| ANTOŠ Karel " Problem of Searching the MST " - from the section: Mathematics and art This article describes searching The Minimum Spanning Tree (MST) of the graph using the Weighted Adjacency Matrix. It describes the Weighting Adjacency Matrix as a new element, and shows how it could be used for searching for the MST of the graph. This creates a new procedure for searching MST of the graph which completes previously known algorithms of searching MST. Proposed Weighted adjacency matrix could be used in similar issues in the field of graph theory, where graphs with weighted edges are given. The procedure is shown on the attached example. |
| BEKESIENE Svajone " Structural Equation Modeling Using the Amos and Regression of Effective Organizational Commitment Indicators in Lithuanian Military Forces " - from the section: Modeling and simulation in engineering and scientific computations The interest in Structured Equation Modeling (SEM) techniques are growing. The recognition of their importance to the scientific research suggests the need to evaluate and compare different types of techniques so that the scientific research designs can be selected adequately. Moreover, second-generation data analysis techniques enable researchers to answer a set of interrelated research questions in a single, systematic, and wide-ranging analysis by modeling the relationships among multiple independent and dependent constructs at the same time. After assessing the area to which these techniques are currently being used in the scientific research, the article presents a consecutively example, which analyzes the same dataset via two very different statistical techniques. After that it compares two modeling possibilities: modeling using Analysis of Moment Structures (AMOS) and statistical software package SPSS. Finally, the article discusses linear regression models and offers guidelines as to when SEM techniques and when regression techniques should be used. |
| BELIBANI Rosalba " The Parametric Architecture Project Towards Cognitive Computing " - from the section: Mathematics and art The work aims to investigate what can be the possible perspectives with the use of algorithms and digital tools in creative architecture, specifically in the process of design and shape control. Moreover, shapes are determined by size and, therefore, by numbers that, accordingly, govern all art forms, including architecture. There is always a relationship between architecture and mathematics, both in conception and transcription. The observation of nature has brought man to question the processes and the organization of nature, taking in its mathematical structure for inspiration and to create works with the same harmonic principles. Today there emerges new and deeper links between mathematics and design, in a contradictory scenario that sees the transformation of architecture as a physical element immersed in a flow of information. A process is taking place whereby mathematics, understood as generating forms, appears as a new genetic code for architecture. Today, architecture makes use of digital tools that support the design and impact the language used allowing for new spatial experiments. The parametric architecture concept often refers to the use of specific software rather than to an organic definition of the relationship between the various parameters during the design phase. The new perspective in the definition of shapes is modeling through algorithms. The geometries by mathematical functions, the mathematical/logical approach and the generation of parametric models enable fast and deep variations of the initial geometries and rapidly obtain forms of great complexities with the repetition of geometric elements. The complex nature of the parametric software allows one to transfer this consistency also during the construction phase, planning and integrating it into the design process through the generation of drawings, and the interaction with the database and the production processes. The new frontier of design process is cognitive computing, a system that acquires information and integrates processes in different ways, through inclusion in the database and through access to the infinite web database. The relationship between the project´s design and mathematics comes today in cognitive computing, that will soon be applied to the design process and is expected to be able to implement the design, construction and management of the entire architectural project. |
| BIBA Vladislav " Applied Mathematics Seminar " - from the section: New trends in mathematical education The paper describes the initial state of basic university courses of mathematics taught at The Institute of Technology and Business in České Budějovice, introduction of new applied mathematics seminar. The model examples especially from part of the ordinary differential equations are presented. |
| BÍLKOVÁ Diana " How Are the Wage Distributions of Czechs and Slovak Different? Comparison: Development, Models and Forecasts " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise The present paper aims at a comparison of wage trends since 2000, focusing on wage level, differentiation and concentration since the adoption of the euro in Slovakia. In this study, theoretical wage models are constructed, using three-parameter lognormal curves, taking into account the minimal wage in both countries. Predictions of wage developments – not just those of the level, variability and concentration of future wages, but also forecasts of the entire wage distribution – employing the methods of time series trend analysis are also a part of the research. |
| BOHDAL Róbert " A Comparison of Normals Calculation for the Construction of Interpolants above Triangular Meshes " - from the section: Algebra and Geometry and Their Applications In this paper, we compare selected methods for calculation of normal vectors, which are necessary for the construction of interpolants above the given triangulation. The normals at individual vertices of the underlying triangulation greatly affect the shape and the smoothness of the resulting interpolation surface. We compare results of selected methods for normals calculation with analytically calculated normals of test functions. We also calculate the difference between the created interpolants and the corresponding test functions. The best results were achieved by the method of calculating normals using the local thin plate interpolation spline. The weighted average method, created by combining Little’s and Max’s method came as the second in order. |
| BRANDI Primo " Math-MAPS a New Road that Opens up a WorldII Part - Elementary Dynamic Models " - from the section: New trends in mathematical education Math-MAPS is a kind of Google maps for mathematics created by Mathematics&Real Life (M&R) with the aim to offer innovative educational pats to the Schools of any order. M&R is a national project of the Department of Mathematics and Informatics of the University of Perugia which promotes education to mathematical modelling as innovation drive. Education to modelling involves a completely new way of approaching Mathematics, based in a dynamic interaction between the real word and mathematical word. Math-MAPS suggests learning highways to connect the different topics. In our paper we will present one of these recommended tracks: the introduction to dynamic models. The contribution is divided in two parts: the first part deals with the discrete case (suitable also for vocational Schools), the second part will illustrate the continuous case. |
| BŘEHOVSKÝ Jiří " Combinatorial Problems in Mathematics Textbooks for Elementary Schools " - from the section: New trends in mathematical education This article describes an analysis of textbooks that contain tasks, which develop combinatorial reasoning of pupils in elementary schools, and the categorization of these tasks. It is a quantitative evaluation that will provide a basis for further research. |
| BRUNETTI Federico A " The Limit as a Resource. Visual Design and Explorations OOf Extreme Space Geometry.From the Graphic Research of M.C. Escher to the Spherical Cameras Application. " - from the section: Mathematics and art The event of a recent exhibition in Milan (2016-2017, curated by Marco Bussagli and Federico Giudiceandrea), give us the opportunity to observe and study the work of M.C. Escher: the ´900 graphic researcher who concerned his intellectual interest to the limits between sight and vision, drawing and geometry, imagination and paradoxes in representation and understanding of space. His texts, letters and rare conferences - as far as his well notorious masterpieces - give us a view of a very interesting path through the osmotic borders between Arts and Science. After quite an half of century of his creative experience - that has been quite fashionably perceived as an “alternative“ research about vision, instead of his rigorous true nature of sharp enquiry overpassing the limits of Euclidean flat screen perspective - the legacy of these iconographyes re-appears in soI am still waiting for the answer, that I sent for the authorization about the declared scientific purposes, from Escher´s Fundation for some artist´s selected quotations and some pictures of his works. In opposite case, my final paper will result as a simple enquiry about the artist´s anyway well notorius works, in comparison with the iconographical legacy inspirating the applications of actual 360° digital VR (virtual reality ) devices. me digital devices defined as spherical digital cameras, in which combined optical wideangles lenses obtaine surrounding 360° (stiched ) virtual maps, that can be so observed by VR / AR (virtual /augmented reality) visors and glasses. |
| BULKOVÁ Kristína " Rubrics as Assessment Tool of Mathematical Open Ended Problems " - from the section: New Trends in Mathematical Education The aim of educational process in mathematics should be focused on developing the student’s mathematical competencies, so they are also useful in the real life. In this paper, a flexible and progressive tool, named rubrics, for the assessment of mathematical problems solutions, is described. The Revised Bloom Taxonomy of Educational Objectives in posing open-ended mathematics problems is reckoning with creating the rubrics for the particular problem solution assessment. The Mathematics B-day contest problems are open-ended problems based on inquiry based learning principles. Rubrics for assessment of selected solutions of the Mathematics B-day contest are used as an example of the rubrics in this paper. |
| BURATTI Giorgio " Art of Geometry. The Use of Perspective in the Woodenchoir of Santa Maria Maggiore in Bergamo " - from the section: Mathematics and Art The choir of Santa Maria Maggiore in Bergamo is a unique furniture in the tradition of wooden choirs because is characterized by a number of innovative solutions resulting from the successful collaboration between the painter Lorenzo Lotto and the inlayer master Giovan Francesco Capoferri. Among the elements of greatest interest are the inlays that decorate the backrests. This paper studies the marquetry Amon violante Tamar. Through the geometrical analysis of perspective will be detailed references to Lombard perspective culture that are due to Bramante’s influence. |
| CAPANNA Alessandra " Claude Fayette Bragdon, Architect. The Fourth Dimension Exposed " - from the section: Mathematics and art At the beginning of 20th century, in the United States of America, some treatise about the diffusion of scientific knowledge, about the notion of space and time, and on the fourth dimension were published. The authors were mathematicians only in some cases. Claude Fayette Bragdon (1866-1946) [1], a valued architect and stage designer, quoted in the renowned book of American Architectural History “The Architecture of America: A Social and Cultural History” (John Burchard and Albert Bush-Brown, 1961), published a chain of essays, books and articles about the higher space geometries and related visualization. The present paper investigates the connections and consequences among the issues that concern the understanding and construction of space in four dimensions and its application in Bragdon’s architectural projects |
| CARSTEA Claudia " Identification Of Sea Turtles Using Image Processing And Neural Arbitration " - from the section: Modeling and simulation in engineering and scientific computations This paper presents a novel neural network application in a rarely explored area related to marine life and the tracking of the mysterious sea turtles. Preservation of marine life is an important integral part of realizing a self sustaining ecosystem, especially the endangered species. Governmental and non-governmental organizations hope that with the availability of relevant information, planning and management, environmental policies could be structured to align with emerging challenges attributed to the ecosystem. In this work, we propose the identification of the eight species of sea turtles using image data obtained from a public database and neural network. Image processing techniques and pattern averaging are applied to images, on which feedforward neural networks are trained. Furthermore, we investigate particle swarm optimization of the designed feedforward neural network, and present comparative analysis based on training time, identification rate, and run time. |
| ČEJKA Jiří " Optimisation of the Line Routing Using the Multi-Criteria Evaluation of Alternatives " - from the section: Modeling and simulation in engineering and scientific computations The paper is concerned with the assessment and design of the transport organization in the town of TÁBOR. The examined issue was the urban public transport analysis focused only on the lines routed in parallel towards Planá nad Lužnicí. The solution designed using the TOPSIS method was based on the carrier and the orderer´s interest in optimizing the above stretch. Based on the results, the draft transport model of the backbone line No. 13 was created and the inappropriate lines were removed. |
| ČEKAN Michal " Description of Membrane Elements for Piezoelectric Materials " - from the section: Modeling and simulation in engineering and scientific computations Most FEA software does not offer elements which incorporate the properties of thin piezoelectric membranes within their libraries. The need to implement piezoelectric materials into mechanical designs has become of increasing importance. This contribution formulates a thin membrane element based on shape function and material properties of AlGaN and PZT materials and compares them to generic Shell 181 finite elements. The element formulation shows promising results for the use of more suitable elements for the description of thin membranes in finite element analysis. |
| CEPPITELLI Rita " Mathematical Models for Food Sanitization Process. " - from the section: Differential equations, dynamic systems and their applications The expression "mild technologies" is used to define those food treatments able to achieve safe food by significantly reducing all the possible negative side-effects. In the specific case of thermal pasteurization and sterilization, the concept of mild technologies is linked to treatments with familiar abbreviations for the consumer: UHT (Ultra High Temperature) and HTST (High Temperature Short Time). Examining the technological parameters (time and temperature) to sterilize milk, we constructed a predictive mathematical model to determine in advance couples time-temperature that will ensure the sanitization of the product with minimizing the degradation of milk quality, in accord with the mild technologies treatments. The proposed model could be applied to other foods and to other food process technologies and could be used in future research projects. |
| CERNAJEVA Sarmite " Application of Information Technologies for Studies of Mathematics in Riga Technical University " - from the section: New trends in mathematical education Utilisation of ICT capabilities in the mathematics studies process facilitates work of teachers and also makes study process more engaging and effective. In order to facilitate the work of teachers and excite students, the Department of Engineering Mathematics created several courses of Mathematics at RTU portal ORTUS, compiled and implemented a series of tests at the ORTUS environment, created Ancillary Course in Elementary Mathematics on the open online platform MOOC and made course of mathematics for pupils of secondary school at RTU ORTUS site. |
| CHEPURNA Olena " Complex Submanifolds of LCK-manifold, Pseudo-Vaisman and Vaisman Manifolds " - from the section: Algebra and geometry and their applications We study(with Berezovski Vladimir and Cherevko Yevhen) the immersions of submanifolds in LCK-manifolds that a tangent space in all points of the submanifolds to be normal to Lee field and we find conditions under which LCK-manifold admits the immersion of complex submanifolds. Also we explore properties of Lee form of Vaisman and pseudo-Vaisman manifold. |
| CHEREVKO Yevhen " Complex Submanifolds of LCK-manifold, Pseudo-Vaisman and Vaisman Manifolds " - from the section: Algebra and Geometry and Their Applications We study(with Berezovski Vladimir and Chepurna Olena) the immersions of submanifolds in LCK-manifolds that a tangent space in all points of the submanifolds to be normal to Lee field and we find conditions under which LCK-manifold admits the immersion of complex submanifolds. Also we explore properties of Lee form of Vaisman and pseudo-Vaisman manifold. |
| CHLÁDEK Petr " Limits of Elektronic Testing of Mathematical Knowledge " - from the section: New trends in mathematical education In the paper we discuss limits of multiple choice testing in Mathematics. This problem is illustrated on disadvantages which appeared during three consecutive years. |
| CIUPALA Laura " Maximum Flow in a Network With an Overestimated Arc Capacity " - from the section: Modeling and simulation in engineering and scientific computations There are several types of problems that can be modeled as maximum flow problems in networks. Sometimes is necessary to determine a maximum flow in a network differing only by an arc capacity (which is reduced by a units) from another network in which a maximum flow is already established. We will describe an algorithm that determines a maximum flow in the new network starting from a maximum flow in the initial network in O(am) time. |
