Rational Type Research Articles

FEATURES OF SOCIO-PSYCHOLOGICAL ADAPTATION IN STUDENTS WITH RATIONAL AND PRALOGICAL THINKING

The article describes the results of a study on the features of the socio-psychological adaptation of students with rational and pralogical types of thinking. The purpose of the study was to identify who has higher rates of socio-psychological adaptation, owners of rational or pralogical thinking.

A-optimal experimental designs for Michaelis – Menten model

Kinetics of simple and complex kinetic reactions is usually described by exponential and rational models. The fractional rational models include the well-known Michaelis – Menten model of enzymatic kinetics. In the presented article A-optimal designs are proposed for the Michaelis – Menten model. The elimination method used to construct A-optimal designs, allowed us to determine the nodes and weights of A-optimal designs separately and thereby extend this approach to other criteria and models of the rational type. It is shown that the nodes of A-optimal designs determined by this method are the roots of the 4th degree algebraic equation with coefficients depending on the model parameters. If the nodes of the A-optimal design are already known, then the weights of the corresponding nodes are determined analytically by the Pukelsheim formula. The properties of the roots as well as the properties of the nodes of A-optimal designs were studied using the Sturm system constructed in the general form for the resulting equation. It is shown that with a certain combination of parameters of the Michaelis – Menten model, the degree of the resulting algebraic equation is reduced to three. A partition of the set of values of the parameters of the Michaelis – Menten model into two subsets has been found. In one of them, the A-optimal design is determined uniquely, whereas for the other one it is necessary to select the optimal node from two possible options. It is revealed that the degree of the algebraic equation is equal to three for points belonging to the curve which is the common boundary of the indicated subsets. Corresponding numerical examples are given to illustrate the results obtained.

Investigating fractal fractional PDEs, electric circuits, and integral inclusions via (ψ,ϕ)-rational type contractions

The fixed point theory has been generalized mainly in two directions. One is the extension of the spaces, and the other is relaxing and generalizing the contractions. This paper aims to establish novel fixed point results of rational type generalized (ψ,ϕ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\psi ,\\phi )$$\\end{document}-contractions in the context of extended b-metric spaces. This will allow us to analyze generalized rational type contraction in a more relaxed and diversified framework in the light of the characteristics of (ψ,ϕ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\psi ,\\phi )$$\\end{document}. Some existing rational-type contractions have been recalled in this direction, and others are defined. New fixed point results have been established by utilizing the properties of ψ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\psi$$\\end{document} and ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi$$\\end{document} and applying the iteration technique. Moreover, the established results are employed to investigate the stability of fractal and fractional differential equations and electric circuits. For the reliability of the established results, examples and applications to the system of integral inclusions and system of integral equations are presented.

Холистическая антропология А.Л. Чижевского в контексте научного и религиозного мировоззрения

The article is devoted to the holistic views of A.L. Chizhevsky on human; fea­tures of their reflection in the philosophical and scientific works of the thinker, as well as in his poetry, are revealed; scientific and religious aspects of the scien­tist’s holistic anthropology are investigated. Analysis of the holistic world­view presented in the metaphysical work “The main beginning of the universe. Cosmic system. Problems”, allows us to state that the holistic approach to the human by Chizhevsky the philosopher is based on his conviction in the impact of the uni­versal principle of circulation on a single electric substrate. A study of the scien­tific works of one of the founders of space natural science suggests that the holistic anthropology reflected in them is based on specific laws that demonstrate human dependence on the environment (solar activity and ionized air). The Chizhevsky-poet forms the reader’s idea of the closest connection between micro- and macrocosm, about the cosmicity of a human being by using vivid images, with­out references to determinism; nevertheless, the anthropocosmic poems of “Leo­nardo da Vinci of the 20th century” are thematically related to his scientific re­search. The relevance of A.L. Chizhevsky’s holistic anthropology to the concept of global evolutionism and the post-classical type of scientific rationality is shown

A Fixed Point Theorem for Non-Self Mappings of Rational Type in 𝔟−Multiplicative Metric Spaces with Application to Integral Equations

