| BENDOVÁ Veronika, BUDÍKOVÁ Marie " Teaching Process of an Applied Statistics Course for Students of the Antropology Study Programme at Masaryk University " - from the section: New Trends in Mathematical Education The point of these proceedings is to describe the teaching process of an applied statistics course that is offered by the Institute of Mathematics and Statistics on the Masaryk University in Brno to students of the Anthropology study programme. Teaching statistics to students of non-mathematical study programmes is in general a difficult matter. Therefore, we aim to make is as easy for the students as possible. To fulfill this goal, we employ a collection of solved statistics exercises, worksheets, along with friendly and open mindset. We succeed in motivating students to use statistical methods in practice despite raised difficulty of the course. |
| BENVENUTI Silvia " Dalí Experience: Salvador Dalí and Maths " - from the section: Mathematics and Art Dalí experience is the title of an exhibition held in winter 2016/17 at Palazzo Belloni, a prestigious historic building in Bologna. The exhibition collected about 200 works, from the "The Dalí Universe" Collection, one of the richest documentations of Dalí´s artistic history, exhibited in an interactive and multimedia path, with the aim of inviting the visitor to an engaging and participatory experience. A good fortune for lovers of ... maths! |
| BÍLKOVÁ Diana " Wage Levels by Regions in the Czech Republic and PPP-Adjusted Wages in Selected European and Non-European Countries " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise The present paper focuses on a comparison of wage levels of the Czech Republic regions. Similar wage-level clusters were created using the methods of cluster analysis. Three regions with the highest and lowest wage levels, respectively, were selected. The wage distribution model for the above regions was created to allow for the comparison of wage development over the past seven years, three-parameter lognormal curves representing the basis of the theoretical wage distribution. |
| BÍMOVÁ Daniela, PIRKLOVÁ Petra " Basic Principles of Orthogonal Axonometry with the Use of Ge " - from the section: New Trends in Mathematical Education Basic Principles of Orthogonal Axonometry with the Use of GeoGebra The contribution introduces the use of dynamic applets created in GeoGebra in teaching the orthogonal axonometry for students of the third year of a Bachelor´s degree Mathematics with a focus on Education. The dynamic applets are used with a big advantage in teaching for students with a lower level of spatial imagination, or for part-time students. The presented dynamic applets show chosen basic principles of the orthogonal axonometry. |
| BRANDI Primo, SALVADORI Anna " A Magic Formula of Nature and Art. PART II " - from the section: New Trends in Mathematical Education In 2003 the Belgian botanist Johan Gielis introduced a new approach for modelling and understanding various natural shapes. The basic result is a single formula, depending on seven parameters, that can describe a large variety of figures. The subject presents interesting aspects from a mathematical point of view. With an appropriate introduction it can be useful for a basic approach to mathematics for undergraduate students. In the paper we illustrate some interesting educational ideas which are related to the magic formula. Moreover we also presents some applications of the formula in design, architecture and graphics. |
| BŘEHOVSKÝ Jiří, PŘÍHONSKÁ Jana " The Ability of Primary School Pupils to Solve Combinatorial Tasks " - from the section: New Trends in Mathematical Education The paper describes the results of a survey which investigated the success rate of primary school pupils in solving basic types of combinatorial tasks that can be used at elementary school and the methods used to solve them. A part of the paper also includes the information on the result of a questionnaire survey focused on primary school teachers in terms of their approach to including and solving combinatorial tasks in teaching mathematics. |
BRUNETTI Federico Alberto The design of tall architectures building assumed for modern architects a particular compositive challenges: not only following the new technical potentiality derived from innovative materials for construction (i.e. iron, steel, reinforced concrete etc.), but also evocating different essential symbols through monolithic shapes. Some recent building sites in Milan offer the opportunity to focus the attention on some evidences in the evolution of design techniques toward the composition of these buildings, in comparison between the XX century analogue orthogonal drafting machine and the actual complex digital 3D (/4D) tools. These two drawing techniques could be considered as the output devices of different algorithms approaching the same gravity challenge to which any architecture design must afford. The verticality of the building structures allows the overlapping of the horizontal floors following the static sciences: the construction and available materials technique could obtain different solutions essentially in reason of calculation process and aesthetical approaches defined by design concept and drawing procedures. |
| BRUNETTI Federico Alberto " The Ideas´ Machine. The Big Science in Search for Young Generation Concepts About Imagination in Physics. The European Cern – CMS Challenge: “Arts & Science Across Italy “ " - from the section: Mathematics and Art The debate about the possible interactions between Science disciplines and Artistic research has recently increased, not only as mere communication method to disseminate complex knowledge into widespread language, but with the aim to generate a matching between these two apparently opposite procedure that realize innovative representation of the world. Some of the most important international Institutions organized conferences, challenges and workshops to improve this bilateral understanding. The CERN (Geneve) promoted a digital Art residential programme named Art@CERN that gathered experts from every country to suggest and propose their experience. But even at high school educational level, several local experiences followed this master example. The CERN – CMS challenge “Arts & Science across Italy “ is part of the European CREATIONS project of Horizon 2020 and is organized by the Italian INFN (National Institute of Nuclear Physics) and the CMS Experiment of CERN in Geneva. The project is aimed at high school students of the third and fourth year of Milan, Florence, Padua / Venice and Naples, lasting two years (2017-2018) and has the aims to bring high school students closer to the world of Science and Research and in particular to the sub- nuclear. The first iconographical and modelling results of the national competition and best result selection has been exhibited in the Museo della Scienza e Tecnologia Leonardo da Vinci in Milan, and further selections are ongoing in other main town of Italy. A first survey of the different tendencies in interpretation of Science research proposed by young students is proposed in this manuscript. |
| BUDÍK Ladislav " Hydrological and Meteorological Data and Modifications of Statistical Distributions - Heuristic Approach " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise The presented paper is dedicated to new approaches of fitting theoretical curves (transformed survival function) to daily average discharges, daily average air temperatures and air humidity and daily precipitation, using generalized log-normal distribution using 5 parameters and modified normal distribution. |
| BUDKINA Natalja, ASMUSS Svetlana " Control Smoothing Splines with Initial Conditions " - from the section: Differential Equations, Dynamic Systems and Their Applications This work is devoted to the problem of optimal control of a linear dynamic system with initial conditions. The main attention is paid to a controlled system reduced to the second order differential equation considered with the cost functional which controls the input function of this system to push a trajectory nearby a set of desired points. We show how the technique of smoothing splines can be adapted for construction of solutions of such problem. |
| CAPANNA Alessandra, MELE Giampiero " Square and Triangular Matrices in Magnaghi-Terzaghi Architectures " - from the section: Mathematics and Art The encounter, in the past editions of Aplimat Conference, with Paola Magnaghi Delfino, daughter of Augusto Magnaghi who, together with his friend and fellow student Mario, founded the Studio Magnaghi-Terzaghi, was an opportunity to start a systematic research on the drawings and projects carried out by these two architects, collaborators of Pietro Lingeri and Giuseppe Terragni, that were two of the most important exponents of Modern Architecture in Milan. In the year of their graduation (1939), the two architects received the assignment from Mr Cicogna to design a residential building from then on known as the Casa dei Nidi (House of the nests). Various books on the History Architecture quote this building as one of the first examples of Italian Modern Architecture, yet the writings have always returned to a single article written by Giuseppe Pagano in 1940 and published in Casabella n. 150. The drawings published in this article have been the starting point for an accurate redrawing, followed by a comparison with the actual survey. The obtained model was thereafter analyzed with the aim to identify the geometric matrices on which the architects based the project of the building. The 80 cm-sided square is the module that allowed the architects to design this architecture. The plan is incorporated into a double square made by 11 x 22 modules and the elevation is 22 x 16 modules. This grid is referred to the classic ad quadratum background, so deep-rooted in the Italian tradition to constitute the basis of the new Italian Rationalist Architecture as theorized by the Grouppo 7. Also in the Bica-Montecatini office building in Via San Giovanni sul Muro - Milano, designed in 1955, the two architects chose the square as a basic module by adopting a 1 x 1 meter grid that generates the shape in plan and scans the rhythm of the façade. For religious buildings, (the Cagnola villa church in Gazzada and San Filippo Neri in Bovisasca district in Milan, designed respectively in 1959 and 1961), instead of the geometry of the square, it is the equilateral triangle at the base of the matrix generating the shape. This regular geometric figure, closely linked to the number three, represents both the concept of stability and the religious concept of the Trinity, The church of Villa Cagnola has a hall-plan with a fully windowed wall that opens the view from the altar to the pre-existing historical park The wall has been designed thanks to the skilful combination of equilateral triangles that compose it. The church of San Filippo Neri has a central hexagonal plan with a series of annexes generated by the same geometrical shape based as well on the geometry of the equilateral triangle. The reference to regular polygons as the principle of the form and the related traditional value of geometric perfection, becomes a model of symbolic rationality, and the courtly instrument of conception of the sacred space. The modern architecture created by the two architects is strongly mathematical in its conception. The square and the equilateral triangle at the base of these architectures show a rationality that binds number, shape and size, generating a modern form that bases its rationalist roots in the classical tradition of the history of Architecture of the past. |
| CEPPITELLI Rita, MARCONI Ombretta " Mathematical Models on Milk, Coffee and Beer. " - from the section: New Trends in Mathematical Education The simple differential equation y´ = ky is an important mathematical model. It is well known in Population Dynamics as the Malthusian Equation and it is familiar to food technologists as Bigelow´s First Law which describes the microbial mortality at constant lethal temperatures.In the paper we focus on the process of thermal sterilization of milk. The Malthusian Equation is also a mathematical model for Newton´s law of cooling or heating. For a body cooling, the rate of heat loss is proportional to the difference in temperatures between the body and its surroundings. In the paper we analyze the data of an experimental study on the cooling of coffee conduced by "Mathematics & Real Life" Project. The measurements of the temperature were taken using a centesimal temperature sensor connected to a computer for automatic data capture. Another simple differential equation is Darcy´s equation, a fundamental mathematical model in the filtration theory. In the paper we are interested in mathematical models derived from Darcy´s law, which are applied to the cross flow microfiltration at constant pressure of beer. These models are then tested using experimental data provided by the Italian Brewing Research Centre of the University of Perugia |
