Problem Of Existence Research Articles

INTENTIONAL APPROACH TO THE INTERPRETATION OF EXISTENTIAL CATEGORIES IN THE “KHIKMETS” OF AKHMET YASSAWI

In the article helped by conceptual and phenomenological research methods, existential categories in the “Diwani Khikmets” by Akhmet Yassawi are studied. The aim of the article is to analyze human existence problems, the meaning of life, the relationship of being and time, true love for the Creator, and the phenomenon of life and death. Although Akhmet Yassawi does not belong to the existentialists, existential categories can be clearly distinguished in the “Khikmets”. The concepts of “The Book of Wisdom” are a storehouse of answers to transcendental questions for people in existential crisis. The main purpose of the “Khikmets” is religious, and Akhmet Yassawi presents “intentional” advice on vital issues such as world creation and human nature (being), using existential categories. When we talk about the intentional meaning of existential categories, we mean the understanding of intentionality in Husserl's phenomenology, which considers the act of orientation as the inclusion of the subject in the analysis of an exclusively given object of philosophizing without distraction to other cognitive constructs. It is this subjective experience and living of the act of contemplation that is vividly expressed in “Khikmets” by Akhmet Yassawi. Akhmet Yassawi talks about such deep and exclusively existential categories as life and death. In modern philosophy, it was existentialism that revived attention to these concepts. From the point of view of existentialists, life, even in a situation of absurdity, is of the highest value. But this is life, always “borderline” with death. Life on the verge of death, loss and the search for the meaning of life are situations that Akhmet Yassawi raised long before the existentialism of the twentieth century. Keywords: Akhmet Yasawi, “Khikmets”, Existential Motives in Intentionality, Transcendental Experiences.

Universality of Euler flows and flexibility of Reeb embeddings

The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. Recently, Tao [38,39] launched a programme to address the global existence problem for the Euler and Navier Stokes equations based on the concept of universality. Inspired by this proposal, in this article we prove that the stationary Euler equations exhibit several universality features. More precisely, we show that any non-autonomous flow on a compact manifold can be extended to a smooth stationary solution of the Euler equations on some Riemannian manifold of possibly higher dimension. The solutions we construct are of Beltrami type, and being stationary they exist for all time. Using this result, we establish the Turing completeness of the steady Euler flows, i.e., there exist solutions that encode a universal Turing machine and, in particular, these solutions have undecidable trajectories. Our proofs deepen the correspondence between contact topology and hydrodynamics, which is key to establish the universality of the Reeb flows and their Beltrami counterparts. An essential ingredient in the proofs, of interest in itself, is a novel flexibility theorem for embeddings in Reeb dynamics in terms of an h-principle in contact geometry, which unveils the flexible behavior of the steady Euler flows. These results can be viewed as lending support to the intuition that solutions to the Euler equations can be extremely complicated in nature.

Using edge cuts to find Euler tours and Euler families in hypergraphs

An Euler tour in a hypergraph is a closed walk that traverses each edge of the hypergraph exactly once, while an Euler family is a family of closed walks that jointly traverse each edge exactly once and cannot be concatenated. In this paper, we show how the problem of existence of an Euler tour (family) in a hypergraph H can be reduced to the analogous problem in some smaller hypergraphs that are derived from H using an edge cut of H. In the process, new techniques of edge cut assignments and collapsed hypergraphs are introduced. Moreover, we describe algorithms based on these characterizations that determine whether or not a hypergraph admits an Euler tour (family), and can also construct an Euler tour (family) if it exists.

On the sticky particle solutions to the multi-dimensional pressureless Euler equations

In this paper we consider the multi-dimensional pressureless Euler system and we tackle the problem of existence and uniqueness of sticky particle solutions for general measure-type initial data. Although explicit counterexamples to both existence and uniqueness are known since [6], the problem of whether one can still find sticky particle solutions for a large set of data and of how one can select them was up to our knowledge still completely open.In this paper we prove that for a comeager set of initial data in the weak topology the pressureless Euler system admits a unique sticky particle solution given by a free flow where trajectories are disjoint straight lines.Indeed, such an existence and uniqueness result holds for a broader class of solutions decreasing their kinetic energy, which we call dissipative solutions, and which turns out to be the compact weak closure of the classical sticky particle solutions. Therefore any scheme for which the energy is l.s.c. and is dissipated will converge, for a comeager set of data, to our solution, i.e. the free flow.

Poisson Stable Motions and Global Attractors of Symmetric Monotone Nonautonomous Dynamical Systems

This paper is dedicated to the study of the problem of existence of Poisson stable (Bohr/Levitan almost periodic, almost automorphic, almost recurrent, recurrent, pseudo-periodic, pseudo-recurrent and Poisson stable) motions of symmetric monotone non-autonomous dynamical systems (NDS). It is proved that every precompact motion of such system is asymptotically Poisson stable. We give also the description of the structure of compact global attractor for monotone NDS with symmetry. We establish the main results in the framework of general non-autonomous (cocycle) dynamical systems. We apply our general results to the study of the problem of existence of different classes of Poisson stable solutions and global attractors for a chemical reaction network and nonautonomous translation-invariant difference equations.

