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The study is devoted to the consideration of the existence of mortality in the works of contemporary Russian-speaking Tatar writers (Salavat Yuzeev, Rustem Sabirov, Shamil Idiatullin, Albina Nurislamova, Guzel Yakhina), on the one hand, influencing the macropoetics of works, contributing to the complication of compositional structures, on the other hand, reflected in micropoetics (complexes of motives that actualize the thanatological code, lexical units expressing anti-vital reflection, the living-dead dichotomy). The mortal dimension is associated with the poetics and aesthetics of magical realism, the features and symptoms of which are found in the works of these authors. Particular emphasis in the article is placed on the interpretation of death in the works of the German art critic Franz Roh, who substantiated the category of anti-vitality as fundamental to magical realism. The poetics of death is associated with the existential orientation of the works. Conclusions are drawn that mortality is one of the main artistic constants in the works of these authors, which contributes to the consideration of the traditions of magical realism in their work.

The article deals with the motivic paradigm of “collecting / packing existence” in the work of B. Pasternak. The study aims to determine its role in the lyrical and philosophical concept of the poet and to identify its structure and connection with the creative system of R.M. Rilke. In the first part of the study, the motif of “collecting existence” appears as one of the basic Pasternak motifs. Further — as a point of contact between the creative concepts of Pasternak and Rainer Maria Rilke. That is how the paradigm forms an intersystem metatext. Rilke’s metatext is also conceptual and relates to the philosophical system of S. Kierkegaard, respected by both poets. Then, based on the analysis of the sub-paradigms of the motif of “collecting existence” in the work of B. Pasternak, it is proved that the paradigm has one of the essential roles in revealing autosystem metatext character of his lyrics, artistic, journalistic, and epistolary prose and forms a poetic and philosophical field. Its repeated reproduction in different genres implements an existential understanding of time and the objectness of the world. It combines the motifs of specific actions, such as collecting cars on the train, things on the road, and people in crowds and gatherings, and imaginative motifs: a collection of abstract realities in man, time, space, and the realities of nature into a picture of the world, both an instantaneous one and imprinted in art for centuries.

The article argues that scientific cosmology, the study of the Universe’s origin, evolution, and structure, remains an essential and integral part of scientific thinking. The article traces the roots of scientific thinking back to ancient Greek philosophy, particularly the work of Plato and Aristotle. These philosophers were the first to provide a clear justification for scientific knowledge, laying the foundation for its development in subsequent centuries. However, modern science no longer accepts their justifications as definitive. This raises the question: how can scientific thinking function without the traditional foundations laid by the Greeks? The article proposes a solution: general concepts can objectively exist as a property of the inherent uniformity and isotropy of space and time. This is not limited to just geometric and physical forms but extends to social, cultural, and other realms. Space can be understood as having dimensions, sets of characteristics used to define an object. These “spaces” are abstract constructs humans create to solve specific problems. The same object can occupy homogenous or heterogeneous spaces, depending on the problem being tackled. Time, unlike space, is irreversible and intrinsically anisotropic. However, it can be considered quasi-isotropic and quasi-homogeneous in some specific cases. The development of these concepts of homogeneity and heterogeneity in both physical (geometric) space and time constitutes the foundation of scientific cosmology.

Introduction. The purpose of the article is to consider the phenomenon of the Home in the philosophical and anthropological aspect, to show the prospects of studying the topology of human existence in the form of the immediate environment and everyday practices, set through ethos as an immanent norm of human existence. To do this, an attempt is made to define the boundaries of the Home as a space of human self-sufficiency, and ethos as a condition for the possibility of understanding communication and connection between the individual and their external environment, which allows us to return to the conceptual consideration of the ultimate foundations of human existence.Methodology and sources. An attempt is made on the basis of a critical analysis of nonclassical and post-classical philosophy (phenomenology, existentialism, structuralism) to consider the process of deconstruction of the foundations of human existence. Based on such concepts as the “Lebenswelt” by E. Husserl, “Dasein” by M. Heidegger, studies of the space of human existence by M. Merleau-Ponty and U. Eko, and definitions of the ethos by P. Bourdieu, the main boundaries of the phenomenon of the Home are determined, which is introduced into the discourse of philosophical anthropology.Results and discussion. The phenomenon of the Home, considered in the anthropological aspect, allows us to interpret the goal of the civilization development process as the “domestication” of being, the construction of an “inhabited world”, in which an individual gets the opportunity to realize their existence in an event with “his others”. The life world is formed as a constant movement of the inhabitants of the home, their active, understanding communication within the boundaries of a common space and a common way of life, its forms and rules, that is, a common ethos.Conclusion. As a condition of the human way of being and its ultimate basis, can be considered Home as a community of I and “its others”, having its own topology, the relationship between which is set by a unique ethos.

The existential and socio-psychological threats to human bodily and emotional existence are observed in the urbanized environment, and the origins of the modern urban crisis are discovered. The author attempts to assess the danger and consequences of urbanization for modern human society. The paper formulates a typology of urban activism in the context of socio-philosophical discourse. The aim of the research is philosophical comprehension of human existence in an urbanized environment. In accordance with the purpose, the tasks are outlined: to characterize the “city man”; to identify the contradictory consequences of urbanization for a modern Human; to determine the influence of urbanization atpeople’s lifestyle; to analyze the typology of the activities of city residents which(the activities) transform the urban environment in the context of modern urbanism. Object: urbanism as a socio-philosophical phenomenon, subject: the existential dimension of Human in an urban environment. Methodology. To achieve this goal, general scientific methods were used: analysis and synthesis, analogies, classifications, as well as philosophical methods of cognition (dialectical and hermeneutic). The method of generalization of philosophical and sociological issueswas applied and in particular by using interdisciplinary approach. The means of visual anthropology (cinematography, photography) are engaged in the study to analyze the documentary series “Homo Urbanus” whichis of special scientific value as a source of important social knowledge. The originality of the study: the existential crisis was studied in the focus of urban anthropology, a classification of types of urban activism was proposed. Practical application. The results of the study can be applied in the future interdisciplinary research, as well as in the urban anthropology studies, in the research of the mutual influence of the city and man, as well as of separate topics of educational courses (“Urban Studies”, “Philosophy”, “Sociology”, “Anthropology”, “Aesthetics of Architecture and Design”, etc.).

The term Quale Mechanics is proposed here as describing the qualitative aspects of Quantum Mechanics that are susceptible of metaphysical considerations. The aim of Quale Mechanics is to distill the quantum discourse to its pillars in order to construct its proper – philosophical in nature – quale discourse. The framework of the discussion is initiated by revisiting the platonic approach of the manner in which knowledge is perceived/processed, and then by discussing the four sapiential stages before arriving at concept of the eide. The sensible-suprasensible dichotomy is exposed by contrasting aistheta to the eide. A discussion on the historical development and the foundation of the pillars of Quantum Mechanics is followed. This includes Planck’s solution for the black-body radiation problem with the introduction of quanta – in conflict with Newtonian physics – followed by Einstein’s explanation of the photoelectric effect and the implications involving the dual nature of light (particle vs. wave) and two generalizations of the quantum character of matter: the planetary model of the atom by Bohr, and the dual particle-wave character of electron demonstrated by de Broglie. The subsequent distillation of these semi-classical concepts into more abstract mathematical concepts by Heisenberg, Born, Dirac and Pauli are then reviewed – with Heisenberg’s uncertainty principle and with the concept of wavefunction as landmarks that unmistakably departs from the classical deterministic view of matter. A representative illustration of these achievements is given by the Casimir effect – with implications for gravity and an illustration of how vacuum can in fact not be considered to be truly void. Quantum Mechanics, as the most accurate mathematical framework which can be employed in order to describe and predict the natural phenomena occurring at the atom-size dimensions of reality, may thus be considered as the root from which the concept of Quale Mechanics is emerged in order to construct the parallel between the metaphysical existence and the quantum physical wavefunction collapse. It is concluded that, within its underlying, Quantum Mechanics is a (hopefully fruitful) reiteration of the Ancient Greek Weltanschauung.