| CERNAJEVA Sarmite, VOLODKO Inta, ILTINA Marija, ILTINS Ilmars " Good Knowledge of Basic Mathematics - a Successful Prerequisite to Study in Riga Technical University " - from the section: New Trends in Mathematical Education The issue viewed in this paper, which affects a multitude of technical universities: an insufficient level of basic mathematical knowledge among students. The 2016/17 centralized State examination, as well as, basic mathematical knowledge examinations done by Riga Technical University have been analyzed. The results show that a large part of students do not have the required level of knowledge in basic mathematics to successfully study calculus. Measures that RTU is using to avert these issues are mentioned. |
| ČIŽMÁR Ján " History of Mathematics published " - invited lecture This presentation is a brief information regarding the first edition of a particularly detailed and comprehensive book on the history of mathematics throughout the duration of its existence, which was published in the Slovak language. It is possible to order the book, in case of interest to purchase it, while delivery will be provided to conference participants directly on the next day of the conference. |
| CHEREVKO Yevhen, BEREZOVSKI Vladimir, CHEPURNA Olena " Conformal Mappings of Riemannian Manifolds Preserving the Generalized Einstein Tensor " - from the section: Algebra and Geometry and Their Applications We study study(with Berezovski Vladimir and Chepurna Olena) conformal mappings preserving the generalized Einstein tensor. We have derived corresponding partial differential equations. Conditions of Integrability are obtained. In addition to the generalized Einstein tensor we get other invariants of the mappings. Also we have proved that orientable compact manifolds equipped by positive definite metric, do not admit conformal mappings preserving the generalized Einstein tensor. Finally, we explored a local structure of Riemann manifolds admitting conformal mapping preserving the generalized Einstein tensor. |
| CIVERIATI Elisa, TERRE Matteo " An Innovative Educational Path on Mathematics and Film Critics for the Flipped Classroom " - from the section: Mathematics and Art In this paper we will discuss an innovative and didactic proposal, experienced in the school year 2016-2017 in a first class of Liceo Scientifico “B. Cavalieri” in Verbania, composed by 28 pupils, in the context of the educational project “Adotta science and art in your classroom”. The educational path link film critics and mathematical beauty using two film π and Vertigo. Our intention is to seek in the panorama of cinema films do not strictly mathematical, but that offer the possibility to be interpreted in a scientific key. Our idea is to be able to disseminate mathematical aspects complex even without resorting to biographical film on mathematicians, which too often put the emphasis on the eccentricity of the character and too little on scientific disclosure. Some innovative aspect of the educational path are summarized and also the teaching method is alternative, because we use the flipped classroom approach. |
| COCCHIARELLA Luigi " On the Identity of Sight(s) in Some Western and Eastern Projective Representations " - from the section: Mathematics and Art In the book “Vie et mort de l’image”, literally ‘life and death of the image’, the French journalist and writer Régis Debray proposed a challenging overview on iconographies and their native cultural contexts. Which calls into question the identity ‘behind the image’. We will focus on some aspects of the adoption of axonometric and perspective representations in Western and (Far) Eastern worlds, in search for clues or evidence revealing identities behind. Keywords: Geometry and Graphics, Projective Symbolic Forms, Eastern and Western Iconography, Image |
| CORONIČOVÁ HURAJOVÁ Jana, MADARAS Tomáš " Do Important Network Actors Form Important Ties? " - from the section: Mathematical Aspects of Network Science and Applications In this contribution, we analyze the location of vertices and edges with respect to maximum betweenness centrality within a graph; along with construction of graphs where the distance of the set of vertices and the set of edges with the maximum betweenness (the betweenness separation) can be arbitrarily high, we also present sufficient conditions for graphs in which this distance is zero, and we discuss the betweenness separation in real-world networks and several models of pseudo-random graphs which use to model complex networks. |
| CSACHOVÁ Lucia, JUREČKOVÁ Mária " Notes to the Problems with Figures at School Mathematics " - from the section: New Trends in Mathematical Education Currently, people are constantly inundated with new information of all kinds. On the road to knowledge, the development of the pupils´ ability to understand and correctly process information from the text implies therefore an increasing importance of the role of schools in this process. Moreover, mathematical education at schools creates a space for understanding the text, which contains charts, diagrams and other forms of images. Visual representations are very important at the time when we are surrounded by "fast" data, so we need to recognize as much information as possible. In our contribution, we focused on the level of graduates of our secondary schools in the area of understanding and the subsequent correct solution of mathematical tasks of this type, which we have named problems with figures. The analysis was made on the basis of nationwide testing T9 from the last six years. In the paper we present some of our findings in this area: a) what is the trend in success in solving problems of this type, b) what the problems with figures can “say” about the mathematical education. Finally, we propose some recommendations connected with these problems for higher education of future teachers of mathematics. If we want to prepare high-quality mathematics teachers at universities, it is necessary to have information from primary and secondary schools about the issues that are problematic and properly warn future teachers of mathematics to these topics. |
| CZIMMERMANN Peter, BUZNA Ľuboš, KOHÁNI Michal " Network Flows as a Tool for Solving Location-Scheduling Problem to Optimize Charging Infrastructure for Electric Vehicles " - from the section: Mathematical Aspects of Network Science and Applications We propose an MIP model to design a private charging infrastructure for a fleet of electric vehicles operating in large urban areas. We derive an IP problem and we show that it is equivalent to a network flow model. We illustrate that the flows in networks can be used in the study of properties of location-scheduling problems related to the design of charging infrastructure. |
| DLOUHÁ Dagmar, HAMŘÍKOVÁ Radka " Our Experience with the Involvement of Students in the Creation of Study Materials " - from the section: New Trends in Mathematical Education In past year we joined a project of the statutory city of Ostrava, which is called The Program focused mainly on supporting education and talent-management in the field of technical and natural science in the statutory city of Ostrava for the year 2017 and 1st trimester of 2018. Within this project we could develop co-operation with our talented students. Currently we have eight students from full-time bachelor, continuing masters and doctoral study. |
| DOBRUCKÝ Branislav, CHERNOYAROV Oleg V., MARČOKOVÁ Mariana, ŠTEFANEC Pavol " Modelling of Matrix System with Fictitious Interling Function Using Instantaneous State Calculation " - from the section: Modeling and Simulation in Engineering and Scientific Computations Abstract. The paper deals with analysis of matrix converter system using discrete instantaneous state calculation method. Because of impulse character of matrix converter, the space-state equations are transformed and discretized into discrete form. Virtual model of matrix converter uses fictitious interlink (DC link), and its model and due to non-linear loads, the fictitious exciting functions are used for creation of discrete model. A new modified method of solution makes possible to determine the state of the system instantaneously. Results of theoretical analysis confirmed by numerical computer simulation are given in the paper. |
| DZENITE Ilona, CERNAJEVA Sarmite, MATVEJES Aleksandrs " The Role of RTU Students’ Survey in Ensuringthe the Quality of Mathematics Studies " - from the section: New Trends in Mathematical Education In the current process of change around the world, questions concerning the improvement of the efficiency and quality of the education system are very appropriate. The quality of higher education needs to be developed and improved for the benefit of students and other beneficiaries of higher education. The authors’ research is dedicated to finding ways of improving studies in Mathematics at Riga Technical University on the basis of surveyed students’ opinions and suggestions. |
| FALCOLINI Corrado, CANCIANI Marco, PASTOR ALTABA Maria " Virtual Reconstruction and Analysis of a Surveyed Model of the Wooden Crucifix of ST. Peter´s Basilica" - from the section: Mathematics and Art The wooden Crucifix of St. Peter’s Basilica in Rome has been recently restored by a group coordinated by L. D’Alessandro and G. Capriotti, under the supervision of P. Zander for the Fabbrica di San Pietro. The work has involved a detailed survey with range based and image based methods to construct a three-dimensional model useful for virtual reconstruction, measures, analysis and documentation. The study includes geometrical models, parametric curves and numerical algorithms. (with M. Canciani and M. Pastor Altaba) |
| FEIJS Loe " B3/S23 Descending a Staircase No. 2 " - from the section: Mathematics and Art This artwork features gliders in cellular automatons playing Conway’s game of life. Each playing field is one basic tile from the fashion pattern known as Pied de poule or Houndstooth. The pattern’s basic tile has a contour consisting of straight line segments and staircases. In the context of the tessellation typology, it must be considered a hexagon. In our work of art, the basic tile is invisibly glued in a manner which is dictated by the tessellation type, thus implementing a Klein bottle topology, as an alternative to the more classical torus. The Klein bottle appears invisible but it comes to life because of the glider. The work is a tribute to the famous painting Nude Descending a Staircase No 2, created by Marcel by Duchamp in 1912. Several other hints to Duchamp’s work are embedded in the artwork. The author has a personal passion for Pied de poule, which is a rich source of aesthetic qualities in fashion and at the same time a playing field for various types mathematical recreations. |
| FERDIÁNOVÁ Věra, BRANNY Michael " Constructions of a Square and a Regular Pentagon Only with a Compass " - from the section: Nothing In 1797, Lorenzo Mascheroni proved that a compass used for constructions has the equal power as using a ruler altogether with the compass. Therefore, it is possible to construct all ruler-and-compass constructions only with the compass itself. The aim of this article is not to prove the theorem but to introduce interesting constructions of a square and a regular pentagon. |
| FERREIRA Manuel Alberto M. " Financially Dependent Pensions Funds Maintenance Approach Through Brownian Motion Processes" - from the section: Statistical Methods in Technical and Economic Sciences and in Practise Abstract. The situation of some pensions funds that are not appropriately auto financed and are thoroughly maintained with an outside financing effort is considered in this paper. In order to represent the unrestricted reserves value process of this kind of funds, a time homogeneous diffusion stochastic process with finite expected time to ruin is proposed. Then it is projected a financial tool that regenerates the diffusion at some level with positive value every time the diffusion hits a barrier at the origin. So, the financing effort may be modeled as a renewal-reward process if the regeneration level is kept constant. The evaluation of the perpetual maintenance cost expected values and of the finite time period maintenance cost are studied for a concretization of this approach when the unrestricted reserves value process behaves as a generalized Brownian motion process. Key words. Pensions fund, diffusion process, Brownian motion process, first passage time, perpetuity, renewal equation. Mathematics Subject Classification: 60J70. |