Objectives: To prove fixed point theorem for non-self mappings of rational type in -multiplicative metric spaces and apply the theorem to solve integral equations. Method: Multiplicative metrically convex is defined in the context of - multiplicative metric spaces to prove fixed point theorems for pairs of non-self mappings using rational type contraction. Findings: The theorem demonstrates that under certain rational type contraction, a unique fixed point exists for non-self mappings in -multiplicative metric spaces. Applications of integral equations shown improved convergence and solution accuracy. Novelty: First fixed point theorem for non-self mappings in -multiplicative metric spaces, introducing a new approach to solving Volterra-Hammerstein integral equations. 2020 Mathematics Subject Classification: 47H10, 54H25. Keywords: Coincidence Point, Nonself Mappings, Rational Type contraction, b-Multiplicative Metric Spaces (b-m ́ms), Volterra-Hammerstein integral equations

Мифические детерминанты политического (Политический проект Платона)

The article is devoted to the explication of the mythological determinants of Plato’s political doctrine. The author raises the question about those axiomatic propositions that underlie the political philosophy of the ancient Greek thinker: what is it, the rudiments of mythical consciousness or the rationality of the nascent philosophical logos? The article shows that there are two opposite answers to this question. One is associated with the tradition of conceptualizing myth as fiction and fantasy (Georg Hegel, Auguste Comte, Feokhari Kessidy), the other with the understanding of myth as a special type of rationality underlying a certain ontological reality (Friedrich Schelling, Alexey Losev, Kurt Huebner). The author shows that modern Platonists are increasingly inclined to the second approach and consider myth as an indispensable element of Plato’s philosophy as such. The central element of his system, the doctrine of ideas, is genetically linked to classical mythology. Plato’s ideas are rationalized supernatural entities, divine substances. This understanding finds comprehensive manifestation in Plato’s political project. The peace of a self-identified being is the ideal of a perfect polis. Justice, on the other hand, is conformity to one’s nature i.e., ultimately, conformity to the divine substance expressed in the idea. Thus, the author concludes, justice in Plato’s project is primarily not a social or political

Segmentation of Chinese consumer preference for wine extrinsic attributes based on stratification and weighted clustering algorithm

Chinese consumers are unfamiliar with the sensory attributes of wine and often pay more attention to the extrinsic attributes of wine that can most directly present information. Therefore, it is crucial to study consumer preferences for extrinsic attributes. This paper proposes a consumer segmentation method based on stratification and weighted clustering algorithm, leveraging data from an anonymous online survey (N = 3179). The AFR model is constructed based on the RFM model to segment wine consumers from the perspective of customer value. This model removes Monetary indicator and adds a new indicator Amount to eliminate multicollinearity caused by the Frequency and Monetary indicators of RFM model. In addition, factor analysis is used to assign weights to clustering indicators, addressing the problems of unequal weighting and strong correlation among the indicators. This allows for a simple, efficient, and precise segmentation of wine consumers at different levels. The method proposed in this article segments consumers into two layers and six categories: the potential layer includes product-oriented type, amorphous type, and cheap-fine type, while the mature layer comprises the rational type, reputation-price type and random type. This research will provide wine producers and distributors with a simple and efficient basis for production and marketing decision-making. Additionally, it can serve as a reference for consumer segmentation in food and other fields.

Rational homotopy type and nilpotency of mapping spaces between Quaternionic projective spaces

The rational homotopy type of a mapping space is a way to describe the structure of the space using the algebra of its homotopy groups and the differential graded algebra of its cochains. An L∞-model is a graded Lie algebra with a family of higher-order brackets satisfying the generalized Jacobi identity and antisymmetry. It can be used to study the rational homotopy type of a space. The nilpotency index of an L∞-model is useful in understanding a space's algebraic structure. In this paper, we compute the rational homotopy type of the component of some mapping spaces between projective spaces and determine the nilpotency index of corresponding L∞-models.