The article explores the problem of human vulnerability and the question of temporal security in Martin Heidegger’s philosophy through a historical-philosophical and philosophical-anthropological analysis. The relevance of the topic is determined by the importance of security in the modern world and its philosophical analysis in the context of the philosopher’s work. In contemporary society, there are numerous threats and chal-lenges that can endanger human security, and it is therefore important to understand the philosophical aspects of this problem in order to more effectively combat it. It is important to note that Heidegger approached the problem of security from a unique philosophical perspective, based on his fundamental ontology and theory of time. This approach allows for a deeper understanding of the philosophical aspects of security and the interaction between humans and the world as a whole. For Heidegger, security does not mean the absence of risks, but rather the abil-ity to master one’s fears and anxieties and learn to live with them. The philosopher’s works note a complex and multifaceted meaning of the relationship to security. An important condition for solving the problem posed in the article is Heidegger’s exploration of the experience of fear and anxiety in everyday life, which he reveals in “Being and Time” (1927). Here, the philosopher highlights the main feature of human existence, which should be sought not in Being itself, but rather in everyday experiences, among which fear and anxiety are just a few examples. The aim of the article is to show how the concepts of vulnerability, anxiety, and fear regarding security are revealed in Martin Heidegger’s philosophical methodology. Another important aspect considered in the article is the relation¬ship between time and security in fundamental ontology. Temporal concepts such as past, present, and future play a key role in understanding security. For Heidegger, time is not simply a linear sequence of events, but rather a fundamental concept that determines our ability to understand our fears and anxieties. In conclusion, the impor¬tance and necessity of returning to the study of Martin Heidegger’s philosophy are emphasized, and the relevance of his views for contemporary philosophers and other researchers is underlined, as his understanding of human vulnerability and temporal security can help us better understand the complexity and uncertainty of our lives and learn to live in a world of dangers and risks. Finally, studying Heidegger’s philosophy can help in the search for answers to current philosophical questions, such as the relationship between human beings, the world, nature, technology, and science, and ways of overcoming the crisis of modern society.

The article postulates the ontological meaning of digitalization, in addition to the obvious technical and political ones. Digitalization is understood as informatization to the utmost extent, i.e. the extension of the action of semantic-syntactic operations to an unlimited number of objects and the expansion of the information and linguistic area (realm) within existence. It is argued that digitalization is the fundamental transformation of existence. The essence of this transformation is the merge of the material and linguistic realms of being. The author stands on an objective and idealistic position in understanding the world. The world is understood as being – a structure which logically exhausts the capacity of existence and consists of three realms: material, linguistic and conscious. The logic of merging the material and linguistic realms is seen in their unification in relation to consciousness. Instead of three, there are two realms – a united material-linguistic one (“materiolanguage”, as the author calls it) versus a conscious one. Ontological inequality emerges: while there used to be a balance of three harmoniously delimited realms in the previous structure of existence, then as a result of the transformation the united material-linguistic area becomes infinitely dominant in relation to the conscious one. Consciousness turns out to be “permanently squeezed” and devoid of its own area, but a fundamentally irreducible ontological link. The unification of matter and language is carried out from the side of the language realm (“expansion of language”). The key idea of the article is that language, according to its inherent intention of signification and the disjunctive movement of detailing definitions, “breaks through” matter itself as a fundamental level of the semantic homogeneity and absorbs the material realm. This penetration leads to the ontological replacement of things, as the author describes it, and deprives consciousness of the harmonizing boundary formed by the material level which distances consciousness from the sociolinguistic realm. The described ontological transformation is regarded as an ontology of absolute evil. In addition to the main conclusion, the problems of transhumanism are touched upon and criticized.

В данной работе для уравнения в частных производных четвертого порядка в прямоугольной области рассмотрена нелокальная обратная задача по поиску неизвестной правой части, которая зависит от одной переменной. Собственные функции и присоединенные функции соответствующей спектральной задачи, и их биортогональные функции полны и образуют базис Рисса в пространстве L2​(0,1). Установлены критерии единственности и существования решения рассматриваемой нелокальной обратной задачи для уравнения четвертого порядка. Единственность решения нелокальной обратной задачи вытекает из полноты системы биортогональных функций. Решение задачи построено в виде суммы ряда по собственным и присоединенным функциям, соответствующей спектральной задачи. Установлены достаточные условия на граничные функции, которые гарантируют теоремы существования и устойчивости решения рассматриваемой задачи. В замкнутой области показана абсолютная и равномерная сходимость найденного решения обратной задачи в виде ряда, а также рядов, полученных почленным дифференцированием по t и x соответственно два и четыре раза, в зависимости от гладкости функции заданными начальными условиями. При этом возникают малые знаменатели, затрудняющие сходимость этих рядов. Доказано, что в зависимости от размера области, множество ненулевых решений выражения в знаменателе не пусто. А также, показано, что если этот знаменатель равен нулю, то данная задача будет иметь нетривиальное решение при однородных условиях. Доказана также, устойчивость решения обратной задачи по нормам пространств L2​,W2n​ и C(Ω±), относительно изменения входных данных.

В последнее время интенсивно изучаются начально – граничные задачи в прямоугольной области для дифференциальных уравнений в частных производных как четного, так и нечетного порядка. При этом в качестве объекта исследования, в основном, берется не вырождающееся уравнение или уравнение, вырождающееся на одной стороне четырехугольника. Начально – граничные задачи (как локальные, так и нелокальные) для уравнений с двумя или тремя линиями вырождения остаются неизученными. В данной работе в прямоугольной области рассмотрено уравнение четвёртого порядка, вырождающееся на трех сторонах четырехугольника и содержащее оператор дробного дифференцирования Герасимова –Капуто. Для этого уравнения сформулирована и исследована одна начально – граничная задача с нелокальными условиями, связывающими значения искомой функции и её производных до третьего порядка (включительно), принимаемых на боковых сторонах прямоугольника. Сначала методом интегралов энергии доказана единственность решения поставленной задачи. Затем, исследована спектральная задача, возникающая при применении метода Фурье, основанном на разделении переменных, к поставленной начально – граничной задаче. Построена функция Грина спектральной задачи, с помощью чего она эквивалентно сведена к интегральному уравнению Фредгольма второго рода с симметричным ядром, откуда следует существование счетного числа собственных значений и собственных функций спектральной задачи. Доказана теорема разложения заданной функции в равномерно сходящийся ряд по системе собственных функций. С помощью найденного интегрального уравнения и теоремы Мерсера доказана равномерная сходимость некоторых билинейных рядов, зависящих от найденных собственных функций. Установлен порядок коэффициентов Фурье. Решение изучаемой задачи выписано в виде суммы ряда Фурье по системе собственных функций спектральной задачи. Исследована равномерная сходимость этого ряда и рядов, полученных из него почленным дифференцированием. Получена оценка для решения задачи, откуда следует его непрерывная зависимость от заданных функций.