| FERRO Luisa " The Alexander Mosaic and the House of Faun (Pompeii Vi 12, 1-8) Geometry Proportions and Art of Composition " - from the section: Mathematics and Art This text analyzes the celebrated Alexander Mosaic, found in the House of the Faun in Pompeii starting from the premise that it may hide the traces of a compositional process based on rules that built its origin, the Ground Zero of any work of art as such. A painstaking process of calculation and precision based on regulators, even surprising symmetries, and aesthetic precision in the placement of figures that projects the represented scene in a well-defined, memorable, selfsufficient and “representational” form. Finally the text analyses the relationship between mosaic and the composition process of the House. |
| FESZTEROVÁ Melánia, HUDEC Michal, PORUBCOVÁ Lýdia, NOGA Henryk " Evaluation of the Qualitative Parameters of Humus and Selected Heavy Metals Content " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise Inorganic impurities are primarily introduced into the soil through human activity or the activity of the natural environment. The impact of heavy metal soil pollution is long-term due to the relatively strong adsorption of many metals by humus and the impact of anthropogenic environmental factors and rock structure. In the case of contaminated soils, it is very important that heavy metals are not absorbed by plants, not only on agricultural land but also on meadows and pastures, due to the fact that heavy metals can then enter the food chain. Humic substances can help improve soil properties, increase production productivity and improve nutrient intake. It is important to examine the mechanisms of sorption and the distribution of heavy metals Pb and Cd in the soil between the fractions of humic substances. The aim of this paper is to describe the characteristics of the qualitative parameters of humus and the selected heavy metal content (Pb, Cd) in the soil. To assess the relationship between chemical factors and heavy metal contents in the soil we used Pearson correlation analysis, which was tested at p < 0.05 and p < 0.01 levels. The content of lead and cadmium heavy metals extracted using HNO3 (cHNO3 = 2 mol.dm-3) and aqua regia was compared using a Student t-test to calculate the differences between the averages to a significance level of α = 0.01. Acknowledgement This work has been supported by the Cultural and Educational Grant Agency (KEGA) under the Grant No. 044UKF-4/2017. |
| FILIPE José António, FERREIRA Manuel Alberto M. " Study of a Collection of Service Time Distributions and Impact in the Respectivo M/g/∞ System Busy Period Parameters " - from the section: Modeling and Simulation in Engineering and Scientific Computations The problems arising when the moments of a particular service time distributions collection, for which the M|G|∞ queue system busy period becomes very easy to study, are presented and it is shown how to overcome them. Some results, precisely about the moment’s computation of random variables with distribution functions given by this collection are given.The busy period “peakedness” and “modified peakedness” for the M|G|∞ queue in the case of those service time distributions are also computed. Key words: Service time, collection, distributions, moments, M|G|∞ queue, busy period Mathematics Subject Classification: MSC 2010: 60K35. |
| GABKOVÁ Jana, JANIGA Ivan " Generalized Linear Model with Software Mathematica® " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise Generalized linear model is used to model the functional dependencies, where one variable is a random variable and the second variable is non-random. |
| GLIVICKÁ Jana " Realising Some Types While Omitting Others Aplimat 2018 proceedings" - from the section: Algebra and Geometry and Their Applications We prove a theorem that combines omitting and realizing of types in one structure. Given two collections of types, we formulate a condition ensuring existence of a model realizing types from the first collection while omitting types from the second one. |
| GLIVICKÝ Petr " A Note on the Problem of Prisoners and Hats " - from the section: Algebra and Geometry and Their Applications We study the famous mathematical puzzle of prisoners and hats. We introduce a framework in which various variants of the problem can be formalized. We examine three particular versions of the problem (each one in fact a class of problems) and completely characterize them as to (non)existence of winning strategies. |
| GOLDŠTEINE Jolanta, POLA Aija, ŠADURSKIS Karlis " Stochastic Analysis of Population Dynamics Subject to Changes at the Random Time Moments " - from the section: The paper presents a mathematical model of a predator-prey population dynamics given in a form of Markov dynamic impulse-type system, allowing discontinuities of trajectories at random time moments. The stochastic approximation procedure allows to analyse the qualitative behaviour of trajectories of the ecosystem. |
| GREBLIČKI Marijana " A Class of Some Third-Metacyclic Finite 2-Groups " - from the section: Algebra and Geometry and Their Applications Third-metacyclic finite 2-groups are groups with a non-metacyclic second-maximal subgroup and all its third-maximal subgroups being metacyclic. Among these groups we are looking for all of those whose non-metacyclic subgroups, including group itself, are generated by involutions. |
| GUNČAGA Ján, KOREŇOVÁ Lilla " Augmented Reality in Mathematics Education for Pre-Service Teachers in Primary Level " - from the section: New Trends in Mathematical Education New technologies with modern method of teaching must be implemented in the university studies. Important part is teacher training study. These technologies make the study more attractive and also it brings bigger motivation an understanding of notions by students. We present in our contribution augmented reality technology as a part of using of mobile technologies in mathematics education b future primary school teachers. |
| HAUDE Lucas " Creating in Interaction with Cellular Automata for Science and Technology Museums" - from the section: New Trends in Mathematical Education The development of technology creates a need for more students following science and technology curricula. Enthusiasm for these subjects is being raised for example by modern science and technology museums, and within schools increased attention is given to subjects like programming. This document describes the design process of an interaction with cellular automata. For interaction design, this means dealing with large sets of settings and a difficulty in offering a clear mental model to the user. |
| HAVELKA René, MUSIL Miloš, HAVELKA Ferdinand, MIHELOVÁ Silvia " Use of Structural Dynamic Modification to Reducing Vibration Level " - from the section: Modeling and Simulation in Engineering and Scientific Computations Dynamic parameters tuning is a required operation when significant vibration of a construction component is expected. Dynamic parameters tuning using structural dynamic modification represents modal-spectral parameters changes by adding substructures to the original to avoid resonances and reduce the level of vibration. Those substructures, which influent mass, stiffness and damping matrices of the original system, can increase or decrease natural frequencies and influents corresponding mode shapes according to the desire behaviour of the structure. Additional tuning of dynamic parameters performed by structural dynamic modification is a useful operation to adapt the structure to changed operation conditions. Modal and spectral parameters of the modified structure can be determined by analytical approach using structural coefficient matrices of modifying substructures and modal parameters of the original structure, that can be obtained experimentally |
| HECKENBERGEROVÁ Jana, ŠILD Petr " Portfolio Optimization for Risk Averse and Risk Seeking Investor " - from the section: Financial and Actuary Mathematics The goal of this work is to optimize portfolio for two types of investors: risk averse and risk seeking investor. The main purpose of optimization is to make the highest profit as possible in investing into the mutual funds with bearable risk corresponding to investor’s profile. As input to this work is selection from equity, bond and commodity funds offered by ČSOB Asset management, because of the largest offer on the Czech market. |
| HEDVIČÁKOVÁ Martina, POZDÍLKOVÁ Alena " Temperament Theory and Statistical Analysis of Temperamental Dependence on Other Factors – Empirical Study " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise Aim of this article is empirical study of temperamental dependence on other factors. Belov’s temperament test and Eysenck’s lability and stability test were used for research. A questionnaire survey was conducted at the University of Hradec Králové at the first and third year students. The Belov’s temperament test focuses on the characteristics, features and behavior of individuals. We use the test to determine the percentage of temperament components (sanguine, choleric, phlegmatic, melancholic). There are twenty questions for each type, which the individual answers yes or no. Some questions are repeated in these four sections (A, B, C, D). The second test from Eysenck determines the lability and stability, as we mentioned above. In other words, extrovert and neuroticism. In the first part correlation analysis will be performed (correlation matrix will be composed) at first, which will be established between each temperament test and age and gender of respondents. In the second part test of independence in PivotTable will be used. The results of the correlation analysis demonstrated the independence of both tests from other variables, such as age and gender, this is as expected. This result has also been confirmed by the test of independence in PivotTable, which confirmed this hypothesis. |
| HOČEVAR Tomaž " Graphlet Counting " - invited lecture Recent technological development in bioinformatics is leading to an increasing amount of data. As a result, there is also a need for new efficient methods for its analysis. Simple improvements such as parallelization are often not enough. Instead, new algorithmic and mathematical insights are required. We speculate that besides enabling analysis of larger datasets, more efficient computational methods in bioinformatics will also spark new analysis methods that were previously unfeasible. Graphlet analysis is an approach to network analysis that captures local network topology based on the frequencies of small induced subgraphs called graphlets. It has been successfully applied to prediction of protein functions, discovery of cancer-related genes, etc. One of the obstacles to the wider use of graphlet analysis is the computational complexity of algorithms for their discovery and counting. We developed Orca, which is based on combinatorial observations that establish relations between individual graphlet counts. These are employed to design an efficient graphlet counting algorithm that outperforms other approaches based on exhaustive enumeration. |
| HOLEŠOVÁ Michaela " Serlio´s, Guarini´s and Meyer´s Constructions of Ovals in Architecture " - from the section: Mathematics and Art When reconstructing some of the buildings with elliptical ground plan, it is often very difficult to unambiguously determine whether an ellipse or an oval was constructed to approximate this ellipse. We deal with Serlio´s and Guarini´s constructions of ovals. F. S. Meyer showed constructions of ovals whose gives very good approximation of the ellipse. We modify Serlio´s and Guarini´s constructions of ovals so that lengths of both axes of the ellipse are preserved. |
| HORSKÝ Richard " The Generalized Solution to a Linear Operator Equation. The Case of Finite Dimension " - from the section: Algebra and Geometry and Their Applications . It is well-known that a system of linear algebraic equations need not have a solution. There is a way allowing to define a solution to such a system which is not dependent on the properties of the linear operator (injective, surjective) represented by the matrix of the system. This leads in special case to the known Least Square Method, however here in rather unusual point of view |
| IANNACE Gino, TREMATERRA Amelia " The Acoustics of the Vanvitelliana Hunting Lodge " - from the section: Mathematics and Art For many centuries, circular and vaulted structures were realised and used for aesthetic and constructive needs as buildings of worship, monumental buildings or courtyards. In vaulted environments, the effects of sound reflection focus on the central area due to the focus of multiple reflections. This paper presents the results of acoustic measurements carried out in a circular plant environment with a vaulted cover of the Vanvitelliana hunting lodge near Lake Fusaro in the north of the city of Naples. In the central area of the room, due to the geometry of the environment, there are focusing sound effects that generate a “flutter echo”. |
