Necessary Conditions For Existence Research Articles

О ДИСТАНЦИИ

The subject of the article is distance, and applications of its analysis, namely: distancial and proximal phenomena and research. The research method is exemplification, explanation of phenomena through characteristic examples, here – distances. Distance has different meanings: distance, detachment, distinction, retreat, distance, alienation, etc., having different natures: physical, figurative, religious, logical, etc. However, if understanding comes late, through distance, then what is the use of it? Depending on the understanding of the infinite, there are two types of distance: 1) a distance leading to an unattainable perfection, an ideal, here infinity turns into emptiness; 2) a distancethat includes the finite and emptiness as ideal moments of movement. The distance is determined through a series of successive approximations, or «near» and «far». In other words, the definition of distance coincides with the definition of truth. For example, K. Levi-Strauss showed that the savage thought as well as modern man, progress occurred not in thinking, but in living conditions. Here people of distant epochs come closer together, through finding a distance between them – this is indicated by the principle of the constancy of distance. An example of a distal study is the definition of the «power distance index», the proximity or remoteness of power from the people. The distances between the past, present and future have ideological significance. Research on this issue notes the reduction of the present time through growth, pressure and acceleration of innovation, alienation from the past and present. A. Einstein, denied the phenomenon of irreversibility, and believed that the division of time into the past, present and future is an illusion. The greatest distance between near and far is created by religion. The article proposes a new trichotomy of truth./false/faith, where faith is the sphere of meaning. Faith forms a distance that transcends human experience – transcendence. Distance and understanding should have a measure – the distance should not be too close or too far, and also go (slip away) into the empty otherworldliness of infinity. Distance correlates with the path, if the path is a necessary condition for existence and understanding, then distance should be a sufficient reason for the path (both understanding and existence). The concept of distance can be attributed to the «dimensional categories» of the synthetic paradigm (the expression of D. V. Pivovarov).

Analysis of a non-integer order compartmental model for cholera and COVID-19 incorporating human and environmental transmissions

Fractional differential operators have increasingly gained wider applications in epidemiological modelling due to their ability to capture memory effect in their definitions; an attribute which lacks in the concept of classical integer derivatives. In this paper, employing the Caputo fractional operator with singular kernel, the co-dynamical model for cholera and COVID-19 diseases is proposed and analyzed, incorporating both direct and indirect transmission routes for cholera. The necessary conditions for existence of the unique solution of the proposed model are studied. Using the results from fixed point theory, Ulam-Hyers stability analysis of the system is performed. The model is fitted to real data from Pakistan and the optimized order of the fractional derivative for which the system fits well to data is obtained. Other numerical assessments of the model are also executed. Phase portraits of the infected classes with different initial conditions and various order of the fractional derivative are obtained in the cases when the reproduction number and . It is observed that the trajectories for the infected compartments tend towards the infection-free steady state when and the endemic steady state when irrespective of the initial conditions and the order of the fractional derivative. Increment in the COVID-19 vaccine efficacy, keeping the vaccination rate fixed at , resulted in a decline in the COVID-19 disease. Also, increasing the COVID-19 vaccination rate, keeping the vaccine efficacy for COVID-19 fixed at , led to a decline in the COVID-19 associated reproduction number. The simulations also pointed out the impact of COVID-19 and cholera vaccinations, direct and indirect transmissions of cholera.

Optimal control and cost effectiveness analysis of contamination associated with aflatoxins in maize kernels, livestock and humans

Aflatoxin contamination poses a significant challenge in food safety and security as it affects both health of consumers and supply chains. Due to health impacts associated with aflatoxin contamination, countries have set standards and restrictions for importing food crops and animal feed, resulting in greater economic losses to farmers, transporters, and crop processors. Three controls, namely good farming practices, biological control and public education and awareness campaigns, have been mostly used in countries where aflatoxin contamination has occurred. Since resources are scarce, there is a need to find the optimal and cost-effective strategy to reduce the burden on farmers. This study aimed to find optimal and cost-effective control strategy to mitigated aflatoxin contamination in maize kernels, livestock and humans. A deterministic model was developed and analyzed for studying the impact of implementing three time dependent controls on the dynamics and control of aflatoxin contamination in maize kernels, livestock and humans. We use optimal control theory to find the necessary conditions for existence of the optimal controls and to determine the optimal strategy for controlling the aflatoxin contamination. We also carry out cost-effectiveness analysis through Incremental Cost Effective Ratio (ICER) to obtain the most effective strategy. Simulation results for the optimal control problem suggest that strategy which involve implementation of all controls performs well than other strategies in controlling the aflatoxin contamination in maize kernels, livestock and humans. Therefore, to control aflatoxin contamination initiatives should focus on good farming practices, biological control and public education and awareness campaigns.