Objective: to study the existential-legal principle in the formation of the personality of a human and a citizen.Methods: the dialectical approach to the cognition of social phenomena led to the choice of the following methods of cognition: formal-logical, comparative-legal, sociological methods.Results: scientific usage includes a methodologically dubious approach associated with the concept of “a person in law”. There seems to be a human and a citizen in law. In this regard, of the most important doctrinal issues referring to a human, attention is drawn by the issue of the role of the existential principle in the formation of the personality of a human and a citizen, which has not been developed by lawyers. Existence covers situations of personal choice that affect the vital problems of a person’s life, their formation as a personality, overcoming objective life difficulties and subjective dissatisfaction in the process of experiencing them. The level of freedom, felt (reflected) by a person and allowing them (giving them the right) to decide for themselves what to do with their life in all its senses, forms an existential right. It is still waiting for its researcher. One of the directions of such research is the formation of subjective rights and obligations outside and before the mediation of relevant social relations by positive law.Scientific novelty: the most important existentialist questions (where we came from, where we are going, what we stand on, what justifies us, what is the meaning of our presence in the world) are not only philosophical questions. They are purely practical. It is no coincidence that discontent is brewing in the Russian public opinion, both in the scientific community and in the mass of thinking citizens, about the lack of a basic ideology. Existentialism gives preference to internal regulators of behavior over external ones and, consequently, this philosophy does not leave much room to legalism and everything related to the use of legislative means. However, the study of the existence involved in the legal sphere, directed to the legal status of the individual, inevitably actualizes the problems of legislative regulation, evaluation of the existing laws for compliance with natural rights and obligations. The aspect which always remains relevant is the prevention of behavior that deviates from the requirements of an external regulator through metered prohibitions and permits of legitimate authorities. The place of the existential principle in the formation of the personality of a human and a citizen is determined in the light of the ratio of general, special and individual spheres, patterns and forms of life activity. The first is dominated by the general laws of natural-scientific and social development reflected in philosophy; the second is dominated by the specific laws of the political and legal movement of societies and states in a definite place and time; the third – by the existence of active personalities.Practical significance: the conclusions and provisions of the article can be used in scientific and legislative activities, in the educational process of universities.

Purpose. The aim of the study is to determine the features of the historical genesis of aesthetic forms of interaction between individuals in the conditions of modern culture, providing significant characteristics of human existence, implemented in interactive and communicative modes of his emotionally colored interaction with the world. Methodology. The methods of textual and content analysis of the material of the primary sources of classical and modern authors, as well as the analysis of some components of the aesthetic matrix of modern culture in terms of parameters that are essential for achieving the stated goal are used. The author turns to the socio-philosophical and sociopsychological analysis of the emotionalization of modern culture. The article uses historical-philosophical and philosophical-anthropological methods for an analytical description of the process of compensatory aestheticization. Results. In this article, based on the analysis of program works of the founder of existential philosophy S. Kierkegaard, the subsequent entry into the space of modern communication culture was carried out in order to conduct a further comparative study of Kierkegaard’s main ideas, and their modern embodiment in the form of emotional existence of a communicative-collective nature. Particular attention is paid in this regard to the meaningful development of the ideas of the Danish thinker by the existentialist philosophers of the last century M. Heidegger and J. Habermas, as well as the most influential researchers in the philosophy of modern sociocultural genesis B. Huebner, J. Ransier. In conclusion, a number of the most significant changes in modern communication culture, inspired by the turn of the interest of a person and society in the emotional side of their own being, are examined, and their specific phenomenology is considered in relation to the reasons that caused these changes. The author enters into a discussion with A. Reckwitz about the society of singularities, putting forward the concept of a society of collective, stereotyped experience. Practical implications. The results of the study can be applied in the field of cultural studies, philosophy of culture, psychology.

The article discusses the philosophical meanings of the concept of «noosphere», reflecting the phenomenon of human presence as an active and productive force on Earth. The relevance of the study lies in the analysis of the ambiguity and inconsistency of interpretations of the term «noosphere», which gives reason to think about its multidimensionality and the possibility of using philosophical science to describe the essential content of the activities of modern society. This approach will qualitatively rethink: what is the «reasonable sphere» in the philosophical dimension, since behind it is the future, more precisely: the future is possible if it begins to prevail on a global scale, as a new level of collective and individual thinking. The rejection of «noospherism» by science is largely due to its moral component, on which it is based, and its life-affirming optimism in critical literature is presented as a utopian idea. At the dawn of a new scientific revolution, prominent scientists predicted a global crisis if the implementation of scientific research is not accompanied by a constant appeal to ethical principles. The purpose of the work is to show the need to comprehend the ideas of the noosphere in the context of a philosophical approach, as the only way to preserve the spiritual foundation of a person in a technological world. Using elements of historical and philosophical reconstruction and the principles of dialectical reflection, the article considers the problem of losing balance between the spiritual and the material, creation and destruction, domination and service, as an inevitable path to a global catastrophe on a planetary scale. The dialectical approach made it possible to more deeply reveal the concept of «noosphere»: the sphere of interaction between the public and the natural reflects the process of the formation of human thinking — from opposing oneself to nature, to finding ways to unite with it, the harmonious coexistence of two principles that complement each other. Using the method of historical analysis, the similarity of the views of thinkers of different eras on the problem of Man in the world and the prospects for his development as an integral and harmonious being in the conditions of modern realities was found. The authors come to the conclusion that the prospect of developing the idea of the noosphere is most productive in the context of the philosophical approach, since philosophy gives the necessary freedom of thought and does not require a rigid attachment to any doctrine. According to the authors, the utopian nature of the concept of the noosphere at the present stage of the development of human society does not mean that its positive experience cannot be applied in the social environment. Moreover, it is the philosophical approach that makes it possible to «reconcile» and combine the moral and value component of the idea of the noosphere with practical science. Major companies around the world are already reconfiguring their technical base, taking into account new environmental requirements, including gentle production methods and a reasonable attitude towards the environment. The prospects of modern science are directed towards «green» technologies, which would be impossible without rethinking the role of humanity in organizing activities that affect nature. The «ecology» of thinking is not only an attempt to solve a number of global problems, but, above all, a new consciousness that seeks to find a way out of existing contradictions using humane methods. In this sense, philosophy turns into a «practical» science, influencing the activities of man and society.

This paper investigates the solvability of the inverse problem of finding a solution and an unknown coefficient in a pseudohyperbolic equation known as the Klein-Gordon equation. A distinctive feature of the given problem is that the unknown coefficient is a function that depends only on the time variable. The problem is considered in the cylinder, the conditions of the usual initial-boundary value problem are set. The integral overdetermination condition is used as an additional condition. In this paper, the inverse problem is reduced to an equivalent problem for the loaded nonlinear pseudohyperbolic equation. Such equations belong to the class of partial differential equations, not resolved with respect to the highest time derivative, and they are also called composite type equations. The proof uses the Galerkin method and the compactness method (using the obtained a priori estimates). For the problem under study, the authors prove existence and uniqueness theorems for the solution in appropriate classes.

The research focuses on the problem of interpretation of such a concept as the origin, which is ultimate for philosophical thought and bases existentially oriented constructions of Franz Rosenzweig and Martin Heidegger. It is argues in this paper the fundamental difference between the interpretations of the origin in “The Star of Redemption» and in «Being and Time”, despite all points of intersection and coincidences that bring closer together dialogical and existential-historical thinking. Such differentiation of positions is determined by the necessity both to neutralize romantic connotations, which expose the origin ( Ursprung ) as abyss ( Abgrund ), and to methodologically clarify the possibility not so much to think as to practically assert a limited and unclosed within itself integral being, including ontological and ethical dimensions. The origin of oblivion and renewal, imposed by Heidegger’s hermeneutics of facticity, is contrasted with Rosenzweig's origin of the “eternal overworld”, reconstructed on the basis of Herman Cohen's religio-philosophical intuitions and his analysis of the infinitesimal as a principle of reality. Rosenzweig’s position, which aims at a correlative consideration of the purely logical content of the infinitesimal quantity (almost-Nothing) and the existential experience of the finiteness of everything, is favorably distinguished by the absence of a one-sided focus on recalling, where fore-running although is declared, but it is immediately restrained by being-towards-death. As a result, Rosenzweig’s dialogism turns out to be free from overestimating what Heidegger’s interpretation calls resoluteness, which in fact is not much different from paralysis in the clearance of being. Cohen’s problem of an infinite task's realization, being actualized in Rosenzweig’s conception, allows to go beyond being-towards-death in juxtaposing the trajectories of initial elements into a true gestalt.