| JANÁK Josef " Parameter Estimation for Scalar 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. Namely, we present another family of estimators of unknown parameters, we show their asymptotic normality and we compare them to the previous family. We also introduce the implementation of all estimators in the program R and on one particular example, we compare the two methods both graphically and numerically. |
| JANČAŘÍK Antonín " Response Devices in Tertiary Education " - from the section: New Trends in Mathematical Education The aim of this article is to introduce the use of voting machines in teaching at university level. We draw on the experience of using this technology in teaching Algebra in Computer Science and Discrete Mathematics at the Faculty of Education, Charles University. Both subjects are taught within a Bachelor´s degree Mathematics with a focus on education and voting facilities are used regularly for several years while teaching students in full-time and combined study. |
JANIGA Ivan |
| JAROŠOVÁ Eva " Destructive R&R Study - Evaluation Problems " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise The paper deals with the estimation of variance components which is part of a study to assess the capability of a measurement system, so called gage study or repeatability and reproducibility (R&R) study. The moment method based on the ANOVA model with random effects is described as well as three related methods for constructing approximate confidence intervals - the modified large sample method, Satterthwaite´s method and the method recommended by Automotive Investment Action Group. The methods are applied on the results of a study where samples of drawn wire were tested for tensile strength Rm. The factorial design with two factors was used and due to the destructive nature of the measurements, twelve drawn wires were produced under different experimental conditions and nine samples from each wire were prepared and divided between three operators. The analysis was performed using two statistical packages - Minitab and Statgraphics - and also SPlus was used to compare the results based on ANOVA with the estimates obtained by the maximum likelihood (ML) and restricted maximum likelihood method (REML). Especially the REML method is recommended for this type of tasks. Due to the negative estimate of the operator´s variance component some problems arose. There are several approaches how to deal with negative variance estimates. Different approaches lead to different results, not only in the determination of confidence limits but also in the estimation itself. It turned out that the confidence intervals yielded by Statgraphics are wrong. |
| KAŇKA Miloš " Lienhard Interpolation Method, Its Generalization and Addition " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise This article is based on the primary publication LIENHARD, H.: Interpolation von Funktionswerten bei numerischen Bahnsteuerungen, furthermore from the publication MATUŠŮ, J. and MATUŠŮ, M.: The Lienhard Interpolation LQ,p – method (see the list of literature), in which the original structure of interpolation was extended. This presented article follows directly on LQ,p – method, which expands LQ,p – method in two ways. The first way relates to the enumeration of elements on the basic matrix of LQ,p – method, with its assistance it is possible to obtain parametric equations of interpolation curve. The other way contains parametric equations of interpolation curve in a situation in which the parameter for each part of the curve is changing at the given interval limited by the extreme (node) points. |
| KASPŘÍKOVÁ Nikola " Data Science and Statistics with Python " - from the section: With Data Science as the recent trend, the tools for efficient manipulation and analysis of data have become important for (training of) professionals in data analysis and statistics. The Python programming language starts to be one of the most popular tools for data analysis, in many cases replacing well-established statistical software packages. We report on a short case study on elementary statistical evaluation of a real-world data on air quality, using Python. |
| KIOSAK Volodymyr, LESECHKO Olexandr, SAVCHENKO Olexandr " Mappings of Spaces with Affine Connection " - from the section: Algebra and Geometry and Their Applications Paper treats geodesic, conformal and holomorphically projective mappings of pseudo-Riemannian spaces. In order to study general patterns of theory of conformity, the authors have found the formulae that connect main tensors, tensor of deformation, Riemannian tensor, Ricci tensor and their first and second derivatives for spaces An and A´n, united by the given mapping. It was achieved by means of modified Norden method. The above-mentioned formulae include such objects as An and A´n with covariant derivatives of the relevant connections. In order to simplify matter, the notions of a shortened mapping and its particular case, a half mapping are introduced. Connection that is characteristic for a half mapping is called a medium connection. Previously-known formulae are largely simplified by a transition to covariant derivatives of a medium connection. |
| KOLISKINA Valentina, ILTINA Marija " Visualization of Mathematical Concepts in Teaching Linear and Vector Algebra to First-Year Engineering Students " - from the section: New Trends in Mathematical Education A method based on the use of dynamical features of PowerPoint to teach linear and vector algebra to first-year students at the Faculty of Mechanical Engineering (FME) at the Riga Technical University (RTU) is proposed in the paper. Power Point has built-in animation features which can be quite helpful for students. This approach is used to explain such topics as matrix multiplication, computation of determinants, vector coordinates in three-dimensional space. The use of dynamical features of PowerPoint is positively evaluated by students. |
| KONEČNÁ Petra, HABIBALLA hashim " Students´ Autoevaluation in the First Year of Science Study Fields Especially in Mathematics (Complex Analysis) " - from the section: New Trends in Mathematical Education In years 2009 – 2012, new Framework Educational Programmes (FEP) were implemented into School Educational Programmes (SEP) and schooling in the Czech Republic. Even though FEP describes compulsory and recommended extensional topics for each study field, it gives more freedom to schools in processing these topics into SEP in comparison to unified curriculum. Thus, huge differences in preliminary knowledge and skills occur between students, even at those from the same study field. This fact is visible in disunited knowledge in basic areas of Mathematics in first year students at universities, which influences the success in study. It was also the reason for making a questionnaire whose aim was to check the orientation in basic areas of Mathematics at students at the beginning of their studies and find, if there is any dependence of results on a type of absolved secondary school or if there are differences at students of different study fields. Currently, thanks to amendment of Higher Educational Act, new study fields are being prepared at all Czech universities. It gives us unique opportunity to create study plans and edit content of subjects to make them correspond as much as possible with the profile of a graduate as well as with preliminary requirements on students. Thus, we decided to analyse data from questionnaires done in years 2011 – 2014 that have not been tested yet and use these results in preparing new study programmes, when it is unique opportunity to create study plans and content of subjects to fit it the best to preliminary mathematical knowledge of students. |
| KONEČNÁ Kateřina " The Leave-One-Out Maximum Likelihood Method for the Priestley-Chao Estimator of Conditional Density " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise The contribution is focused on a kernel estimation of conditional density. Kernel smoothing is still popular non-parametric method, in theory as well as in practice. The Priestley-Chao estimator of conditional density is introduced and the statistical properties of the estimator are given. The smoothing parameters called bandwidths play a significant role in kernel smoothing. This is the reason for suggesting the methods for their estimation. The typical approach - the cross-validation method - is supplemented with the leave-one-out maximum log-likelihood method. The performance of the suggested methods is compared via a simulation study and an application on a real data set. |
| KOROBIICHUK Igor, KARACHUN Volodimir, MEĹNICK Viktorij, ASAFTEJ Olena, SZEWCZYK Roman " The Three-Measurable Problem Change of Coordinates Functions of Floater Suspended in Acoustic Environment " - from the section: Modeling and Simulation in Engineering and Scientific Computations The constructed analytical model of elastic-stressed state of a floated gyroscope gimbal. Clarified the pattern of elastic displacement of the gyroscope gimbal under the action of the penetrating acoustic radiation. Analyzed the possibility of manifestation of local features. The obtained values of the coordinate functions of the floated gyroscope gimbal provide the possibility of manifestation, in the operating conditions, of the effect of selectivity of the angular motion of an aircraft, components of acoustic vibration of its surface in the form of the formation of a systematic measurement error. |
| KOŤÁTKOVÁ STRÁNSKÁ Pavla, KOŠŤÁLEK Josef " Verifying the Authenticity of the Accounting Data Using the Benford´s Algorithm " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise This article describes examples of such algorithms, which is basing on the knowledge of American physics Benford. Benford´s law describes the behavior of empirical values, when the size of the relative frequency digits forms a numeric or financial data. The aim of the article is a description of the model that is capable of decomposition on single digit figures. The digits are calculating relative to frequency and those are then comparing to the probabilistic model respectful of Benford´s law. |
| KUČERA Petr, PÍŠOVÁ Jitka, VACKOVÁ Petra " Regularity Criterion for Local in Time Existence of Strong Solutions to the Navier-Stokes Equations with Navier´s Type Boundary Conditions " - from the section: Differential Equations, Dynamic Systems and Their Applications In this contribution we deal with the system of the Navier-Stokes equations with boundary conditions of the Navier´s type on the bounded smooth convex domain. The main theorem gives condition for local in time existence of strong solutions to this system. This result is modification of results of Robinson et al. for solutions of the Navier-Stokes system on the whole space or on the space-periodic domains. |
| LANGEROVÁ Martina " On Impulsive Control of the Second Order Periodic Problems " - from the section: Differential Equations, Dynamic Systems and Their Applications In this work we formulate conditions on optimal impulsive control of the second order periodic problem with a variational structure. Control impulses at given times represent special external forces and put the conservative system into a periodic motion. This problem is modeled on a system of charged planar pendulums without friction which are subject to external forcing terms including impulses of Dirac type. We use the variational approach. |
| LORENZI Marcella Giulia " Spatial Relationships Addressed with Geometrically Exacting Constructions: an Illuminating Experience in Math and Art by John Edmark. " - from the section: Mathematics and Art Inspired by nature, American artist, designer and Stanford University professor John Edmark creates stunning mathematical sculptures that take life through strobe light. |
| LORENZI Marcella Giulia,SCHIAVELLO Francesco " Nature Inspired Architectures and Jewels Parametric Design " - from the section: Mathematics and Art The concept of “geometric form” aroused from the observation of forms already existing in Nature. These can be sources of inspiration for artists. We present some design projects in which architectures and jewels are created in this framework, modelled using parametric processes and softwares. |
