graphic method
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How is the movement of bodies recorded, traced, captured? How is the perception of movement decomposed, analyzed, and then reconstructed through signs, lines, and diagrams? This article traces how, with the help of engineers and collaborators, Etienne-Jules Marey’s self-styled “graphic method” innovated upon existing instruments and photographic apparatuses in order to capture not just the movement of horses’ legs but something of the biomechanical essence of animal movement through the technique of “chronophotographie.” Although inspired by Edward Muybridge’s photographs of horses in motion, for Marey the photographs were not the end result. What he achieved were new ways of transcribing the phenomena of bodily motion. Unlike previous physiologists who thrived on vivisection in the laboratory, Marey took ever greater pains to examine the principles of animal movement in the wild, and built an open-air “station physiologique” in a Parisian park for this purpose. One legacy of Marey’s chronophotographic technique was in the documentation and dissection of human movement, and became acknowledged precursors of the wave of Taylorism which would sweep industrial research in the early 20th century. But another legacy is the capacity to transcribe the phenomena of movement into other forms, externalizing perception across other media.

The aim of this paper is to study, from a topological and geometrical point of view, the iteration map obtained by the application of iterative methods (Newton or relaxed Newton’s method) to a polynomial equation. In fact, we present a collection of algorithms that avoid the problem of overflows caused by denominators close to zero and the problem of indetermination which appears when simultaneously the numerator and denominator are equal to zero. This is solved by working with homogeneous coordinates and the iteration of self-maps of the Hopf fibration. As an application, our algorithms can be used to check the existence of multiple roots for polynomial equations as well as to give a graphical representation of the union of the basins of attraction of simple roots and the union of the basins of multiple roots. Finally, we would like to highlight that all the algorithms developed in this work have been implemented in Julia, a programming language with increasing use in the mathematical community.

This study explores the correlation between two variables and to demonstrate a simple graphic method to assess their degree of correlation. Following the lead of early English biometricians, it has been tacitly assumed that the studied variables develop in the same direction: when variable A’s measurements are higher from one object to another, the measurements of variable B, also are higher. The customary measure of co-relation relies on a least squares fitted trend line, then assuming that the trend is more real than, and has priority over the individually recorded data. The situation changes when measurements of variables develop in opposite directions: The very first data set I used to perform a correlation analysis was a study of student grades achieved and the percentage of their having missed classes: the more a student was absent from class, the lower were his achieved grades. In that situation the accepted model of correlation analysis – the mathematically fitted straight line and the squared distance of each student’s record from that line - was not appropriate. The usual correlation coefficient contradicted visual evidence of those data because the model underlying that situation treats the individual data as having more reality value than the general trend, but not as deviations or errors. The visual appearance, the graph of that situation, resembles a rectangular triangle, formed by the horizontal and vertical axis as its catheters, and the hypotenuse formed by a line through and representing the highest data points. This image justifies the expression “Triangular correlation”.

The results of the analysis of the properties of components of residual marine fuels (RMF) are described. The stability areas of marine fuels are determined using ternary phase diagrams VisRes - ULSD – LGOCC, Asphalt – ULSD – LCGO, Asphalt – ULSD – LGODC. The graphic method for determining the stability of A.B. Stankiewicz based on SARA analysis is used to describe the stability of RMF on the basis of VisRes - ULSD – LGOCC. The areas of stability, instability, and metastability of marine fuel are presented on the graph according to the Stankiewicz method, which can be used to predict the stability of RMF.

Research background: The presented article analysis major impacts of corona crisis on global and subsequently Slovak economy. It divides major impacts into several basic categories. These categories are presented in the methods part of the article. First of all, we analyze and discuss economic impacts, subsequently shocks in supply and demand and at last impacts of policies. These categories contain wide literature research in order to offer complex overview of the topic. The results and discussion part offers comparison of three important economic indicators. Namely gross domestic product, inflation rate and unemployment rate in periods before, during and shortly after the corona crisis. Some of the selected countries play major role in global economy – China, United States and European union. Other selected economies have the most direct impact on Slovak economy like Germany, Czech Republic, Hungary, Poland and Austria. For complex overview, we also included results of Euro area and Italy as a country with the worst course of pandemic. Purpose of the article: Major purpose of presented article is description of major impacts of corona crisis on Global and Slovak economy. The need to shut down individual parts of economies and in some cases total lock down results in important damages. The article underlines these damages. Methods: Among the methods used in this article, the most important one have descriptively analytical character. We also used other methods of formal logic like analysis, graphic method, comparison and synthesis. Findings & Value added: Overview of the major corona crisis impacts on Slovak and global economy during corona crisis.