Introduction. The perception of death is inextricably linked with subjective experience, the feeling of the inevitability of this phenomenon. Theoretical analysis. Existential modes, such as fright, despair, fear, anxiety, actively studied in the corresponding philosophical trend, are the main aspects that determine this or that view on death in the context of personal experience of the phenomenon of the fi niteness of human existence. Modern reality makes its own adjustments to every phenomenon of human existence, however, the attitude towards death results from the infl uence of existential modes, formed by the emerging philosophy of existentialism, but perceived through the prism of the given of the 21st century. The purpose of this scientifi c work is to identify the structures and mechanisms of the infl uence of existential experiences on the perception of the phenomenon of death in the context of complex data of modern reality. To achieve this goal, materials of existential philosophy were used, primarily the works of the Danish philosopher Seren Kierkegaard. The concept of despair, which is important for this thinker, has a clear correlation with the psychological health of a modern person, in addition, the feeling of despair expresses an attitude towards one’s own death. Conclusion. The novelty of this work consists in identifying the dependence of aspects of existential philosophy in the formation of the perception of death in the modern world.

This article discusses the problems of integrating artificial intelligence into the legal and ethical field, as well as issues related to the existential status of this phenomenon. The author analyzes possible variations in the existential, legal and ethical statuses of artificial intelligence, also relying on the features of the object of study, in particular on its potential presence, both in a weak and strong form. The purpose of the work is to model the main specifics and problematic aspects of the introduction of artificial intelligence in areas where person is a dominant subject. In the study, preference is given to a strong form of artificial intelligence, since it is in the presence of such an ontological unit that problems arise in the field of law, morality and existence (the relationship between a person and artificial intelligence). The existential problem is related to the possibility of assigning a certain status to artificial intelligence: equal to a person, identical to him, standing above/below a person, etc. Legal issues are related to the existential, so some problematic issues (for example, the assigned status) intersect. In addition, the legal legitimacy of the artificial intelligence ​​self, as well as the necessary legislative changes resulting from this, is relevant in this problematic field. Ethical issues are related to the question of the formation and possibility of morality in artificial intelligence. Research methodology. In this work, the dialectical method is used. It allows you to identify and analyze the contradictions that arise both within the very phenomenon of artificial intelligence, and within the framework of its hypothetical introduction into society and the existence of an individual. The modeling method allows one to form a set of ideas about problematic moments and possible crisis situations that can be caused by the integration of artificial intelligence into society, in particular, in its strong form. The method of analysis and synthesis allows penetrating deeper into the essence of the problem associated with assigning the status of an ontological (existential) unit to artificial intelligence. The ethical approach allows us to analyze the possibility of creating a «programmed morality». Together with the psychological approach, it involves the formation of ideas about the potential complexities of the relationship between a person and artificial intelligence, which has the status of a person. Results. The principles of comfort and safety are dominant (repressive) in terms of the hypothetical creation of a strong artificial intelligence. At present, the principle of the anthropomorphic organization of artificial intelligence is dominant. Technological singularity, in particular also initiated by the advent of artificial intelligence, has a number of requirements for its implementation (not only dynamics, but also frequency and depth of integration). The phenomena of mass character and fear of innovation are an inhibitor of the formation of scientific and technological progress, including the emergence of a strong artificial intelligence. The instrumental nature eliminates the need to consider the relationship to artificial intelligence as being-with-other. In the aspect of strong artificial intelligence, the problem of existence with the other-as-other arises, and the impossibility of the identity of the «other» and «other» arising from this. Legal issues are represented by a number of controversial issues: the citizenship of a strong artificial intelligence, its social and legal status, the need for separate legislative acts, etc. The anthropomorphic ideal/standard is identified as ineffective for artificial intelligence and the concept of «programmed morality».

A nonlinear boundary value problem for a third-order nonlinear equation with multiple characteristics is studied in the article in a curvilinear domain. The unique solvability of the problem is proved. The uniqueness of the solution to the boundary value problem is proved by the energy integral method using some elementary inequalities. An auxiliary problem is considered for the existence of a solution, for which the Green function is constructed. By solving an auxiliary problem, the original problem is reduced to a system of Hammerstein integral equations. The solvability of a nonlinear system is proved by the contracting mapping method.

The fractional differential equations play important roles due to their numerous applications and also for the important role they play not only in mathematics but also in other sciences. In the present research work, we build up the explicit solutions to linear fractional q-differential equations with the q-Caputo fractional derivative of real order a > 0. To speak more precisely, we will achieve our main results we use that this Cauchy type q-fractional problem is equivalent to a corresponding Volterra q-integral equation. After that, by using the method of successive approximations is applied to solve the Volterra q-integral equation we construct the the explicit solutions to linear fractional q-differential equations. In the same way we have the more general homogeneous fractional q-differential equation with the Caputo fractional q-derivative of real order a > 0 and we give other The (Mittag-Leffler) q-function. Finally, some examples are presented to illustrate our main results in cases where we can even give concrete formulas for these explicit solutions.

This article investigates the connection between two positive logarithmically convex sequences {M̂n} and {Mn}, which define respectively the Carleman classes of functions infinitely differentiable on the set J and sequences {bn} specifying the values of the function itself and all its derivatives at some point x0 ∈ J. The results obtained are more general than those previously known, and explicit constructions of the required functions are proposed with estimates for the norms of the functions themselves and their n derivatives in the Lebesgue spaces Lr (J), not only for the classical case r = ∞ but also for any r ≥ 1. Obviously, Mn ≤ M̂n is always observed. Here the sequences {M̂n}, for which equality holds, are indicated and specific examples are given.

The paper is devoted to the transformation of concept of death in philosophy and theology of XX century. We analyze the influence of Martin Heidegger’s version of the statement about human mortality on Christian theology. For Heidegger, death is the "existential of totality" in the structure of Dasein; death determines and embraces the totality of human existence. Death leaves man "open," or necessarily pointing to something beyond himself, ultimately to being itself. In Christian theology the new understanding of death is presented in theology of Karl Rahner, Eberhard J?ngel and Sergei Bulgakov. Death, for Rahner, is a personal act embodying our personhood and freedom and our responsibility of love and faithfulness. We recognize the notion "theonomous death". It is both an act of freedom and an act of Grace, for as the fullest self-communication of God, it is the Grace of Christ that, as one existentially open to divine self-communication, exposes the hearer of the word. Eberhard J?ngel seeks an understanding of man's death which is not concerned with his preservation but with the presence of God to man in death. The meaning of man's death lies not within himself and his survival, but beyond him, in God who is all in all. Death is "an anthropological passive". We discuss also the problem of theological language about death. According J?ngel Christian language about death is a "word from beyond death". In the analysis of the problem of death in the theology of S.N. Bulgakov, we note his attempts to develop a positive attitude towards death. Death is understood not as "some ontological misunderstanding", but as arising from the foundation of the universe. The centre of Bulgakov's understanding of death is its incorporation in the antinomy of the divine kenosis. We argue that if Heidegger accentuates Being toward death as running ahead of possibility , Christian theologians conceptualize death as dying with Christ.

Inverse problems of finding the right-hand side of a partial differential equations arise when an external source is unknown or impossible to measurement, for example, the source is in a high-temperature environment or underground. The partial differential equations with mixed derivatives by time and space variables are usually called pseudo-parabolic equations or Sobolev type equations. Pseudo-parabolic equations occur in mathematical modeling of many physical phenomena such as the motion of non-Newtonian fluids, thermodynamic processes, filtration in a porous medium, unsteady flow of second-order fluids, etc. This paper is devoted to investigate the unique solvability of two inverse problems for a linear one dimensional pseudoparabolic equation. The inverse problems consist of recovering the right hand side of the equation depending on the space variable. An additional information for the first inverse problem is given by an final overdetermination condition and for the second is given by an integral overdetermination condition. Under the suitable conditions on the initial data of the problem, the existence and uniqueness of a classical solution to these inverse problems are established. By using the Fourier method, the explicit formulas of a solutions are presented in the form of a series, which make it possible to perform the necessary numerical calculations with a given accuracy.