| LÖSTER Tomáš " Comparison of Results in Determining 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 paper is to compare results of cluster number determination in using of different clustering methods. To comparison were used 19 selected real datasets from The UCI Machine Learning Repository (http://archive.ics.uci.edu/ml/datasets.html). On the basis of these analyzes, it can be said, that in case of the high level of variable variability, in situation, that the individual clusters are overlaped each other, it is better to use the Mahalanobis distance measure in process of cluster number determination. The best results were obtained using the CHF coefficient and Davides Bouldin index. Their success rate was, especially when using the centroid method, 54, 55 % in the case of the CHF coefficient (54, 55%) and 59, 09 % in case of the Davies-Bouldin index (59, 09%). |
| LUDVÍK Pavel, MORÁVKOVÁ Zuzana " Two Numerical Approaches to the Non-Linear " - from the section: New Trends in Mathematical Education Our contribution is meant to be an example of multidisciplinary approach to the teaching of numerical methods. By employing the Michaelis-Menten’s model for enzyme kinetics, we show a practical application of numerical methods in biochemistry. Given the experimental data, we find a dependence of a reaction rate on a concentration of a substrate. In a preliminary section, we derive and explain The Michaelis-Menten kinetics from behaviour of biochemical reactions. In a first part, the problem is linearized and then solved by the least squares method. In a second part, we do not use linearization and solve the original problem by the Newton’s method for systems of non-linear equations. We conclude our contribution with a comparison of both approaches and results. We also offer several problems for students to clarify and deepen their understanding of the linearization. Our solution is provided in a form of a thoroughly commented MATLAB Code. |
| LUMINET Jean-Pierre " Gravitational Music " - from the section: Mathematics and Art Since the 1960s a growing number of composers have engaged with scientific research and have tried to incorporate their understanding of various models and theories into their musical works. Among them, Hèctor Parra (b. 1976) has been particularly impressed by the recent developments of gravitational physics and astrophysics, namely the part of astronomy which deals with gravity rather than light. Black holes, gravitational waves (first detected in September 2015), cosmology, or quantum gravity models belong to such fields of intensive research, bringing surprising new concepts such as the coarse-graining of space-time, multiverse or holographic principle. In this framework we have collaborated in the conception of a large piece for soloist ensemble, orchestra and electronic devices, which tries to transpose gravitational phenomena into a new form of contemporary music. |
| MAGNAGHI-DELFINO Paola, NORANDO Tulia " Geometrical Analysis of a Design Artwork Coffee Table Designed by the Architect Augusto Magnaghi-Delfino " - from the section: Mathematics and Art The 1960s and 1970s saw Italian interior design reach its pinnacle of stylishness, and by that point, with Pop and post-modern interiors, the phrases "Bel Design" and "Linea Italiana" entered the vocabulary of furniture design. In all the works of the architect Augusto Magnaghi-Delfino we find strongly a geometric component typical of those years in architecture and design. The Magnaghi-Terzaghi architectural firm from 1950 designed sophisticated lounge set and coffee tables with oval top for industrial production. For his home (Caboto Street, in Milan), Augusto Magnaghi- Delfino preferred to assign to his trusted artisan in Carrara the construction of a prototype in marble and iron. The unusual shape of the top table and the single leg and the lack of the original drawing stimulated our interest in trying to recreate the draw of the top and the leg. For the components of the leg and the top table, we considered alternative solutions: ellipse, polycentric curves, quartic curves, and superellipse. In our opinion, quartic curve fit the points of our template of leg and superellipse the points of the top, with good approximation to Magnaghi’s curves. |
| MAGRONE Paola, BRANCALEONI Fabio, CARLINI Alessandra, FALCOLINI Corrado, GARGANO Maurizio, TEDESCHINI-LALLI Laura " Towards a Diffused (Open Air) Museum in the Historical Center of Rome. University Third Mission Involving Art, Architecture, Mathematics " - from the section: Mathematics and Art Diffusion of scientific culture is a “third mission” aiming at fostering and updating scientific citizenship, as defined in the Horizon2020 European program. We experienced a new way of spreading scientific culture, by exploiting artefacts of Cultural Heritage widely available in Rome, and promoting scientific trips. Such field-trips, open to a large public, draw on the beauty of these artefacts and the sense of belonging they instill, to explain a scientific aspect. We initiated Scientific trips ([1]) on the occasion of 2014 European Science Week, and then maintained them regularly under different institutional settings. Today this approach has been taken over in various Italian towns. The main features of our approach are direct experience, embodied learning and knowledge. Here we describe two of our trips: Modularity and symmetries in Rome, where we observe the geometric compositions of the Roman Marmorari, or "cosmati", in the medieval Roman churches. We invite visitors to make on-field surveys of the floor patterns, with the purpose to ascertain modularities and repetitions. The second guided visit, Under the bridges of Rome, more than one story, is a walk along the banks of the Tiber. Bridges are important: in ancient Rome the word “Pontifex” referred to the Authority who could decide of the construction of a bridge. The walk unfolds under the bridges of the historical district, from the Tiberina isle to Castel Sant’Angelo, with the observation of the evolution of constructive techniques, narration of historical facts, geological evolution, floods and overflows of the river. References [1]The scientific trips on the site www.formulas.it http://www.formulas.it/?page_id=7902 Promoters and collaborators of this project: Tedeschini Lalli Laura, Brancaleoni Fabio, Carlini Alessandra, Falcolini Corrado, Gargano Maurizio, Magrone Paola |
| MALACKÁ Zuzana " Hankel Transform and Free Vibration of a Large Circular Membrane " - from the section: Differential Equations, Dynamic Systems and Their Applications Integral transforms are a powerful apparatus for solving initial value and boundary value problems for linear differential equations. Paper is primarily attended to Hankel integral transform and shows a utilization of the integral transforms for solving partial differential equation- the equation of vibration of circular membrane. |
| MAREK Patrice, VÁVRA František " Comparison of Home Team Advantage in English and Spanish Football Leagues " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise Home team advantage in sports is widely analysed phenomenon. This paper builds on results of recent research that - instead of points gained - uses goals scored and conceded to describe home team advantage. Using this approach, the home team advantage is random variable that can be described by trinomial distribution, and it is possible to use Jeffrey divergence and test for homogeneity of parallel samples to compare and test home team advantage of different leagues. The paper also introduces procedure that is based on identification of all distances between home advantages of leagues. These distances are later used to construct disconnected graph with components that contain leagues with similar home team advantage. Procedures are demonstrated on five top level English football leagues and two top level Spanish leagues from the 2007/2008 season to the 2016/2017 season. |
| MAREK Jaroslav, NEDVĚDOVÁ Marie " Comparing EEG Signals and Emotions Provoked by Images with Different Aesthetic Variables Using Emotive Insight and Neurosky Mindwave " - from the section: Mathematics and Art The paper is part of a broader study to verify hypotheses about the relationship between aesthetic characteristics and the emotions that an image provokes. Klinger and Salingaros stated, that aesthetic impression of an image was determined by the variables „Life and Complexity“. They proposed the hypothesis, that by measuring L and C for patterns in the image, it is possible to determine the overall impression of the image. We will not use a survey where respondents would communicate their emotions, but we will use EEG signal monitoring devices. These devices are known as Brain-Computer Interface and allow us to measure human brain activity. We will try to measure emotions provoked by images using the above BCIs. The main objective is to compare options and outputs from different BCIs when examining emotions in images with different aesthetic characteristics. These devices differ in the number of sensors and the possibility of getting raw data. The first device is the Emotiv insight and offers five EEG sensors, the second device is the Neurosky mindwave and offers two EEG sensors. For Emotiv insight, wave measurement is a paid service; only the characteristics derived from them can be obtained directly. These characteristics are: Engagement, Excitement, Interest, Relaxation, Stress, Focus. The Neurosky mindwave offers delta, theta, alpha, beta, and gamma wave tracking. Based on the Klinger-Salingars approach, images with different values of aesthetic characteristics L and C were generated. From these images, we selected paintings to analyze the suitability of using EEG-devices to measure audience emotions. |
| MARKOŠOVÁ Mária " Network Model Inspired by the Real Data – Functional Brain Networks " - from the section: Mathematical Aspects of Network Science and Applications In this paper we studied degree distributions of functional brain networks, which a re extracted from the real fMRI measurements of young healthy participants at three different correlati on thresholds of voxel activity. To explain how the degree distribution changes with the decreasi ng threshold, we created a dynamic network model. The model reflects how initially scale-free networ ks change their structure, manifested in the degree distribution, due to the processes of the netwo rkgrowth and edge addition. |
| MATVEJEVS Andrejs, CARKOVS Jevgenijs " On Subjected to Rapid Random Extractionstwo-Sex Population Growth " - from the section: Differential Equations, Dynamic Systems and Their Applications The paper analyzes a model for isolated population with sexual reproduction under assumption that the extractions are random and going at random time moments. Applying the approximative procedures of stochastic analysis we construct an ordinary differential equation for population dynamics in the mean and a linear stochastic differential equation for deviations on the mean trajectories. This approximative model permits to analyze a population growth as the Gaussian process with mean and variance given by ordinary differential equations. |
| MIKEŠ Josef " Some Algebraic Properties of Tensors " - from the section: Algebra and Geometry and Their Applications This paper is devoted to the study of some algebraic properties of tensors on manifolds. |
| NICOLA Susana, MENDONCA Jorge, PINTO Carla " Active-Learning Techniques in Math Courses in Engineering Degrees: the Pursuit for a New Engineer Profile " - from the section: New Trends in Mathematical Education In this work, we present new teaching-learning methodologies of Mathematics in Engineering Degree courses. The traditional way of teaching mathematics is based on a ´teaching by telling´ approach, especially in the early years of the courses. It is characterized by classes with many students, where they are exposed to the contents of a single discipline. Recently, there has been an increasing interest by engineering professionals and bodies to accredit engineering degrees in promoting change in this paradigm. The new teaching paradigm proposed here consists of the implementation of the following strategies: adaptation of the curricula of the course, using ´active-learning´ (AL) as a pedagogical approach, to solve real-world engineering problems~[1]. In this article, we focus on two AL methodologies, namely the eduScrum method~[3] and Jigsaw~[2]. The first creates an environment where students are masters of their knowledge, increasing their initiative to learn and entrep reneurship. The second develops in students more responsibility/autonomy and notion of belonging, hardly achieved when working alone. Some results of the implementation of these methods in ISEP´s bachelor degrees, will be presented. |
| NOVÁK Michal, BORBAR Hashem, CRISTEA Irina, JUN YoungOUNG Bae " Properties of Reduced Meet Ideals in Lower BCK-Semilattices " - from the section: Algebra and Geometry and Their Applications In our paper we include some new results on lower BCK-semilattices, which are a special class of BCK-algebras. We concentrate on a specific class of ideals of lower BCK-semilattices. We make use of some recent results on weak closure operations on ideals of lower BCK-semilattices or relative annihilators in lower BCK-semilattices obtained by Jun et al. |
