| AHMAD Israr " Reduced-Order Synchronization Criterion for Coupled Chaotic Systems Using a Generalized Robust Active Control " - from the section: Differential equations, dynamic systems and their applications This paper is devoted to study the problem of reduced-order synchronization of a fourth order and a second order chaotic system with the presence of unknown external disturbance. A generalized robust active control is proposed and sufficient algebraic conditions are derived to compute suitable linear controller gains that accomplish the closed-loop stability for reduced-order synchronization. The Routh–Hurwitz criteria and Lyapunov stability theory are used to study the conditions of the globally exponential reduced-order synchronization. Numerical simulations are presented to demonstrate the effectiveness of the proposed reduced-order synchronization scheme. |
| ANTOŠ Karel " How to apply Creative Approach in finding the Greatest Common Divisor of Natural Numbers " - from the section: New trends in mathematical education This article focuses on one of the important purpose of school mathematics, namely how to make the student to be a better math problem solver. It discusses the possibilities and strategies in solving problems. It shows that the research approach in the field of mathematical research is a method that enables pupils and students to make experiments and find solutions to various mathematical problems. It shows further that an important aspect of education is to make pupils and students to know the creative aspect of mathematics as a way to self-finding solutions of different mathematical problems. This creative approach is shown here on the problems of finding the greatest common divisor of natural numbers. |
| BÁLINT Vojtech " Minimization of the Parallelepiped for Packing of Three Cubes in Dimension 6 " - from the section: Algebra and geometry and their applications Two new results can be found in this paper: minimal volume of box into which is possible pack any two or three 6-dimensional cubes with total volume 1. |
| BAYERL Erik " Interactive Textbooks in Mathematics education - What does it mean for students? " - from the section: New trends in mathematical education iBook technology reflects demands of the modern era by innovating ways of access and it also creates comprehensive, multimedia, interactive, dynamic and attractive study materials which are available on computers on the Internet, tablets and smart-phones, as the latest electronic platforms. Whilst the creation and use of iBook textbooks in Mathematics education abroad is a standard and the attention is focused on verifying efficiency and effectiveness, Math as an iBook textbook in Slovakia is not yet developed. This paper discusses the process of preparation and concepts of iBook textbooks – collection of exercises with solutions focusing on isometries. The pilot version of the collection was introduced to students of a grammar school. The aim of this work is to describe students’ opinions on the interactive collection of exercises with solutions and its potential use at their mathematical education. The analysis of students’ opinions is important for authors of the iBook, mostly form the point of view of their statements on strengths and weaknesses, potential opportunities and threats, therefore it resulted in a SWOT analysis, that shall become the fundamental pillar for the creation of iBook textbooks – collection of exercises with solutions in Geometry. |
| BÍLKOVÁ Diana " Trimmed L-moments in Modeling Wage Distribution " - from the section: Statistical methods in technical and economic sciences and in practise L-moments and their estimations lack some robust features that belong to the TL-moments. TL-moments represent an alternative robust version of L-moments, which are called trimmed L-moments. This paper deals with the use of TL-moments in the construction of models of wage distribution. Three-parametric lognormal curves represent the basic theoretical distribution whose parameters were simultaneously estimated by three methods of point parameter estimation and accuracy of these methods was then evaluated. |
| BOHÁČ Zdeněk " Is a Large Amount of Study Materials a Benefit " - from the section: New trends in mathematical education BOHÁČ Zdeněk, (CZ), DOLEŽALOVÁ Jarmila, (CZ), KREML Pavel, (CZ) Keywords and phrases : Study, mathematics, study materials Mathematics Subject Classification: Primary 97U50 At present, students are flooded with a large amount of study materials. In addition to traditional printed textbooks and university textbooks, they have access to a wealth of materials in electronic form. However, not all materials are suitable and flawless. Any binding texts, or curricula, which would specify for individual fields of study and types of schools what and how much to teach, do not exist. This is in direct conflict with wide possibilities of mobility which present-day students have. Another question that concerns mathematical teaching texts is a conflict between mathematical correctness and comprehensibility for students. This problem arises especially in connection with the fact that for many years, input knowledge of students has already had a downward trend. In consequence of a large amount of study materials, students rely on the fact that required study materials on all themes can be found via the Internet (however only seldom they are able to assess whether these materials are suitable for them). A considerable number of various instructions on how to solve problems, work sheets, syllabi, etc. eventually turn out to be counterproductive, because students