Some properties of Glisson distances in the upper half-plane

The author compares the Gleason distance with the distance of Euclid in the unit disk in the upper half plane. The concept of “the Gleason distance” was formulated in the work of H.S. Bear [1] The Gleason distance is defined as follows (see [1]): d = sup |f(z2)-f(z1)|, f(Z)εB1(K) where B 1 (K) is the unit ball in the space of bounded analytic in K functions. The author of the article proves that in the circle K the distances of Gleason and Euclid are equal only when the points are opposite. He found necessary and sufficient conditions, when the distances are equal for the two given points which are symmetrical about the ordinate axis.

Investigation of the convergence of the integration algorithm with the choice of the variable of integration at each step using the example of a Luneberg lens

The paper describes an integration algorithm with a choice of a variable at each step in the numerical construction of ray trajectories in a medium with a given dependence of the permittivityon coordinates. The convergence of the calculations to the exact solution is estimated using the example of the problem of calculating the trajectories of rays in a Luneberg lens. It is shown that with a decrease in the grid step, convergence to the exact solution is observed. Purpose. Assess the convergence to an exact solution of an integration algorithm with a choice of a variable at each step using the example of the problem of calculating ray trajectories in a Luneberg lens. Results. The trajectories of rays incident parallel to the ordinate axis and the trajectories of rays incident at an angle to the ordinate axis are calculated. It is shown that with a decrease in the grid step, convergence of the results to the exact solution is observed. Practical significance. It is shown that an integration algorithm with a choice of a variable at each step provides the construction of ray trajectories with an error in the coordinate not exceeding the grid step for the problem of ray propagation in a Luneberg lens.

Financial Strategy Formulation and Implementation under Economic Uncertainty: Ukrainian companies’ case

Factors of economic uncertainty are considered. Economic uncertainty factors’ effect on financial managerial decisions is studied. Financial strategy matrix is proposed on the basis of a sample of Ukrainian companies. The proposed financial strategy matrix covers both financial and market goals – according to the BSC methodology. Thus, in the proposed tool, financial goals are reflected by the level of leverage A/E (Assets-to-Equity), market goals in turn are represented by ROA level; combination of the financial goal (A/E) and market goal (ROA) produces ROE, i.e. level of value creation for stakeholders. Within the proposed methodology financial strategy uses an analytical tool that combines financial and market goals of the enterprise, where the abscissa axis plots ROA level, the ordinate axis plots A/E level. The algorithm of making managerial decisions on financial strategy is described on an example of a company from selected sample – PJSC “Carlsberg Ukraine” – over 2014-2018. A set of managerial decisions targeted at further financial and market position is proposed.

Corrigendum

The Editor-in-Chief has been informed that in the article ?Comparisons of Quantemol and Morgan LXCat cross section sets for electron-neutral scattering and rate-coefficients: helium and water?, FACTA UNIVERSITATIS, Series Physics, Chemistry and Technology Vol. 17, No 2, 2019, pp. 145-159, DOI: https://doi.org/10.2298/FUPCT1902145M, the cross sections for electron-impact excitation of helium in Figure 1b) are wrongly presented. The values of the cross section in the ordinate axis are marked in the interval from 10-1 to 101 (in units 10-16 cm2), and should be from 10-2 to 100. We apologize for that oversight. After further discussion with the corresponding author, the Editor-in-Chief has decided to publish a corrigendum with corrected Figure 1. Link to the corrected article: https://doi.org/10.2298/FUPCT1902145M <br><br><font color="red"><b> Link to the corrected article <u><a href="http://dx.doi.org/10.2298/FUPCT1902145M">10.2298/FUPCT1902145M</a></b></u>

A New Version of Schauder and Petryshyn Type Fixed Point Theorems in S-Modular Function Spaces

In this paper, using the conditions of Taleb-Hanebaly’s theorem in a modular space where the modular is s-convex and symmetric with respect to the ordinate axis, we prove a new generalized modular version of the Schauder and Petryshyn fixed point theorems for nonexpansive mappings in s-convex sets. Our results can be applied to a nonlinear integral equation in Musielak-Orlicz space L p where 0 < p ≤ 1 and 0 < s ≤ p .