Filippov's Solution and Finite-Time Stability of Stochastic Systems for Discontinuous Control

In this paper, a suite of theoretic tools is provided for discontinuous control design and finite-time stability analysis of a class of stochastic differential systems. The notion of Filippov&#x0027;s solutions for stochastic differential systems is proposed, and the corresponding solution existence problem is explored. The classical It&#x00F4; differentiation formula is generalized for quasi-<inline-formula><tex-math notation="LaTeX">$C_{0}^{2}(\mathbb {R}^{n},\mathbb {R})$</tex-math></inline-formula>-class functions along Filippov&#x0027;s solutions of stochastic differential systems, and two involved set-valued stochastic integrals are introduced with a study on their properties. Some finite-time stability results of stochastic differential systems are revealed with Filippov&#x0027;s solutions, and one of them is applied to neural synchronization, together with case simulations.

ОБРАЗ ЛЮДИНИ КАТАСТРОФИ У РОМАНІ ДЖУЛІАНА БАРНЗА «ВІДЧУТТЯ ЗАКІНЧЕННЯ»

ОБРАЗ ЛЮДИНИ КАТАСТРОФИ У РОМАНІ ДЖУЛІАНА БАРНЗА «ВІДЧУТТЯ ЗАКІНЧЕННЯ»

THEORETICAL AND LEGAL FOUNDATIONS THE ESSENCE AND CONTENT OF ENVIRONMENTAL EDUCATION

The article considers scientific and doctrinal approaches to the definition of the term "environmental education". The author's approach to the content of the concept of environmental education is offered. Its special features and their content side revealing essence of ecological education are distinguished. The important place of environmental education as system forming factor and fundamental element within the framework of sustainable development strategy realization and necessity of introducing the basics of environmental knowledge within the framework of all levels of education is underlined. It is stressed that environmental education is an important element of education and solving environmental tasks of the society and the state. The main goals of ecological education are defined among which one of the main goals is, in the author's opinion, orientation on preparation of professional staff, capable to solve existent ecological problems effectively.

DEVELOPMENT STAGES, OPPORTUNITIES AND CHALLENGES OF THE HOTEL BUSINESS AND HOTEL TYPE ESTABLISHMENTS: GEORGIAN EXPERIENCE

One of the essential and reliable guarantees for the further development of the tourism potential of Georgia, of course, is the development and expansion of the hotel business and hotel-type establishments, because Georgia, as a country of four seasons, has excellent tourism opportunities and has the chance to be active throughout the year.&#x0D; The article's primary purpose is to study and explore the role and importance of the hotel business in Georgia, both in terms of the development of the Georgian tourism market, the society involved in this area, and the formation of financial income in the country. The economy as a whole.&#x0D; Despite the significant successes and results already achieved in this field, as evidenced by the highest ratings of leading and influential international organizations, where Georgia, at different times, as an essential tourist center, as well as individual hotels, is often in advanced positions, the problem is that the hotel industry market in Georgia is still in the process of formation and cannot fully meet the complex needs of customers with different levels, abilities, tastes, and needs.&#x0D; The article analyzes the stages of formation and development of the hotel business and hotel-type establishments in Georgia; current state, features, and development opportunities; analysis of statistical data and results; Existing risks, challenges, and problems, ways to overcome them and prospects, compliance with international standards and impact on the sustainable development of the country's tourism market.

Existence of extrinsic polyharmonic maps in critical dimensions

Given two closed Riemannian manifolds M of dimension 2m and N⊂RK, we study the existence problem of extrinsic m-polyharmonic maps in a fixed free homotopy class from M to N. We prove that any energy-minimizing sequence in a fixed free homotopy class subsequently converges locally in Wm,2 to a smooth extrinsic m-polyharmonic map except possibly at most finitely many energy concentration points. Moreover, at an energy concentration point we show that there exists a non-constant smooth extrinsic m-polyharmonic map from R2m to N by blow-up analysis. As a consequence, when the homotopy group π2m(N) is trivial, we prove that there always exists a minimizing extrinsic m-polyharmonic map in every free homotopy class in [M2m,N]. This generalizes the celebrated existence results for harmonic maps (m=1) and biharmonic maps (m=2). The main technical ingredient is an ϵ-regularity for an energy-minimizing sequence, which is new for m-polyharmonic maps and should be of independent interest.