The algorithms for the Eulerian cycle and Eulerian trail problems for a multiple graph

In this paper, we study undirected multiple graphs of any natural multiplicity $k>1$. There are edges of three types: ordinary edges, multiple edges and multi-edges. Each edge of the last two types is a union of $k$ linked edges, which connect 2 or $(k+1)$ vertices, correspondingly. The linked edges should be used simultaneously. If a vertex is incident to a multiple edge, it can be also incident to other multiple edges and it can be the common end of $k$ linked edges of some multi-edge. If a vertex is the common end of some multi-edge, it cannot be the common end of another multi-edge. We set the problem of finding the eulerian walk (the cycle or the trail) in a multiple graph, which generalizes the classical problem for an ordinary graph. We formulate the necessary conditions for existence of an eulerian walk in a multiple graph and show that these conditions are not sufficient. Besides that, we show that the necessary conditions of existence of an eulerian cycle and eulerian trail are not mutually exclusive for an arbitrary multiple graph, that is why it is possible to construct a multiple graph where two types of eulerian walks exist simultaneously. Any multiple graph can be juxtaposed to the ordinary graph with quasi-vertices, which represents the structure of the initial graph in a simpler form. In particular, each eulerian walk in the multiple graph corresponds to the eulerian walk in the graph with quasi-vertices. The algorithm for getting such a graph is formulated. Also, the auxiliary problem of finding the covering trails with given endpoints in an ordinary graph is studied. Two algorithms are obtained for this problem. We elaborate the algorithm for finding the eulerian walk in a multiple graph, which has the exponential complexity. We suggest the polynomial algorithm for the special case of a multiple graph and show that the necessary conditions are sufficient for existence of an eulerian walk in this special case.

Existence and uniqueness of limits at infinity for homogeneous Sobolev functions

We establish the existence and uniqueness of limits at infinity along infinite curves outside a zero modulus family for functions in a homogeneous Sobolev space under the assumption that the underlying space is equipped with a doubling measure which supports a Poincaré inequality. We also characterize the settings where this conclusion is nontrivial. Secondly, we introduce notions of weak polar coordinate systems and radial curves on metric measure spaces. Then sufficient and necessary conditions for existence of radial limits are given. As a consequence, we characterize the existence of radial limits in certain concrete settings.

Gradient-based descent linesearch to solve interval-valued optimization problems under gH-differentiability with application to finance

In this article, gradient based descent line search scheme is proposed to solve interval optimization problems under generalized Hukuhara differentiability. The innovation and importance of these concepts are presented from practical and computational point of view. The necessary condition for existence of critical point is presented in inclusion form of interval-valued gradient, without transforming it into real valued function. Suitable efficient descent direction is chosen based on the monotonic property of the interval-valued function and specific interval ordering. Mathematical convergence of the scheme is proved under the assumption of Inexact line search for interval optimization problem. The theoretical developments are implemented with a set of interval test problems in different dimensions. A possible application in finance is provided and solved by our proposed scheme.

Сутність і структура індивідуально-психологічної готовності фахівців соціальної сфери до роботи з вразливими категоріями населення

The article, based on the analysis of scientific literature, theoretically substantiates the essence and structure of the individual and psychological willingness of specialists in the social sphere to work with vulnerable categories of the population. It has been established that the individual and psychological willingness of social sphere specialists to work with vulnerable categories of the population is a unique, inimitable combination of physiological, mental and psychological qualities of the individual, which determines the individual lifestyle and allows effective professional activity. Vulnerable categories of the population are that part of the human community of a particular society, which during this period of time or on an ongoing basis has the highest risk of falling into difficult life circumstances due to the influence of adverse external or internal factors and needs help, support and protection from the state, state and non-state bodies, institutions and organizations, as it is unable to provide itself with the necessary conditions for existence without outside help. The structure of the individual and psychological willingness of social sphere specialists to work with vulnerable categories of the population has been determined as a dynamic combination of two components: psychophysiological (abstractness, criticality, flexibility and creativity of thinking; emotional stability; strong-willed determination) and psychological (tolerance, communicativeness, reflexivity and other personality qualities).