To reconstruct a critique of the ontological proof of the existence of God in Schelling’s philosophy I examine his interpretation of the ontological argument by Anselm of Canterbury and Descartes as well as Schelling’s assessment of the critique of the Kantian ontological proof of the existence of God. I propose a reconstruction of Schelling’s account of undoubted being which cannot be deduced from the concept of the totality of all that is possible and therefore must come before any thought. He interprets reason as having an ecstatic nature which posits precedent undoubted being. This enables Schelling to formulate his own version of the thesis on the unity of being and thought, whereby being comes first and thought is only second. Against this background I analyse Schelling’s interpretation of the Kantian account of the ideal of reason. Schelling, on the one hand, agrees with Kant that being is not a real predicate, hence real existence cannot be deduced from essence in the sense of “what.” But, on the other hand, in contrast to Kant, he believes that real existence of the individual absolute must be assumed, which would be the subject for all possible predicates and whose being is ecstatically posited by reason as being external to itself. I raise the question of the relevance of Schelling’s thought for modern ontology, above all in overcoming ontotheology. Proceeding from the works of J. F. Courtine and L. Tengelyi I single out two aspects of Schelling’s doctrine that are relevant to my subject: (1) the priority of existence over essence in God’s being and (2) the fundamental irreducibility of God to a necessarily existent being, i.e. God’s freedom. It is evident that, in his interpretation of Kant, Schelling somewhat simplifies his train of thought and leaves it unclear how Kant links the concepts of necessary being and the supremely perfect being. It is also evident that Schelling’s concepts of “contingency,” “contingent necessity,” “the whole experience” need further study.

In this paper, we study the solvability of some non-local analogs of the second initial-boundary value problem for multidimensional hyperbolic and parabolic equations of the second order. We prove the existence and uniqueness theorems of regular solutions (which have all Sobolev generalized derivatives that are summable with a square and are included in the equation). Some generalization and amplification of the obtained results are also given.

The study of equations of mathematical physics, including inverse problems, is relevant today. This work is devoted to the fundamental problem of studying the solvability and qualitative properties of the solution of the inverse problem for a quasilinear pseudoparabolic equation (also called Sobolev-type equations) with memory term. To date, studies of direct and inverse problems for a pseudoparabolic equations are rapidly developing in connection with the needs of modeling and control of processes in thermal physics, hydrodynamics, and mechanics of a continuous medium. The pseudoparabolic equations similar to those considered in this work arise in the description of heat and mass transfer processes, processes of non-Newtonian fluids motion, wave processes, and in many other areas. The main types of the inverse problems are: boundary, retrospective, coefficient and geometric. The boundary and retrospective inverse problems lead to the study of linear problems. In turn, the statements related to the study of coefficient and geometric types bring to the nonlinear problems. Coefficient inverse problems are divided into two main groups: coefficient inverse problems, where the unknown is a function of one or several variables, and finite-dimensional coefficient inverse problems. In this article the existence and uniqueness of a weak and strong solution of the inverse problem in a bounded domain are proved by the Galerkin method. Also we used Sobolev’s embedding theorems, and obtained a priori estimates for the solution. Moreover, we get local and global theorems on the existence of the solution.

Inverse problems of determining the right-hand side of a differential equation arise in the mathematical modeling of many physical phenomena, when an external source or some of its parameters acting to the motion of the process are unknown or unacceptable for measurement, for example, the source is in a high-temperature environment or underground, etc. This paper deals to study the solvability of an inverse problem for a nonlinear pseudo-parabolic equation (sometimes they called Sobolev-type equations) with p-Laplacian and damping term with variable exponent. The inverse problem consists of determining a coefficient of the right-hand side depending only on time. Additional information for this investigated inverse problem is given as an integral overdetermination condition. Under the suitable conditions on the exponents and on the data the global and local in time existence of a weak solutions to the inverse problem are established. The existence of a weak solution proved by the Faedo-Galerkin method. The global and local in time a priori estimates for the Galerkin approximations are obtained. On the basis of a priori estimates and by using compactness theorems and the monotonicity method, the convergence of the Galerkin approximations to the solution of the initial inverse problem is proved.

Purpose. The paper is aimed at studying the peculiarities of the Oleksandr Kulchytskyi’s doctrine of human, taking into account the context of European philosophy and especially in comparison with the paradigm of philosophizing in the Lviv-Warsaw school. The theoretical basis of the study is determined by Kulchytskyi’s scholarly works in the field of philosophy and philosophical anthropology, as well as the latest researches that reinterpret the influence of Twardowski’s theoretico-methodological ideas on the formation of the philosophical worldview of the Ukrainian thinker. Originality. Based on the appeal to primary sources, Kulchytskyi’s philosophical doctrine of human in the unity of its basic principles and theoretico-practical results is reconstructed. The ways of forming the key ideas of his philosophical anthropology are determined, their originality is substantiated, despite the cooperation with Twardowski’s school, as well as despite numerous discussions and researches of Western European philosophico-anthropological, existentio-ideological and socio-psychological issues. Conclusions. It is found out how the philosophical worldview of Oleksandr Kulchytskyi was formed and how he gradually came from the research of the human psyche within the framework of anthropological structural psychology to the realization of the need to study philosophical anthropology. The personalistic features of his philosophical doctrine of human are characterized; in particular, attention is paid to the distinction between the concepts of person and personality, determining the importance of the social factor for the formation of human worldview, didactic aims of anthropological studies. It is shown how in Kulchytskyi’s philosophical anthropology the analysis of the existentio-worldview dimension of human existence, manifested in different spiritual situations and socio-cultural conditions that influence the specifics of thinking and the nature of the personality mentality, acquires special importance. The originality of Kulchytskyi’s arguments about human in the context of both Ukrainian philosophy and in general European philosophical thought is stated.

The aim of this paper is to study the solvability of solutions of non-local problems with integral conditions in spatial variables for high-order linear parabolic equations in the classes of regular solutions (which have all the squared derivatives generalized by S. L. Sobolev that are included in the corresponding equation) . Previously, similar problems were studied for high-order parabolic equations, either in the one-dimensional case, or when certain conditions of smallness on the coefficients are met equations. In this paper, we present new results on the solvability of non-local problems with integral spatial variables for high-order parabolic equations a) in the multidimensional case with respect to spatial variables; b) in the absence of smallness conditions. The research method is based on the transition from a problem with non-local integral conditions to a problem with classical homogeneous conditions of the first or second kind on the side boundary for a loaded integro-differential equation. At the end of the paper, some generalizations of the obtained results will be described.

New sufficient conditions for the existence and uniqueness of a periodic solution of a system of differential equations equivalent to the Rayleigh equation are obtained. In contrast to the known results, the existence proof of at least one limit cycle of the system is based on applying curves of the topographic Poincare system. The uniqueness of the limit cycle surrounding a complex unstable focus is proved by the Otrokov method.

В работе рассматривается обратная задача для гиперболического уравнения третьего порядка. Ставится обратная задача, состоящая в определении неизвестного коэффициента, зависящего от времени. В качестве дополнительной информации для решения обратной задачи задаются значения решения задачи во внутренней точке. Доказывается теорема существования и единственности решения обратной задачи. Доказательство основано на выводе нелинейной системы интегральных уравнений типа Вольтерра второго рода и доказательстве его разрешимости.