| COCCHIARELLA Luigi " Back to the Babel Tower, Warning and Archetype " - from the section: Mathematics and Art As graphic educators, looking at the city as a special case in the field of architectural configurations, we should not avoid considering the links between forma urbis and forma mentis, and consequently the vision behind the built settlements, either plan-based or sprawl-based - whose variety reminds the Babylonian archetype - together with the role of image in supporting urban design, so evoking a sort of genetic-iconic materialism, and the role of Geometry and Graphics in creating and supporting our whole idea of city. Probably no artificial human systems show a complexity level comparable with that of a city. Almost every disciplinary field and activity takes place in the city, as well as it contributes to form and to transform the city. From the point of view of an architect, whose main focus is on space, namely a space where human beings can live, the city is a special kind of spatial system, and consequently, of architecture. That is consistent with one of the most impressive and complete modern definitions of architecture, proposed by William Morris, who stated that it concerns every spatial transformation of the terrestrial crust finalized to provide adequate places for living to human beings. More recently, the idea has been significantly reconfirmed by Jan Lubicz-Nycz with the neologism urba-tecture, and it has been also analyzed in the very well-known book - we could say a revolutionary best-seller - titled The Architecture of the City, by Aldo Rossi. Given the complexity of the city, no exhaustive analyses are really possible, and in fact this is not our purpose, as well as any attempt to investigate the relationships between Mathematics and the city could defeat even the most brilliant and talented researcher. Instead, given our interest in Geometry and Graphics, we would like to focus more strictly on space. Although a city can not be reduced to a pure geometrical configuration, Geometry can be seen as a meta-structure representative of the physical, sensory, and symbolic components of a urban space, working as a special glue making each urban context real, unique and different from any other. We could say that without geometrical identity urban spaces collapse into a literary form. |
| CUMINO Caterina " Origami Pythagorean Tree, Natural Numbers´ Powers, Sum and Series " - from the section: New trends in mathematical education Origami is a very versatile tool for hand-on made mathematical activities in every school degree. Origami technique has many strengths: it allows to visualize mathematics, it shows maths from other points of views, it is lived as a game by students and it is cheap. Any straight fold on the paper produce (segments of) lines and so it is natural to apply origami in teaching geometric subjects according to the well known van Hiele model , at any educational level from kindergarten to university as shown in many projects. But it is possible to use origami also for arithmetical topics. In this paper we would like to show an example of lesson (for students aged 10-13) about powers and sum of powers, with an output about series for the highschool students. In this workshop we propose an origami model to visualize the concept of a°=1 and to show that with this tool, in addition to the rules about product and quotient of powers, one can deduce the formula for the sum of the first n powers of a given natural number. Using an original origami model of the Pythagorean tree introduced by A. Bosman in 1942, students can visualize the problem and research the solution on their behalf. They have the opportunity to create the formula and not only to learn it! We remark that, even if the focus of this lesson are powers, the same model can be used to introduce fractals and also Pythagora Theorem. Authors: Caterina Cumino and Maria Luisa Spreafico |
| DEMCHENKO Hanna " Optimality Conditions for Scalar Linear Delayed Differential Equations " - from the section: Differential equations, dynamic systems and their applications In the contribution is considered a linear differential equation with a control function and a delay together with a problem on minimizing of an integral-type functional. The second Lyapunov´s method is used to solve the problem. |
| DOBIAS Vaclav " Using Semantic Differential for Measuring Changes in Understanding Selected Concepts by Respondents " - from the section: Statistical methods in technical and economic sciences and in practise The article focuses on the analysis of semantic differential data based on the assessment of the global similarity of keywords. This method finds out the mutual distances of keywords in the semantic space. The calculation of this distance, creation of corresponding matrix of distances and application of cluster analysis for graphical representation of the keywords similarity in the form of dendrograms are described in the article. Using the comparison of the pretest and posttest dendrograms, changes in perceiving of selected keywords by respondents were identified. |
| DOBRUCKÝ Branislav " Analytic Solution of the Multi-Resonant Electrical Circuit under Impulse Supply " - from the section: Modeling and simulation in engineering and scientific computations The paper deals with analytical solution which make possible to estimate instantaneous state of dynamical system in any time instant. Analytical model of the multi-resonant converter filter uses Laplace-Carson transformation with complex operator p. The method described in the paper using transient component separation makes it possible to use both steady state- and transient components to generate of total time waveforms of chosen output state variables or other quantities. The steady state component is created using response of AC input voltage during the first one half-period. Results of theoretical analysis confirmed by numerical computer simulation are given in the final paper. |
| DOTLAČILOVÁ Petra " An Application of Polynomial Functions of Different Order in Smoothing of Mortality Curves: the Case Study of Bulgaria and Czechia from 1960 to 2010 " - from the section: Financial and actuary mathematics In this paper we use classical polynomial functions of 2nd, 3rd and 4th order for smoothing the mortality curves at advanced ages (60–110 years of life) in the case of Bulgaria and Czechia. Classical polynomial functions are good approach as a supplement to weighted moving averages and commonly used models for smoothing variance in the age-and-sex-specific death rates. Our results are compared with each other using adjusted index of determination and it will be shown that the quality of smoothing is at very good level in the case of Bulgaria and Czechia. |
| DRAŽENSKÁ Emília " On the Crossing Numbers of Several 8-Vertex Trees with Paths and Cycles " - from the section: The crossing number of a simple graph G is the minimum number of edge crossings in any drawing of G in the plane. Garey and Johnson have proved that compute the crossing number for a given graph is a very difficult problem, it is NP–complete problem, in general. There are several classes of graphs for which crossing numbers have been studied. We extend these results by giving the exact values or upper bounds of crossing numbers of some graphs. |
| DZENITE Ilona " Mathematics Teaching Problems and Its Solution at Riga Technical University " - from the section: New trends in mathematical education Mathematics is one of the basic subjects in all academic programs at Riga Technical University (RTU). At the same time it is one of the subjects which causes the most problems for many students. The main reasons are the students’ insufficient knowledge of elementary mathematics, the students’ disinterest and lack of motivation. In this article we present a description of a series of actions which are used in RTU for solving the above-mentioned problems. |
| FAILLA Gioia " Linear Triangulations of Polytopes " - from the section: Algebra and geometry and their applications The most important term orders on the set of monomials of the polynomial ring S=K[x1,..,xn],K a field,are the lexicographic order L and the reverse lexicographic order R. The linear order L is introduced in [4]on the set T of r- indexed variables of the presentation K-algebra of in the rth-Veronese square free ,the subring of S generated on K by all monomials in r -square free variables x1,…,xn .In the paper [1] the authors considered the LL-universal Groebner basis GLL for the toric deal I of K[T] ,universal with respect all linear orders on the set T of variables and the lexicographic order on the set of monomials of the polynomial ring K[T] of the presentation . They proved that the degree is 2 or 3. In this talk we compute the initial complexes [3]in correspondence of the GLL and we study the triangulations of the representing polytopes. Combinatoric properties of the triangulations are studied. In particular, for n>4, the LL- order builds to initial simplicial complexes more complicated that for n=4, depending from the degree of the Groebner basis of the toric ideal.Since such triangulations depend from the chosed term order , it is a fertile field to explorer in the direction of varying the term order and to check properties whether the reverse lexicographic order R is applied. Starting from the founded polytopes in the paper, in [2] the author obtained new applications in art field. References [1]G. D’Agui-G. Failla Afrika mathematika, Série 3,Volume 20, 2008, 131-146 [2]V. Iorfida,Compositions of polytopes arising from linear orders, Aplimat 2017 [3]B. Sturmfels, Groebner bases and convex polytopes,Univ. Lectures Series,Amer. Math.Soc.,Vvol.8,(1995) [4] R. Villarreal,Monomial Algebras,Pure and Applied Mathematics,Marcel Dekker ,Inc. New York,vol.238(2001) |
| FALCOLINI Corrado " Parametric Planar Sections of a Point Cloud with applications in Cultural Heritage " - from the section: Mathematics and art Given a discrete (“Point Cloud”) representation of a surveyed object it is possible to analyze its three dimensional features with the help of several planar sections. Some original algorithm is presented and applied to specific cases of interest in archaeology or architecture such as reconstruction of fragmented objects or symmetry detection. |
| FECHOVÁ Erika " Utilization of Software Means at Solving Differential Equations in Teaching Technical Subjects " - from the section: New trends in mathematical education The present time brings a great surge in the use of information and communication means, the application of which can be found in almost all areas of our lives. They are important means of modernization in educational process. The paper deals with the possibility of using application software in educational process of natural science and technical subjects. Suitability of utilization of computer means is presented at solving the problem from electrical engineering – solving differential equations of second order and describing time dependencies. |
| FERDIÁNOVÁ Věra " New Tools for Monge Projection in GeoGebra " - from the section: New trends in mathematical education GeoGebra is a dynamic mathematics software for all levels of education that brings together geometry, algebra, spreadsheets, graphing, statistics and calculus in one easyto- use package. It also is a rapidly expanding community of millions of users located in just about every country. GeoGebra has become the leading provider of dynamic mathematicsl software, supporting science, technology, engineering and mathematics (STEM) education and innovations in teaching and learning worldwide.[2] Materials created in GeoGebra can be stored or shared on official website. Worksheets, materials and tools are the most shared files there. All these materials should support development of spatial imagination. However, this is the ability most students lack, which results in having problems with understanding simple tasks in descriptive geometry [1]. Thus we decided to create a new tool that would help to improve teaching Monge projection. Tool constructions are based on a simple algorithm rule - if it is possible to create an "algorithm" from a construction, it is possible to create a tool. We have created 3 tools for Monge projection that can draw three basic elements used almost in every task: a point, a straight line, a plane. The process of creation is described in paper in details, thus it is possible to use this manual for defining own tools or for modification of created ones. [1] Gittler, Georg, and Judith Glück: Differential transfer of learning: Effects of instruction in descriptive geometry on spatial test performance. Journal of Geometry and Graphics 2.1 (1998): 71-84. [2] URL: http://www.geogebra.org. |
| FERREIRA Manuel Alb " First order Differential Equations Induced by the Infinite Servers Queue with Poisson Arrivals Transient Behavior Probability Distribution Parameters Study as Time Functions " - from the section: Statistical methods in technical and economic sciences and in practise The M|G| queue system state transient probabilities, considering the time origin at the beginning of a busy period, mean and variance monotony as time functions is studied. These studies, for which results it is determinant the hazard rate function service time length, induce the consideration of two differential equations, one related with the mean monotony study and another with the variance monotony study, which solutions lead to some particular service time distributions, for which those parameters present specific behaviors as time functions. |
| FILIPE José Antón " Preferences Relations and Consumer Theory " - from the section: Differential equations, dynamic systems and their applications In this paper an interesting application of mathematics in economics is presented: the formulation of the theory of consumer basic problem, grounded on the concept of preferences relation and operationalized with optimization tools. |
| FJODOROVS Jegors " Imitation of the Nonlinear Processes via Copulas " - from the section: Statistical methods in technical and economic sciences and in practise Our research studies the construction and estimation of copula-based semi parametric Markov model for the processes in different fields of science. As a rule analyzing the dependence structure of stationary time series regressive models defined by invariant marginal distributions and copula functions that capture the temporal dependence of the processes is considered. This permits to separate out the temporal dependence (such as tail dependence) from the marginal behavior (such as fat tails) of a time series. For example, dealing with utility company data we have found the best copula describing data - Gumbel copula. As a result constructed algorithm was used for an imitation of low probability events (in a hydro power industry) and predictions. |
| FLOREA Olivia " Approach of the dynamical systems using the transfer function " - from the section: Differential equations, dynamic systems and their applications In this paper it is studied the behavior of a dynamical system using the transfer function. This study is used in the theory of automatic regulation. Using Simulink environment from Matlab software is analyzed the behavior of some dynamical systems. |
| FLORKOVÁ Michaela " An Analysis of Students´ Use of Mathematical Models in Solving Tasks with Real-Life Context " - from the section: Despite the general tendency to emphasize the importance of mathematics in solving daily-life problems, students’ difficulties with such tasks still widely persist. Mathematics education should be focused on making students learn how to mathematize real-life situations by means of mathematical models. Also, it seems wise to incorporate team work in mathematics education, for while solving problems in groups students have to communicate and provide proper arguments. In this research study we present results of a content analysis conducted on students’ solutions of two mathematical tasks related to gas consumption in households and gas distribution costs. The analysis was focused on how 204 students, aged 16-18, working in 51 groups of four, mathematically modelled the given real-life situations. Their solutions’ were analysed in terms of four main stages of the modelling cycle by Kaiser (real situation, real world model, mathematical model, and mathematical results). The results of the analysis indicate that students experienced serious difficulties at all four stages of the modelling cycle. Most students failed at the very first stage of the cycle, i.e. they misunderstood the real-life situation, its conditions and consequences. We assume this is closely associated with the reading comprehension skills of the students. Also, the interpretation of the obtained mathematical results was absent in students’ solutions, which suggests that students neglected proper verification of their mathematical model. Although we expected students to go through the stages of the modelling cycle sequentially, their solutions demonstrated that students often skipped some of the stages. |
| FULIER Jozef " Continuity of a Function of Several Variables and a Generalization of one Counterexample. " - from the section: New trends in mathematical education Abstract. The submitted paper discusses the issue of teaching university students about the limits and continuity of a function of several variables. Our attempt was to find a cohesive view on one group of interesting counterexamples related to the function which was studied in detail by the well-known Italian mathematician G. Peano in 1884. We provide a proof of a simple proposition which is further broadly applicable in proposing analogous counterexamples with other functions. Also, we generalize the range of validity of a noteworthy counterexample. |