Necessary conditions for existence of an additional integral in the problem on motion of a solid body with a fixed point in the flow of particles bounded by an ellipsoid revolution surface

Рассматривается задача о движении в свободном молекулярном потоке частиц твердого тела с неподвижной точкой, ограниченного поверхностью эллипсоида вращения. Получены необходимые условия существования в этом случае дополнительного аналитического первого интеграла, независимого с интегралом энергии.

Nonlinear Liouville-type theorems for generalized Baouendi-Grushin operator on Riemannian manifolds

We are concerned with differential inequalities of the form $$ -[d_{M_2}(y_0,y)]^{2\rho_2}\Delta_{M_1} u-[d_{M_1}(x_0,x)]^{2\rho_1}\Delta_{M_2}u\geq V |u|^p\mbox { in } M_1\times M_2, $$ where $M_i$ ($i=1,2$) are complete noncompact Riemannian manifolds, $(x_0,y_0)\in M_1\times M_2$ is fixed, $d_{M_1}(x_0,\cdot)$ is the distance function on $M_1$, $d_{M_2}(y_0,\cdot)$ is the distance function on $M_2$, $\Delta_{M_i}$ is the Laplace-Beltrami operator on $M_i$, $V=V(x,y) > 0$ is a measurable function, and $p>1$. Namely, we establish necessary conditions for existence of nontrivial weak solutions to the considered problem. The obtained conditions depend on the parameters of the problem as well as the geometry of the manifolds $M_i$. Next, we discuss some special cases of potential functions $V$. The proof of our main result is based on the nonlinear capacity method and a result due to Bianchi and Setti (2018) about the construction of cut-off functions with controlled gradient and Laplacian, under certain assumptions on the Ricci curvatures of the manifolds.

On pseudofrobenius imprimitive association schemes

An (association) scheme is said to be Frobenius if it is the (orbital) scheme of a Frobenius group. A scheme which has the same tensor of intersection numbers as some Frobenius scheme is said to be pseudofrobenius. We establish a necessary and sufficient condition for an imprimitive pseudofrobenius scheme to be Frobenius. We also prove strong necessary conditions for existence of an imprimitive pseudofrobenius scheme which is not Frobenius. As a byproduct, we obtain a sufficient condition for an imprimitive Frobenius group G with abelian kernel to be determined up to isomorphism only by the character table of G. Finally, we prove that the Weisfeiler-Leman dimension of a circulant graph with n vertices and Frobenius automorphism group is equal to 2 unless $$n\in \{p,p^2,p^3,pq,p^2q\}$$ , where p and q are distinct primes.

The existence of a triangle when its three elements are known

The problem of the existence of a triangle with respect to three given elements in some cases can be very difficult. For example, Brokard's problem about the existence of a triangle, given its three bisectors [1], has a long history [3] and solved only in 1994 [10]. We include in the number of elements: three sides, three angles, three heights, three medians, three bisectors, radii of the circumscribed and inscribed circles, and perimeter. In total, there are 186 different problems of the existence of a triangle with three given elements and for 116 problems are given sufficient conditions (for some sufficient and necessary conditions of existence) when a triangle can be construct by a compass and a ruler, and the remaining 70 problems when it is impossible to construct a triangle by a compass and a ruler. The authors list these 70 problems and indicate for which of them the necessary and sufficient conditions for the uniqueness of the existence of a triangle with three prescribed elements have found.