| PALENČÁR Jakub, KUBIŠ Milan, PALENČÁR Rudolf " Modeling and Synthesis of Control the Process of Casting " - from the section: Modeling and Simulation in Engineering and Scientific Computations This article is focused on modeling and design of thermal control of distributed parameter systems. Partial differential equations describe the dynamics of these systems. Currently, to solve these equations using numerical methods, concrete the finite elements method. The numerical model was created based on the finite elements method using software COMSOL Multiphysics, which is adequate for modeling the process of casting. This software was linked with MATLAB & Simulink environment, where control of temperature fields in casting mold was simulated. Linked software provides for foundry practice to include the possibility of controlling the process at the very beginning of the design and by the can reduce the cost of casting production. |
| PASÁČKOVÁ Jana " Weak Property B and Property B of System of Four Nonlinear Difference Equations " - from the section: Differential Equations, Dynamic Systems and Their Applications We investigate a system of the four nonlinear difference equations, where the first equation obtain a neutral term. We state sufficient conditions for system to have the weak property B and the property B. |
| PAVLENKO Oksana, CARKOVS Jevgenijs " On Interspecific Competition of Logistic Populations with the Assumption of Rapid Random Contacts " - from the section: Differential Equations, Dynamic Systems and Their Applications The famous mathematical model for competition of two populations was studied by A.J.Lotka and V.Volterra as the system of ordinary differential equations for the mass densities of two species dependent on time, rates of growth in absence of intraspecific and interspecific competition, asymptotic masses of the species when they grow separately, and the coefficients that characterize the influences of one species to another defining a decreasing opportunity of growth. Note that this model assumed a time-continuous contact of populations. Later, the model was converted into the Ito stochastic differential equations. In our paper we analyze the stochastic modification of the two-species competition model, using the following assumptions. Our model supposes that the populations come into contact at random time moments and time intervals between contacts are independent exponentially distributed random variables with expected value, which is a small positive parameter. The impacts of the populations against each other are also sufficiently small and dependent on a sequence of identically Uniform(0,1)-distributed random variables, independent on time. Applying the asymptotic methods of the contemporary stochastic analysis we construct the average differential equations and the stochastic differential equations for the Gaussian deviations of the random trajectories on the corresponding solutions of the average equations. |
| PINTO Carla " How to Embrace the New Teaching Methodologies in Math Courses in Engineering Degrees " - invited lecture The skills needed in the 21st century have suffered a radical change with respect to the ones required in the 20th century and behind. It is observed a shift from manufacturing to emphasizing information and knowledge services. Knowledge is assumingly more specialized and is expanding exponentially. Information and communication technology change the way we learn, the nature of how work is done and perceived, and the role of social relationships. Companies nowadays require shared decision-making, information sharing, collaboration, innovation, and speed. To be successful, students have to be proficuous communicators, share, and use information to solve complex problems, adapt and innovate in response to new problems, and create new knowledge. Einstein used to say “We must revolutionize our thinking, revolutionize our actions.” The proposed new teaching paradigm consists in the implementation of the active-learning methodology (AL), by working in real world engineering problems. In the AL framework, students achieve competences, namely critical thinking, agility and adaptability, communication, collaboration, initiative (autonomy), analysis and conceptualization of information, curiosity and imagination. Students are an active part of their learning process and the teacher acts as a guide by proposing new research directions, methods, and tools. It is well known that teacher-centered learning has limitations, namely the learning process stops upon its expected delivery. Teacher-centered learning fosters a culture of learner’s dependency on the supervising instructors and teachers. On the contrary, the main goal of AL is to create strong self-directed learners. Engineering students lack essential competences in a world of rapidly changing and dynamic working environments. The later require constant creativity, analytical thinking, perfectionism and adherence to tight deadlines. This could influence negatively their future careers. Knowledge cannot be perceived any longer as the end of a goal of an engineering study, it has to be felt as an on-going activity of learning-to-think and learning-to-learn. This will promote a new design for an Engineer profile, one which encompasses an Engineer willing to manage the tools that our lifestyle requires, for all Engineering areas: electromechanical, electrochemical, informatics, amongst others. |
| PIRKLOVÁ Petra, BÍMOVÁ Daniela " Parallel Illumination in GeoGebra " - from the section: New Trends in Mathematical Education The paper introduces several parallel illumination problems solved using geometric GeoGebra software. The solution of the problem both in 3D and in 2D can be identified in GeoGebra at the same time. As a result it provides students better imagination of the problem submission and furthermore its solution. |
| PISKOŘOVÁ Zuzana, BAŠTINEC Jaromír, LABOUNEK René " Improving the Sensitivity of Tractography Using Microstructure Modeling and Pseudo-Inversion " - from the section: Modeling and Simulation in Engineering and Scientific Computations Tractography is a method to map white matter bundles within brain tissue based on diffusion MRI techniques. It seems to be a promising way of detecting white matter structure in vivo, however, method seems to be prone to false positives if standard methods of tractography are used. The paper promises to explore the possibilities of optimization techniques which would enable to include more informative models to the tractography procedure by filtering out false positives from a set of candidate tracts. To detect anatomically plaussible tracts, inverse problem from matrix equation $mathbf{y=Ax}$ is solved with help of pseudo-inversion technique. However, pseudo-inversion seems to be inappropriate for system of such dimensions and conditioning. |
| POBOČÍKOVÁ Ivana, SEDLIAČKOVÁ Zuzana, ŠIMON Ján " Comparative Study of Seven Methods for Estimating the Weibull distribution Parameters for Wind Speed in Bratislava - Mlynská dolina " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise In this paper the Weibull distribution is used to describe the wind speed data collected in Bratislava-Mlynská dolina in the period of the years 2005-2009. The parameters are estimated using seven methods: the maximum likelihood, method of moments, empirical method, power density method, least squares method and weighted least squares method with two weight factors. Their performance is compared using the root mean square error and coefficient of determination. It was observed that the weighted least squares method perform the best, followed by the maximum likelihood method and the method of moments. |
| POTŮČEK Radovan " The Sum of the Series of Reciprocals of the Quadratic Polynomials with Integer Roots " - from the section: Modeling and Simulation in Engineering and Scientific Computations This contribution is a follow-up and a completion to the previous author´s papers dealing with the sums of the series of reciprocals of quadratic polynomials with non-zero roots. We summarize these results and deal with the sum of the series of reciprocals of the quadratic polynomials with zero roots. We derive the formulas for these sums and verify them by some examples evaluated using the computer algebra system Maple 16. |
| POZDÍLKOVÁ Alena, MAREK Jaroslav " Spatial Lag Model for Apartment Prices in Pardubice Region " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise The article is devoted to modelling the relationship of apartment prices between neighbouring small municipalities within the Pardubice region. A spatial lag model will be used for the calculation, and the unknown parameters will be estimated us-ing the least squares method. This model is often used to describe geo-informational phenomena. |
| PROCHAZKOVA Jana, MARTISEK Dalibor " Notes on Iterative Closest Point algorithm " - from the section: Algebra and Geometry and Their Applications Point clouds are commonly used in many areas of technical practice. Nowadays, the common applications are in the area of autonomous cars and 3D terrain or object modelling. During the scanning process, the scanning device or object is moving. So, the problem of precise point cloud registration arises. In this article, we describe Iterative Closest Point (ICP) algorithm that is suitable for fine registration. We introduce some of the improvements that leads to higher precision, speed computation and efficiency. We also tested the ICP algorithm on the noisy point clouds to process the registration. |
| RAGUŽ Andrija, BARIČ PISAROVIČ Gordana, VOJVODIČ ROZENZWEIG Višnja " On Normal Assumptions on Demand Function and Its Elasticity " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise In this presentation we consider the demand function D=D(p), where p is price of a certain good and we introduce some natural assumptions on D in terms of the corresponding elasticity coefficient. We derive some properties of D which follow from the normal assumptions, and we provide economic interpretation and application. We also present some classes of of functions which satisfy the normal assumptions. |
| RAK Josef " Numerical Solution of a Special Singular Integral Equation of the Second Kind " - from the section: Differential Equations, Dynamic Systems and Their Applications This paper shows the method for numerical solution of a Fredholm integral equation of the second kind which has kernel function with a special type of singularity. The numerical solution is based on a Nyström method with a singularity subtraction technique. It requires a singular integral to be computed. Here the singular integral is converted to a non-singular one and a standard numerical quadrature is used. |
| REBENDA Josef " An Application of Bell Polynomials in Numerical Solving of Nonlinear Differential Equations " - from the section: Differential Equations, Dynamic Systems and Their Applications Partial ordinary Bell polynomials are used to formulate and prove a version of the Faa di Bruno´s formula which is convenient for handling nonlinear terms in the differential transformation. Applicability of the result is shown in two examples of solving the initial value problem for differential equations which are nonlinear with respect to the dependent variable. |
| RICHTARIKOVA Daniela " Sinusoid Characteristics in Applets " - from the section: New Trends in Mathematical Education The paper deals with visualisation of sinusoid characteristics. It discusses the importance of visualisation and interactive manipulations in the process of understanding the heart of the matter as the essential stage to acquire higher levels of knowledge and skills. Combining different teaching and learning aids and methods helps not only to supply but also develop various styles of cognition. |
| RIHOVA Elena, MALEC Miloslav " Fuzzy C-Means Clustering. Technique and Evaluating Results. " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise The present study aims to provide a better understanding of the fuzzy C-means clustering, their technique and evaluating their results. In order to do so, the fuzzy C-means clustering technique was described in detail, than those technique was applicated on the data sets, as generated, as real. In doing so, novel insights into the key drivers of fuzzy C-means clustering and evaluating of fuzzy clustering results. |
