встановлено, що у вестибулярних ядрах усіх досліджуваних видів переважають мультиполярні нейрони. Крім них, наявні також веретеноподібні нервові клітини. У всіх досліджуваних тварин найбільші розміри перикаріонів нейронів зафіксовано в nucl. vestibularis dorsolateralis. У канюка звичайного найбільша щільність нейронів – у nucl. vestibularis ventrolateralis, у той час як в інших досліджуваних видів найбільшу щільність нервових клітин зафіксовано в nucl. vestibularis ventromedialis.

An attempt to analyze unclear facts and processes that took place during adoption of the Ukrainian spelling of 1928, is made. A previously commonly unknown letter of the State Spelling Commission Presidium member is taken into account. This letter states that Mykola Skrypnyk, Head of the Spelling Commission, repeatedly acted in the unfair manner in order to adopt unjustified and «revolutionary» changes to the Ukrainian spelling: he used to involve stranger persons to vote for the spelling, insisted on the ill-grounded expansion of the use of «ґ» in spite of the Ukrainian language practice, entered into Presidium a person who was not an expert in linguistics, and did not invite a Presidium member to the sessions. The author of this letter expresses displeasure by these actions and estimates the changes to the Ukrainian spelling carried out by Mykola Skrypnyk, as a «revolution». It is conjectured that there are no grounds to treat the Pravopys-1928 as legitimate and scholarly justified.

This article is dedicated to European Court of Human Rights (ECHR) case law on freedom of peaceful assemblies. The author analyzes the circumstances in which the ECHR may admit that the state interferes with the right to peaceful assembles and whether this interference is legitimate from the prospective of European Convention. According to the ECHR case law, either act or nonfeasance of general or individual character taken before, during, or after the peaceful assembly could be considered as an interference in the right to peaceful assemble even if such actions had no apparent effect on the actual conduct of peaceful assembly, or formally legally not related to its consequences. The interference may also be recognized when the authorities take no necessary actions related to conduction of peaceful assembly in cases where such actions could be reasonably expected. In order to verify that the interference with the right to freedom of peaceful assembly meets the conditions of the Convention, the Court uses the special three-part test. The interference does not violate the Convention if it is prescribed by the law, has at least one legitimate aim, and is necessary in the democratic society. As to the first requirement, the general practice of the ECHR is used. The restriction on peaceful assembly would be considered as prescribed by the law if the law is accessible and sufficiently precise to enable the citizen to foresee the consequences of his or her behavior, whether lawful or not. It is very hard for applicant to prove that the restriction of the right to freedom of peaceful assembly does not pursue one of the legitimate aims of the Convention. The ECHR in most cases does not question the reference of the state to one of the legitimate aims under the Conventions. The only possible way for the applicant to prove that the restriction does not pursue one of the legitimate aims is to provide Court with the strong evidence that the reference given by the state is purely formal and another hidden aim exists that is not prescribed by the Convention. Interference with the freedom of peaceful assembly must also meet the criteria of necessity in a democratic society. In practice, this means, first of all, that the state should demonstrate a sufficient degree of tolerance for peaceful gatherings, proportionally balance the interests of the members of the assemblies and those who do not participate in them, and be ready to fulfill the positive responsibilities of the state during the peaceful gatherings.

The technological phenomenon of artificial intelligence transforms B2B marketing and approaches to the formation of product value, sales and service. The case study allowed the author to examine and summarize the experience of large companies in integrating artificial intelligence into the sales management system, marketing and service. The article identified three problems of B2B companies’ sales system: incomplete, unreliable data, lack of interaction between marketing and sales systems, dynamic growth of personal data volume. The study proves economic efficiency of the integration of artificial intelligence, which solves these problems. The future of marketing was identified based on the latest trends in the B2B segment. In the future, industrial marketing will be determined by the accuracy, reliability of customer information, a high level of accuracy of demand forecasts, a shortened cycle of trade agreements, increasing level of effectiveness of cooperation between marketing and sales departments. The integration of artificial intelligence into sales management will finally complete the era of digital marketing in the B2B segment and will be the beginning of the era of “human” marketing. The latter will mean that in the context of a regulated digital private B2B data market, marketing will be focused on human needs with an accurate predictable understanding of customer needs.