| GATTON Matt " Conventionalized Distortions in Upper-Palaeolithic Cave Art: Calculations of the Keystone Effect " - from the section: Mathematics and art Upper-Palaeolithic cave artworks sometime display conventionalized distortions: sliver-thin heads and enormous protruding bellies. Prehistorians have grappled with the reasons for these distortions, given that no animal in the archeological record was so disfigured, and have produced a number of explanations: pregnancy, bloating and death. Countervailing arguments — How, exactly, can a male horse be pregnant? — largely dismantled these explanations decades ago, but no viable explanation was offered as a replacement, so the question was largely abandoned. During the course of recent experiments with reconstructions of simple, animal-hide, Palaeolithic tents, a potential explanation arose. When light passed through small holes in the animal hides and fell upon non-parallel surfaces within the darkened tents it caused projected images to distort (the keystone effect) in a manner similar to the conventionalized distortions seen in the cave artworks. The optical distortions of a horse documented inside a camera obscura are presented side-by-side with Paleolithic artwork. This study measures the keystone distortion evident in the famous ‘Second Chinese Horse’ in the Axial Gallery of la Grotte de Lascaux (Dordogne, France). |
| GLIVICKÝ Petr " Shepherdson´s Theorems for Fragments of Open Induction " - from the section: Algebra and Geometry and Their Applications By a well-known result of Shepherdson, models of the theory IOpen (a first order arithmetic containing the scheme of induction for all quantifier free formulas) are exactly all the discretely ordered semirings that are integer parts of their real closures. In this paper we prove several analogous results that provide algebraic equivalents to various fragments of IOpen. |
| GOLDSTEINE Jolanta " On Gaussian Approximation for the Stationary SIS Model with Random Contact Rate " - from the section: Differential equations, dynamic systems and their applications The paper deals with a mathematical model of the classical dynamic epidemic susceptible-infected-susceptible (SIS) model for the population community given by a scalar differential equation with dependent on an impulse type compound Poisson process of large intensity. Applying the stochastic asymptotic approximation procedure we deduced the approximative stochastic differential equations for the steady stay stationary process and discussed the probabilistic characteristics of the infected population dynamics. |
| GREBLICKI Marijana " Classification of Second-Metacyclic Finite 2-Groups " - from the section: Algebra and geometry and their applications Second-metacyclic finite 2-groups are finite 2-groups with some non-metacyclic maximal subgroup and with all second-maximal subgroups being metacyclic. According to a known result there are only four non-metacyclic finite 2-groups with all maximal subgroups being metacyclic. The groups pointed in the title should contain some of these groups as a subgroup of index 2. There are seventeen second-maximal finite 2-groups, four among them being of order 16, ten of order 32 and three of order 64. |
| GRIRA Sofiane " Enhancement Effects of a Learning Management System on Student Learning " - from the section: New trends in mathematical education This paper describes an investigation of the enhancement effects of using MyMathLab (MML) in math courses for engineering students.In this paper we compared the student´s results with and without using MyMathlab and how MyMathLab´s features improved student´s performance in math courses. In addition, the benefits and difficulties of using MyMathLab were discussed. Finally, we examined student responses to the uses of MyMathLab. |
| GUNČAGA Ján " Statistical Analysis of the Level of Mathematics at Slovak Lower Secondary Schools " - from the section: New trends in mathematical education In educational practice, there are different ways of measuring pupils’ knowledge. Despite the fact that there are different opinions of the forms of examining and marking students it is indisputable that the verification of the achieved knowledge is an important component of the educational process. It not only provides important information on the level of achieved abilities to a student and his/her parents but it is also a form of control for a teacher who can, on the basis of them, assess the efficiency of the teaching methods used. Regularly carried out in Slovakia by the National Institute for Certified Educational Measurements in Bratislava (NICEM), centrally implemented testing is irreplaceable in this process. The aim of the nation-wide testing is to objectively compare the performances of pupils within the subjects tested and, based on the results, to give schools feedback about their level as compared to other schools in Slovakia. In our contribution we would like to focus on the comparison of the results of the nation-wide tests T9 in mathematics from the years 2011-2016, which were provided by NICEM for statistical processing. The tests measured the pupils’ skills of applying basic mathematical principles and procedures in both the mathematical context and real life. |
| HAŠKOVÁ Simona " Insight into the Art of Solving a Practical Geometric Task " - from the section: Algebra and geometry and their applications The article presents and compares three approaches to the problem solving of a practical geometric task: the standard mathematical approach, the experimental solution and the mathematical “art” solution; the last two stated illustrate the unconventional and inventive approach to the solution of the problem. The step-by-step solutions are presented in the form of a case study and serve as an inspiration to the teachers of a linear algebra or geometric class. |
| HECKENBERGEROVA Jana " Plug-in Problem in Discrete GNSS-PIM Algorithms " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise The aim of the contributed paper is to find a solution of plug-in problem in Discrete GNSS-PIM algorithms. Global Navigation Satellite Systems - Position Integrity Monitoring(GNSS-PIM) algorithms determine train position and verify its safeness. Plug-in problem has to be solved, when covariance matrix of GNSS positions is unknown and we would like to use its estimate instead. Confidence area for variance components and insensitivity region for the test in a given alternative are derivated first as a necessary part of the plug-in problem solution. If the confidence area is a subset of insensitivity region, then the estimate of covariance matrix can be considered as precise enough to be use in the Discrete GNSS-PIM algorithm instead of a real covariance matrix. |
| HINTERLEITNER Irena " On 4-planar Mappings onto Almost Quaternionic Hermitian Spaces " - from the section: Algebra and geometry and their applications In this paper we study 4-planar mapping of almost quaternionic spaces. This mapping generalize geodesic, quasigeodesic and holomorphically projective mappings of Riemannian and Kählerian spaces. We obtained the new fundamental equations of 4-planar mappings onto almost quaternionic Hermitian spaces. |
| HLAVÁČOVÁ Irena M. " Derivatives in physics in Novel Appearance – Several Applications for Math Lectures " - from the section: New trends in mathematical education The paper proposes a collection of various interesting and important applications of derivatives in physics. Apart from the most common applications in mechanics, namely instantaneous velocity and acceleration, less known extreme search is introduced not only in mechanics but also in optics and quantum mechanics. Some not so common views on electrodynamics problems are enclosed in the survey. Examples from mechanics are presented in detail in order to emphasize novelty in their solution. Other examples are given in a brief form – either only the most important step is presented (application of the Faraday’s law) or they are only named to remind their key ideas. |
| HOLEŠOVÁ Michalela " Minimal Generating Sets for Associated Ideals of Monomial Curves " - from the section: Algebra and Geometry and Their Applications We deal with associated prime ideals of monomial curves in a nne space. We search conditions for concrete descriptions of minimal generating sets for associated prime ideals of monomial curves. We show some results also about associated prime ideals as set-theoretic complete intersections. |
| HORSKÝ Richard " Ill Posed Problems. Application to the Time Series Analysis " - from the section: Many problems in mathematics and applied science take the form of an operator equation. The operator is usually a matrix or a difference, differential or an integral operator. It turns out that a great number of such problems are ill-posed which means that the solution either does not exist or it is not unique or it is unstable. In time series analysis the ill-posedness is demonstrated by the non-stationarity of a stochastic process. The typical example of such a process is the random walk. Keywords: ill-posed problem, regularization, symmetrization, random walk. |
| HOSKOVA-MAYEROVA Sarka " Pseudo Regular Rings Derived from Multiplicative Hyperrings " - from the section: Algebra and geometry and their applications The theory of hyperstructures has been introduced by Marty in 1934 during the 8thCongress of the Scandinavian Mathematicians. Marty introduced hypergroups as a generalization of groups. We introduce notation of pseudo regular rings and obtain some properties of such rings. Further, ee will proceed by considering a multiplicative hyperrings R, we obtain the smallest equivalence relation eta*, such that the quotient R/eta*, the set of all equivalence classes, is a pseudo regular ring. Finally, we characterize pseudo regular and strongly regular relations on R and obtain several results on the topic. |
| HYRÁNEK Eduard " " - from the section: Statistical methods in technical and economic sciences and in practise Watching the performance of tourism facilities there are especially number of beds of facility, number of visitors, number of overnight stays, the average number of nights spent and revenues from accommodation. The paper is focused on selected hotels in Nitra region and an important indicators of performance options. The collected data for years 2013 and 2014 are compared with the overall figures for those years in the Slovak Republic and considering the performance of sector in the Nitra region and in the Slovak Republic. The aim of the paper is to evaluate the effectiveness, efficiency and productivity of selected hotel facilities in the Nitra region on the basis of financial and other indicators using data envelopment analysis (DEA) by the size of input’s and output’s indicators. These indicators can be several species. |
| IORFIDA Vincenzo " Compositions of Polytopes Triangulated by Linear Orders " - from the section: Algebra and geometry and their applications We are interestd to convex polytopes and their triangulations realized starting by initial complexes linked to different term orders. We consider term orders on the set of monomials of a polynomial ring S=K[x1,..,xn],K a field,are the lexicographic order L and the reverse lexicographic order R.The linear order L is introduced in [4] on the set T of r- indexed variables appearing in the rth-Veronese squarefree ,the subring of S generated on K by all monomials of S in r-squarefree variables ,useful in many subjects of combinatorics and convex geometry. In the papers [1],[2] the authors considered the LL-universal Groebner basis GLL for the toric deal I of K[T] of the second Veronese square free ring ,universal with respect all linear orders on the set T of variables and the lexicographic order on the set of monomials of the polynomial ring K[T]. They proved that the degree is 2 or 3 and they compute the initial complexes with respect the LL –term order and the triangulations of the polytopes arising from the initial monomials of the toric ideal, when the degree is 2 or 3. In this paper, in order to construct geometric forms that can be utilised in the field of ingeneering, or business, or art and architecture ,following the previous triangulations, we obtain new interesting configurations,composing the triangulated polytopes. More precisaly, for n=6, we utilize bipyamidals for obtaining new models that offer multidisciplinary approaches in the teaching of scientific disciplines. References [1] G.D’Agui-G.Failla Afrika mathematika,Série 3,Volume 20,2008, 131 -146 [2] G. Failla, Linear triangulation of polytopes, Aplimat 2017. [3] B. Sturmfels, Groebner bases and convex polytopes,Univ.Lectures Series,Amer. Math.Soc.,Vvol.8,(1995) [4] R. Villarreal,Monomial Algebras,Pure and Applied Mathematics, Marcel Dekker ,Inc. New York,vol.238(2001). |
| JAJCAYOVA Tatiana " Computer Assisted Search for Graphs with Prescribed Degrees and Cycle Structure " - from the section: Mathematical Aspects of Network Science and Applications In this paper we introduce theoretical results, as well as computer experiments and algorithms to produce and analyze data of cycle spectra of Moore graphs and graphs close to Moore graphs, i.e. graphs with small excess. The results of these experiments where used to improve lower bounds for (k,g)-graphs, and to study a structure of subgraphs induced by excess vertices |
| JANÁK Josef " Asymptotic Normality of Parameter Estimates for Stochastic Differential Equation of Second Order " - from the section: Differential Equations, Dynamic Systems and Their Applications In this contribution, we are improving and extending some previous results on the parameter estimation for stochastic differential equation of second order, which were previously published last year. Namely, we are focusing on asymptotic normality of estimators, which is the main result of the paper. |
| JANČAŘÍK Antonín " Fractals, Robots and Matematics Education " - from the section: New trends in mathematical education The aim of this paper is to present an interdisciplinary project that was developed within the frame of a diploma thesis. The first author of this paper is the supervisor of the thesis, the second author is the author of the thesis. The goal of the developed interdisciplinary project was to verify whether the topic of fractal geometry can be used in teaching mathematics at upper secondary schools. For these ends robotics kit LEGO Mindstorms NXT was used. A robot was constructed and used by pupils to draw fractals. The results of the experiment show that fractal geometry has the potential of being a meaningful interdisciplinary topic whose use at upper secondary school level is possible and can support development of mathematical and algorithmic thinking of pupils as well as their awareness of the intricacies and beauties of real world. |
| JANIGA Ivan, GABKOVÁ Jana " Tolerance Charts in Statistical Process Control " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise The article analyzes the process of tightening screw fasteners. Tolerance diagrams are used in a process control, because in this case, they are more appropriate than the control charts which are used by the firm. |
| JÁNSKÝ Jiří " Polynomials with the Schur Property and Their Characterizations " - from the section: Differential equations, dynamic systems and their applications The paper discusses a distribution of the zeros of the polynomial egin{equation*} p(lambda)=lambda^{k}-alpha lambda^{k-m}-eta end{equation*} with respect to the unit circle. This problem is of a theoretical as well as practical importance which motivated many authors to formulate necessary and sufficient conditions guaranteeing the location of all the zeros of $p(lambda)$ inside the unit circle. Using various approaches, different forms of conditions ensuring this property have been obtained. We give here an overview and comparisons of these conditions, and show equivalence between some of them. |
| JAROŠOVÁ Eva " Control Charts for Processes with Fluctuating Mean " - from the section: Statistical methods in technical and economic sciences and in practise Control charts for processes in which the variation of sample averages arise due to other causes than the inherent within-sample variation are examined. The control chart with extended limits and modified control chart are applied on a real industrial process and the operating characteristic and average run length are calculated. The analysis is based on the random-effect model. |
| JUKL Marek " Almost Geodesic Mappings of the First Type Onto Symmetric Spaces " - from the section: Algebra and geometry and their applications In the contribution of authors V. Berezovski, M. Jukl, L. Juklová, new fundamental equations of canonical almost geodesic mappings of the type π 1 onto symmetric spaces are obtained. |
| JURSA Andrej " Fast Algorithm for Finding Clique Number of Scale-Free Networks and Sparse Graphs " - from the section: Mathematical Aspects of Network Science and Applications In the graph theory the maximum clique problem is NP hard. There are many algorithms attempting to solve it. In this paper we present a new algorithm specially targeted for solving maximum clique problem in scale-free networks and sparse graphs. We use the general algorithm developed by Östergård in 2002 as a base for our new algorithm. In our algorithm the search process has been improved by an eective initial heuristic. First, preliminary clique size is computed and then the graph is reduced by the k-core decomposition, where k is the size of the preliminary clique. Subsequently, greedy algorithm for coloring is used upon induced subgraph of selected vertex. Our new algorithm solves maximum clique problem for an arbitrary graph, but together with the above mentioned and some other, less signi cant pruning techniques, the algorithm performs exceptionally well on scale-free networks and sparse graphs. Its functionality has been tested on many real graphs as well as randomly generated graphs. |
| KABÁT Juraj " Number of Theoretical Plates in a Distillation Column " - from the section: Modeling and simulation in engineering and scientific computations The number of theoretical plates (NTP) is the basic process parameter of every plate column. All the methods that deal with NTP are based on the idea that every plate represents one theoretical equilibrium stage. The paper is focused on the Lewis-Matheson method. The calculation of NTP through the Lewis-Matheson method is demonstrated by the solving of the multicomponent mixture separation problem. |
