Rational Type Research Articles

A connection between the classical r-matrix formalism and covariant Hamiltonian field theory

We bring together aspects of covariant Hamiltonian field theory and of classical integrable field theories in 1+1 dimensions. Specifically, our main result is to obtain for the first time the classical r-matrix structure within a covariant Poisson bracket for the Lax connection, or Lax one form. This exhibits a certain covariant nature of the classical r-matrix with respect to the underlying spacetime variables. The main result is established by means of several prototypical examples of integrable field theories, all equipped with a Zakharov–Shabat type Lax pair. Full details are presented for: (a) the sine–Gordon model which provides a relativistic example associated to a classical r-matrix of trigonometric type; (b) the nonlinear Schrödinger equation and the (complex) modified Korteweg–de Vries equation which provide two non-relativistic examples associated to the same classical r-matrix of rational type, characteristic of the AKNS hierarchy. The appearance of the r-matrix in a covariant Poisson bracket is a signature of the integrability of the field theory in a way that puts the independent variables on equal footing. This is in sharp contrast with the single-time Hamiltonian evolution context usually associated to the r-matrix formalism.

Religious Faith And The Types Of Rationality

The purpose of this article is to determine the nature of religious faith and various types of rationality, with special emphasis on instrumental rationality, to characterise the link between faith and reason, and to reveal the insufficiency of instrumental reason in the sphere of faith. Instrumental reason is limited to the practical pursuits, which forces man to rely on a different type of mental activity in other spheres of life, such as religiousness. The paper is divided into three parts. The first section presents the nature of religious faith (religious faith as a psychological attitude of the followers and as a set of theses accepted in a given religion; existential and cognitive dimension of faith; the relationship between faith and revelation; assertion of religious truth). The second section outlines the nature of modern rationality (pluralism of rationality, its types, instrumental reason). The third section focuses on the relationship between religious faith and human reason (ratio, substantial reason, intellect).

ON THE ISSUE OF ESTIMATING ECONOMIC LOSSES IN THE CARRIAGE OF CARGO TRANSPORTATION WITHIN A LARGE INDUSTRIAL UNIT

The article deals with topical issues of estimation of the general economic losses from freight transport. The purpose of the study is to estimate the economic losses incurred in the carriage of goods by road within a large industrial unit, taking into account all the costs and the amount of damage. Methodology. In the course of the study, the methods of field observations, scientific search, intellectual and statistical data analysis were applied.Findings. Separate calculation methods and methods are used as a basis for development, which are used in European and CIS countries. It is established that considerable material damage is caused to objects and elements of transport and urban infrastructure. Industrial sites (cities and other settlements) are subject to harmful environmental impacts. They incur considerable losses and carriers, using vehicles in difficult road conditions. Road accidents (road accidents) involving freight vehicles also cause damage to the region's economy, carriers, road owners, third parties.Quantitative assessment is a set of separate economic calculations of different costs and amounts of damage. An assessment was made and appropriate calculations were made to determine the cost of repairs, restoration, reconstruction and operation of the road farm; for repair, restoration of rolling stock, damage due to underutilization of its performance; damage from road accidents and costs of eliminating the consequences of an accident; reduced environmental costs.The originality is that for the first time an extended method of calculation (quantification) of total damage, which is inflicted by road freight transport to the infrastructure and transport network of regions, industrial units, cities and other settlements, is proposed.The practical value is that the quantitative assessment will allow an objective assessment of the economic damage, costs and losses of freight transport systems. Implementation of the proposed developments will facilitate the choice of more efficient options for the organization of transportation, the application of more rational types of rolling stock, the complete or partial elimination of the harmful effects of road transport.