are not acquainted with them and often are not able to choose rightly. The result is chaotic preparation for examinations and lessons in general. If we realize how low the number of students coming from secondary schools with the habit of consistent and systematic work is, we cannot be surprised at the low number of hours devoted by them to preparation for lessons and examinations. References: [1] URL: http://www.studopory.vsb.cz/ [2] URL: http://www.vsb.cz/714/ Current address Zdeněk Boháč, doc. RNDr. CSc., VŠB – TU Ostrava, Department of Mathematics and Descriptive Geometry, 17. listopadu 15, 708 33 Ostrava – Poruba, +420 597 324 182, zdenek.bohac@vsb.cz Jarmila Doležalová, doc. RNDr. CSc., VŠB – TU Ostrava, Department of Mathematics and Descriptive Geometry, 17. listopadu 15, 708 33 Ostrava – Poruba, +420 597 324 185, jarmila.dolezalova@vsb.cz Pavel Kreml, doc. RNDr. CSc., VŠB – TU Ostrava, Department of Mathematics and Descriptive Geometry, 17. listopadu 15, 708 33 Ostrava – Poruba, +420 597 324 175, pavel.kreml@vsb.cz |
| BOHDAL Robert " Improvement of Character Set Detector Chardet " - from the section: Nothing There are many encoding schemes which represent characters in text files. If the program displaying these texts cannot determine the right encoding, the text may become unreadable. Thanks to the widely spread universal character set detector from Netscape, it is possible to display text correctly in any software on any device. Language models for the automatic character set detection have been created only for a small group of languages. Our aim was to create language models for more countries so that the probability of successful determination of the encoding increased. The most problematic was the increase in accuracy of detecting the character set for languages using ISO-8859-1 encoding. The original algorithm was not sufficiently precise, and we have therefore designed a different procedure |
| BRUNETTI Federico A " Through the Screen. Concepts and Typologies of Digital Vision Experience. " - from the section: Mathematics and art The recent development of several new technologies in the area of visual digital applications- and even wearable smart-glasses devices- demonstrates the actuality of the visual thought in the human knowledge, and also the strategic power of computational systems applied for the image interactions. But in the proliferation of tools, and specific different research and complex patents competences, is often difficult to recognize some essential design lines that are – at least at present- taking shape in common fields, or heterogeneous direction of development of these innovations. In this short overview, instead of positioning the focus on the subject of the observation experience - i.e. the human eye- it is suggested to set the digital screen at the fulcrum of a comparative essay, with the aim to identify the converging value – from geometry, optics, visual arts, design, IT etc.- to the image conceived as an algorithm. |
| BUDKINA Natalja " S. ASMUSS, J. BREIDAKS, N. BUDKINA. On Approximation of Density Function by Shape Preserving Smoothing Histospline " - from the section: Statistical methods in technical and economic sciences and in practise The problem of approximation of a density histogram is considered as the problem of smoothing histopolation with weights under some additional restrictions, which are obtained from the properties of given histogram. The paper suggests the method for solving of the problem of histopolation when solution preserves some shape properties such as positivity, monotonicity and/or convexity. These conditions are considered as the positivity/negativity constraints on the derivative (or the derivatives) of approximants. The approach is illustrated by some numerical examples. |
| BŘEHOVSKÝ Jiří " Forms of the Problem Presentation in the School Practice " - from the section: New trends in mathematical education Břehovský J. (CZ), Knobloch R. (CZ): The contribution describes the case study that deals with the influence of the form of the problem presentation on the pupils’ understanding of its assignment taking into account the level of the reading achievement abilities of the pupils. It is a qualitative evaluation that will provide the base for the further more long terms investigation. |
| CAPANNA Alessandra " Exploring Expo Geometric Exploits " - from the section: Mathematics and art International world fairs are temporary events in which world countries show themselves in a relative narrow space, in buildings constructed on purpose, usually following the main theme of the exposition. These temporary buildings, by their very ephemeral essence, transient, of rapid construction and consumption, express summarily the image of the historical present through a representation of progress and modernity, using the geometry as a means of symbolic abstraction and as materialization of "aesthetic" choices. The different nations participate to the world fairs in order to show their best characteristics, often coinciding with the achievements in the various fields of knowledge, by giving to the architects the task of representing that with amazing pavilions, exploits of imagery and manufacturing competency. From time to time those buildings, became urban icons. Starting from an historical introduction of some of the most famous and relevant, from a geometric point of view, pavilions, we will explore the last world fair architecture. Expo 2015 was held in Milan, Italy, from May 1st to October 31st, 2015, and its main theme was Food for the planet. Although it is noticeable, in this expo just ended, that geometries represent mainly the configuration of the exteriors, some pavilions occur anyway as objects for which the search for the form is addressed starting from strong geometric figures. It may be noted that in some cases the volumes and in others the surfaces determine the external images of the pavilions and in some cases also the character of the interior. We will examine only some of the pavilions - it would occur a book to deal with all – exploring the geometric exploits of this edition of the world fairs. |