| KAŇKA Miloš " B-spline Base Functions, Cox-de Boor Recursive Formula, B-spline Curves Clamped, Open, Closed " - from the section: Modeling and simulation in engineering and scientific computations This work deals with the construction of planar B-spline curves that are constructed piecewise, i.e., segment-wise, in comparison with their final (complete) graph. The task for segmented construction of planar B-spline curves was assigned by Swedish company MIR in Enskede. During the cutting process with laser or water beam sometimes occur a situation when the course of the whole curve (cutting track) is not desired, and course of only a part of the curve is preferred. Along with the MIR firm requirements, a special attention is paid to clamped, open and closed B-spline curves, which are frequently used in aplications. For segmented construction of planar B-spline curves, the author of this article invented a program, which makes solving problems on this type of construction easier. |
| KASPŘÍKOVÁ Nikola " EWMA Based LTPD Variables Sampling Plans and Cost Models " - from the section: Statistical methods in technical and economic sciences and in practise The calculation of the recently proposed unknown standard deviation case LTPD acceptance sampling plans minimizing the mean inspection cost per lot of the process average quality, when the design of the variables sampling plans is based on the exponentially weighted moving average statistic is addressed. The design of the plans is recalled first. Then the economic efficiency of the plans in comparison with the attributes inspection plans is discussed using cost model considering difference in variable and fixed cost. |
| KLŮFA Jindřich " Multiple Choice Question Tests in Mathematics for Entrance Exams " - from the section: New trends in mathematical education The causes of differences of average number of points in the test in mathematics between test variants in entrance examinations are studied in present paper. The analysed data are the results of 4614 students in mathematics in 2013 at University of Economics in Prague. Different statistical methods (test of hypothesis, ANOVA, correlation, regression) were used for this analyse. Calculations were performed using MS Excel. |
| KMEŤOVÁ Mária " Geometry Education in Historical Context " - from the section: New Trends in Mathematical Education The lecture is aimed to analyse our way of geometry teaching in a historical context. We deal with questions: How was the geometry curriculum influenced by new developments in science, mathematics and geometry itself? How can we partly compensate the newly reduced geometry teaching hours and content of curriculum by using appropriate computer programs for creative thinking and investigation in geometry? |
| KONEČNÁ Kateřina " Application of Hedging on Natural Gas Prices " - from the section: Financial and actuary mathematics The following paper examines hedging on natural gas. Natural gas is for a modern society vitally important. Furthermore, it is assumed due its advantages over other carbohydrates that the dependence will even increase. However, some disadvantage is incorporated with the product. The price instability poses significant price risk. We tried to apply naive portfolio, OLS, copula and wavelet in order to find an optimal hedge ratio. Subsequently, the ability to protect against undesirable price movement were compared. |
| KONEČNÁ Petra " Analysis of Efficiency of Entrance Examination Based on Permeation in the First Year of Study " - from the section: New trends in mathematical education Article extends partial outcomes received in year 2016, in which the author tries to answer the question, based on the monitoring of the admission procedure strategy, interest in studies and permeation in the first year of study in selected undergraduate Bachelor´s degree programmes, whether the entrance examination is able to guarantee reduction in academic failure rates and increasing number of successful graduates. In this extending article authors process needed data of all Bachelor´s degree programmes and put them through more-detailed analysis. Based on results of analysis, they also try to classify study programmes according to permeation as well as other common features. |
| KOŤÁTKOVÁ STRÁNSKA Pavla " Dynamic Model of Tax Assignment for Yield Tax on Personal Income From Dependent Activities " - from the section: Financial and actuary mathematics The fundamental changes that accompany the allocation of taxes were due to the changing political situation or a reflection of the political cycle and a non-system approach in the creation of modifications. The aim of the paper is to create a dynamic model. The assembled a dynamic model will be a tool for specifying the expected proceeds from the selected tax revenues (e.g. yield tax on personal income from dependent activities). Assembled model will be simulated on a change to the selected criteria. |
| KOTLASOVÁ Michala " Applying Discrete Mathematics in Situational Informatics Tasks - It Students’ Perspective " - from the section: The paper reports on findings of a research among IT students focused on the impact of passing an undergraduate course of discrete mathematics on students’ ability to recognize concepts, principles and methods used in discrete mathematics in situational informatics tasks. The performance in solving such problems, ability to find discrete mathematics in these tasks and also the use of knowledge gained in the course of discrete mathematics were studied and are discussed in the article. |
| KOVÁČ Tomáš " COMPARING THE EFFECTS OF CONSTANTS FOR GALIUM NITRIDE BASED ON THE CHARGE OF A THIN MEMBRANE " - from the section: Modeling and simulation in engineering and scientific computations The contribution focuses on the comparison of constants in the compliance matrix of a mechanical model based on magnitude of the resulting charge when a thin piezoelectric membrane of circular cross section made from aluminum gallium nitride is loaded. The article compares 15 sets of varying mechanical constants used in numerical analysis when determining the magnitude of the charge. The constants were obtained from different sources in world databases. The numerical results of each set were compared with experimental results and conclusions were drawn. |
| KOVÁR Martin " Mathematical Model of Serum PSA-Urinary Sarcosine Depencency and Its Impact On Tumor Geometry " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise Coming out from the well-known Brunn-Minkowski Theorem and its immediate consequence, the isoperimetric inequality, we attempt to reveal the geometrical information regarding the prostate tumor, hiding behind the dependency between the two biomarkers - serum prostate specific antigen (PSA) and urinary sarcosine. |
| KRČMÁROVÁ Monika " Integrating the History of Algebra in the Mathematics Class " - from the section: New trends in mathematical education The paper deals with the use of history of algebra in mathematics classroom. We describe our experience with the integrating of the history of mathematics. We used the single and double false position method in the historical problems to solve linear equations in the high school. We present also some examples of solving quadratic equations by completing the square from historical point of view. They could be used in the classroom too. |
| KROUPA Lukáš " Statistic of Quasi-Periodic Signal With Random Period - First Application on Vocal Cords Oscillation " - from the section: Statistical methods in technical and economic sciences and in practise In this paper we will introduce problem of statistics of quasi-periodic signal in relation to detection of the vocal cords pathology from audio recording or objective assessment of phonation quality. Quasi-periodic signal is assumed to be continuous bounded signal which repeatedly crosses given level (e.g. zero level) in direction from below to above this level. In following example, notice subtle differences of periods. First step is definition of distribution function of period lengths and its relation to distribution function of immediate frequencies. To avoid problems caused by existence or non-existence of moments, quantile expression of these moments is used. Next, approach for application on vocal cord diagnostic by classification of periods and frequencies to common and anomalous is devised. Developed probability model of vocal cord oscillation and its similarity to normal distribution as well as possible further development and application is discussed in the conclusion. |
| KURUCOVÁ Zuzana " The Use of Statistical Methods in Verification of a New Educational Model for Safety Specialists at Selected Higher Schools " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise This paper presents the design of a new educational approach in the area of Occupational Safety and Health (OSH) while taking into consideration specifications of the above mentioned field. Efficiency of the newly proposed approach in the preparation of future safety specialists has also been experimentally verified. The outcomes of our experiment were evaluated by means of non-parametrical statistical methods. The research was done in 2011-2014 and its aim was to propose an optimal model of education in the OSH area through the analysis of the current state in the field. |
| LALATTA COSTERBOSA Cecilia " The Smart Greenhouse:Photonic Crystals to Control Indoor Temperatures " - from the section: Mathematics and Art Smart Greenhouse is the prototype of a greenhouse, built in compliance with the parameters of the Parametric Hybrid Wall PHW method (Aplimat 2016 "The smart Greenhous"). The aim of the project is to achieve the optimization of the greenhouse indoor condition by means of a semi-automated control. A device able to independently manage the micro temperatures exploiting the combination of a biodegradable elastic polymer integrated to a Photonic Crystals film. |
| LOMBARDI Ilaria " Numerical Simulations for Acoustics Improvement of Roman Theatre of Cassino " - from the section: Mathematics and art In the present work are shown the results of acoustic measurements inside the Roman theatre of Cassino, in its present state. The theatre is only in part rebuilt, missing scene walls. The theatre is used for musical performances. To improve the acoustic characteristics have been studied, with the aid of a software for the acoustics architectural, the effects of installation of reflective screens on the scene. The numerical results show an improvements of the acoustic characteristics especially in the central area of the cavea. |
| LÖSTER Tomáš " Comparison of Different Ways How to Determine the Optimal Number of Clusters in Cluster Analysis " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise Cluster analysis is a multivariate statistical method which main aim is to classify objects into groups called clusters. Classification of objects into groups is a natural requirement of various scientific disciplines. There are a lot of methods which can be used to classification of objects into clusters, in the current scientific literature. The main aim of this article is to compare selected ways, which can be used to determine the optimal number of clusters. We used generated files for evaluation of coefficients. These files were generated in different conditions. It can be said, that CHF coefficient is one of the best coefficient for finding the optimal number of clusters. Euclidean distance measure is more useful in different conditions in comparison with Mahalanobis distance measure in clustering process. |
| MADARAS Tomáš " On Properties of Length-Scaled Betweenness Centrality " - from the section: Mathematical Aspects of Network Science and Applications The length-scaled betweenness centrality of a vertex $x$ in a graph $G$ is the sum of reciprocally distance-normalized relative numbers of shortest paths in $G$ which have $x$ as an inner vertex. We explore selected basic properties of this local graph invariant along with properties of graphs having the same length-scaled betweenness for each of their vertices; we also provide several estimates on the average length-scaled betweenness of a graph, and show its relation to Harary index. |
| MAGNAGHI Paola " Matemartiamo: Maths&Art Competition " - from the section: Mathematics and art The authors are engaged in interdisciplinary research initiatives of the FDS Laboratory (Formation, Didactics, and Science Communication) of the Mathematics Department of the Politecnico di Milano. The most important aim of the FDS laboratory has always been to contribute at the revaluation of the role which mathematics naturally play in the liberal arts. Historically mathematics always constituted an integral part of the liberal arts, in all meaning, which this term has had through the centuries. Nowadays in the Italian secondary schools, the students still believe that there are two different learning population which have alternative interests and goal: the scientific and the humanistic studies and careers. The connection between Mathematics and Figurative Arts is an argument that only recently had investigated by Italian mathematical researcher and populariser as Bruno D’Amore, Michele Emmer, Mauro Francaviglia, Piergiorgio Odifreddi. However, high school’s teachers, who generally do not exhibit any bias towards the other teaching arguments, develop each of the cultural trails in a separate way, nor do they feel the lack of connections. For many years, as FDS active members, we did many interdisciplinary projects with high school students of different orientations and we are convinced more and more that these experiences contributes significantly to increase the wealth of skills of the students. A chance to experience their creativity by producing an artwork in which they express mathematical laws is the first step towards the enjoyment of mathematics that we want students to feel. Among all the projects we did, the authors realised many educational projects oriented to connect learning experiences of Maths to other educational experiences in Humanities and in Art world. The aim of these interdisciplinary projects is mostly to reach students that are not otherwise be reached and we try to transform their opinions or prejudices about the role of Maths and Arts in the real world. Some of the projects we did provide new challenges for those students already considered successful. The idea to hold a contest on the theme of Art and Mathematics was born in one of our FDS meetings and strengthened through the exchange of experiences had in Tortona during the event of award ceremony of the Competition “Adotta Scienza e Arte nella tua classe”. In 2015-2016, FDS Laboratory published the competition MatemArtiAmo (Math&Arts) for pupils of secondary schools and freshmen of Politecnico di Milano in order to let them experience mathematical concepts by way of artworks’ creation. The contest provided six sections: Painting, Graphics, Photography, Literature, Sculpture and Video. We received one hundred or so artworks, especially in the section of Painting and Graphics. Most of all artworks’ authors went to secondary schools of almost all Italian regions and, in our opinion, some of their artworks are very interesting. The artworks were exhibited at the Politecnico di Milano and many of them were awarded during the ceremony that concluded the exhibition. In this paper, we describe production and operating methods of the contest and we describe the content and the meaning of some prize winning artworks. |
| MAGRONE Paola " Ellipses and Ovals in the Physical Space of St. Peter´s Square in Rome. " - from the section: Mathematics and art We discuss the 3D spatial and perceptive implications of the geometry at urban scale of Peter´s Square in Rome. The case study of Bernini´s project for the colonnade is exemplary for showing the relation between the geometry of the plan and its spatial development. Moreover it can be used to show the geometric differences of an ellipse and ovate. In scholarly literature, the difference between ellipses and ovate in architecture has been showed several times through an analytic investigation or by comparing the original drawings and the relief of the actual state, focusing on a 2D analysis of the plan. Here we propose to observe the geometry of St Peter´s square from another point of view, taking into consideration the plan along with the elevation, moving in the three-dimensional space of the city. We will show that the geometry of the circle affects intentionally the perception of the walking visitor. There is a traditional ambiguity of use between the terms ellipse and oval, especially in touristic literature and some school textbooks. These specific mathematical properties, of one curve respect to the other, were well known at the time and were obviously intentionally exploited in the design of the square along with the colonnade. We also report of a "geometric flash mob" we organized for the European Researcher´s Night of 2015 with www.formulas.it, a group of mathematicians and architects of the Department of Architecture of Roma Tre University. The activity, started by us and some of our students, and involved tourists in perceptive appreciation of the shape, and the anthropomorphic measurements of the square, building a human chain to measure its amplitude to a startling precision. Joint work with Alessandra Carlini |
| MAJOVSKÁ Renata " Mathematical Literacy Supported by Computer Tools " - from the section: New trends in mathematical education Modern technologies affect all areas of human life but mathematical education resists their influence. In this paper we present some experiences with using mathematical programs, online calculators and interactive tools at the Faculty of Economics VŠB-TU in Ostrava. The special attention is paid to the knowledge engine Wolfram|Alpha. We carried out the research to assess the appropriateness of the use of electronic products in teaching. The results of this research are presented. |