ІНТЕГРОВАНИЙ КУРС «МИСТЕЦТВО» ЯК ІНСТРУМЕНТ РОЗВИТКУ КРИТИЧНОГО МИСЛЕННЯ ЗДОБУВАЧІВ ПОЧАТКОВОЇ ОСВІТИ

For more than ten years, modern psychology and pedagogy have preferred effective and original educational tools, the main purpose of which is to reveal the potential of modern art, the development of critical thinking that can be used in the study of various school subjects. Modern society, like life, is very demanding, it needs citizens who are able to think flexibly and dynamically, are able to navigate the variability of life, can make unusual decisions. Critical thinking of contemporary art is a jewelry tool for understanding the new educational paradigm focused on the adaptation of free communication in the world. Life proves that thanks to creativity, flexibility, the ability to generate new ideas, society will be easier to navigate in the most difficult times. How to prepare primary school students for life activities and fruitful work? Why should teachers and their students understand contemporary art? Scientific research (Kolotilo O.) proves that the main tasks of teaching an integrated course «art» are to reveal creative talents, stimulate artistic and figurative thinking, education of aesthetic taste of the individual in early school age and later independent life. In the process of a brief review of the history of modern art, the development of cultural values, the development of artistic and figurative thinking is formed on the basis of the idea of «beautiful». The demand for creative, intellectually developed people is very high.The classification of types of thinking has its origins in the works of Aristotle, who built the sphere of «speculation» and «pure reason» on a system of universal abstractions. Psychologists, in turn, consider several types of thinking: visual, concrete and abstract, intuitive and critical thinking. The scientific prism of intellectual and practical activity emphasizes the unity of thinking with the feelings of perception of the world around. Thanks to critical thinking, the child goes beyond sensory cognition. L. Masol, S. Zhupanin and F. Shchegel agree that the methodological basis for understanding the essence of the artistic image are the philosophical provisions of the theory of knowledge, interpret thinking as a holistic expression of human essence, where feelings and imagination provide diversity of implementation. Each of us is an artist, and creativity brings us great pleasure. In art, a person gets many opportunities to express their feelings and emotions. Creative talents in children are no longer perceived as internal uncontrolled processes. Creativity – a constant companion of child development, and in a broader sense – a necessary condition for existence. With the help of an integrated art course introduced by the New Ukrainian School, primary school students expand their knowledge of the ideas and features of contemporary art and develop skills to implement various components of contemporary art in their professional activities. Key words: critical thinking, creativity, subject learning, creativity, abilities, art, New Ukrainian School

Self-Sustaining Oscillations With an Internal Two-Fuzzy Inference System Based on the Poincaré–Bendixson Method

The generation of self-sustaining oscillations at the output of nonlinear systems without tracking a reference signal is under investigation. In this study, we proposed an internal double fuzzy inference system to generate an asymptotically stable limit cycle or self-oscillations for the second-order systems. The fuzzy system has been synthesized by invoking the Poincaré–Bendixson theorem, which states sufficient and necessary conditions of existence of an attracting periodic orbit at the output of the closed-loop system. This theorem was also used for design; that is, we set the tuning rules of the fuzzy controller. The effectiveness of the proposed controller is corroborated by numerical simulations and experiments made in a single-link pendulum system.

Money and Economic Growth Revisited: A Note

In an important but neglected paper, Begg (1980) attempted to solve the puz-zle of monetary super-neutrality in the steady-state. Super-neutrality was shown to depend on two sufficient conditions, only one of which is necessary. Begg argued that a more general specification restores monetary non-super-neutrality. This note suggests an additional sufficient condition for super-neutrality. The demand for real balances must be modeled as a de-creasing function of the real interest rate. This has implications for models as-suming a steady-state. Harkness (1978) had already shown that the extra suf-ficient condition is a necessary condition for existence.

О существовании и устойчивости решений типа «кольцо» уравнений нейронного поля Амари с периодической микроструктурой и функцией активации Хевисайда

In the present research, existence and stability of ring solutions to two-dimensional Amari neural field equation with periodic microstructure and Heaviside activation function are studied. Results on dependence of the inner and the outer radii of the ring solutions are obtained. Necessary conditions for existence and sufficient conditions for non-existence of radial travelling waves are formulated for homogeneous neural medium and neural media with mild periodic microstructure. Theoretical results obtained are illustrated with a concrete example based on a connectivity function commonly used in the neuroscience community.

Fixed point theorems to generalize FR- contraction mappings with application to nonlinear matrix equations

In the present paper, we introduce the notion of generalize FR-contraction and establish some fixed point results for such mappings, which extend and generalize the result of Alam and Imdad (J. Fixed Point Theory & Appl., 17(4) (2015), 693-702), Sawangsup et al. (J. Fixed Point Theory, 2016 (2016), 1-15) and many others. Our results reveal that the assumption of M-closedness of underlying binary relation is not necessary condition for existence of fixed point in relational metric spaces. We also derive some N-order fixed point theorems from our main results. As an application of our main result, we find a solution of a certain class of nonlinear matrix equations.