Some studies on Lorentz transformation matrix in non-cartesian co-ordinate system

The Lorentz matrices for transformation of co-ordinates in Cartesian system are presented for the cases when the relative velocity between two reference frames is along X , Y and Z axes. The general form of the matrix for transformation of co-ordinates from unprimed to primed frame has been deduced in case of Cartesian co-ordinate system with the help of the above matrices. This matrix has not been transformed to the cases of cylindrical and spherical polar co-ordinates due to the fact that the calculations are cumbersome and lengthy. Hence, considering the relative velocity between two frames along a co-ordinate axis the transformation matrix has been found out for cylindrical and spherical co-ordinates.

Power Spectrum for Surface Description of Corroded Ship Structure From Laser Scan

Strength of corroded marine structures is in the industry traditionally assessed using average thickness reduction together with the assumption of a uniform surface. In academia it is however realised that the surface texture will influence the strength where the effect of the irregular surface is considered through various parameters such as reduced material properties, roughness, geometrical ratios and thickness distributions. In this paper, the objective is to present a power spectrum which describes the corroded surface topography. Therefore, power spectra of surface and thickness are produced from 3D laser scan of real corroded mild steel specimens from a 30 year old ship using Fast Fourier Transform (FFT). The frequency distribution describes the spatial variability, wherefrom the autocorrelation function (ACF) is deduced. A log-log fit is made to the power spectrum, where the interception with the ordinate axis describes the corrosion severity. This way of describing the surface pattern of the corrosion deterioration may serve as input to novel ways of calculating corroded strength and fatigue initiation as well as simulation of corroded surfaces.

Classification and ordination of lime trees in the south of the Tyumen Region

The paper contains a classification of lime trees according to the method of Brown-Blanke and ordination based on isolated syntaxonomic units in the southern part of the Tyumen Region. The material for this study was 115 geobotanical descriptions of the lime trees in the southern part of the Tyumen Region. Syntaxonomic diversity of lime trees on the territory of three regions in the south of the Tyumen Region in the system of ecological and floral classification includes 8 associations and 6 variants belonging to 3 orders, 3 unions and 2 classes: Asaro europaei - Abietetea sibiriacae and Brachypodio pinnate - Betuletea pendulae . Forests of the selected associations and variants are distributed by various relationships to humidification conditions from the more humid to the steppe forests. To study the syntaxonomic diversity of lime trees, a multifactorial gradient analysis was used, where a combination of several environmental factors was simultaneously considered. Average values for four soil scales of D.N. Tsyganov and two scales of A.Yu. Korolyuk discovered 12 patterns of syntaxonomic units that revealed a certain pattern of distribution on the ordinate axis with concentration from dry forests to moist forests. The main gradient factor of location in the ecological area of lime trees associations is the presence of moisture in the soil.

Weighted Orthogonal Distance Regression for Tire Models Parameters Identification

Determining the parameters in existing tire models (e.g. Magic Formula (MF)) for calculating longitudinal and lateral forces depending on the tire slip is often based on standard least squares techniques. This type of optimization minimizes the vertical differences in the ordinate axis between the test data and the chosen tire model. Although the practice is to use this type of optimization in adjusting those model parameters, it should be noted that this approach disregards the errors that have been committed in the measurement of tire slips. These inaccuracies in the measured data affect the optimum parameters of the model, producing non optimum models. This paper presents a methodology to improve the fitting of mathematical tire models on available test data, taking into account the vertical errors together with errors in the independent variable.

The Planetary Vibroexciter with Elliptic Inner Race

We present a method determining analysis of workflow of the planetary vibroexciter, allowing by constructing three-dimensional graphs obtained in MathCAD, combine several line graphs in one. Improves the availability the results of theoretical analysis, the influence of the main parameters of the vibroexciter on its dynamic characteristics. The use of a planetary vibroexciter with elliptic inner race gives substantial advantage in generated driving force against an analog vibroexciter, equipped with a round inner race with the same dimensions and initial parameters. Selecting the mode of setting the spider axis of a planetary vibroexciter in one of focal points of elliptic inner race leads to the increase of generated driving force, 2.2 times on abscissa axis and 2.4 times on ordinate axis, against the central position of the spider axis. This proves the effectiveness of the elliptic planetary vibroexciter use. 1.6 times increase of focal length results in directly proportional increase of driving force projection on ordinate axis, and 2.1 times increase of driving force projection on abscissa axis.