Constructive arithmetics in Ore localizations enjoying enough commutativity

This paper continues a research program on constructive investigations of non-commutative Ore localizations, initiated in our previous papers, and particularly touches the constructiveness of arithmetics within such localizations. Earlier we have introduced monoidal, geometric and rational types of localizations of domains as objects of our studies. Here we extend this classification to rings with zero divisors and consider Ore sets of the mentioned types which are commutative enough: such a set either belongs to a commutative algebra or it is central or its elements commute pairwise. By using the systematic approach we have developed before, we prove that arithmetic within the localization of a commutative polynomial algebra is constructive and give the necessary algorithms. We also address the important question of computing the local closure of ideals which is also known as the desingularization, and present an algorithm for the computation of the symbolic power of a given ideal in a commutative ring. We also provide algorithms to compute local closures for certain non-commutative rings with respect to Ore sets with enough commutativity.

Perception, Logic and Plurality of Rational Representations of the World

The article covers such issues as the relevance of the theory of perception as a multi-level information processing, the methodological role of the concept of representation and the relation of neurodynamic structures to subjective experience. The author critically reviews the philosophical presumptions underlying the various concepts of “local rationality,” the core of which is constituted by the belief that large ethnic cultures generate or are based on their own rationality and their own logic. Three statements are successively considered: (a) thinking is based on the inherent rules of rationality, (b) logic is an extract of rationality, and (c) types of rationality are geographically consistent with large ethnocultural communities. Empirical arguments are presented that demonstrate equivocality (if not falsity) of the first two theses. In particular, firstly, it is shown that the genuine rationality of thinking lies not in following the rules that are immanent to it, but in the development of thinking and, more broadly, cognitive operations towards optimization of certain indicators of the cognitive or motor system that are important for survival and adaptation. In addition, this rationality is multivariate, and the choice between variants is often weakly determined or even random. Thus, the first statement turns out to be refuted. Secondly, by reference to the well-known experiments, it is shown that most people do not explicitly follow some declared logical rules in solving even logical or mathematical problems, and yet there is reason to consider their behavior rational. The third thesis, as shown with some limited empirical material, appears to be partially confirmed. Nevertheless, the demonstration of the doubtfulness of the first two theses makes the conclusion that different nations have different logics insufficiently substantiated.

A review of cost–benefit analysis and multicriteria decision analysis from the perspective of sustainable transport in project evaluation

Transport decision processes have traditionally applied cost–benefit analysis (CBA) with benefits mainly relating to time-savings, and costs relating to infrastructure and maintenance costs. However, a shift toward more sustainable practices was initiated over the last decades to remedy the many negative impacts of automobility. As a result, decision processes related to transport projects have become more complex due to the multidimensional aspects and to the variety of stakeholders involved, often with conflicting points of view. To support rigourous decision-making, multicriteria decision analysis (MCDA) is, in addition to CBA, often used by governments and cities. However, there is still no consensus in the transport field regarding a preferred method that can integrate sustainability principles. This paper presents a descriptive literature review related to MCDA and CBA in the field of transport. Among the 66 considered papers, we identified the perceived strengths and weaknesses of CBA and MCDA, the different ways to combine them and the ability of each method to support sustainable transport decision processes. We further analysed the results based on four types of rationality (objectivist, conformist, adjustive, and reflexive). Our results show that both methods can help improve the decision processes and that, depending on the rationality adopted, the perceived strengths and weaknesses of MCDA and CBA can vary. Nonetheless, we observe that by adopting a more global and holistic perspective and by facilitating the inclusion of a participative process, MCDA, or a combination of both methods, emerge as the more promising appraisal methods for sustainable transport.