| CEJKA Jiří " Application of Mathematical Methods in Transport and Logistic Area " - from the section: Statistical methods in technical and economic sciences and in practise The issue of mathematical methods currently represents one of the possibilities to eliminate the rising costs in the technological process. In the paper the authors have analyzed some of the operation research methods that can be used in transport processes. The paper also includes an overview of authors who have dealt with using mathematical techniques in transport-technological processes in both passenger and freight transport. |
| CEPPITELLI Rita " State Preference Models and Jointly Continuous Utilities. " - from the section: Statistical methods in technical and economic sciences and in practise In the present work, we study the possibility to represent the preorders defined by the characteristic linear operators of financial (or economic) markets represented in the States Preference Model perspective by applying classical theorems of the existence of jointly continuous utilities. We conduct our exam by a strongly application-oriented mood. Indeed, by introducing the classic setting of Arrow-Debreu State Preference Model and its recent generalization to the sphere of Schwartz Linear Algebra in distribution spaces, we address the problem of extending some fundamental results of finite dimensional State Preference Decision Theory to a new case, characterized by a hard type infinite linear-topological dimensionality. In this case a representation theorem for submetrizable k_omega-space is applied. |
| CERETKOVA Sona " Inquiry Based Mathematics Education(Statistical Evaluation of One Part of Pupils Questionnaire Survey) " - from the section: New trends in mathematical education The aim of this contribution is to present the results of 143 pupils’ questionnaire survey on mathematics classes at secondary schools in Slovakia and their statistical evaluation. Mathematics teachers of these pupils were exposed to professional development courses of IBL pedagogy in mathematics. The retrieved part of the questionnaire deals with the Inquiry Based Learning (IBL) moments and/or episodes during the mathematics lessons. The Stuart-Maxwell test has been used for questionnaire survey evaluation. The survey is a part of the research within the 7FP project PRIMAS. |
| CLAUDIA-GEORGETA Carstea " Object Oriented Dynamic Model for A Human Resource System-Based on Components " - from the section: Modeling and simulation in engineering and scientific computations The purpose of this paper is to simulate the process for human resource management in a distributed network, based on a visual modeling language. The system is divided in specific components like: subtask of personal records, tracking working hours, improving staff skills. The case study deals with organize the design process in a way that programers can understand the system and with creating a decision support. |
| COCCHIARELLA Luigi " Perspective Reliefs in Italian Renaissance. Visual Styles and Geometrical Paradigms " - from the section: Mathematics and art Abstract. The history of perspective is about space, with the aim at finding principles and procedures to represent it on a bi-dimensional support, namely, the picture plane. The story had its decisive start, or a re-start, in the early Italian Renaissance. But in parallel, a new story was starting, aiming at extending perspective beyond the canvas and creating three-dimensional perspectival environments, either by theatrical scenes, or by architectural and urban spaces, together with sculptural representations, on which we would like to focus our attention. The introduction will look at the almost coeval development of perspective painting and perspective relief, starting from Saint George and the Dragon by Donatello (1416-1420), also in comparison with some analogous experiences carried on in architecture and urban contexts. The following section will focus on the iconographic style of the perspective set adopted in the bas-reliefs as well as in the high-reliefs in XV century, trying to reach a basic classification with the help of some selected artworks. Geometrical paradigms are the topic of the third section, where we will discuss projective principles and operational procedures, according to the theoretical sources at that time. The last section is dedicated to a real case studio, namely the relief of the Annunciazione by Benedetto da Majano (1490. Monteoliveto, Naples). Two perspective reconstructions will be proposed, one based on a survey from life, one based on a photogram. The reconstructions are both carried on by homological procedures. The Conclusion will reaffirm the role of perspective as symbolic form across visual arts. Key words. geometry and art, perspective, perspective relief, projective geometry, architecture, sculpture, graphic representation Mathematics Subject Classification: Primary 00A05, 00A66, 01A05, 51N05; Secondary 97U99. |