| ŠABÍKOVÁ Henrieta, JUDINOVÁ Lenka, ČERETKOVÁ Soňa " Rubrics as Self-Assessment Tool of Mathematical Education " - from the section: New Trends in Mathematical Education The source of the majority of disputes, misunderstandings and disagreements in a mathematics teacher-pupil relationship is testing, evaluation and classification of pupils. These parts of education are nowadays marked by defects which are an outcome of constant changes in lives of teachers, pupils and their parents. The focal point of education is no longer just acquirement of facts and but also development of teaching quality, creation of a good base for lifelong learning, increase of creativity, communication, digital literacy, the ability to resolve problems. The feedback accommodated to these demands on learning in a 21st century school should be new trend in university education of next generation mathematics teachers. According to a conventional approach, evaluation is solely an assessment of learning results, but evaluation ought to support the progress of the learner, as well as the process of learning itself. At any rate, the teacher should evaluate pupils’ outputs while providing them with a space for self-assessment. Our experiment gives answers to fundamental questions: Are pupils currently able to evaluate their own knowledge and skills? Do they underestimate or overestimate themselves? Is self-assessment affected by their age or gender? Results of the experiment could be the initial motion for changing the current approach of teachers, for preparing next generation of mathematics teachers to evaluation of pupils and pointing it to the right direction of change – to the developing assessment and to new assessment tools, e.g. Assessment Rubrics |
| ŠADURSKIS Karlis, CARKOVS Jevgenijs, GOLDŠTEINE Jolanta " Stochastic Approximation Procedure for Isolated Population in Fast Oscillated Random Environment " - from the section: Differential Equations, Dynamic Systems and Their Applications The paper deals with logistic type population mathematical model given in a form of Markov impulsive differential equation controlled by fast oscillating ergodic Poisson process. Applying the stochastic approximation procedure we construct and analyze an ordinary differential equations for mean value of population size and stochastic Ito differential equation for random deviations on mean values. |
| ŠEDIVÁ Blanka, PELANTOVÁ Helena, BUGÁŇOVÁ Martina " Normalization Techniques for Univariate Biostatistics Analysis " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise The biostatistical processing of metabolomic data includes a number of mathematical and statistical methods. The series of preprocessing steps is necessary apply before application the univariate or multivariate approaches for identifications of statistical significant factor. The usually proprocessing workflow includes methods of correction baselines, methods of binning the continuous signal to discrete datasets, the normalization of dataset and elimination of outliers in samples. We encounter mainly the problems of great variability of biological material and the high dimension of information. The goal of this article is using simulation Monte Carlo approach for analysis of influence of normalizations proceses to the results of univariate statistical methods. In our study four methods of normalization are compared - normalization by sum, normalization to creatinine, quantile normalization and probabilistic quotient normalization. The results simulation experiments studies have shown that PQN and quantile normalization are most robust than suma normalization or creatinine normalization, especially in case a small number of metabolites with a large fold change is presented. |
| ŠIMPACH Ondřej, DOTLAČILOVÁ Petra " Stochastic Extrapolation of Mortality Rates in the Czech Republic with an Impact on Probability and Number of Surviving " - from the section: Financial and Actuary Mathematics The aim of this paper is to compare the results of stochastic (autoregressive integrated moving averages) and deterministic (linear regression) extrapolations of logs of age-and-sex-specific mortality rates in the Czech Republic with impact on selected characteristics of mortality tables – probability and number of surviving. Research shows that selected ARIMA models provide more precise extrapolation of the analysed characteristics mainly in advanced ages and they are much less biased. Deterministic models are useful mainly in lower ages and up to 65 years. |
| SIVÝ Július, FRONC Marek, BORTŇÁK Dušan, VÉGH Daniel, KRÁLIK Marián " Crystal, Molecular and Electronic Properties of (E)-1-((5´-Bromo-[2,2´-Bithiophen]-5-YL)Methylene)-2-(Perfluorophenyl)Hydrazine " - from the section: Mathematics and Physics in Contemporary Science and Technique The pentafluorophenyl group is an important constituent not only in biological chemistry, but also in analytical, material and polymer chemistry, catalysis, dynamic combinatorial chemistry, and reaction development. We reported here the structures of new hydrazine, C15H6BrF5N2S2, which crystallizes as racemate in the space group P-1. The C— S, C— F and the N—H bonds are presented. The dihedral angle between the thiophene rings is 3.33 (0.19 )° and the side ring (C1 to C6) is 9.29 (18) and 10.73 (18)°, respectively. The crystal structure is slightly stabilized by the intramolecular N—H···F and intermolecular N—H···F, C—H···F hydrogen bonds as H-atoms donor, link the molecules into dimers along the b axis. Calculations of the NBO analyses (DFT/B3LYP/cc-pVDZ, single point geometry) were performed. |
| ŠKRABÁNEK Pavel, MAREK Jaroslav " Models Used in Fuzzy Linear Regression " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise The paper summarizes fuzzy linear models that were introduced in fuzzy regression analysis. The exhaustive review is extended with new models. This contribution is intended as a guide for implementing known fuzzy regression methods. However, it can be used as an inspiration for researchers developing new approaches. |
| SMETANA Bedřich, CHVALINA Jan " Groups and Hypergroups of Artificial Neurons " - from the section: Algebra and Geometry and Their Applications When we study structure of the most used artificial neural network - multilayer perceptron and functionality of artificial neuron, there is possibility using several ways to describe function and neural network properties on the basis of known algebraic structures, vector spaces and graphs theory or properties of relations. Using certain analogy with relations between descriptions of differential equations certain quality there is developed access to new view point on these subjects. In this paper some concepts of description and modelling systems of neurons are investigated. |
| ŠOVČÍKOVÁ Petronela " Cooperation in Teaching and Learning Analytic Geometry " - from the section: New Trends in Mathematical Education Cooperative or small group learning is widely recognized as pedagogical practise that promotes learning and socialisation across a range of curriculum areas from primary school to high school and college. Our research was realized in two classes. There were 42 pupils (18 pupils in the first class and the 24 pupils in the second class). The main aim of this research was to verify our hypothesis: Can pupils accomplish better results when they cooperate with someone similar? |
| STAŠ Michal " Cyclic Permutations: Crossing Numbers of the Join Products of Graphs " - from the section: Algebra and Geometry and Their Applications The crossing number cr(G) of a graph G is the minimal number of edge crossings over all drawings of G in the plane. In the paper, we extend known results concerning crossing numbers for join of graphs of order six. We give the crossing number of the join product G + D_n, where the graph G consists of one 4-cycle and two leaves, and D_n consists on n isolated vertices. The proof is done with the help of software that generates all cyclic permutations for a given number k, and creates a graph for a calculating the distances between all (k-1)! vertices of the graph. Finally, by adding some edges to the graph G, we are able to obtain the crossing numbers of the join product with the discrete graph D_n for other graphs. |
| SZABOVÁ Zuzana, KRBÁLEK Milan " Two Methods for Estimating Number of Interacting Vehicles " - from the section: Modeling and Simulation in Engineering and Scientific Computations Knowledge of an interaction range in particle systems, especially in vehicular traffic could significantly contribute to modeling of traffic flow. When determining distribution of microscopic quantities like time-clearances, knowledge of interaction range is essential, since the course of the distribution function may vary with degree of interaction (number of actively followed vehicles). Therefore we aimed our interest at statistical detection of an interaction range in particle systems. Combination of simulation methods, analytical predictions of headway distribution and correlation analysis led to several observations. We show, that interaction range depends on both resistivity and type of repulsive potential. Next we discuss generally-accepted premise (on a short range of traffic interactions), which does not correspond to traffic reality as will be demonstrated by means of correlation analysis. Such observations bring a new insight into a theory of traffic dynamics. Moreover we introduce method for detection of number of actively followed vehicles based on perturbation function. This novel approach could acknowledge results obtained by method based on correlation analysis. |
| TEDESCHINI LALLI Laura, MAGRONE Paola, SCIROCCHI Antonio, TRICARICO Daniele " When Turin Came to Rome: a Walk in the Prati District and Its Symmetries " - from the section: Mathematics and Art Symmetry is the property of invariance with respect to any transformation of an object that leaves distances unchanged. Such a transformation is called “isometry”. Isometries make it possible reduce complex shapes in primary forms. In particular, all information about a symmetrical object can be reduced to the description of a portion of the object, together with the transformation of the space that will reconstruct its entire aspect. From a computational point of view, this description is short, as it occupies less memory, and yields light on what can be legitimately called “less complex”. Architecture has exploited symmetries also to speed the design and realization processes of artifacts. In this study we show how in the early twentieth century buildings of the Prati district of Rome, isometries have been used systematically on the large urban scale and on the smaller scale of decorations. On urban scale, symmetries usually suggest some privileged directions, for instance as vanishing point of a large scale perspective. Prati was planned when the King moved from Turin to Rome, as Rome became the Capital of the new Kingdom of Italy, to host the functionaries and employees,. We think the choice of orientation of the symmetric plan is significant. We show its urban symmetries never align on the view of the adiacent Vatican city, (still the capital of another State). Many of the buildings of Prati also carry decorative friezes. We will look in particular at the front of the Courthouse. (with P. Magrone, A. Scirocchi, D.Tricarico) |
| TEREŇOVÁ Zuzana " Lines on Complete Intersection of Two Quadrics in P4 " - from the section: Algebra and Geometry and Their Applications In this paper we investigate a complete intersection of two quadrics in the projective 4-space over an algebraically closed field. This quartic surface contains one singular line. We determine all the lines on these surfaces and the arrangement of these lines. |
| TOMICZEK Petr " Forced Duffing Equation with a Non-Strictly Monotonic Potential " - from the section: Differential Equations, Dynamic Systems and Their Applications This article is devoted to study the existence of a solution to the periodic nonlinear second order ordinary differential equation with damping u´´(x) + c u´(x) + g(x, u) = f(x), x in [0, T]; u(0) = u(T), u´(0) = u´(T) ; where c in R, a quotient g(x,s)/s lies between 0 and c^2/4 + (pi/T)^2 and a potential is a non-strictly monotonic function. The technique we use are variational method and critical point theorem. |