The Existence Paradigm and the Antinomy of the Liar in Mathematical Economics

Early contributions in Walrasian general equilibrium analysis led to logical problems that are remnants of the foundations debate in mathematics. The problem of existence of equilibrium in a competitive economy was at the core of this research program. This was however a loaded question since it admits different methodological approaches and interpretations. By tracing back the problem to the foundations of mathematics this paper aims to identify logical implications of the existence paradigm in Walrasian theory. Grounded on a bird’s eye overview of the history of ideas in early mathematical economics, the distinction is made between different interpretations of the question in relation with axiomatics and models of competitive economies. This leads to the conclusion that in general equilibrium theory, the problem set to provide consistency or existence proofs entails logical implications about the antinomy of liar and the rationale of doctrines in economics.

Религиозно-философские диалоги в романе Достоевского «Бесы»

Philosophical dialogue as a genre generated by ancient culture has become an integral part of F. M. Dostoevsky’s novels. There it acquired a distinctly religious character. In this sense, the theory of M. M. Bakhtin about polyphonic dialogue in Dostoevsky’s novels does not allow to fully explain its (dialogue’s) mystical-religious content, and even more so the hidden author’s modality – Christian assessment (“pointing finger, passionately raised”). Moreover, the question of faith in the polyphonic dialogue is not raised at all. Bakhtin confines himself to the dialogue of the “speech activities” of the subjects, the characters’ minds “in the realm of the word”, “the image of the idea” as a “living event”. The article highlights a special religious and philosophical dialogue in Dostoevsky’s novel on the example of Demons. It is proved that the characters of such a dialogue philosophize, i.e. act not only as those with external, effective, psychological characteristics, but as spokesmen for a certain intellectual activity, an established concept of life, which they usually translate into philosophemes, mental images. Religious-philosophical dialogue is also present when conducted at the level of metaphysical depths, with a creed, a manifestation of religious feeling, when the question of the Absolute is being resolved. Deep drama, appeal to the eternal problems of existence, the ultimate expansion of the artistic space of the topics, the subjects of dialogue limit the plot peculiarities and the characters’ details. There is a feeling of a direct connection between the two minds in the darkest corners of the man’s spirit: “Here the devil is fighting with God, and the battlefield is the hearts of people” (XIV, 100).

Orlicz–Lorentz function spaces equipped with the Orlicz norm

We investigate Orlicz–Lorentz function spaces equipped with the Orlicz norm generated by any Orlicz function and any non-increasing weight function. As far as we know, this is the first time such a general research is conducted. First we show some basic properties of the Orlicz norm, including its equality to the Amemiya norm, the problem of attainability of infimum in the definition of the Amemiya norm and a formula for the norm of a characteristic function. Then we find criteria for the order continuity and strict monotonicity and we study the problem of existence of order linearly isometric copies of l^{infty }.

Probing the Geometry of Correlation Matrices with Randomized Measurements

The generalized Bloch decomposition of a bipartite quantum state gives rise to a correlation matrix whose singular values provide rich information about non-local properties of the state, such as the dimensionality of entanglement. While some entanglement criteria based on the singular values exist, a complete understanding of the geometry of admissible correlation matrices is lacking. We provide a deeper insight into the geometry of the singular values of the correlation matrices of limited Schmidt number. First, we provide a link to the framework of randomized measurements and show how to obtain knowledge about the singular values in this framework by constructing observables that yield the same moments as one obtains from orthogonal averages over the Bloch sphere. We then focus on the case of separable states and characterize the boundary of the set of the first two non-vanishing moments by giving explicit constructions for some of the faces and extremal points. These constructions yield a connection between the geometry of the correlation matrices and the existence problems of maximal sets of mutually unbiased bases, as well as SIC-POVMs.

The Relevance of the Practice of Ifá Divination in Ola Rotimi’s The Gods are not to Blame

The custom of Ifá divination is common among the Yorùbá of Western Nigeria, and among Africans generally. This paper attempts an evaluation of the relevance of the practice of Ifá divination in the selected play of Ola Rotimi to Yorùbá culture and metaphysics. This is purposely to attain a greater and more profound awareness of its role as a symbol of communal and cultural identicalness. Using The God Are Not to Blame (1975) as an illustration, the paper contends, in a poignant manner, that the elements of Yorùbá Ifá divination, through oracular devices, well manifested in the structuring principles of Rotimi’s work. This is analyzed from spiritual and mythological angles. With an overwhelming lucidity, the paper posits that actions in the play are influenced by an assumption that any collective catastrophe or adversities are the outcomes of disharmony between disparate cosmos. The aforementioned includes a detailed interrogation of the rationality and logic of these beliefs as Rotimi presents them. Through the ambiance of the various events in the play, the paper establishes that the practice of Ifá divination in Yorùbá land is not only a way of life but has also transcended traditional, Christian, and Muslim traditions and beliefs. Finally, while recognizing the enduring popularity and artistic forte of Rotimi’s magnum opus, the paper broadens spasmodically our perception of the pervasiveness and practical relevance of the practice of Ifá divination as means for rectifying evil destiny, regulating what the future holds and resolving problems of existence in Yorùbá culture and metaphysics.