| DELIGIANNAKI Katherine " Statistical View on the “Golden Bug” Story of E.A.Poe " - from the section: Mathematics and art In the story Golden Bug of E.A.Poe we can meet with problem of connecting measurement. Unknown coordinates of treasure can be calculated by Least squares method. In this article our attention has been given to describe confidence domain by using statistical methods. To modeling of uncertainty coordinates, the model of indirect connecting measurement will be used. |
| DEMLOVA Marie " Algorithms for Minimal Automata Congruences " - from the section: Algebra and geometry and their applications A linear algorithm for finding the minimal automaton congruence containing a given relation will be shown. |
| DI CARLO Biagio " Tensegrity Structures and Design Science " - from the section: Mathematics and art The ancient art of weaving related to the reciprocal frame joint of Leonardo reveals the starting point to understand design science structures. We can expand this starting point toward resonant tensegrities and rigid-deresonated tensegrities, polyhedra and geodesic spheres, obtaining in this way the visual pattern called DST (Design Science Tetrahedron). The five basic weaving cells mostly used in bidimensional space are: the two-way cross unit, the three-way triangle unit, the two-way square plane weave unit, the five-way pentagon weave unit, the three-way hexagon weave unit. If we use the helical reciprocal frame joint we can move platonic and archimedean solids in a three dimensional space, getting weave-like polyhedra modules. In this way three-dimensional weaving can be seen as an extension of conventional flat weaving. When tension and compression are used together to form tensegrity structures, the qualities of each are used to their best advantage. Rock, brick, cement, and other hard, rigid materials work most efficiently when compressed. Rope, steel cable, elastic cord,and other flexible materials are best suited to be tensed. Materials under tension tend to increase in strength as they approach their breaking point. The combination of rigid compression and flexible tension is also common in nature. Our bodies, with their rigid bones and flexibleligaments and tendons are examples oftensegrity structures. The reciprocal frames of Leonardo can be considered as forerunners to rigidtensegrity structures, which can themselves be considered the forerunners to geodesicstructures. The rigid tensegrity systems turn out to be apparently more complex thanreciprocal and geodesic structures but in reality the only difference regards the systems of joints. |
| DOLEŽALOVÁ Jarmila " Is a Large Amount of Study Materials a Benefit? " - from the section: New trends in mathematical education BOHÁČ Zdeněk, (CZ), DOLEŽALOVÁ Jarmila, (CZ), KREML Pavel, (CZ) Keywords and phrases : Study, mathematics, study materials Mathematics Subject Classification: Primary 97U50 At present, students are flooded with a large amount of study materials. In addition to traditional printed textbooks and university textbooks, they have access to a wealth of materials in electronic form. However, not all materials are suitable and flawless. Any binding texts, or curricula, which would specify for individual fields of study and types of schools what and how much to teach, do not exist. This is in direct conflict with wide possibilities of mobility which present-day students have. Another question that concerns mathematical teaching texts is a conflict between mathematical correctness and comprehensibility for students. This problem arises especially in connection with the fact that for many years, input knowledge of students has already had a downward trend. In consequence of a large amount of study materials, students rely on the fact that required study materials on all themes can be found via the Internet (however only seldom they are able to assess whether these materials are suitable for them). A considerable number of various instructions on how to solve problems, work sheets, syllabi, etc. eventually turn out to be counterproductive, because students are not acquainted with them and often are not able to choose rightly. The result is chaotic preparation for examinations and lessons in general. If we realize how low the number of students coming from secondary schools with the habit of consistent and systematic work is, we cannot be surprised at the low number of hours devoted by them to preparation for lessons and examinations. References: [1] URL: http://www.studopory.vsb.cz/ [2] URL: http://www.vsb.cz/714/ Current address Zdeněk Boháč, doc. RNDr. CSc., VŠB – TU Ostrava, Department of Mathematics and Descriptive Geometry, 17. listopadu 15, 708 33 Ostrava – Poruba, +420 597 324 182, zdenek.bohac@vsb.cz Jarmila Doležalová, doc. RNDr. CSc., VŠB – TU Ostrava, Department of Mathematics and Descriptive Geometry, 17. listopadu 15, 708 33 Ostrava – Poruba, +420 597 324 185, jarmila.dolezalova@vsb.cz Pavel Kreml, doc. RNDr. CSc., VŠB – TU Ostrava, Department of Mathematics and Descriptive Geometry, 17. listopadu 15, 708 33 Ostrava – Poruba, +420 597 324 175, pavel.kreml@vsb.cz |