Optimal control analysis of Taenia saginata bovine cysticercosis and human taeniasis

Bovine cysticercosis and human taeniasis are neglected food-borne diseases that pose challenge to food safety, human health and livelihood of rural livestock farmers. In this paper, we have formulated and analyzed a deterministic model for transmission dynamics and control of taeniasis and cysticercosis in humans and cattle respectively. The analysis shows that both the disease free equilibrium (DFE) and endemic equilibrium (EE) exist. To study the dynamics of the diseases, we derived the basic reproduction number R0 by next generation matrix method which shows whether the diseases die or persist in humans and cattle. The diseases clear if R0<1 and persist when R0>1. The normalized forward sensitivity index is used to derive sensitive indices of model parameters. Sensitivity analysis results indicate that human's and cattle's recruitment rates, infection rate of cattle from contaminated environment, probability of humans to acquire taeniasis due to consumption of infected meat, defecation rate of humans with taeniasis and the consumption rate of raw or undercooked infected meat are the most positive sensitive parameters whereas the natural death rates for humans, cattle, Taenia saginata eggs and the proportion of unconsumed infected meat are the most negative sensitive parameters in diseases’ transmission. These results suggest that control measures such as improving meat cooking, meat inspection and treatment of infected humans will be effective for controlling taeniasis and cysticercosis in humans and cattle respectively. The optimal control theory is applied by considering three time dependent controls which are improved meat cooking, vaccination of cattle, and treatment of humans with taeniasis when they are implemented in combination. The Pontryagin's maximum principle is adopted to find the necessary conditions for existence of the optimal controls. The Runge Kutta order four forward-backward sweep method is implemented in Matlab to solve the optimal control problem. The results indicate that a strategy which focuses on improving meat cooking and treatment of humans with taeniasis is the optimal strategy for diseases’ control.

A Multiplication Technique for the Factorization of Bivariate Quaternionic Polynomials

We consider bivariate polynomials over the skew field of quaternions, where the indeterminates commute with all coefficients and with each other. We analyze existence of univariate factorizations, that is, factorizations with univariate linear factors. A necessary condition for existence of univariate factorizations is factorization of the norm polynomial into a product of univariate polynomials. This condition is, however, not sufficient. Our central result states that univariate factorizations exist after multiplication with a suitable univariate real polynomial as long as the necessary factorization condition is fulfilled. We present an algorithm for computing this real polynomial and a corresponding univariate factorization. If a univariate factorization of the original polynomial exists, a suitable input of the algorithm produces a constant multiplication factor, thus giving an a posteriori condition for existence of univariate factorizations. Some factorizations obtained in this way are of interest in mechanism science. We present an example of a curious closed-loop mechanism with eight revolute joints.

THE IMPORTANCE OF THE ORGANIZATION OF ACCOUNTING AND CLASSIFICATION OF ACCOUNTING

The article considers the current state of methodological tools for the formation of financial statements, based on the interests of consumers of such reporting and the current state of the domestic economy. On the basis of the organization of accounting the necessary general theoretical provisions and methodology of formation of system of the accounting administrative reporting are defined, following which it will be possible to speak about existence of necessary conditions of formation of a qualitative information base for acceptance of administrative decisions. A description of the range of users, which allows to limit the various options for financial reporting, taking into account their real needs and interests. Depending on the specific features of the company and the content of financial statements, the justification of categories according to the content of information. The place and significance of financial reporting in the process of forming macroeconomic indicators and determining the directions of classification of financial statements based on the results of spectral analysis of information interests of users of accounting information at the local level and at the macro level of the state as a user of information. For business entities, financial statements are allocated, which reflect information on ordinary and extraordinary activities with the appropriate details. The degree of automation of the management and accounting system, which is divided into automated, partially automated accounting and manually compiled, is considered. It is noted that the considered areas of grouping of financial statements take into account the information interests of users of accounting information both at the local level of individual enterprises and at the state level as users of information in the formation of macroeconomic indicators, which will improve their quality and improve the range of indicators.

Dyakonov surface magnons and magnon polaritons

We predicted one Dyakonov surface magnon (DSM) and two Dyakonov magnon polaritons (DSMPs) localized at the antiferromagnet (AF)-air interface. Their concise dispersion equations and necessary conditions of existence were obtained. The DSM is the magnetostatic limit of the first DSMP, which are situated inside the AF reststrahlen frequency band. The second DSMP has no magnetostatic limit and lies outside the frequency band. The specifical frequency ranges occupied by the DSM and DSMPs were analytically found. The DSMPs are hybrid-polarization surface polaritons and the DSM is a hybrid-polarization surface magnetostatic mode. The first DSMP possesses large attenuation constants so that it is highly localized at the surface. Compared with it, the second DSMP exhibits relatively small attenuation constants. According to the features of polarization obtained for either DSMP, we used the TE and TM radiations incident on the AF surface to calculate attenuated total reflection (ATR) spectra, respectively. These ATR spectra not only further prove the existence of the DSMPs but also demonstrate their observability in experiment. However, the DSM should be detected by means of a light-scattering technique.