| MAREK Patrice " Effects of Rule Changes and Three-point System in NHL " - from the section: Statistical methods in technical and economic sciences and in practise There are two main reasons for changing rules in the ice hockey. The first reason is a safety of players and spectators and the second reason is an attractiveness of matches. This paper studies effects of rule changes that were made because of the second reason, e.g., allowing a two-line pass, narrowing a neutral zone, overtime in the case of a tie match. Rule changes are analyzed from two perspectives the first one is a distribution of goals scored in a match and the second one is a relative number of ties after a 60-minute regulation time. All seasons since the last big expansion of the NHL in 1979 are used in this analysis. The second part of this paper is dedicated to study of the three-point system that is often named as a cure for a high number of ties in the NHL. This system was earlier introduced in the world´s most important ice hockey leagues, i.e., in the Czech Republic, Finland, Germany, Russia, Switzerland and Sweden and its effect in these leagues is analyzed. |
| MAREK Jaroslav " Mathematical Linguistics and Greek Translation of the “Raven” by E. A. Poe " - from the section: Mathematics and Art The poem Raven of E. A. Poe is not only exciting story about meeting an ill man and a raven, about meeting a live with a disappointment, but a great occasion for comparing a texts. Translations of Raven exists in every language across whole world probably. In this article values of linguistics characteristics will be calculated. Our attention has been given to looking for similarities and differences among four Greek translation of Raven and of original text. |
| MARKOŠOVÁ Mária " Analyticaly Solvable Model of the Scale Free Growing Network with Hierarchy " - from the section: Mathematical Aspects of Network Science and Applications It is well known, that the preferential node attachment leads to the scale free network structure. Less is, however, known about the local processes leading to the hierarchical node organization. Our previous studies have shown, that adding new edges in a certain pattern creates complex scale free network with hierarchy. These studies were preferably numerical. In this paper we look for a minimal analytically solvable model of growing scale free hierarchical network. We define a minimal number of local processes leading to the hierarchical scale free structure and derive dynamical equations by which the evolution of network is driven. |
| MAŤAŠOVSKÝ Alexander " Remarks on the Local Intersection Multiplicity of Plane Curves " - from the section: Algebra and Geometry and Their Applications The two dimensional version of Bézout´s theorem states the global number of common points of two projective algebraic plane curves. This result says nothing about the connection between the multiplicity of $C$ on $U cap V$ and the multiplicities of $C$ on $U$ and $C$ on $V$. Denote $r$ resp. $s$ the multiplicity of common point $C$ on $U$ resp. $V$. Then there is the following inequality for multiplicities $i(U,V;C)geq rcdot s$. The aim of the paper is a characterization of equality. In particular, we give an equation for improving the inequality to equality. |
| MATVEJEVS Andrejs " On Diffusion Approximation for the Van Der Pol Oscillator Subject to Random Impulse Perturbation " - from the section: Differential equations, dynamic systems and their applications The paper deals with a mathematical model of the Van der Pol oscillator given by second order differential equation dependent on an impulse type compound Poisson process of large intensity. Applying the stochastic asymptotic approximation procedure we deduce the approximative stochastic differential equations for the phase and amplitude of vibrations. These equations permit us to analyze an existing capability and to describe the probabilistic characteristics of a stationary amplitude, and to discuss the behavior of a vibration phase. |
| MELE Giampiero " Perspective and Proportions in the Montefeltro Altarpiece of Piero Della Francesca " - from the section: Mathematics and art The aim of this research is to highlight the architect’s creative skills while designing an artifact that refers to the divine model. Perspective representation is the means by which everything is seen in proportional relationships, producing an artificial image that filters reality through another system of metric relations. After a brief investigation of the historical context of the Holy Conversation, the paper deepens the study of proportion and perspective. Piero’s painting is a rectangle composed of 6x10 square modules, whose sides are equal to 8/10 of the Urbino foot (38.3541 cm). The horizon line is placed at a height of 4 modules, and the square 6x6 acts as the basic unit for a Latin cross church plan whose nave’s area is equal to three 6x6 squares, and whose transept is composed of one 6x6 square and two 4x6 rectangles. At last 4x6 rectangle produces a space containing the apse with lacunars. The point of view of the perspective is 15 modules away from the picture plane. The way to highlight the geometrical construction in relationship with the measure of the architecture and perspective, allow us to formulate hypotheses and collect results to some doubtful points set previously by historians. The research is a part of the National Research project: PRIN Architectural Perspectives: digital preservation, dissemination and study . |
| MENCÁKOVÁ Kristýna " Solving a Higher-Order Discrete Equation " - from the section: Nothing In this paper we will find two linearly independent solutions of a linear discrete homogenous equation of the (m+2)-order. These solutions are a special functions called delayed discrete cosine and delayed discrete sine. There is given a representation of an initial problem and a nonhomogenous linear equation. |
| MIKEŠ Josef " On Conformal Mappings onto Einstein Spaces " - from the section: Algebra and geometry and their applications We study (with N. Guseva and I. Hinterleitner) conformal mappings of Riemannian manifolds onto Einstein manifolds under minimal condition of the differentiability class of manifolds in question. We obtain new results for this problems. |
| MILIN ŠIPUŠ Željka " Promoting Collaboration in Mathematics Education in Croatia " - from the section: New Trends in Mathematical Education In this talk I would bring in focus various forms of collaboration in the field of mathematics education in Croatia. A recently started project at the Department of Mathematics, University of Zagreb, aims to address the issue of underachievement in basic competences in mathematics, primarily by so called “overlooked middle” of upper secondary students. Therefore, as one of its target goals, it tries to enhance collaboration and flow of ideas between educational and research communities. Although the projects focuses on enhancing mathematical concepts of upper secondary education, it also relies on e.g. results of the research conducted at the Faculty of Science which investigates the use of mathematical concepts in physics and in real life contexts in order to promote ideas related to interdisciplinary approaches in learning and teaching of mathematics. Finally, I will also present beliefs of mathematics education students on the nature of mathematics, on learning of mathematics and on relevance of its various areas for their future teacher profession. |
| MORAOVÁ Hana " Differences in Classroom Practices in Ordinary and a Clil Mathematics Lesson " - from the section: New Trends in Mathematical Education The goal of the paper is to show the specifics of communication and practices in a CLIL mathematics lesson in contrast to a mathematics lesson conducted in a mother tongue. The reported research is conducted within the frame of the international Lexicon Project. A CLIL lesson must have dual focus (mathematical and language objectives) and thus we must expect some significant differences in classroom practices and communication patterns. For these reasons, the authors of the paper use Czech Lexicon to describe several CLIL lessons and look for what specific aspects of a CLIL lesson do not have a corresponding term in the Lexicon. Lexicon is a book of reference, a lexicon that provides the needed terminology as well as examples of what is meant by different terms used for the description of classroom practices in a mathematics lesson. The aim of the study is to point to the fact that teachers who face the situation of teaching mathematics through a foreign language should be familiar with practices that will be different from a traditional mathematics lesson and thus it will need more of their and their pupils’ attention. Moreover, pupils must be allowed extra time to get used to these new practices and patterns to develop a new classroom culture – the culture of a CLIL mathematics lesson. The results of the presented analysis illuminate the specifics of teaching mathematics in CLIL, and thus they are useful both for CLIL teachers and teacher trainers. |
| MOSKALIUK Stepan " Category Analysis of Nonlinear Schroedinger Equations and Its Applications " - from the section: Differential equations, dynamic systems and their applications This talk, on the one hand, is an introduction to category theory, a theory of structures and powerful organizing principles with many applications. On the other hand, the Category of the basis of differential invariants of Schroedinger group is constructed. We also present an extended discussion of the basic definitions and properties of Schroedinger category and its functors, with many illustrating and motivating examples from various areas of nonrelativistic quantum dynamic systems. |
| MOŠNA František " Statistical Tools in Excel " - from the section: New trends in mathematical education Use of computer technologies has become an integral part of statistics education at all levels of schools. This paper shows how the widespread program MS Excel can be used for teaching/learning of statistics. Statistical calculations in Excel are enabled through following three main options – statistical functions, add-in Analysis ToolPak and graphical tools. In one example relating to correlation it is shown that Excel can also be used for calculating of multiple and partial correlation and regression. Excel remains a good tool not only for scientific work but also for teaching statistics in schools and universities. It can substitute statistical programs even in relatively advanced topics. |
| NÁHLÍK Tomáš " Analysis of Video Files Using Information Entropy " - from the section: Statistical methods in technical and economic sciences and in practise The real-time experiments, especially biological experiments, provides us huge amount of data. They can be of different type; some of them are images, or video-files. Problem with biological experiment is that it cannot be repeated under exactly the same condition. Once the experiment is done we need to mine all possible data. But it can happen that the quality of data is poor or is changed during the experiments. Then it is necessary to enhance or improve obtained data. |
| NAŠTICKÁ Zuzana " An Analysis of Students´ Use of Mathematical Models in Solving Tasks with Real-Life Context " - from the section: New Trends in Mathematical Education Despite the general tendency to emphasize the importance of mathematics in solving daily-life problems, students’ difficulties with such tasks still widely persist. Mathematics education should be focused on making students learn how to mathematize real-life situations by means of mathematical models. Also, it seems wise to incorporate team work in mathematics education, for while solving problems in groups students have to communicate and provide proper arguments. In this research study we present results of a content analysis conducted on students’ solutions of two mathematical tasks related to gas consumption in households and gas distribution costs. The analysis was focused on how 204 students, aged 16-18, working in 51 groups of four, mathematically modelled the given real-life situations. Their solutions’ were analysed in terms of four main stages of the modelling cycle by Kaiser (real situation, real world model, mathematical model, and mathematical results). The results of the analysis indicate that students experienced serious difficulties at all four stages of the modelling cycle. Most students failed at the very first stage of the cycle, i.e. they misunderstood the real-life situation, its conditions and consequences. We assume this is closely associated with the reading comprehension skills of the students. Also, the interpretation of the obtained mathematical results was absent in students’ solutions, which suggests that students neglected proper verification of their mathematical model. Although we expected students to go through the stages of the modelling cycle sequentially, their solutions demonstrated that students often skipped some of the stages. |
| NORANDO Tullia " Matemartiamo: Maths&Art Competition " - from the section: Mathematics and art The authors are engaged in interdisciplinary research initiatives of the FDS Laboratory (Formation, Didactics, and Science Communication) of the Mathematics Department of the Politecnico di Milano. The most important aim of the FDS laboratory has always been to contribute at the revaluation of the role which mathematics naturally play in the liberal arts. Historically mathematics always constituted an integral part of the liberal arts, in all meaning, which this term has had through the centuries. Nowadays in the Italian secondary schools, the students still believe that there are two different learning population which have alternative interests and goal: the scientific and the humanistic studies and careers. The connection between Mathematics and Figurative Arts is an argument that only recently had investigated by Italian mathematical researcher and populariser as Bruno D’Amore, Michele Emmer, Mauro Francaviglia, Piergiorgio Odifreddi. However, high school’s teachers, who generally do not exhibit any bias towards the other teaching arguments, develop each of the cultural trails in a separate way, nor do they feel the lack of connections. For many years, as FDS active members, we did many interdisciplinary projects with high school students of different orientations and we are convinced more and more that these experiences contributes significantly to increase the wealth of skills of the students. A chance to experience their creativity by producing an artwork in which they express mathematical laws is the first step towards the enjoyment of mathematics that we want students to feel. Among all the projects we did, the authors realised many educational projects oriented to connect learning experiences of Maths to other educational experiences in Humanities and in Art world. The aim of these interdisciplinary projects is mostly to reach students that are not otherwise be reached and we try to transform their opinions or prejudices about the role of Maths and Arts in the real world. Some of the projects we did provide new challenges for those students already considered successful. The idea to hold a contest on the theme of Art and Mathematics was born in one of our FDS meetings and strengthened through the exchange of experiences had in Tortona during the event of award ceremony of the Competition “Adotta Scienza e Arte nella tua classe”. In 2015-2016, FDS Laboratory published the competition MatemArtiAmo (Math&Arts) for pupils of secondary schools and freshmen of Politecnico di Milano in order to let them experience mathematical concepts by way of artworks’ creation. The contest provided six sections: Painting, Graphics, Photography, Literature, Sculpture and Video. We received one hundred or so artworks, especially in the section of Painting and Graphics. Most of all artworks’ authors went to secondary schools of almost all Italian regions and, in our opinion, some of their artworks are very interesting. The artworks were exhibited at the Politecnico di Milano and many of them were awarded during the ceremony that concluded the exhibition. In this paper, we describe production and operating methods of the contest and we describe the content and the meaning of some prize winning artworks. |
| NOVÁK Michal " A Class of Hyperlattices Induced by Quasi-Ordered Semigroups " - from the section: Algebra and geometry and their applications There exist numerous generalizations of the concept of a lattice. In the hyperstructure theory, e.g. (join / meet) hyperlattices, hypersemilattices or $H_v$-semilattices are studied. In our paper we study a class of all these hyperstructure concepts which is derived from quasi-ordered semigroups by means of a simple universal construction. |
| NOVOTNÁ Jarmila " Parameters Influencing Word Problems Difficulty " - from the section: New Trends in Mathematical Education The paper presents the methodology and preliminary results of a 3-year project GAČR 16-06134S Context problems as a key to the application and understanding of mathematical concepts. The project aims to identify linguistic, psychological and mathematical parameters of context problems influencing their difficulty, describe those influences on primary school pupils’ success and the relationships between levels of linguistic and mathematical competence at different ages. Via linguistic, psychological and mathematical analyses of word problems in textbooks, international mathematical surveys and existing research results, about 71 linguistic psychological and structural parameters influencing word problems difficulty were identified. Seven parameters have been selected for the first stage of research: Pa. Formulation of numerical information in words or in numerals, Pb. (Mis)leading triads of numbers, Pc. Functional relationships, Pd. Order of information, Pe. Presence of false implication, Pf. Length of the text, Pg. Several levels of communication. Pairs of word problems differing in only one of the parameters have been created. They will be used with pupils of Grade 3 through to 9 from four Prague primary schools to find out how exactly the parameters influence the success rate of pupils and their solving strategies and mistakes. After presenting a theoretical framework consisting of word problems and related research, the paper concentrates on the methodology of research and presents illustrations of pairs of word problems differing in one parameter. For each parameter, we hypothesise how it will influence the solution and success rates. Finally, possible uses and implications of future research results are given. |