Психология восприятия: трансцендентальная перспектива

Using the meta-empirical foundations of the transcendental approach to the study of perception, the author organizes and generalizes the theoretical and empirical data of modern foreign and domestic perceptual studies (about 1,000 sources) in the following areas: methodological and methodical aspects of the modern perceptual psychology; correlation of types of scientific rationality in the modern perceptual psychology; the process of perception as a special function of the psyche, etc. The paper identifies the core methodological and methodical trends in the development of the modern perceptual psychology: expanded requirements for the lack of bias, accuracy and reliability of experimental studies; ontologization of the research subject; complexity and crosscutting features of the research system; the active use of modern technological opportunities, including the renovation of classical research methods. The author substantiates the methodological necessity of a brand new resource for studying perception from the proper positions of meta-empirical foundations — a transcendental approach, in which the directly sensory process of perception is positioned as a process of form generation helping to distinguish the generative quality of this process and capture its diffe­rence from the structural qualities of other information processes. Against the modern trends in the positioning of perception as an auxiliary stage of latent representation and categorization of objects of the external world, the author shows the relevance and identifies the means of distinguishing perception as a special function of the psyche. The paper substantiates the transcendental type of scientific rationality, alternative to the epistemological paradigm of cognition.

Random fixed point theorems in Banach spaces applied to a random nonlinear integral equation of the Hammerstein type

The purpose of this paper is to define a new random operator called the generalized ϕ-weakly contraction of the rational type. This new random operator includes those studied by Khan et al. (Filomat 31(12):3611–3626, 2017) and Zhang et al. (Appl. Math. Mech. 32(6):805–810, 2011) as special cases. We prove some convergence, existence, and stability results in separable Banach spaces. Moreover, we produce some numerical examples to demonstrate the applicability of our analytical results. Furthermore, we apply our results in proving the existence of a solution of a nonlinear integral equation of the Hammerstein type.

The Problem of Harmonization of Linguistic Pictures of the World (The Case of Western European and Chinese Medicine)

The article discusses the problem of coexistence of different types of rationality, different scientific and linguistic pictures of the world as well as the problem of the adoption by one culture of another culture’s scientific picture of the world with accompanying transformations of the linguistic picture of the world of the recipient culture. The article deals with the experience of mutual research and collision between Western and Chinese traditions, using the example of medical science. The author examines the problem of the transfer of scientific medical knowledge from Western to Chinese culture in the context of a radical mismatch of scientific and linguistic pictures. The articles considers two different approaches to the translation of Western medical terminology into Chinese, developed at different times by English translators Benjamin Hobson and John Fryer. Hobson was focused on harmonizing new terminology with the usual concepts of the world language picture of the recipient. Fryer preferred to introduce new specific terms, artificially created directly for the needs of a new scientific picture of the world. In the field of medical terminology, the first of the two approaches turns out to be more viable, since it is more focused on its “end users” – Chinese doctors who study Western medicine in order to use its methods in their medical practice. Therefore, there is only partial applicability of the approaches, methods and terminology developed in one tradition for the evaluation and development of another tradition.

Is the Conceptual Eurocentrism So Much Frightening?

The article is a response to the criticism of “conceptual Eurocentrism” expressed in the paper by A.A. Krushinsky at the Round Table on the Geography of Rationality on April 25, 2019. It deals with the main thesis of A.A. Krushinsky that in cross-cultural philosophical studies the Western conceptual matrix currently defines a single conceptual space for all participants, the language of Western philosophy acts as a trans-civilizational language in the world philosophy. The author of the article agrees with the main thesis, however she does not agree with its arguments and two consequences: (a) it is necessary to consider Western rationality as “rationality as such,” and (b) there is no multi-polarity in the current philosophy though there are a lot of traditions of philosophical discourse, which identify and articulate themselves by means of Western conceptuality (that is why we may speak on so-called “philosophical geography” only). The arguments do not stand comparison with the search of future philosophy, conducted now by the world philosophical community. The search is aiming to equality of all philosophical traditions. The article proves that conceptual Eurocentrism is not so much a danger as an objective necessity. Its spread is a manifestation of tendency to creative mutual borrowing of cultural inventions. The tendency always had place, but it was not so obvious in the conditions of preglobal history. The consequences of Krushinskiy’s thesis are refuted by the evidence that the Western philosophers denied to use the concept universal rationality and began studies of the various types of rationality. The author also provides an example of the creative borrowing and use of European concepts “rationality,” “positive knowledge,” “truth,” “scientific method,” “hypothesis” by the Indian philosopher of science B. Seal, who applied these concepts to the Indian material.