Block-Graceful Designs

In this article, we adapt the edge-graceful graph labeling definition into block designs and define a block design V , B with V = v and B = b as block-graceful if there exists a bijection f : B ⟶ 1,2 , … , b such that the induced mapping f + : V ⟶ Z v given by f + x = ∑ x ∈ A A ∈ B f A mod v is a bijection. A quick observation shows that every v , b , r , k , λ − BIBD that is generated from a cyclic difference family is block-graceful when v , r = 1 . As immediate consequences of this observation, we can obtain block-graceful Steiner triple system of order v for all v ≡ 1 mod 6 and block-graceful projective geometries, i.e., q d + 1 − 1 / q − 1 , q d − 1 / q − 1 , q d − 1 − 1 / q − 1 − BIBDs. In the article, we give a necessary condition and prove some basic results on the existence of block-graceful v , k , λ − BIBDs. We consider the case v ≡ 3 mod 6 for Steiner triple systems and give a recursive construction for obtaining block-graceful triple systems from those of smaller order which allows us to get infinite families of block-graceful Steiner triple systems of order v for v ≡ 3 mod 6 . We also consider affine geometries and prove that for every integer d ≥ 2 and q ≥ 3 , where q is an odd prime power or q = 4 , there exists a block-graceful q d , q , 1 − BIBD. We make a list of small parameters such that the existence problem of block-graceful labelings is completely solved for all pairwise nonisomorphic BIBDs with these parameters. We complete the article with some open problems and conjectures.

Bounded Solutions of Difference Equations in a Banach Space with Asymptotically Constant Operator Coefficient

We study the problem of existence of a unique bounded solution for a difference equation on the half axis with asymptotically constant operator coefficients in a Banach space. Necessary and sufficient conditions for the existence and uniqueness of bounded solutions are obtained for equations with and without initial condition.

Spiral Waves: Linear and Nonlinear Theory

Spiral waves are striking self-organized coherent structures that organize spatio-temporal dynamics in dissipative, spatially extended systems. In this paper, we provide a conceptual approach to various properties of spiral waves. Rather than studying existence in a specific equation, we study properties of spiral waves in general reaction-diffusion systems. We show that many features of spiral waves are robust and to some extent independent of the specific model analyzed. To accomplish this, we present a suitable analytic framework, spatial radial dynamics, that allows us to rigorously characterize features such as the shape of spiral waves and their eigenfunctions, properties of the linearization, and finite-size effects. We believe that our framework can also be used to study spiral waves further and help analyze bifurcations, as well as provide guidance and predictions for experiments and numerical simulations. From a technical point of view, we introduce non-standard function spaces for the well-posedness of the existence problem which allow us to understand properties of spiral waves using dynamical systems techniques, in particular exponential dichotomies. Using these pointwise methods, we are able to bring tools from the analysis of one-dimensional coherent structures such as fronts and pulses to bear on these inherently two-dimensional defects.

Sociocultural Aspect of Functioning of Toponymic Legends in Central Kazakhstan (Expeditions Materials 2012, 2017)

The article is devoted to the problem of existence and analysis of the current state of legends and toponymic legends of Central Kazakhstan. The material was the texts recorded by the authors on expeditions to the Karaganda region in 2012 and 2017. The current state of the folklore of Central Kazakhstan is marked by the functioning of certain genres: legends, wedding poetry, proverbs, toponymic legends. The main layer of the functioning of folklore samples falls on legends and toponymic legends. It is concluded that the Kazakh legends are characterized by a specific informative function. The main plot-forming component is the character, around which all the material is united, the plots themselves, as a rule, are single-motive, do not contain fantastic elements and are designed as a narration about the recent past. The paper notes that toponymic legends explain the names of localities and are associated, as a rule, with the names of famous people. The specificity of the names is the use of speaking names or similarity with natural phenomena. The authors argue that the active functioning of folklore samples indicates a favorable folklore situation and the prospects for further research on the sociocultural aspect of Kazakh non-fairytale prose.

The Existence Problems of Solutions for a Class of Differential Variational–Hemivariational Inequality Problems

In this work, we used reflexive Banach spaces to study the differential variational—hemivariational inequality problems with constraints. We established a sequence of perturbed differential variational–hemivariational inequality problems with perturbed constraints and penalty coefficients. Then, for each perturbed inequality, we proved the unique solvability and convergence of the solutions to the problems. Following that, we proposed a mathematical model for a viscoelastic rod in unilateral contact equilibrium, where the unknowns were the displacement field and the history of the deformation. We used the abstract penalty method in the analysis of this inequality and provided the corresponding mechanical interpretations.