On Certain Fixed Points for (α,φ,F)-Contraction on S_b- Metric Spaces with Applications

This work establishes unique fixed point theorems (UFPT) for self mapping in complete S_b-metric spaces (S_b-MS) with the concept of (α,φ,F)-contraction in the context of S_b-MS Furthermore, we show how the results may be used and present applications to integral equations and homotopy theory. Introduction: In previous work authors were discussed fixed pointon various metric spaces with F -contractions, α-type almost -F- contractions, α-type F -Suzuki contractions, (φ, F)-contraction, F - weak contractions, α −ψ-contractive type, α −ψ-Meir-Keeler contractive mapping, α-ratonal contractive mappings, (α, β) − (φ,ψ)-rational contractive type mappings. Objectives: Finding the unique fixed point for self mapping in S_b-MS, via (α,φ,F)-contraction. Methods: with the help of α- admisible mapping, (φ, F)-contraction, α type F -contraction and (α.φ,F)-contraction we have fixed point findings in complete S_b-metric spaces. Results: we obtained unique fixed point results via (α,φ,F) contractive type for self mapping in complete S_b-MS. Conclusions: In this article, Contractive mappings of the (α,φ,F) type are used to show certain fixedpoint results in the context of S_b-MS, along with appropriate example that illustrate the key findings. Appications to integral equations and homotopy are also offered.

A Revised Fuzzy Differential Equations Using Weakly Compatible Self-Mappings in Revised Fuzzy Metric Spaces

In this paper, we demonstrated certain coincidence point and Common Fixed Point [briefly, CFP] findings under the rational type weakly compatible revised fuzzy-contraction conditions in full Revised Fuzzy Metric spaces [briefly, RFMSs] utilizing the "triangular property of revised fuzzy metric" with examples in this work. We also provided Revised fuzzy differential equations [briefly, RFDEs] as an application and demonstrated that the solution of the RFDEs has a unique CFP of the integral operators B,C and g. This new path of weakly-compatible Revised fuzzy-contraction with the use of RFDEs in RFM space will be crucial. With different sorts of weakly-compatible Revised fuzzy contraction conditions for self-mappings and different forms of differential equations in the context of RFMSs, this approach may be expanded and developed in diverse directions.

A Revised Fuzzy Differential Equations Using Weakly Compatible Self-Mappings in Revised Fuzzy Metric Spaces

In this paper, we demonstrated certain coincidence point and Common Fixed Point [briefly, CFP] findings under the rational type weakly compatible revised fuzzy-contraction conditions in full Revised Fuzzy Metric spaces [briefly, RFMSs] utilizing the "triangular property of revised fuzzy metric" with examples in this work. We also provided Revised fuzzy differential equations [briefly, RFDEs] as an application and demonstrated that the solution of the RFDEs has a unique CFP of the integral operators and . This new path of weakly-compatible Revised fuzzy-contraction with the use of RFDEs in RFM space will be crucial. With different sorts of weakly-compatible Revised fuzzy contraction conditions for self-mappings and different forms of differential equations in the context of RFMSs, this approach may be expanded and developed in diverse directions.

Rational homotopy type of projectivization of the tangent bundle of certain spaces

PurposeThe paper aims to determine the rational homotopy type of the total space of projectivized bundles over complex projective spaces using Sullivan minimal models, providing insights into the algebraic structure of these spaces.Design/methodology/approachThe paper utilises techniques from Sullivan’s theory of minimal models to analyse the differential graded algebraic structure of projectivized bundles. It employs algebraic methods to compute the Sullivan minimal model of P(E) and establish relationships with the base space.FindingsThe paper determines the rational homotopy type of projectivized bundles over complex projective spaces. Of great interest is how the Chern classes of the fibre space and base space, play a critical role in determining the Sullivan model of P(E). We also provide the homogeneous space of P(E) when n = 2. Finally, we prove the formality of P(E) over a homogeneous space of equal rank.Research limitations/implicationsLimitations may include the complexity of computing minimal models for higher-dimensional bundles.Practical implicationsUnderstanding the rational homotopy type of projectivized bundles facilitates computations in algebraic topology and differential geometry, potentially aiding in applications such as topological data analysis and geometric modelling.Social implicationsWhile the direct social impact may be indirect, advancements in algebraic topology contribute to broader mathematical knowledge, which can underpin developments in science, engineering, and technology with societal benefits.Originality/valueThe paper’s originality lies in its application of Sullivan minimal models to determine the rational homotopy type of projectivized bundles over complex projective spaces, offering valuable insights into the algebraic structure of these spaces and their associated complex vector bundles.