| ORSZÁGHOVÁ Dana " Mathematical Tasks with Applications and Their Presentation Via Information Technology " - from the section: New trends in mathematical education In this paper authors focused on the interconnection of three areas: how to link together knowledge in mathematics, economics and computer science? To use mathematics, economics and informatics in the one complex task - this is the difficult problem for students who enter the university in the first year. Students have to solve tasks that are formulated in the study subject mathematics and some problems appear in the topic of the function with two variables. We also present the results of the questionnaire survey about the skill level of university teachers to use IT tools. |
| PÁLENÍKOVÁ Kitti " Examples of Good Practices of Experiential Learning and Students’ Opinions on experiential learning " - from the section: New trends in mathematical education The present research is focused on constructivist approach in mathematics instruction referred to as experiential learning. The research presents findings of a questionnaire survey concerning with students’ attitudes towards particular workshops they took part in, and popularity of science subjects. The workshops were designed following the experiential learning theory, with emphasis on learners’ active work. The workshops’ topics were chosen with intention to show students where geometry learnt at school can be applied, and to make them experiment and observe actively in order to find patterns for solutions of linear Diophantine equations. |
| PAUN Marius " Tropical Geometry " - from the section: New trends in mathematical education Starting from a simple problem of flow we construct the context in which the Tropical Geometry is working and we present some applications of this algebraic geometry. Low level examples constitute a very good model of how difficult and modern mathematics can be used in teaching. |
| PAVLENKO Oksana " On Diffusion Approximation for the Van Der Pol Oscillator Subject to Random Impulse Perturbation " - from the section: Differential equations, dynamic systems and their applications The paper deals with a mathematical model of the Van der Pol oscillator given by second order differential equation dependent on an impulse type compound Poisson process of large intensity. Applying the stochastic asymptotic approximation procedure we deduce the approximative stochastic differential equations for the phase and amplitude of vibrations. These equations permit us to analyze an existing capability and to describe the probabilistic characteristics of a stationary amplitude, and to discuss the behavior of a vibration phase. Keywords. The Van der Pol oscillator, random oscillations, diffusion approximation. |
| PAVLIKOVA Sona " Ivertibility of Graphs with Perfect Matching. " - from the section: Algebra and geometry and their applications In this paper we investigate invertibility of graphs with perfect matching, i. e. graphs having unique 1 - factor. We recall the new notion of the so-called negatively invertible graphs investigated by the authors in the recent paper by Pavlikova and Sevcovic. In the full proceeding paper we characterize all graphs with perfect matching on 6 vertices with respect to their positive and negative invertibility. |
| PEŠKA Patrik " On semisymmetric projective Euclidean spaces " - from the section: Algebra and geometry and their applications In this paper we (with Josef Mikeš and Almazbek. A. Sabykanov) study n-dimensional semisymmetric projective Euclidean spaces. Semisymmetric spaces are spaces with affine connection ∇ in which curvature tensor R satisfies condition, RᵒR = 0. These spaces are generalization of symmetric spaces for which the covariant derivative of curvature tensor is vanishing, i.e. ∇R = 0. Symmetric spaces begin to study P. A. Shirokov and É. Cartan. The name semisymmetric was explicitly introduced from paper by Sinyukov. In his paper he studied geodesic mappings of symmetric and semisymmetric spaces, and later in this field continuous Mikeš who obtained new results. The geometry of symmetric and semisymmetric spaces plays important role in Riemannian manifolds and their generalizations. The great interest in semisymmetric spaces had Nomizu hypothesis which was out casted later. Projective Euclidean spaces were investigated in many different ways. These spaces are geodesically equivalent to Euclidean spaces. Components of affine connection of symmetric projective Euclidean spaces obtained P. A. Shirokov. In our paper, we find new properties of semisymmetric projective Euclidean spaces. |
| PILOUS Derek " Reaction Time of Simple Categorization of Subclasses of Functions " - from the section: New trends in mathematical education In last decades, there is a tendency to use general psychological mathods of research in mathematics education. In our contribution we present mostly quantitative results of our first study focused on measuring of reaction time and accuracy of respondents in specially developed task - categorization of mathematical objects, specifically one subclass of class of functions. Particular hypotheses and interpretations of process of decision in this task, based on statistical analysis, are proposed. |
| PLOTHOVÁ Lucia " 1. An Analysis of Students´ Use of Mathematical Models in Solving Tasks with Real-Life Context, 2.An Analysis of Errors in Algebraization of a Math Word Problem and the Rosnick-Clement Phenomenon " - from the section: New trends in mathematical education 1. Despite the general tendency to emphasize the importance of mathematics in solving daily-life problems, students’ difficulties with such tasks still widely persist. Mathematics education should be focused on making students learn how to mathematize real-life situations by means of mathematical models. Also, it seems wise to incorporate team work in mathematics education, for while solving problems in groups students have to communicate and provide proper arguments. In this research study we present results of a content analysis conducted on students’ solutions of two mathematical tasks related to gas consumption in households and gas distribution costs. The analysis was focused on how 204 students, aged 16-18, working in 51 groups of four, mathematically modelled the given real-life situations. Their solutions’ were analysed in terms of four main stages of the modelling cycle by Kaiser (real situation, real world model, mathematical model, and mathematical results). The results of the analysis indicate that students experienced serious difficulties at all four stages of the modelling cycle. Most students failed at the very first stage of the cycle, i.e. they misunderstood the real-life situation, its conditions and consequences. We assume this is closely associated with the reading comprehension skills of the students. Also, the interpretation of the obtained mathematical results was absent in students’ solutions, which suggests that students neglected proper verification of their mathematical model. Although we expected students to go through the stages of the modelling cycle sequentially, their solutions demonstrated that students often skipped some of the stages. 2. The purpose of this research was to examine the basic algebraic skills of students, and to identify errors they make when solving a simple math word problem. The research was conducted among 103 first graders of a secondary comprehensive school aged 15-16 and 135 first-grade university students. The research instrument was a short three-item test. Despite proper acquisition of the algorithm for solving linear equations, in algebraization of the math word problem altogether 35.93% of the secondary school students and as much as 72.59% of the university students were unsuccessful. The reversal error occurred in 27.18% of the incorrect secondary school students’ solutions and in 35% of the incorrect university students’ solutions of the word problem. The students’ low success rates could be caused by their miscomprehension of the texting of the word problem, which is associated with their reading comprehension skills. The reversal error occurred due to mechanical procedures employing no deeper thinking. Many of the errors can be remedied by teaching students to verify and interpret their results back into the non-mathematical language. |
| POLCEROVÁ Marie " Method to Programmatically Generate a Large Number of Assignments for Students and to Assess Their Results in MATLAB " - from the section: New trends in mathematical education This paper discusses one method of generating large number of different individual assignments for students, their fully automated electronic assessment and its role and possibility in computer-aided teaching of mathematics at technical higher education institutions. This paper describes methodology and the specific realization, including programs written in MATLAB and examples of inputs and outputs. Also this article summarizes current experience with this method and discusses evaluations in mathematics. |
| PORUBA Jakub " New Tools for Monge Projection in GeoGebra " - from the section: New trends in mathematical education co-author with Ferdianova GeoGebra is a dynamic mathematics software for all levels of education that brings together geometry, algebra, spreadsheets, graphing, statistics and calculus in one easyto- use package. It also is a rapidly expanding community of millions of users located in just about every country. GeoGebra has become the leading provider of dynamic mathematicsl software, supporting science, technology, engineering and mathematics (STEM) education and innovations in teaching and learning worldwide.[2] Materials created in GeoGebra can be stored or shared on official website. Worksheets, materials and tools are the most shared files there. All these materials should support development of spatial imagination. However, this is the ability most students lack, which results in having problems with understanding simple tasks in descriptive geometry [1]. Thus we decided to create a new tool that would help to improve teaching Monge projection. Tool constructions are based on a simple algorithm rule - if it is possible to create an "algorithm" from a construction, it is possible to create a tool. We have created 3 tools for Monge projection that can draw three basic elements used almost in every task: a point, a straight line, a plane. The process of creation is described in paper in details, thus it is possible to use this manual for defining own tools or for modification of created ones. [1] Gittler, Georg, and Judith Glück: Differential transfer of learning: Effects of instruction in descriptive geometry on spatial test performance. Journal of Geometry and Graphics 2.1 (1998): 71-84. [2] URL: http://www.geogebra.org. |
| POTŮČEK Radovan " The Sum of the Series of Reciprocals of the Quadratic Polynomials with One Negative and One Positive Integer Root " - from the section: Modeling and simulation in engineering and scientific computations We dealt with the sum of the series of reciprocals of the quadratic polynomials with one negative and one positive integer root. We derived the formula for the sum of this series using harmonic numbers. We also stated two simple cases of this formula. We verified this result by computing 100 various sums by using the CAS Maple 16. |
| POZDÍLKOVÁ Alena " Usage of Artificial Intelligence and Spectral Analysis for Predicting the Behavior of Stock Prices " - from the section: Financial and Actuary Mathematics In this paper methods of artificial intelligence and spectral analysis to build an algorithm for predicting the behavior of stock prices are applied. Spectral decomposition of a time series was calculated using known methods based on Fourier transformation. The results obtained from periodogram analysis simply provide information about periodicities. Significance analysis was not performed and we worked with four frequencies. This spectral information is then used in clustering of data. Comparison of behavior of price oscillation in clusters was carried out. The presented contribution aims to describe a new algorithm for predicting the behavior of stock prices. The clustering algorithm is based on spectral analysis and SOM. The whole procedure is tested on selected time sections of Dow Jones Industrial Averages, where the algorithm is performed. Results of analysis and final discussion, presented in the Case Study, show that the new method successfully signalizes the trend of stock market prices. |
| PŘÍBORSKÝ Jan " Some Properties of Causal Structures " - from the section: We introduce and study a new notion, causal venue, which is a slight modification of causal site, defined by J. D. Christensen and L. Crane in 2005. In fact, we omit the assumption of anti-reflexivity of the causal relation and the necessity of the presence of the least element in the spatial relation. As we show and discuss, our modification of the studied algebraic causal structure potentially solves some limitations of its original version. |
| PŘIBYL Jiří " Heuristic Strategy Systematic Experimentation " - from the section: New trends in mathematical education The paper describes a heuristic strategy for problem solving called Systematic experimentation. The strategy is described and illustrated by several problems. In our conception we count Systematic experimentation strategy among experimental strategies. The fundamental definition of this strategy is based on systematic exhausting of all potential results. The strategy Systematic experimentation is an advisable option for the pupil to solve a problem that is to be solved through a straight-forward way. |
| PROCHÁZKOVÁ Jana " Free Form Deformation Methods - Theory and Practice " - from the section: Algebra and geometry and their applications Solid modeling is one of the essential techniques used in common 3D studios (Maya, Rhinoceros, Blender). The editing or modification of the solids is often done using free-form deformation (FFD). In our article, we present two different techniques of the FFD. Firstly, we outline Sederberg´s scheme based on Bernsteins polynomials that is the headstone of the method. Secondly, we describe the method NURBS FFD that is more complex and is independent on the shape of the object hull. |
| RÁBOŇOVÁ Petra " Polynomial Calibration with Use of Linearized Model wiht Errors in Variables, and Kenward Roger Type of Approximation " - from the section: Statistical methods in technical and economic sciences and in practise Calibration is a set of tasks which gives the relationship between a reference device and a calibrated device (if some special conditions are fullfilled). This relationship is described by the transformation function and represented by the transformation curve. In the contribution we assume that the transformation curve is a polynomial of degree k. Therefore, we focus on the polynomial calibration. We use a method based on linearized errors-in-variables model and Kenward-Roger type approximation for obtaining the transformation curve. Calibration process can be divided into two parts: 1) creation of the calibration model (calibration of the device), 2) application (use) of the calibration model (measuring by calibrated device). In the contribution we estimate parameters of the transformation function and their confidence region by the mentioned methods and we also show the use of the transformation curve in the measuring process. |
| RAGUZ Andrija " Are Business Cycles Phase Transitions? " - from the section: Differential equations, dynamic systems and their applications In this note we interpret the well-known one-dimensional Cahn-Hilliard functional as the model for achieving the dynamic equilibrium over large periods of time in given national economy with known initial aggregate economic parameters. The economy is viewed as the dynamical system, without strict separation to exogenous and endogenous variables, but with assumed existence of business cycles (viewed as "phases" or "states"), which bring both balance and imbalance to the state of the economy. Our conclusions are based on a number of results obtained by A. Raguz outside the economic context, which are related to standard analysis of Cahn-Hilliard functionals in one dimension. Mathematical apparatus used is Gamma convergence of functionals defined on appropriately chosen space of functions, as well as the relaxation method in the variational calculus over the space of Young measures. We prove that under relatively mild assumption on double well potential function and the optimal profile function we can indeed deduce both economic interpretation of the mentioned model and the desired equilibrium state of the national economy in terms of balancing the usual economic parameters. |
| RAK Josef " Numerical Computing of Singular Integrals in Integral Euqations " - from the section: Modeling and simulation in engineering and scientific computations This paper shows three possible methods to numerically compute a special singular integral in an integral equation of the second kind. The methods are isolation of the singularity, singularity subtraction and substitution. All methods are compared with their error behavior and numerical examples. The main aim is to show, that the subtraction method, which is usable in multidimensional problems, has good error behavior. |
| RIHOVA Elena " Fuzzy Clustering Application on Direct Marketing Case " - from the section: Statistical methods in technical and economic sciences and in practise There are many marketing campaigns made by banks, nowadays. However, every of those campaigns has just one and only goal. This goal is a success, i.e. the client subscribes the deposit. In this paper we are trying to determinate the success of the campaign with fuzzy clustering help (if the campaign was sucessfull or not). Real world data were collected from a Portugauese direct bank marketing campaign in 2012. |