The Problem of the Typology of Rationality in Muslim Culture

The typology of rationality is one of major issues of modern philosophy. In an attempt to provide a typology to Oriental materials, a researcher faces additional problems. The diversity of the Orient as such poses a major challenge. When we say “Oriental,” we mean several cultures for which we cannot find a common denominator. The concept of “Orient” involves Arabic, Indian, Chinese, Turkish and other cultures, and the only thing they share is that they are “non-Western.” Moreover, even if we focus just on Islamic culture and look into rationality in this context, we have to deal with a conglomerate of various trends, which does not let us define, with full confidence, a common theoretical basis and treat them as a unity. Nevertheless, we have to go on trying to find common directions in thought development, so as to draw conclusions about types of rationality possible in Islamic culture. A basis for such a typology of rationality in the context of the Islamic world was recently suggested in A.V. Smirnov’s logic of sense theory. However, actual empiric material cannot always fit theoretical models, and the cases that do not fit the common scheme are interesting per se. On the one hand, examination of such cases gives an opportunity to specify certain provisions of the theory and, on the other hand, to define the limits of its applicability.

Rational maps from Euclidean configuration spaces to spheres

In this note we give an algorithm to determine the rational homotopy type of the free and pointed mapping spaces $\map(F(\br^m,k),\bs^n)$ and $\map^*(F(\br^m,k),\bs^n)$. An explicit description of these spaces is given for $k=3$. The general case for $n$ odd is also presented as an immediate consequence of the rational version of a classical result of Thom.

Almost formality of manifolds of low dimension

In this paper we introduce the notion of Poincare DGCAs of Hodge type, which is a subclass of Poincare DGCAs encompassing the de Rham algebras of closed orientable manifolds. Then we introduce the notion of the small algebra and the small quotient algebra of a Poincare DGCA of Hodge type. Using these concepts, we investigate the equivalence class of $(r-1)$ connected $(r>1)$ Poincare DGCAs of Hodge type. In particular, we show that a $(r-1)$ connected Poincare DGCA of Hodge type ${\mathcal A}^\ast$ of dimension $n \le 5r-3$ is $A_\infty$-quasi-isomorphic to an $A_3$-algebra and prove that the only obstruction to the formality of ${\mathcal A}^\ast$ is a distinguished Harrison cohomology class $[\mu_3] \in {\mathsf{Harr}}^{3,-1} (H^*({\mathcal A}^\ast), H^*({\mathcal A}^\ast))$. Moreover, the cohomology class $[\mu_3]$ and the DGCA isomorphism class of $H^*({\mathcal A}^\ast)$ determine the $A_\infty$-quasi-isomorphism class of ${\mathcal A}^\ast$. This can be seen as a Harrison cohomology version of the Crowley-Nordstrom results [D. Crowley, J. Nordstrom, The rational homotopy type of $(n-1)$-connected manifolds of dimension up to $5n-3$, arXiv:1505.04184v2] on rational homotopy type of $(r-1)$-connected $(r>1)$ closed manifolds of dimension up to $5r-3$. We also derive the almost formality of closed $G_2$-manifolds, which have been discovered recently by Chan-Karigiannis-Tsang in [K.F. Chan, S. Karigiannis and C.C. Tsang, The ${\mathcal L}_B$-cohomology on compact torsion-free ${\rm G}_2$ manifolds and an application to `almost' formality, arXiv:1801.06410, to appear in Ann. Global Anal. Geom.], from our results and the Cheeger-Gromoll splitting theorem.