Calculation of the main operational characteristics of a tethered high-altitude ship-based system

Objectives. Currently, UAVs are actively used in many military and civilian fields such as object surveillance, telecommunications, radar, photography, video recording, and mapping, etc. The main disadvantage of autonomous UAVs is their limited operating time. The long-term operation of UAVs on ships can be ensured by tethered high-altitude systems in which the power supply of engines and equipment is provided from the onboard energy source through a thin cable tether. This paper aims to select and justify the appearance of such system, as well as to calculate the required performance characteristics.Methods. The study used methods of systemic and functional analysis of tethered system parameters, as well as methods and models of the theory of relations and measurement.Results. The issues of design and implementation of new generation tethered high-altitude ship-based systems were considered. A rational type of aerodynamic design for unmanned aerial vehicles was determined based on existing tethered platforms. The optimal architecture of the tethered system was defined and justified. The paper presents the appearance and solution for placement onboard the ship, and describes its operation. The main initial parameters for designing high-altitude systems such as take-off weight, optimal lift altitude, maximum power required for operation, structure of the energy transfer system, as well as deployment and lift time to the design altitude were selected and calculated.Conclusions. The methodology for calculating the necessary characteristics described in the paper can be used for developing and evaluating tethered high-altitude systems. These systems are capable of performing a wide range of tasks, without requiring a separate storage and launch location, which is especially important in the ship environment. The system presented herein possesses significant advantages over well-known analogues.

Ariadne's Thread Metacognition for emancipatory rationality in education

Emancipatory rationality in education empowers individuals and promotes social justice.Metacognition and critical thinking play vital roles in supporting this approach by encouraging learners and professionals to reflect on their thinking processes, question assumptions, and develop the ability to engage critically with information. The research presented in this paper falls within the action research framework, which provides for theinvestigation to be conducted in the field based on close collaboration between researchers and practitioners. Action research aims to generate improvement and change in the context in which it is implemented. The roots of this approach can be found in Dewey’s criticism of the traditional separation of knowledge and action and in Freire’s idea of conscientization, the process of developing critical awareness through reflection and action. In their view, learning depends upon uncovering real problems and actual needs. Starting from four criticalincidents, the paper demonstrates how reflective practices based on metacognition can be used to train education professionals. Metacognitive work is essential for analyzing problems and responsibilities and identifying any distortions preventing educational action from responding effectively to people's needs. When faced with an educational problem, the professional needs to be able to use two forms of rationality: heuristic-reflective andemancipatory. The first type of rationality guides through the investigation of the experience to build the necessary knowledge to interpret and manage it. The second makes the educator an agent of transformation and change.

Some notes on spaces realized as classifying spaces

In this work, we are concerned with the realization of spaces up to rational homotopy as classifying spaces. In this paper, we first show that a class of rank-two rational spaces cannot be realized up to rational homotopy as the classifying space of any n-connected and π-finite space for n≥1. We also show that the Eilenberg-Mac Lane space K(Qr,n)(r≥2,n≥2) can be realized up to rational homotopy as the classifying space of a simply connected and elliptic space X if and only if X has the rational homotopy type of ∏rSn−1 with n even.