In this paper, an initial-boundary value problem for the equation of forced vibrations of a cantilever beam is studied. Such a linear differential equation of the fourth order describes bending transverse vibrations of a homogeneous beam under the action of an external force in the absence of rotational motion during bending. The system of eigenfunctions of the one-dimensional spectral problem, which is orthogonal and complete in the space of square-summable functions, is constructed by the method of separation of variables. The uniqueness of the solution to the initial-boundary value problem is proved in two ways: (i) using the energy integral; (ii) relying on the completeness property of the system of eigenfunctions. The solution to the problem was first found in the absence of an external force and homogeneous boundary conditions, and then the general case was considered in the presence of an external force and inhomogeneous boundary conditions. In both cases, the solution of the problem is constructed as the sum of the Fourier series. Estimates of the coefficients of these series and the system of eigenfunctions are obtained. On the basis of the established estimates, sufficient conditions were found for the initial functions, the fulfillment of which ensures the uniform convergence of the constructed series in the class of regular solutions of the beam vibration equation, i.e. existence theorems for the solution of the stated initial-boundary value problem are proved. Based on the solutions obtained, the stability of the solutions of the initial-boundary value problem is established depending on the initial data and the right-hand side of the equation under consideration in the classes of square-summable and continuous functions.

Purpose. The paper is aimed at analyzing in a comparative way the philosophical conceptions of the human, proposed by Ludwig Wittgenstein and Martin Heidegger as the main representatives of the analytic and continental tradition of philosophizing in the XXth century. The theoretical basis of the study is determined by Wittgenstein’s legacy in the field of logical and linguistic analysis, as well as Heidegger’s existential, hermeneutical, and phenomenological ideas. Originality. Based on the analysis of the philosophical works of Wittgenstein and Heidegger, the initial principles of their anthropological concepts in the unity of transcendental preconditions, essential foundations, and correlations to the world in the technosphere are reconstructed. It is demonstrated that, despite the difference in the explanation of the peculiarities in the interpretation of the realm of the transcendental (as an extra-linguistic) and basic characteristic of the inner world of human, both philosophers emphasized the understanding of the human being through the prism of language and the need for anthropologization of science and technology. Conclusions. Wittgenstein and Heidegger developed their own original considerations on the nature of human being, which fully conform to the basic theoretico-methodological principles of their philosophical conceptions. The former focused on how language reflects a human’s world and serves as a means of expressing their knowledge and aspirations. The latter, on the contrary, interpreted the world as a reflection of language that expresses itself through human. As a supporter of analytic methodology and, accordingly, of accuracy in formulations, Wittgenstein came to the concept of the unspeakable in the process of reflection on the being of human over the language. But in Heidegger’s existential discourse, which is full of metaphors and neologisms, being of human is limited by the concept of Nothing. As a consequence, it is noted that the ontological status of values is transcendental to the world according to Wittgenstein, but it is immanent to the world, according to Heidegger. It is argued that the Austrian thinker developed a linguo-psychological approach to the study of human through the prism of the mental, but the German philosopher comprehended the human on the basis of the concept of self in the ontological sphere. It has been demonstrated that both thinkers have pointed to the challenges faced by humans in the development of science and technology while emphasizing the importance of substantiating their anthropological foundations.

The paper is devoted to the study of the solvability of nonlocal problems with an integral variable $t$ condition for the equations $$u_{tt}+(\alpha\frac{\partial}{\partial t}+\beta)\Delta u=f(x,t)$$($\alpha$, $\beta$ are valid constants, $\Delta$ is Laplace operator by spatial variables). Theorems are proved for the studied problems existence and non-existence, uniqueness and non-uniqueness solutions (having all derivatives generalized by S. L. Sobolev included in the equation).

The article is devoted to identifying the specifics of Russian philosophy through the analysis of F. M. Dostoevsky and L.N. Shestov’s texts. The stylistic features of the two philosophers have been considered, their ways of philosophizing and denying of the cult of reason have been examined. The analysis is carried out using additional literature of French existentialism (were used such philosophers who wrote in similar styles as philosophical essays). To date, there are many researches in which study features of Russian philosophy. It is noted, that one of them are imagery, inseparable connection between philosophy and faith and criticism of rationalism. The excessive cult of reason leads to such problems in the history as the creation of the hydrogen bomb, the environmental crisis and so on. The revolt against reason and the state of groundlessness are a response to the processes of modern rationalization and technocratization, an attempt to go beyond the limits of the usual paradigm, to get out of the closed subjectivity. Thus, it’s necessary to define the limits of the reason and develop a new way of philosophizing, for this reason it is proposed to consider the concept of groundlessness in the philosophy of L.N. Shestov, which makes the attempt to construct a philosophy, avoiding strict logic and excessive rationality.

Each personality contains a part of the fullness and depth of the World and the completeness of it depends on personality’s own abilities and talents. Each «I» has the right to consider itself valuable and can claim to have a dialogue with another personality. A personality can evaluate and contain various cultures, knowledge and beliefs, science and religions. Each personality actualizes what can be called the development of thought throughout time. Moreover, not only «in the time» in sense of Newton’s and Einstein’s physics, but, mainly, in what we call «the time of the appearance of the Savior», «Shakespeare’s time », «our time». That is, a set of conditions under which historical events occur. All these times are characterized by their own way of thinking and their own level of knowledge. And their own laws of existence. This means not only the factual existence, but also that exists in the imagination of the individual. At the same time, imaginary reality can more affect a person’s worldview than actual reality. The development of thought throughout time brought a lot of useful things to a person, but also a lot of disastrous ones, such as conflicts and wars, global catastrophic risk, world-wide pre-crisis ecology problems, and a lot of other troubles – all these that can direct a person’s thought towards dreams and imagination. Current problems of time, of course, disappear and are absorbed by Eternity. Eternity embraces and completes all time and existence. However, if you connect your imagination, then an inquisitive, free thought can assume the existence of the Pre-Eternal. Absolute, God. Just assume that He controls us, but we must trust Him with many of our concerns. Existence is a fundamental category. You can exist in reality or in imagination…or in the reality of imagination. The author considers the conversation about existence for himself not yet complete...

The present research was based on modern psychological studies. The article features the structure and contents of the existential theory. The structure of the theory is presented in the framework of the concept coined by A. V. Yurevich, while its contents are represented in the context of the existential and phenomenological philosophical traditions. The paper focuses on three elements in the structure of the existential psychological theory. The central one includes a generalized image of psychological reality, its central category, corresponding phenomena, basic concepts, the system of relations between them, basic statements, etc. The peripheral elements are represented by theoretical and empirical components. The third component features the implicit part. The generalized image of the psychological reality is represented by the concept of "Dasein", its central category being "the existence". The author described the basic concepts and auxiliary statements of the theory. The basic statements of the theoretical part of the existential approach are the key provisions and principles of existentialism as formulated by J.-P. Sartre. The auxiliary statements belong to A. Camus and V. Frankl. The authors clarify the conceptual formation of existential theory, starting with E. Husserl’s phenomenology and moving on to modern psychology. The authors believe that the establishment of existential theory contributed to the development of the existential tradition in psychological counseling practice.

For a mixed elliptic-hyperbolic type equation with characteristic degeneration, the first boundary value problem in a rectangular region is investigated. The criterion for the uniqueness of the solution of the problem is established. Earlier, in proving the uniqueness of solutions of boundary value problems for equations of mixed type, the extremum principle or the method of integral identities was used. The uniqueness of the solution to this problem is established on the basis of the completeness of the system of eigenfunctions of the corresponding one-dimensional spectral problem. The solution of the problem is constructed as a sum of a series in the system of eigenfunctions. When we proved the convergence of the obtained series, the problem of small denominators of a more complicated structure than in other known works arose. These denominators contain a parameter depending on the lengths of the sides of the rectangle in the hyperbolic part of the domain and the exponent of the degree of degeneration. In this connection, estimates are established about separation from zero with the corresponding asymptotics, in cases where this parameter is a natural, rational and algebraic irrational number of degree two. If this parameter is not an algebraic irrational number of degree two, then the solution of the problem as a sum of a series does not exist. Using the obtained estimates, the uniform convergence of the constructed series in the class of regular solutions is justified under certain sufficient conditions with respect to the boundary functions. The stability of the solution of the problem with respect to the boundary functions in the norms of the space of summable functions and in the space of continuous functions is also proved.