| ROUBÍČEK Filip " Assessing a Teacher’s Competence for Implementation of Inquiry Based Mathematics Education From a Discussion of Open Geometrical Situations " - from the section: New Trends in Mathematical Education This study is focused on the possibility to assess and develop primary teachers’ abilities to implement some principles of inquiry based mathematics education into their teaching practice. The requirements on a primary teacher and their competence are assessed through a joint discussion of open geometrical situations presented through Concept Cartoons. Teachers’ written comments and notes and verbal statements expressed in the discussion of four geometrical problems were analysed and presented. |
| ROZEHNALOVÁ Petra " Homogenization on Domains With Holes " - from the section: Differential equations, dynamic systems and their applications Homogenization is a mathematical technique which can be use for mathematical modeling of mechanical behavior of materials with fine structure (composite material, finely perforated material etc.). In this paper we describe homogenization based on unfolding operator, we briefly state properties of such operator and present an example of its usage. |
| RÝPAROVÁ Lenka " On Global Geodesic Mappings of Quadrics of Revolutions " - from the section: Algebra and geometry and their applications We (with J. Mikeš) studied geodesic mappings of special surfaces of revolution. It is proved that quadrics of revolution (except a circular cylinder) admit nontrivial geodesic mappings and deformations, in which they remain rotational. Surfaces (except circular cylinder and sphere) obtained in these geodesic deformations are no longer quadrics. |
| ŠABÍKOVÁ Henrieta " High School of Business Pupils´ Background and Mathematical Competences " - from the section: New Trends in Mathematical Education Pupils´ background and their mathematical competences could be considered as basic factors that influence their high school study success. Based on previous teaching experience, characteristics of pupils´ background include origin (town or village), gender and number of pupils in their last class at the elementary school. Pupils´ mathematical competences could be characterized by their results of the entry exam in mathematics and by their math grade point average at the elementary school. The structure of pupils´ background and their mathematical competences will be analysed at the general and bilingual section of high school of business. This analysis should be initial resource of the experiment focused to bilingual English-Slovak mathematics education at high school of business and expected pupils results in mathematics. |
| SAFARIK Jan " Solution of weakly delayed linear discrete systems in $mathbb{R}^3$ " - from the section: In the paper we investigate weakly delayed linear discrete systems with constant delay $$x(k+1) = Ax(k) + Bx(k-m), k = 0, 1, dots, m,$$ in $mathbb{R}^3$. Conditions for the system to be a weakly delayed system are given and the initial problem is explicitely solved in one of possible cases. |
| SALVADORI Anna " Math-MAPS a New Road that Opens Up a WorldI Part - Dynamic Models without Derivatives " - from the section: New trends in mathematical education Math-MAPS is a kind of Google maps for mathematics created by Mathematics&Real Life (M&R) with the aim to offer innovative educational pats to the Schools of any order. M&R is a national project of the Department of Mathematics and Informatics of the University of Perugia which promotes education to mathematical modelling as innovation drive. Education to modelling involves a completely new way of approaching Mathematics, based in a dynamic interaction between the real word and mathematical word. Math-MAPS suggests learning highways to connect the different topics. In our paper we will present one of these recommended tracks: the introduction to dynamic models. The contribution is divided in two parts: the first part deals with the discrete case (suitable also for vocational Schools). |
| SAMKOVÁ Libuše " Observing How Future Primary School Teachers Reason and Generalize: the Case of Number Triangles and Concept Cartoons " - from the section: New trends in mathematical education The contribution focuses on the possibility to use an educational tool called Concept Cartoons as a diagnostic instrument in problem solving and problem posing activities of future primary school teachers. The aim of the presented study is to observe which aspects of future primary school teachers´ knowledge related to reasoning and generalization could be investigated through Concept Cartoons that are based on a substantial learning environment called "Number triangles". |
| SCHREIBEROVÁ Petra " Mathematical Education with Worksheets (with P. Volny) " - from the section: New trends in mathematical education We present our practical experiences with using of worksheets during education of Mathematics at VŠB - Technical University of Ostrava. We prepared worksheets for the students. These worksheets cover all main mathematical courses in the bachelor study program. We asked the students to answer a few questions concerning the worksheets. The feedback from students is presented in the paper and we also discuss our practical experiences with the worksheets. |
| SEDIVA Blanka " The Principles of Random Matrix Theory and Their Application to the Portfolio Choice " - from the section: Statistical methods in technical and economic sciences and in practise In this paper, we use random matrix theory to analyse eigenvalues and see if there is a presence of pertinent information by using Marčenko–Pastur distribution. Thus, we analyse cross correlations between price fluctuations of different stocks using methods of random matrix theory. Moreover, we try to clean correlation matrix from noisy elements to see if the gap between predicted risk and realized risk would be reduced. The cleaned correlation matrix was used in portfolio optimization problem. This analysis is a way to understand the correlation structure. |
| ŠIMPACH Ondřej " Deterministic and Stochastic Extrapolation of Death Rates in the Czech Republic with an Impact on Probability of Dying and Tabular Number of Deaths " - from the section: Financial and actuary mathematics The aim of this paper is to compare the results of deterministic (linear regression) and stochastic (autoregressive integrated moving averages) extrapolations of logarithms of age-and-sex-specific death rates of the Czech population with impact on key characteristics of mortality tables – probability of dying and tabular number of deaths. The result is that the optimized stochastic ARIMA models provide more realistic results about the future development of the analysed characteristics and they are much less biased. Deterministic models have problems in applications on variable data, which can be expected especially in the highest ages. |
| SIVÝ Martin " Seismic Response of Elevated Liquid Storage Tanks " - from the section: Modeling and simulation in engineering and scientific computations The paper deals with the seismic analysis of elevated liquid storage tanks with the aim to compute the response of the structure to earthquake loading. In the seismic analysis, the unfavourable mode of oscillation is computed by the analytical and numerical approach. The computation of the response to the seismic event is performed by spectrum analysis with El Centro earthquake response spectrum plot and results are compared by time-history analysis using El Centro accelerogram. All analyses are carried out by FE method in software ANSYS. |
| SLÁDEK Václav " Comparison of Robust Estimates " - from the section: Modeling and simulation in engineering and scientific computations The aim of this paper is to analyze properties of robust estimates which estimate the mean value and variability of a distribution and to compare properties of these estimates. This will provide background for selection which robust estimate is better estimate of an unknown parameter in specific situation. Properties of estimates are estimated by robust bootstrap. Considered robust estimates have relatively similar properties. If we dispose of a large sample, our selection can be based only on the mean value of estimate. |
| ŠMARDA Zdeněk " Semi-Analytical Approach to Solving Partial Differential Equations " - from the section: Differential equations, dynamic systems and their applications In the present paper an analytic solution of partial differential equations is deduced with the help of the differential transform method (DTM). General formalae of (n+1) - dimensional DTM are given. To illustrate the capability and efficiency of the method two examples are solved. The method can be easily applied to many initial and boundary value problems and is capable of reducing the size of computational work. |
| SMETANA Bedřich " Ompatible Relations on State Sets of Quasi-Automata " - from the section: Algebra and geometry and their applications Using analogy with relations between hypergoups and automata there is developed access to relations between these subjects. In this paper some concepts of compatible relations on state sets of quasi-automata are investigated. |
| SMETANOVÁ Dana " The Regularization by Constant Functions of Lagrangiangs Linear in First Derivatives " - from the section: Algebra and geometry and their applications In this paper we study case of the Lagrangians affine in first derivatives in first order field theory (for example Dirac field Lagrangian is of this type). By the regularization procedure we mean the process how to find appropriate Lepagean equivalent for given Lagrangian (in the sense of the geometric meaning of the regularity). The theory is illustrated on an example in dimension 4. The relations to multisymplectic forms are discussed. |
| SOPKULIAK Peter " Validation and Convergence of the Adaptive Monte Carlo Method Toward the Law of Propagation of Uncertainty Applied on Specific Point of Chosen Subscale of Its-90 " - from the section: Modeling and simulation in engineering and scientific computations The article briefly describes the approach of evaluating calibration using the adaptive method of Monte Carlo and the subsequent validation by the law of uncertainties when applied on the primary realization of the temperature scale, with emphasis on measurement with standard platinum resistance thermometer (SPRT) illustrated by the range (0 ÷ 660) °C of the international temperature scale (ITS-90). |
| SPREAFICO Maria Luis " Origami Modeling for Architectural Shapes: Mathematical and Design Investigation " - from the section: Mathematics and art Origami is the ancient Japanese art of paper folding. Despite its long history, the majority of its scientific and technological applications have come within the past 50 years. Advances in mathematics and computer science have paved the way for new analysis of the folding process and design techniques, which now allow to realize structures with specified properties, in a predictable and precise way, far beyond the art itself. We expose a research experience in this context. Analyzing mathematically the pure forms of the roof system generated by portions of developable surfaces, we construct 3D origami models of these architectural shapes. As we investigate applications in many fields, we are making experience with various types of materials beginning with cardboard engraved by laser or die cut. Authors: Caterina Cumino, Maria Luisa Spreafico, Ursula Zich. |
| ŠUMNÝ Timotej " ABOUT CONSTRUCTION OF TRIANGLE GIVEN BY INSCRIBED CIRCLE, LENGTH OF ONE SIDE AND ONE OTHER PARAMETER " - from the section: New trends in mathematical education In the learning process of geometry, we have a many types of task for triangle construction. But is only a few tasks which are typical and those types are solving on the mathematics lessons. With using the ICT on the learning process, we can solve unusual geometric task.In thos paper we are focused on a geometric problem about construction triangle if we know value of side c, radius of inscribed circle ρ and other parameter. For solve this problem we use a locus of point. |
| SVOBODA Zdeněk " Representation of Solutions of Nonhomogenous Second-order Linear Differential Systems with Constant Delays " - from the section: Differential equations, dynamic systems and their applications In the paper the representations of solutions to initial problems for n-dimensional nonhomogeneous second-order linear differential equations with delays is given. The results are derived by means of special matrix delayed functions. |
| TALAMANCA Valerio " Folding Cubic Roots: Margherita Piazzolla Beloch´s Contribution to Elementary Geometric Constructions " - from the section: Mathematics and art Paper folding, or origami, has been known for centuries as a fine art form, a way to transform a piece of paper into something beautiful. In the last 30-40 years it has been undestood that paper folding can also be an important scientific and technological tool. It has contributed to create new fields of research, in particular related to technological frameworks, with the exploitation for example of the properties of the so called flat origami. Some of this topics were described in a previous article by Paola Magrone In this work we examine its application to classical geometric construction, with special regard to the contribution of Margherita Piazzolla Beloch, who, already in 1934, realized that paper folding was a powerful tool when dealing with geometric configurations. Of the many geometrical problems studied by the ancient Greek only three gained enduring fame: doubling a cube, trisecting an angle, and squaring the circle. They owe their celebrity chiefly to the fact that they withstand every attempt to be solved by ruler and compass, the classical instruments, for centuries. In the nineteenth century, it was proven that was actually impossible to solve them only using ruler and compass. Margherita Piazzolla Beloch was the first one to realize that it is possible to solve the problem of doubling the cube using paper folding. The solution was achieved by creating a new fold, fold which in turn enabled Piazzolla Beloch to construct also the root of any given cubic polynomial. Joint work with Paola Magrone |
| TEDESCHINI-LALLI LAURA " Imperial Roman Cochlear Columns and Their Historical Narrative Friezes " - from the section: Mathematics and art Cochlear columns (colonna Trajana, colonna Antonina) in imperial Rome bore the historic visual narration of battles, victories and conquers by emperors. This was possible as a long sculpture narration evolved along a helical frieze, permitting representation without aberration or visual distortion, due to the locally euclidean property of the surface. Moreover, we also describe the narrative correspondences relating to the vertical periodicity of the subjacent helix. joint work with Alessandra Carlini, architect |
| TEICHMANN Dušan " A Contribution to Shortest Path Algorithms in Transport Networks With Capacity Limitations of Edges " - from the section: Mathematical Aspects of Network Science and Applications The article presents modifications of two well-known pathfinding algorithms – Ford algorithm and Floyd algorithm. The presented modifications enable to find a shortest path which satisfies pre-defined capacity limitations – for example the limitations resulting from known measures and weight of a shipment we want to transport. |
| TEREK Milan " Regional Incomes Structure Analysis Based on Compex Survey Data " - from the section: Statistical methods in technical and economic sciences and in practise The paper deals with the analysis of complex survey data by construction of empirical probability mass function, empirical cumulative distribution function and estimation of medians in domains with aid of sampling weights adjusted regarding to nonresponse. The estimates of median whole gross household incomes for eight Slovak regions on the basis of European Union statistics on income and living conditions in Slovak republic data are calculated and compared. |
| TICHÁ Marie " Observing How Future Primary School Teachers Reason and Generalize: the Case of Number Triangles and Concept Cartoons " - from the section: New Trends in Mathematical Education The contribution focuses on the possibility to use an educational tool called Concept Cartoons as a diagnostic instrument in problem solving and problem posing activities of future primary school teachers. The aim of the presented study is to observe which aspects of future primary school teachers´ knowledge related to reasoning and generalization could be investigated through Concept Cartoons that are based on a substantial learning environment called "Number triangles". |
| TOLNAY Marián " Simulating the Environment of Cutting Processes " - from the section: Modeling and simulation in engineering and scientific computations In this article, paired parallel processed signals and neural networks were used to describe the overall behavior of a system (emergence) which cannot be otherwise predicted based on each individual element of the system on its own. Artificial neural networks are used when the rules of a given solution to a possible situation are not completely known, or are too complex to describe exactly. Artificial neural networks are most commonly used in recognition and classification of patterns (images) into categories (pattern recognition and classification). With neural networks it is possible to predict solutions to very diverse associative problems. If it is possible to formulate the problem as an associative task, it is possible to incorporate artificial neural networks. Training the neural network requires knowledge of the experimental processes involved. The most basic building block of a neural network is the model of the neuron. This contribution utilizes a feedforward artificial neural network. |
| TORRE MATTEO " Impossible Pictures: when Art Helps Science Education " - from the section: Mathematics and art The paper talks about the use of the impossible figures in science education discovering, in particular, the great artistic and communicative value of the artworks of Oscar Reutesvärd, that long before Escher and Penrose had drawn triangles and stairs impossible through a conscious use of "Japanese" perspective. In the last part of paper are also analyzed the links between art and impossible figures showing how over the centuries their communicative power has been (more or less) deliberately used by artists such as W. Hogarth, or of Op Art, which tried to involve the observer deceiving his eyes and his brain. |