Certain Applications via Rational Type Contraction Fixed Point Theorems in Ab-Metric Spaces

Certain Applications via Rational Type Contraction Fixed Point Theorems in Ab-Metric Spaces

Carbohydrate digestion in the stomach of horses grazed on pasture, fed hay or hay and oats

Concentrations of starch, mono- and disaccharides, fructans, hemicellulose and cellulose were analysed in feed and gastric digesta of horses in relation to acid insoluble ash as a marker indigestible in the stomach. Twenty-four horses were allocated to pasture 24 h/d (PST; n = 4), hay ad libitum (HAY; n = 8), hay ad lib. and oats at 1 g starch/kg body weight (BWT)/meal (OS1; n = 6) and hay ad lib. and oats at 2 g starch/kg BWT/meal (OS2; n = 5). One horse was excluded from the analysis. The horses were fed the ration a minimum of 34 days. Following euthanasia and dissection, digesta was sampled from Pars nonglandularis (PNG) and Pars glandularis (PG). Oat starch concentration in gastric digesta decreased from 309 to 174 g/kg dry matter (DM) in OS1 (44 %-reduction) and from 367 to 261 g/kg DM in OS2 (29 %-reduction) (P < 0.001). Glucose, fructose and sucrose disappeared from gastric digesta distinctly more in PST, HAY and OS1 than in OS2. In PST and HAY, sucrose concentration was completely cleared (P < 0.001). The concentration of fructans was reduced predominantly in PST (84 %-reduction) and HAY (54 %-reduction), mainly in the PNG (P < 0.05). Fructan degradation did not occur in the high-starch diet (OS2). Some evidence for fibre degradation was observed in PST (P < 0.01). Soluble carbohydrates disappear from the stomach dependent on the type of ration, which may lead to changes in the composition of the gastric microbial community and the endogenous response.

Regression dependence of the number growth dynamics of the biogas plants in Ukraine

The global environmental crisis forces the countries of the world to introduce and use new alternative means of energy production, in particular methods of extraction and processing of biogas to provide energy to the population. Therefore, the determination of the regression dependence, which describes the dynamics of the increase in the number of biogas plants and can be used when forecasting the number of such plants, is an urgent scientific and technical task. The purpose of the research is to determine the regression dependence, which describes the dynamics of the increase in the number of biogas plants and can be used when forecasting the number of such plants, with the aim of increasing the prevalence of the use of renewable energy sources, saving fossil energy sources and simultaneously reducing the intensity of environmental pollution. During the research, the method of regression analysis of the results of one-factor experiments and other paired dependencies was used with the selection of a rational type of function from the sixteen most common options according to the criterion of the maximum value of the correlation coefficient. Regression was carried out on the basis of linearizing transformations, which allow reducing the non-linear dependence to a linear one. The coefficients of the regression equations were determined by the method of least squares using the developed computer program "RegAnalyz", which is protected by a certificate of copyright registration for the work. An adequate regression relationship was obtained, which describes the dynamics of the increase in the number of biogas plants and can be used when forecasting the number of such plants. A graphical dependence was built that describes the dynamics of the increase in the number of biogas plants and allows to visually illustrate this dynamic and show sufficient convergence of theoretical results with actual data. It was established that the increase in the number of biogas plants in Ukraine during 2012-2019 grew according to a hyperbolic dependence.

ANALYSIS OF STUDENTS' PERSONALITY TYPES AND ITS INFLUENCE ON MATHEMATICAL PROBLEM SOLVING ABILITY

This research aims to analyze students in solving problems based on personality type using personality type instruments, problem solving, and interviews. The research results show: (1) understanding the problem, the Guardian wrote down sufficient and necessary conditions; (2) make a solution plan, the subject is able to determine the information to solve the problem; (3) in carrying out the plan, the subject worked on the questions according to the steps but not precisely. (1) understand the problem, the idealist subject only writes down what is asked; (2) make a solution plan, the subject is able to determine the formula; (3) carrying out the plan, the subject uses a formula that has been prepared previously, even though the calculation is wrong. (1) understand the problem, Artisan type subjects write down all available information very clearly; (2) make a solution plan, the subject determines the formula. (3) carrying out the problem solving plan, the subject is able to solve the problem. (1) understanding the problem, the rational type subject does not write down sufficient and necessary conditions; (2) make a solution plan, the subject is able to determine the steps to solve it; (3) carry out problem solving plans, be skilled in algorithms and accurately answer questions.

Realization of Lie algebras of derivations and moduli spaces of some rational homotopy types

Realization of Lie algebras of derivations and moduli spaces of some rational homotopy types