| TORRE Matteo " Trajan´s Column: Math, Art and Cryptograph " - from the section: Mathematics and Art The history of civilization testifies to the interaction of Physics and Mathematics with Art and the influence that such disciplines have on it and on artists. Even Ancient Rome was not insensible to the charm of art and understood its great communicative and universal character. One of the most significant artworks is the Trajan Column, in particolar his frieze, because it is an artistic and scientific example of how mathematics can help art popularization to the people. In this paper I propose a cryptographic interpretation of the mathematical model of the Trajan Column frieze; the ideas came from the listening to a talk during Aplimat 2017 by Prof. Laura Tedeschini-Lalli “On imperial roman cochlear columns”. The interpretation identifies in the scytale, one of the oldest transposition methods of cryptography known and probably the only cryptographic instrument that has been successful whit this method, the main source of inspiration for the artist who made the frieze of the Trajan’s Column. The vertical alignment of episodes and key images guarantees an easy interpretation of the scenes and an immediate understanding of the ideological message of the frieze and, in my opinion, uses the column diameter not only as a reading key, but also as a cryptographic key to the message symbolic that you want to convey to the observer. This cryptographic interpretation opens up new interpretative scenarios not only for the Trajan’s Column, but also for other cochlid columns and other monuments containing a historiated frieze with continuous narration. |
| TOSHI Andrea " Twines, Knots, Mazes: an Rncounter with Paola Levi Montalcini Across Art and Mathematics " - invited lecture In 1974 the Italian artist Paola Levi Montalcini (twin sister of biologist Rita Levi Montalcini, Nobel prize winner in 1986) asked a young friend who had just graduated in mathematics to look at some of her recent works that had been created through the etching of copper sheets and to recount his impressions about them. Such was the beginning of a common quest for a language that could express the intuitions that bind the world of art and that of mathematics. A dialogue that started from the figures that evoked some of the so-called «catastrophies» described by René Thom in book that had recently been published (Stabilité structurelle et morphogénese, W.A. Benjamin, Reading Mass. 1972) and would be developed through the years in the light of the thinkings by great personalities who in the past had explored these border territories. |
| ŤOUPAL Tomáš, ŠEDIVÁ Blanka " Possible Comparison Between Two Time Series " - from the section: Statistical Methods in Technical and Economic Sciences and in Practise This paper is focused on the possible methodologies for comparing two time series by estimating the probability that both time series will increase or decrease (of course in probability) in the same time. It can be considered as the specific measure of dependence (more precisely concordance) between two random variables with non-parametric approach. Then the problem may arise with a statistical inference. The main idea of this approach is based on the transformation of observed data set into increasing and decreasing movement and then the Markov model (Markov chain) of transitions (increasing-increasing, increasing-decreasing, decreasing-increasing, decreasing-decreasing) is used with the removal of the assumption of independence. |
| TREMATERRA Amelia, IANNACE Gino " The Acoustics of the Longobard Church of Santa Sofia in Benevento " - from the section: Mathematics and Art This paper presents the results of acoustic measurements carried out in the Longobard church of Santa Sofia in Benevento (Italy). The church is on a central plan, with a diameter of 23.5 m. In the centre there are six columns, placed at the vertexes of a hexagon and connected by arches which support the dome; around this central hexagon there is a second decagonal ring, with eight pillars of white limestone blocks interspersed with layers of bricks and two columns immediately after the entrance. The acoustic measurement were done with a sound source on the altar, and the microphone points in the area were seat people. The average value of reverberation time at the frequency of 1.0 kHz was about 1.5 seconds, so the church can be used for good listening of symphonic music. |
| VACHÁLEK Ján, NELICHER Markus, VAŠEK Pavol, ŠIŠMIŠOVÁ Dana, VOLENSKÝ Tomáš " Quality Comparison Between Hybrid Regularized Exponential Forgetting Algorithm with Alternative Covariance Matrix and Selected Standard Long-Run on-Line Identification Methods of Industrial Systems " - from the section: Modeling and Simulation in Engineering and Scientific Computations This paper deals with comparing the quality of standardly used ON-LINE identification algorithms like directional forgetting and regularized exponential forgetting with the hybrid algorithm of exponential forgetting algorithm with an alternative covariance matrix. It points also to the behavior of selected algorithms in different deployment conditions and different run times. Particularly interesting for us is the long-run deployment, which correlates with use in the industry. Based on the obtained results, there will be decisions taken, about the suitability of the hybrid regularized exponential forgetting algorithm with an alternative covariance matrix for selected industrial deployment scenarios. |
| VÁCLAVÍKOVÁ Zuzana " Prototypes in Planimetrics " - from the section: New Trends in Mathematical Education The paper is focused on the detection of a tendency of primary and secondary schools´ students to have a prototypical thought in planimetrics. The summary of the results which have been reached by questionnaires given to the selected schools are described (if the way used by students to sketch the specified units is similar to what they may have seen in the textbooks, eventually to results of their teachers, or if it depends on, for example, left-right orientation, sex, age or type of studied school). |
| VÁGOVÁ Renáta, KMEŤOVÁ Mária " The Role of Visualisation in Solid Geometry Problem Solving " - from the section: New Trends in Mathematical Education Visualising in mathematics is usually connected with drawing pictures or diagrams because these help learners to find a solution to the problem. The purpose of this paper is to provide qualitative research experiment on visualisation of hidden spatial objects during solid geometry problem solving. Subsequently, we offer a way how the teacher can easily demonstrate the problem via GeoGebra software and thus support the learner in problematic steps of problem solving. The usage of an interactive geometry software provides a great opportunity to demonstrate the correct image that leads to the solution. |
| VALA Jiří " Computational Optimization of Material Choice for Thermal Containers of Advanced Buildings " - from the section: Modeling and Simulation in Engineering and Scientific Computations Optimization of performance of thermal containers of advanced buildings stimulates the multidisciplinary research, covering civil and mechanical engineering studies, material testing and physical, mathematical and computational analysis, up to the implementation of algorithms. This paper pays attention namely to the hot-wire identification of thermal characteristics of materials, with references to more general optimization tools. |
| VALLO Dusan, DURIS Viliam " GeoGebra and Logarithmic Spiral in Educational Process " - from the section: New Trends in Mathematical Education In this paper, we introduce with an usage of dynamical geometry software Geogebra in teaching Mathematics and in teachers training education. For this purpose, we concerned with some specific curves like spirals, especially logarithmic spiral. In software environment, we demonstrate some properties of this curve and its application in metal engineering. Some didactical remarks are included in the paper, too. |
| VANKÚŠ Peter, DILLINGEROVÁ Monika " New Trends In Teaching Functions at University Level " - from the section: New Trends in Mathematical Education In our paper we focus on one of the key concepts of Mathematical Analysis – the functions. We present results of our survey, realized on the sample of 91 students. During this survey we analysed their solutions of selected tasks and identified some major misconceptions the students have in the area of the functions. In the paper we then propose some new trends those can help to avoid these misconceptions and improve students’ knowledge. |
| VARGA Marek, NAŠTICKÁ Zuzana " Creative Use of Mathematical Strategies in Proofs in Undergraduate Calculus " - from the section: New Trends in Mathematical Education Mathematical theories could be developed neither without mathematical proofs, nor without mathematical creativity. Undergraduate students should be, thus, shown multiple proofs of fundamental theorems of various mathematical branches, creatively applying various techniques and strategies. In this paper we present altogether nine proofs of Lagrange’s Mean Value Theorem, employing various strategies which, in general, are useful in problem solving. |
| VARGOVÁ Michaela, SLAVÍČKOVÁ Mária " Secondary Mathematics Misconception as a Main Obstacle in Solving Higher Mathematics Problems" - from the section: New Trends in Mathematical Education Paper deals with the most common misconception in secondary mathematics and its influence on solving tasks of higher mathematics. We provide several examples from our pedagogical experiences, main misconceptions connected to the mentioned examples and our solutions for possible re-education of mentioned misconceptions. |
| VELICHOVÁ Daniela " Surface Measures Revisited on the Boundaries of Mathematics and Art " - from the section: Mathematics and Art Paper brings few reflections on the attempts to confront mathematical and artistic approach to measuring various aspects of creativity, imagination and our understanding of aesthetic values hidden in the produced artefacts in fine art and in science, mathematics namely. Phenomena that are carriers of these subtle values enable comparison of the concepts of measures and measurement strategies in maths and art. Short revision of the surface measure definitions and its application within the two environments is presented, together with continuous efforts of finding their common features and differences. |
| VERESS-BÁGYI Ibolya, KOREŇOVÁ Lilla " The Usage of Mobile Devices in The Students’ Mathematics Learning " - from the section: New Trends in Mathematical Education Mobile devices enables university students to develop innovative learning methods. The question is that can they exploit these potentials, do they know the relevant online curriculums, platforms and applications and do they have incentive for integrating mobile devices in their math learning process? In our survey, we searched the answers for these above issues. Our pilot survey suggests that the theme is very actual, arouses interest and we have to pay particular attention to the future research. |
| ZAHRÁDKA Jaromír, SEIBERT Jaroslav " On the Hosoya Index for the Molecular Graphs of Helicenes " - from the section: Algebra and Geometry and Their Applications The matching of an undirected graph is a subset of such that no two edges of are adjacent in. The Hosoya index of a graph is given by the number of all matching of. This number is one of the most interesting topological index in chemistry. Helicenes are extremal hexagonal chains with a simple graph representation as an important subclass of benzenoid molecules. We obtain the exact formula for the Hosoya index of the molecular graphs of helicenes as a function of the number of hexagons in it. |
| ZAWISLAK Stanislaw, KOPEC Jerzy " Theatre, Love and Graphs " - from the section: Mathematics and Art In the paper, utilization of graphs in theatre-related issues is discussed. World-wide known plays are analysed: W. Shakespeare’s “Measure for measure”, M. Camoletti’s “Boeing, Boeing” and Jarosław Murawski’s “Humanka”. The graphs represent relations among the heroes however they could be a part of scenography. Graph-based modelling allows for deeper understanding of attitudes and dependencies between dramatis personae, additionally unexpected visions of the plot are obtained.New type of graphs has been proposed - so called: maggraphs, where vertices are graphs. Adequqte edges represent general relation between these grapgs representing - in discussed case - power, society and church. Unexpected relevance of graph-based modelling to drama issues was achieved. |
| ZEITHAMER Tomáš R., POSPÍŠIL Jiří " General Theory of Retail Gravitation Field " - from the section: Mathematics and Physics in Contemporary Science and Technique The work examines space weather phenomena that affect the transfer of mass, momentum, jerk, energy and charge of heliospheric magnetized plasma into the geosphere and its sub-spheres. In addition to phenomena involving transfers between individual parts of the geosphere, space weather also affects biological and technological systems found both in the heliosphere and below the Kármán line, as well as biological and technological systems on the ground. The economic implications of the transfer mechanisms for space business are also discussed. |
Number of registered papers: 143 |
Last change: 06.03.2018 |