| ŤOUPAL Tomáš " Trend Component Analysis of Time Series " - from the section: Statistical methods in technical and economic sciences and in practise This paper deals with the problem of trend component estimation particularly for economic time series. The proposed approach could be used in many applications e.g. GDP, unemployment, stock markets etc. There will be presented one method using orthonormal system generated by Gram-Schmidt orthonormalization process from some available linearly independent sequence of time series or functions in an inner product space. Obtained results are then applied to the real data sets of the foreign trade and consumer price index. |
| TREMATERRA Amelia " Virtual Reconstruction and Sound Field Simulation of Odeon of Posillipo " - from the section: Mathematics and art Campania coast during Imperial Rome period, due to healthy climate and beauty of landscape was an ideal place to host residences of Roman patricians. In this paper is reported the virtual reconstruction and the sound field simulation of Odeon of Posillipo. This analysis is performed using a software for architectural acoustic. The sound field simulation gives information that the Oden was used for speaking. |
| TURŇA Ľubomír " Rupture Formation and Phase Transition as a Possible Consequence of Limiting Environmental Conditions " - from the section: Differential Equations, Dynamic Systems and Their Applications Abstract. Any activity in any environment or device often produces waste and changes of the environment. The paper aims to analyze this process on a simple model and determine the conditions of the change of environment characteristics by means of the model parameters. Results of analyzing the coexistence of biological species in their various relationships, such as cooperation, competition and antinomy, have been known within the mathematical ecology for almost a century. The same mathematical apparatus of evolution equations can be used for monitoring the coexistence of inanimate entities, for example: in particle physics theories, in the behavior of gases and thermodynamics, quantum generator, in the theory of management and so on. The contribution follows the use of mathematical tools, for example: in the area of information technology, and the analysis of interacting stakeholders and groups in the socio-economic environment. |
| UGHI Emanuela " From Leonardo´s Ycocedron Abscisus Vacuus to the Football: a Geometric Journey " - from the section: New trends in mathematical education Teaching methods usually require students to look at pictures and drawings related to some mathematical subject, but the manipulation of a concrete model is much more appealing, so that this paper wants to offer a teaching proposal to offer the students the possibility to realize concrete models of a football, so discovering and better mastering its geometric structure. |
| ÚRADNÍČEK Juraj " Investigation of Frictional Stick Slip and Sprag Slip Mechanisms Leading to Disc Brake Noise Vibration and Harshness Effects " - from the section: Modeling and Simulation in Engineering and Scientific Computations Paper describes mechanisms of vibration of disc brake components which can leads into noise effects known as brake Noise Vibration and Harshness (NVH). Stick slip and Sprag slip physical effects are mathematically described under simplifying physical assumptions. Self-excited vibration due to stick slip effect and stability conditions are defined using 1 degree of freedom mechanical system. Response is obtained by numerical solution of ordinary differential equation. Sprag slip mechanism is demonstrated through multiple degree of freedom elastic system defined by the Finite Element Method (FEM). Kinematic and dynamic behavior is simulated in Multibody dynamics (MBD) simulation system using Algebraic-differential equations solver. |
| UTANO Rosanna " Mixed Product Ideals and Simplicial Complexes " - from the section: Algebra and geometry and their applications MIXED PRODUCT IDEALS AND SIMPLICIAL COMPLEXES 1 UTANO ROSANNA MESSINA UNIVERSITY rosanna.utano@unime.it Keywords: squearefree monomial ideals; simplicial complexes, polytopes. 2010 AMS Mathematics Subject Classification: 13C15, 13F20 Extended Abstract. Let I be a squarefree monomial ideal of the polynomial ring K[x1,…,xn]. We can consider I as the Stanley Reisner ideal of a simplicial complex ΔI, on the set of vertices x1,…,xn and whose faces are defined by ΔI = {{x_i1, ..., x_ik}|i1 <... More precisely, we study two classes of mixed product ideals, IrJr and Ir +Jr, where Ir (resp. Jr ) is the ideal of K[X,Y] generated by all the squarefree monomials of degree r in the variables X (resp. Y). If the ideal has the form IrJr or IrJr-1+ Ir-1Jr then it is the generalized graph ideal of a complete bipartite graph, whose set of vertices are X and Y. If the ideal has the form Ir +Jr, as before, the structure of the associated simplicial complex Δ is not difficult to understand, being the join Δ1* Δ2 of two disjoint simplicial complexes consisting of the (r-1)-skeletons of two (r-1)-simplices on the sets of vertices X and Y respectively, with Ir =IΔ1 and Jr = IΔ2 . We refer to [1] for basic properties of Stanley-Reisner ideals. We want to study the simplicial complexes and polytopes associated to these ideals ([2]). Even for the simplest examples several properties arise. We examine low values of n and m, and some examples will cover the other classes. References 1. W. Bruns, J. Herzog, Cohen-Macaulay Rings, Cambridge University Press, Rev. Ed. (1997). 2. G. Restuccia, R. H. Villarreal, On the normality of monomial ideals of mixed products, Comm. Alg., 29 (8), (2001) 3571--3580. 3. B. Sturmfels, Groebner bases and convex polytopes, Univ. Lectures Series, Amer. Math.Soc., 8 (1995). 4. R. Villarreal, Monomial Algebras, Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, Inc. New York, 238 (2001). 1 Rosanna Utano Università di Messina, Dipartimento di Scienze matematiche e informatiche, Scienze fisiche e Scienze della Terra, Viale Ferdinando Stagno d’Alcontres, 31, 98166 Messina (Italy) E-mail: rosanna.utano@unime.it |
| VÁCLAVÍKOVÁ Zuzana " Gamification and Game-Based Learning – How to Implement They Into Education " - from the section: New trends in mathematical education The use of games in the education process is, in our country, usually associated with ICT or digital tools. This paper attempts to clarify the concepts of gamification and game-based learning in connection with the informal, as well as the formal, education process, especially in cases of non-ICT or e-learning. The examples of implementation of gamification and game-based learning in Ostrava´s Science and Technology Center will be introduced. The examples will focus on use in science teaching, but the concept can be successfully used in any subject, and, using the interdisciplinary link, several courses can even be covered in one game. |
| VALA Jiří " Computational Prediction and Optimization of Thermal Consumption in Buildings " - from the section: Modeling and simulation in engineering and scientific computations Application of advanced materials, structures and technologies in building structures stimulates the development of new approaches to the physical, mathematical and computational analysis of both new and reconstructed buildings. In this paper the physical and mathematical analysis of a building as a thermal system leads to the design of the original robust and effective numerical algorithm for the evaluation of thermal insulation and accumulation properites of buildings with the aim of optimization of energy requirements to artificial heating. |
| VALKOVIČ Vojtech " " - from the section: This article focuses on calculation of deflection, bending moments and transverse forces of the beam deposited on a elastic foundation for changing the stiffness of soil. |
| VALLO Dušan " Constructivist Approach to Double Integral via GeoGebra Environment " - from the section: New trends in mathematical education The aim of this contribution is to bring some inspiration how to use dynamical geometry software Geogebra in teaching Mathematics and in teachers training education. For this purpose we concerned with some difficult stereometrical problems of computation of volume of intersection of two cylinders. We demostrate numerical computing of double integral via interactive graphics and spreadsheet environment. Some didactical remarks are included in the paper, too. |
| VARGOVÁ Michaela " Infinite Series in Circles " - from the section: New trends in mathematical education In our opinion, one of the obstacles that students face in relation to the concepts of convergence is the confusion and misconception of terms infinite and unbounded. In the paper we show examples of infinite series whose convergence is easily seen from the figures and can be rigorously justified, for instance, by using integral test or direct comparison test. These visual representations may help students overcome some difficulties related to the thorough understanding of this concept. |
| VAVRÍKOVÁ Lucia " Mathematics, Garden and Landscape Architecture " - from the section: Mathematics and art In this contribution we discuss students approach teaching and students project devoted to gardens and landscape architecture. We discuss mathematics and its selected topics applied to gardens and mindscape architecture in the world. |
| VELICHOVÁ Daniela " 1.Modelling free-form curves and surfaces by means of Minkowski point set operations 2. Reconstruction of 3D object dimensions from videorecords " - from the section: Algebra and geometry and their applications 1. Some basic intrinsic properties are described for a two-parametric family of surface patches generated by means of Minkowski combinations of two free-form curve segments. Illustrations of interesting forms and variations of these basic forms for particular values of parameters are presented. 2. Information is given about determination of specific characteristic geometric properties of objects from recordings of 3D scenes obtained by means of available camera equipment, which are regarded as relevant image records for the criminalistics explorations. Newly developed tool for 3D reconstruction CamWitt, an interactive tool for the filtration of data recordings and 3D reconstruction is shortly described. Possible generalizations of presented reconstruction methods for development of algorithms of videogrammetry for reconstruction of moving objects from video-records taken by stable camera systems are discussed. |
| VISNYAI Tomáš " Remarks on Strongly Separately Continuous Functions f: ℓ^p → R " - from the section: Differential equations, dynamic systems and their applications In this paper are investigated the strongly separately continuous functions defined on l^p. We show the sufficient condition when the strongly separately continuous function defined on l^p is continuous and some properties of limit function of sequence of strongly separately continuous functions on l^p. |
| VOLNY Petr " Mathematical Education with Worksheets (with P. Schreiberova) " - from the section: New trends in mathematical education We present our practical experiences with using of worksheets during education of Mathematics at Vv SB - Technical University of Ostrava. We prepared worksheets for the students. These worksheets cover all main mathematical courses in the bachelor study program. We asked the students to answer a few questions concerning the worksheets. The feedback from students is presented in the paper and we also discuss our practical experiences with the worksheets. |
| VOLODKO Inta " Application of Information Technologies for Studies of Mathematics in Riga Technical University " - from the section: New trends in mathematical education Utilisation of ICT capabilities in the mathematics studies process facilitates work of teachers and also makes study process more engaging and effective. In order to facilitate the work of teachers and excite students, the Department of Engineering Mathematics created several courses of Mathematics at RTU portal ORTUS, compiled and implemented a series of tests at the ORTUS environment, created Ancillary Course in Elementary Mathematics on the open online platform MOOC and made course of mathematics for pupils of secondary school at RTU ORTUS site. |
| VOŠTINÁR Patrik " Developing Mathematical Mobile Applications without Programming Skills " - from the section: New trends in mathematical education In this article we are focusing on developing mathematical mobile applications without programming skills. We will show you how to create mathematical application in environment App Inventor. |
| VYSOKÁ Jana " Example of Mathematical Modeling in High Schools " - from the section: New trends in mathematical education The aim of this paper is to suggest an expansion of preparation of learning materials designed for university students who have chosen advanced mathematics as an elective, or for high school students who are engaged in mathematics beyond compulsory curriculum. Students will work with a simple example of mathematical modeling in solving simple transport tasks. In this work, we will pay attention to the issue of traffic flow modeling from a macroscopic perspective. First, we derive a mathematical model in the form of partial differential equations and then we will focus on solving this equation using the method of characteristics. Interpretation is presented in a way that should be easily grasped by students. |
| ZAHRÁDKA Jaromír " The Fibonacci Numbers for the Molecular Graphs of Two Types of Bent Hexagonal Chains " - from the section: Algebra and geometry and their applications The Fibonacci number of an undirected graph is given by the number of subsets of such that no two vertices in are adjacent. This number is one of the most popular topological index in chemistry, which is called as the Merrifield-Simmons index there. Hexagonal chains are the graph representations of an important subclass of benzenoid molecules. In this contribution we follow our previous results on the Fibonacci number of the linear hexagonal chains. We obtain exact formulas for the Fibonacci numbers of two types of bent hexagonal chains. |
| ZAWISLAK Stanislaw " Dedicated Computer Programs Visualizing Some Graph Theory Problems as Learning Enhancement " - from the section: New trends in mathematical education In the paper, dedicated computer programmes are described which visualizes the graphs as well as visual the performance of particular algorithms. The considered problems are e.g. bi-criteria TSP - monitoring of evolutionary algorithm and distinguishing of Pareto front, checking of graph isomorphism, drawing of self-complementary graphs in different manner. The programs are written by students and can be utilized in didactics to improve a teaching process. |
| ŽDÍMALOVÁ Mária " Mathematics and Its Applications in the Architecture and Urban Design of Selected Parts of Mexico " - from the section: Mathematics and art Abstract. In this contribution we discuss mathematics and its applications in architecture and urban design. We prepared with students projects devoted to the selected parts of the states of Mexico. The aim was to consider different approaches and types of considerations devoted to the architecture and urbanism: colonial architecture, earthquakes, big monumental city and antient architecture and their connection to mathematics and history. |
| ZICH Ursula " " - from the section: New trends in mathematical education Caterina Cumino, Maria Luisa Spreafico, Ursula Zich: We present a set of guided tours and educational workshops, based on the interplay between mathematics and architecture, with the double purpose of making architecture accessible and observe mathematics in the surrounding world. The halls of a magnificent baroque royal residence become classrooms, where visitors are led to discover architectural shapes and to understand their geometry with the use of various origami modeling activities, rigorously supported by mathematics (descriptive geometry and basics in analytic and differential geometry). This way of introducing architectural elements, figures and geometric properties is intuitive, practical and unconventional and presents undoubted advantages even for people with disability (for example, visually impaired persons): visitors can produce by origami technique and touch with their hands the shapes just observed, in the spirit of "learn by doing", in a new teaching language and knowledge sharing. The proposed activities are tailored to students of all school levels, but also to a broad audience of visitors and families, taking into account the different levels of knowledge of participants. |
| ZIGUNOVS Maksims " The Solution Of The Heat Conduction Equation In 3d Anisotropic Environment And Possibilities Of Its Improvement " - from the section: Modeling and Simulation in Engineering and Scientific Computations Abstract. This manuscript presents a new method of creating heat conduction solution for the anisotropic space by considering each included heat transfer material’s physical characteristics. This manuscript also provides descriptions of new possibilities to make these calculations less time consuming, less time costing and to provide advantages strictly connected to the computer quantity involved in the calculation process. |
| ŽILKOVÁ Katarína " The Impact Of Ibooks on Geometric Conceptions of Students About Isometries " - from the section: New Trends in Mathematical Education The aim of this paper is to describe the experience of the implementation of iBook textbooks into geometric education, to analyze the data obtained and to summarize the impact of the use of iBook textbooks on learning outcomes. According to our findings, we can conclude that the learning outcomes through iBook textbooks are not only comparable with the traditional forms of education, but in some aspects, have showed a positive impact, particularly when solving the tasks aimed at higher cognitive processes. |
Number of registered papers: 200 |
Last change: 12.02.2017 19:46:49 |