DEVELOPMENT OF THE CLASSIFICATION OF THE CYBER SECURITY AGENTS BOUNDED RATIONALITY

The subject are the bounded rationality agents of cyber security system. The purpose of this work is is to build a classification system for agents of a cybersecurity system with limited rationality. The tasks: consideration of the decisionmaking process by agents in cybersecurity systems, analysis of various manifestations of bounded rationality of agents of the cybersecurity system, introduction of classification features of bounded rationality, formal presentation of bounded rationality of various types, combining agents with various types of bounded rationality into a whole classification system. Results. Presents approaches to the classification of the concept of rationality in relation to cybersecurity systems. Such types of rationality are considered as strong, semi-strong, weak. Further classification of types of rationality is carried out on the basis of the place of manifestation of rationality. For this, the decision-making process in the cybersecurity system has been considered, formal relations have been introduced, which characterize its various stages. Such types of bounded rationality as informational, methodological, predictive, evaluative and conditional are considered. The ratio of the considered types of rationality is presented. Conclusion: A comparison of various types of bounded rationality, based primarily on its place in the decision-making process, made it possible to propose a classification scheme of bounded rationality characteristic of agents of the cybersecurity system. The result of the formalization of the description of bounded rationality is presented, which can be used as the basis for the development of models of behavior of interacting agents of cybersecurity systems.

Rational homotopy theory of spaces 1-connected by shape

A rational shape type and a strong rational shape type are defined for the class of spaces 1-connected by shape. This class is a natural generalization of the class of 1-connected spaces for which the rational homotopy theory was constructed in work [10]. With the use of the category of inverse systems, the result in [10] on the equivalence of homotopy theories is extended onto the class of spaces 1-connected by shape.

Contractions with rational inequalities in the extended b-metric space

In this paper, we prove some fixed point theorems for contractions of rational type in the setting of the extended b-metric spaces. We present some examples to illustrate the validity of our results. Our results improve and generalize a number of fixed point results in the literature.

Senderos que se bifurcan. Patrones de acceso a la vida política y experiencia militante en la UNLP

Los autores analizan la experiencia política de los militantes de la Universidad Nacional de La Plata a partir de los datos que surgen de entrevistas realizadas con militantes de diferentes agrupaciones. De acuerdo con la exploración, el ingreso al campo político universitario se resumen en tres modelos de trayectoria que denominan militancia o politización por el «legado», a través del «conflicto» y por «contacto». Apoyados en las mismas fuentes, se analiza la tensión entre los perfiles del militante «emancipador» y el militante visto como «calculador racional». Se concluye que ambas identificaciones conviven guiadas por dos tipos de racionalidades: la «comunicativa», ligada a la prosecución de objetivos emancipatorios, y la «estratégica», vinculada a fines de construcción, de distribución y de ejercicio de poder.

An Ethic of Organizational Responsibility? Decoupling in the light of Weberian Types of Rationality

An Ethic of Organizational Responsibility? Decoupling in the light of Weberian Types of Rationality

Exact single traveling wave solutions to generalized (2+1)-dimensional Gardner equation with variable coefficients

We firstly apply the trial equation method to generalized (2+1)-dimensional Gardner equation to reduce the nonlinear partial differential equation into ordinary equation. Then by the complete discrimination system for polynomial method, the classification of the exact single traveling wave solutions is presented. This is the first time that the two methods are applied to integral-differential equation. In the classification, we can see that the equation has rational function type solutions, solitary wave solutions, triangle function type periodic solutions and Jacobian elliptic functions solutions with double periodic, which are impossible to be obtained by other methods. Moreover, to ensure the existences of these solutions, concrete examples are also constructed with specific parameters. To the best of our knowledge, the results presented in the paper are brand new and can not be found in any other papers.

SOME COMMON FIXED POINT RESULTS FOR RATIONAL CONTRACTION TYPE VIA THE C-CLASS FUNCTIONS ON METRIC SPACES

The purpose of this paper is to prove some common fixed point results for rational contraction type via the C-class functions on metric spaces. As an application, we study the existence of solutions to the system of nonlinear integral equations.