Purpose. The article is aimed to show the specificity and heuristic value of the humanism of the French existentialist J.-P. Sartre, represented both in his early works, where the isolationist position prevailed, and considering his evolution to various types of collective responsibility and attempts to build a universal morality on the basis of ontological integral humanity. Theoretical basis. Taking into account the relevance of the topic of person’s searching for authentic existence in the modern world, the author analyzes the concept of Sartre’s humanism, which remains poorly researched in the Ukrainian philosophical space, since most of his works of the later period remained untranslated and unknown to the Ukrainian community. That is, there is a need to consider the phenomenon of a human and his/her basic characteristics, which ultimately determine what type of humanism deserves further support and development. The author places the existentialist dimension of a human being, which is one of the most important determinants of human behavior and the ways of human self-determination of his/her existence, in the context of the general development of the humanistic tradition of modern anthropology. Originality. The article substantiates the thesis that Sartre’s position concerning humanism is conditioned by the specificity of his understanding of the authentic human existence as a constant self-transcendence, the person’s realization of the project that makes a person the creator of the values. Therefore, Sartre’s humanism can only be understood in the context of this self-construction and responsibility of a person for his/her choice. The author proved that although this concept was subsequently changed, the basic intention of the Sartre’s approach remains the same. Thus, having combined the existentialism and Marxist understanding of the historical process, Sartre nevertheless emphasizes that the primal intentionality of human existence (project or transcendence) is decisive in all subsequent actions and doings, despite the fact that real practice may demonstrate deviations and even regression concerning humanity. Having defined the universality of the human situation in the world as the presence of certain a priori restrictions, the philosopher comes to the recognition of intersubjectivity, which allows him to reach a new type of morality, which defines "integral humanity" or "full-fledged human" as its goal. Conclusions. The interpretation of humanism by early Sartre relied on the idea of a person as such, who is in constant transcendence (going beyond), constantly constructing him/herself; he/she is oriented towards the future (but it is a pure future, unplanned and undefined). In this case, a person is the creator of the values and their legislator in this world. At the same time, the late Sartre emphasized that since a person exists in a society where he/she is usually in a state of alienation, the question under which conditions and by what means is it possible to reproduce and realize a truly humanistic dimension is inevitable. Sartre’s position is based on the fact that there is a primal need for self-realization, to be human.

In this article, the first boundary problem for the mixed type equation with two degeneration lines at a half-strip in the class of the regular and limited in infinity decisions is discussed. The criterion of uniqueness for the stated problem was formulated by the methods of a spectral analysis.The solution of a problem is constructed in the form of a series on eigenfunctions of the corresponding one-dimensional eigenvalues problem. At justification of the uniform convergence of the constructed series there was a problem of small denominators. The estimation for the separation from zero of a small denominator with the corresponding asymptotics was provided in connestion with mentioned problem in the present paper.This assessment at some sufficient conditions on boundary function allowed to prove convergence of the constructed series in a class of the regular solutions of this equation. In difference from other works of similar subject is the criterion of uniqueness and existence of the solution of the stated problem to be proved at all positive values of the parameters entering the equation, not necessarily equal. Such fact is an important consequence of the received result that the constructed solution everywhere in the considered area is the solution of the equation. Therefore the line of change-type of the equation as a special one is eliminated.

This work is a collection of brief essays and aphorisms, which despite the apparent diversity are parts of a common explanatory principle based on the anthropological dualism between truth and value. Being a mental monad, every phrase, however, internally echoes other mini-texts, and therefore, the author does not leave attempt to link them internally. In this work, he combined the “logical quirks” of paradox and irony with some ideas drawn from his future book on philosophical anthropology, on which he is currently working.

The article is devoted to the study of the solvability of boundary value problems for third-order Sobolev-type differential equations of the third order with two time variables (such equations are also called composite-type equations or equations not solved for the derivative). The peculiarities of the equations under study are, firstly, that the differential operators acting at the time derivatives are not assumed inverse, and, secondly, that the statements of boundary value problems for them are determined by the coefficients of these differential operators. For the problems proposed in the article, we prove existence and uniqueness theorems for regular solutions (solutions having all weak derivatives in the sense of Sobolev involved in the equation). The technique of proving the existence theorems is based on a special regularization of the equations under study, a priori estimates, and passage to the limit.

In this paper, the intervals of change in the exponent of the degree of degeneration of a mixed-type equation with characteristic degeneration are established. The first boundary problem and the modified boundary problem (analogue of the Keldysh problem) with the conditions of periodicity are correctly set. In the case of the first problem, a criterion for the uniqueness of its solution is manifested. It is shown that the solution of the analogue of the Keldysh problem is unique up to a term of a linear function. Solutions are constructed as the sum of series of eigenfunctions of the corresponding one-dimensional spectral problem. In justifying the convergence of a series representing the solution of the first boundary-value problem, the problem of small denominators of a more complex structure arises in the class of regular solutions of this equation than in previously known works. The estimate on separation from zero is established with the corresponding asymptotic. Based on this estimate, sufficient conditions are found for the boundary functions to substantiate the uniform convergence of the series and their derivatives up to the second order inclusive.

The inverse problems for finding the initial condition and the right-hand side were studied for the heat transfer equation. A solution of the initial boundary value problem for the inhomogeneous heat transfer equation with sufficient conditions for the solvability of the problem was constructed in the first place. On the basis of the solution of the initial boundary value problem, a criterion for the uniqueness of the solution of the inverse problem to determine the initial condition was established. The study of the inverse problem of finding the right-hand side of the component, which depends on time, is equivalent to reducing to the unique solvability of the Volterra integral equation of the second kind. In view of the unique solvability of the given integral equation in the class of continuous functions, we obtained theorems for the unique solvability of the inverse problem. The solution of the inverse problem to determine the factor of the right-hand side, depending on the spatial coordinate, was constructed as a sum of the series in the system of eigenfunctions of the corresponding one-dimensional spectral problem; the criterion of uniqueness was established, and the existence and stability theorems of the solution of the problem were proved.

Modern scientific discourse, basing on the postnonclassical scientific world picture and on the permanent-transitive fluctuations of the postmodern period, still includes such eternal questions as the problem of a man, human life and health, the fundamental factors of the world and human being in the world. Life is the only biologically possible way of human being in the world. Its value lies not only in the specificities of existing biological forms and various manifestations, which are nevertheless a unique phenomenon of being in their totality, but also in the possibility of self-reflection, conscious experience of the phenomenon itself and the ability to form symbolic pictures of the existential world on this basis. The purpose of the article is to examine the transformation of scientific discourse on the concept of “living” within the framework of the formation and development of religious and ethical studies. To achieve this purpose, the author analyzes the categorical framework of the concept of “living”. Analyzing classical philosophical and modern scientific approaches to the definition of the concept of “living”, the author distinguishes two main approaches to the definition of life: substrate and functional. In the article the main attention is focused on the analysis of religious and bioethical discourses in the study of “living”. Bioethical discourse proceeds from the need for identifying moral norms and imperatives that can answer the question of the limits of the existence of “living” and determine the moral possibilities of impact (expansion or narrowing) on these limits. One of the fundamental problems of bioethics is the problem of life as a value. In modern bioethical discourse there are two main points of view in this regard. The first may be named the ethics of the sacrality of life or life as the highest value (sanctity of life), the second – the ethics of the quality life (quality of life). The sacrality of life implies an attitude to the phenomenon of “living” as to the object of exceptional weight, of the most important value, and on this basis requires a reverent attitude to it. This approach has the most clear and full representation by modern religious discourse. The religious content of the bioethical discourse on “living” is manifested, firstly, in approval of the objective ontological status of the human personality by the Christian personalism; secondly, in the teachings of Christian theologians who claim the beauty and righteousness of life created by God, where nature and human are understood as something sacral, and therefore the actions against them are sinful and unacceptable; thirdly, the basis of human life is rooted in the spiritual world of human himself related to the divine transcendence. In is concluded that modern religious and ethical discourse forms a system of categories and concepts that describe applied ethical conceptual constructs in order to form a person’s moral attitude to all living. The proposed author’s approach allowed establishing the essence of modern bioethical discourse in the study of “living”.

