Axiological Dimension of the Concept of the Soul in Pamfil Yurkevych’s Philosophical Works

In the article, the author analyses Pamfil Yurkevych’s vision of the interaction between the heart and the reason as well as analyzes his axiosphere, which is absolutely necessary for the development of our country. The author argues that Pamfil Yurkevych is the founder of the axiosphere, which was in compliance with the European Continental Philosophy’s understanding of the being-with-other (Mit-Sein) and it remains also relevant nowadays. Therefore, the main emphasis in the article is placed on the value component of Pamfil Yurkevych’s philosophical reflection and significance of the concept of the soul as a bearer of axiological foundations for the development of spirituality in society. The author interprets the concept of the soul as the interaction between the heart and the reason. At the same time, the heart is a kind of value filter, and the reason plays the role of an instrument of intentional activity in the field of values, involvement in which enables the real development of society. The author relies on the representation, interpretation and analysis as operations of cognition with the help of which it is possible to reproduce a holistic picture of Pamfil Yurkevych’s axiosphere and prove its significance for the formation of value priorities in the contemporaneity.

Speech Influence Mechanisms and Models in Polycode and Polymodal Text (Using the Example of Regional Television Sports Coverage)

This article analyzes speech influence mechanisms and models in polycode and polymodal text. As an example, we took a sports coverages aired on regional television, since it is a polycode and polymodal composing. The publication presents speech influence mechanisms and models proposed by various researchers. Taking into consideration various points of view it can be assumed that speech influence in television sports coverage occurs through the information sharing on two levels proposed by A.A. Leontiev. This process is carried out either by introducing new knowledge about reality into the field of values of the recipient, on the basis of which he will change his behavior or his attitude to this reality, or by changing the field of values of the recipient without introducing new elements.

Speech Influence Mechanisms and Models in Polycode and Polymodal Text (Using the Example of Regional Television Sports Coverage)

This article analyzes speech influence mechanisms and models in polycode and polymodal text. As an example, we took a sports coverages aired on regional television, since it is a polycode and polymodal composing. The publication presents speech influence mechanisms and models proposed by various researchers. Taking into consideration various points of view it can be assumed that speech influence in television sports coverage occurs through the information sharing on two levels proposed by A.A. Leontiev. This process is carried out either by introducing new knowledge about reality into the field of values of the recipient, on the basis of which he will change his behavior or his attitude to this reality, or by changing the field of values of the recipient without introducing new elements.

New Parameterizations of \(\mathrm{SL}(2,\mathbb{R})\) and Some Explicit Formulas for Its Logarithm

Here we demonstrate some of the benefits of a novel parameterization of the Lie groups $\mathrm{Sp}(2,\bbr)\cong\mathrm{SL}(2,\bbr)$. Relying on the properties of the exponential map $\mathfrak{sl}(2,\bbr)\to\mathrm{SL}(2,\bbr)$, we have found a few explicit formulas for the logarithm of the matrices in these groups.\\ Additionally, the explicit analytic description of the ellipse representing their field of values is derived and this allows a direct graphical identification of various types.

Domain decomposition preconditioners for high-order discretizations of the heterogeneous Helmholtz equation

We consider one-level additive Schwarz domain decomposition preconditioners for the Helmholtz equation with variable coefficients (modelling wave propagation in heterogeneous media), subject to boundary conditions that include wave scattering problems. Absorption is included as a parameter in the problem. This problem is discretized using $H^1$-conforming nodal finite elements of fixed local degree $p$ on meshes with diameter $h = h(k)$, chosen so that the error remains bounded with increasing $k$. The action of the one-level preconditioner consists of the parallel solution of problems on subdomains (which can be of general geometry), each equipped with an impedance boundary condition. We prove rigorous estimates on the norm and field of values of the left- or right-preconditioned matrix that show explicitly how the absorption, the heterogeneity in the coefficients and the dependence on the degree enter the estimates. These estimates prove rigorously that, with enough absorption and for $k$ large enough, GMRES is guaranteed to converge in a number of iterations that is independent of $k,p$ and the coefficients. The theoretical threshold for $k$ to be large enough depends on $p$ and on the local variation of coefficients in subdomains (and not globally). Extensive numerical experiments are given for both the absorptive and the propagative cases; in the latter case, we investigate examples both when the coefficients are nontrapping and when they are trapping. These experiments support (i) our theory in terms of dependence on polynomial degree and the coefficients; and (ii) the sharpness of our field of values estimates in terms of the level of absorption required.

ENTERPRISE SUBSYSTEMS INTERACTION UNDER PURPOSEFUL CONTROL OF PRODUCT QUALITY

The purpose of the paper is to study the interaction of social-economic, organizational and engineering subsystems of industrial enterprises during purposeful control of product quality. There is offered an interaction scheme of enterprise subsystems at product quality support. The simulation carried out allowed defining a difference between the values of managing impacts ensuring the reachability of the ends specified for a stationary state of enterprise activities and in the planned period of time for a time dependent of activities with the use of real data. To ensure actual reachability of the required values of the ends in the field of quality one requires to specify their increased values, in this connection there is introduced an idea of a gain factor. In the example considered for two values of product quality there is defined a field of values corresponding to gain factors showing a level of value increase of the ends required in the field of quality to ensure their actual reachability. With the use of fields revealed a possibility appeared to offer different variants of values of gain factors during managing solutions making. The directions for the further investigations connected with the analysis of operator structure to change values of enterprises subsystems in the course of the assurance of ends manageability in the field of quality are defined.

The field of values of Jones matrices: classification and special cases

The concept of field of values (FoV), also known as the numerical range, is applied to the 2 × 2 Jones matrices used in polarization optics. We discover the relevant interplay between the geometric properties of the FoV, the algebraic properties of the Jones matrices and the representation of polarization states on the Poincaré sphere. The properties of the FoV reveal hidden symmetries in the relationships between the eigenvectors and eigenvalues of the Jones matrices. We determine the main mathematical properties of the FoV, discuss the special cases that are relevant to polarization optics, and describe its application to calculate the Pancharatnam-Berry phase introduced by an optical system to the input state.