This article investigates the problems which arise when the concept of possible worlds is applied to modal and existential judgments about God. In presentday logic, philosophy and linguistics, modal statements are conventionally understood as coordinating the situation described or relationships between situations with possible worlds. Existential statements are in this case seen as coordinating what is being stated by default with reality. But a judgment about God does not always imply a link between His existence or His possession of certain properties and some concrete world or even the whole array of possible worlds. Having studied the problem, the author of the paper has come to the conclusion that semantics of possible worlds is compatible with preferable (from the point of view of theism) readings of diffi cult cases of the type in question if one of the two requirements is met, namely if these statements are not assigned the sense of the truth or they are understood as hidden metaphors.

Purpose. To examine the existential anthropology of G. Marcel and E. Minkowski, in order to demonstrate the necessity of distinguishing the universal-spiritual, as human in human being, apart from the individual-existential in him, and to reveal the hierarchical correlation of biosocial, existential and spiritual spheres in personality. Theoretical basis. Within existential philosophy the author differentiates two separate traditions and proceeds from the insufficiency of the distinction of existential sphere, proposed by phenomenological tradition, showing the necessity of its correlation with the spiritual sphere as a sphere of humanity, proposed by non-phenomenological tradition of G. Marcel and E. Minkowski. Originality. The author presents the anthropological conception of G. Marcel and E. Minkowski, in which human personality is understood as unity of individual-existential and universal-spiritual, which requires a special trans-empirical field of culture, which contains senses, images and symbols of humanity. Also, the author presents the recent developments of existential thinkers in distinguishing existential and spiritual dimensions, both not reducible to the physical and social dimensions. Conclusions. In both existential traditions, the specifically human was founded as a trans-biological and trans-social phenomenon, which appears as indefinable and non-predetermined. But in first tradition (M. Heidegger, J.-P. Sartre), humanity is understood as an existence, as a unique individuality, "project", variant of humanity, equivalent to other variants, and universal is understood as a community of human condition in the world. While in the second tradition (G. Marcel, E. Minkowski, also V. Frankl), the universal is understood as spiritual. Thus, horizontal level of our private existence, as the process of movement from birth to death, is supplemented by vertical of human, universal ideals and images. Humanity appears as a task, on the way to which human being transcends beyond the limits of his individual "self" to the "super-individual", through inclusion into spiritual community, into universal culture.

Introduction. The article discusses the problem of a limited personal world. Its topicality is justified by a specific spiritual and historical situation in the modern world when a man and the humanity can no longer accept or follow the old-time values, which have now been undermined. Moreover, there is a necessity to have the landmarks that would aid one in orienting one’s inner world, since it is becoming ever more obvious that the reliable support is found only in the single available authentic being – the within. By reflecting on various metaphors of human psychological rigidity, the author is discussing the potentialities and traits of the inner existence free from limitations and constraints. The aim of the research is to analyze and try to discover the limitations and obstacles preventing one from implementing their individual existential projects, as well as elucidating the basic psychological mechanisms, encumbering deeper awareness of one’s own existential core.Materials and Methods. To achieve this goal, the methods of theoretical analysis and generalization of the interdisciplinary literature has been undertaken. Philosophical, sociological, psychological, psychopathological as well as fiction literature has been analyzed. Out of empirical methods, observation was used to observe the phenomena of the inner life of the psychological patients with the follow-up induction and synthesis of the facts obtained. Interdisciplinary approach was used, as well as the principle of theory-practice interconnection, situation specific approach, existentialism as a methodological concept, synergetic approach.Results. Conceptions related to overcoming inner closedness and conformity are developed from existential perspective. Wholeness is understood as integrity of cognitive, emotional and volitional aspects of human psyche. Man is understood as a being that gains its wholeness and overcomes limitation on its way beyond any imposed boundaries, be it outer or inner. In this sense, existential philosophy of the German thinker and psychiatrist Karl Jaspers with his metaphor of the shell reveals itself as anthropology of vulnerability. Overcoming constrains on its way to integrity and wholeness man inevitably faces vulnerability. In this encounter he comes to a new quality of self-awareness. From this perspective man is understood as becoming, a becoming being.Discussions and Conclusions. This understanding of wholeness and integrity, and man as a vulnerable and becoming being draws our attention to the problem of the loss of the sense of being in the modern world. The sense of being is a transcendental to a subject sense of being encompassing the subject himself. These conclusions are aimed at solving the existential sort of issues within psychological consultancy sessions. That is aimed at rediscovering the ability to experience being without adapting to other’s evaluations; rediscovering the original sense of existence through the growth in awareness of oneself, other people and the world.

The subject of this article is Heidegger's existentially-ontological consideration of human being (Dasein) as the transcending structure. This article proves the conclusion that the interpretation of Heidegger's intentional consciousness as “transcendence” means going beyond Husserl's phenomenology. Consequently, raising an issue of intentionality as a specific kind of Being (rather than cognition) Heidegger in contrast with Husserl considers the latter not as the consciousness immanent act, but as the act of transcending, or ecstasis, which being “isomorphic to Husserl's structure of intention” is regarded as ontological (rather than epistemological or academic) phenomenon. Specifically, Heidegger regards the act of transcending as the ecstatic temporality, and, therefore, as the fundamental aprioristic structure of the human Being. Significantly, this ecstatic temporality corresponds to “«the horizon of understanding, which ontologically belongs to Dasein”. Furthermore, Heidegger characterizes the above-described structure as the “openness” (openness of things existent to Dasein and vice versa) and interprets it as the basic phenomenon, and as the initial research subject in his phenomenological ontology. Moreover, this structure of the human being has a twofold interpretation: as the Being of things existent (Dasein), or as the aprioristic condition of this Being, hence it “internally” grounds “the possibility of ontology” in principle.

In the rectangular domain, the initial-boundary value problem for the Helmholtz equation and its non-local modifications are studied and the inverse problems for finding its right-hand side are studied. The solutions of direct problems with nonlocal boundary conditions and inverse problems are constructed in explicit form as the sums of orthogonal series in the system of eigenfunctions of the one-dimensional Sturm-Liouville spectral problem. The corresponding uniqueness theorems for the solution of all set problems are proved. Sufficient conditions for boundary functions are established, which are guaranteed by the existence and stability theorems for the solution of the proposed new problem statements.

In mathematical modeling of continuous media with memory, we deal with equations that describe a new type of wave motion, something between ordinary wave diffusion and classical wave propagation. There are fractional differential equations, which are the basis for the most mathematical models describing a wide class of physical and chemical processes in the fractal geometry of the Nature. The paper presents a new moisture transfer equation with a fractional Riemann – Liouville derivative that generalize the Aller – Lykov equation. The first boundary value problem for the generalized moisture transfer equation is considered. To prove the uniqueness of a solution we employ the energy inequalities method; an a priori estimate is obtained in terms of the fractional Riemann – Liouville derivative. The existence of the solution for the problem is proved by the Fourier method.