| DORDA Michal " A Model for Design of Public Transport Network with Predefined Route Headways " - from the section: Modeling and simulation in engineering and scientific computations The presented article deals with the problem of planning public transport networks. The problem is solved by means of linear programming methods. Results got by solving the original mathematical models often require consequent corrections in order to put the results in practice. Problems may arise if we want to keep regular headways on a route (time intervals between the consecutive connections of the route). The headway can be calculated on the basis of the cycle time of the route and the number of the vehicles that are assigned to the route. The presented model differs in the fact that the model takes into account only feasible values of the headway on the route. Vehicles are allocated according to the feasible headways; their values are predetermined. The total number of the vehicles assigned to the routes forms the optimization criterion. The model is created for transport companies having a heterogeneous vehicle fleet. The heterogeneous vehicle fleet is the fleet consisting of different kinds of the vehicles (for example buses and trams). Moreover, individual vehicles of the same kind can differ in their capacity. The presented mathematical model takes into account both of these facts. |
| DOTLAČILOVÁ Petra " Smoothing of Mortality Curve: The Usage of Moving Averages and Gompertz-Makeham Function in the Case of the Czech Republic " - from the section: Financial and actuary mathematics Our paper discusses the possibilities of levelling the age-specific death rates of the Czech population using different lengths of moving averages and the Gompertz-Makeham (G-M) function. Moving average is a technique that belongs between the simpler one, G-M function between the most used approaches for levelling of mortality curves at higher ages. These approaches are very useful in the conditions of the Czech Republic. The lengths of moving averages were used according to Czech literature and empirical studies and finally set to 3, 9 and 19 values with different weights. The best results of smoothing by moving averages is achieved with the use of moving averages of 19 values, on the other hand we lose most initial observations. The G-M functions were estimated in STATA software and results are different e.g. in comparison with 19 values length moving averages. Results from this study will be used for future research to implement this technique into extrapolation script that will be able to smooth the values and then extrapolate them to the highest ages (110 years or above). |
| DRAŽENSKÁ Emília " The Crossing Numbers of Cartesian Products of Seven Vertex Graphs with Path " - from the section: There are known the crossing numbers of Cartesian products of paths, cycles or stars with many connected graphs on at most six vertices. In this paper, we determine the crossing number of Cartesian products of several graphs on seven vertices and seven edges with paths. |
| ECSI Ladislav " On the Stress Solution of Hypoelastic Material Based Models Using Objective Stress Rates " - from the section: Modeling and simulation in engineering and scientific computations Although hypoelastic material based models in general do not have constitutive equations in terms of finite strain measures, there is an exception, when they are loaded elastically only. The proper objective rate form of the material model then can be obtained by objective time derivation of this particular constitutive equation. Such constitutive models do not exhibit any of the well documented spurious material behaviour, which will be demonstrated in an analytical study using the Jaumann rate of the Cauchy stress. |
| EDEKI Sunday O. " The Variance Gamma Model as a Difference of Two Gamma Processes in Option Pricing " - from the section: Financial and actuary mathematics The Variance-Gamma (VG) process is a three parameter stochastic process with respect to a Brownian motion. In this paper, we present a detailed study of the VG process expressed as a difference of two gamma processes. We obtain the basic moments of the process using the characteristic function of the VG process with regard to the parameters of a differenced gamma processes. Also, the Levy-Khintchine formula for the process is derived via the Frullani’s integral. Finally, a modified European call option VG model incorporating difference of two gamma processes is proposed. |
| FABBRI Franco " The birth of Adotta Scienza e Arte nella tua classe a project for teaching and popularisation of science " - from the section: Mathematics and art FABBRI Franco L., (IT), BATTISTINI Lorenza, (IT), BOCCARDI Beatrice, (IT), CAVICCHI Veronica, (IT), CAVINA Marco, (IT), GIURGOLA Giliola, (IT), GIANSANTI Stefania, (IT), LORENZI Marcella G., (IT), NAPOLEONE Maria, (IT), PAROLINI Giovanna, (IT), SARTORI Renato, (IT), SEVERI Alice, (IT), SOLARI Amerigo, (IT), TORRE Matteo, (IT) Abstract. “Adotta Scienza e Arte nella tua classe” (“Adopt Science and Art in your class”) is a project for the students of the Italian secondary schools. Presented in its core design at the Aplimat Conference, February 2012, the project is now in its fourth edition. Starting from an aphorism on science chosen among a hundred, the students put themselves to the test drawing science, guided by the teacher along an educational path that practices the links between science and art. In the last years, 186 schools have joined, from all the Italian provinces, involving more than 400 classes, 286 teachers and 6294 students. 1726 original artworks have been published on the web. Numerous ancillary activities have been made, including exhibitions of the students’ artworks, local competitions, local and networking activities. A second project “Adotta Scienza e Arte nella scuola primaria” (“Adopt Science and Art in the primary school”) was derived and adapted from the first for pupils from the age of 6 to 10, promoted by Esplica-no profit in collaboration with CIRD-UNI Udine and other associated partners. The article describes the milestones of “Adotta Scienza e Arte nella tua classe”, presented and illustrated through several works created by the students among those most in evidence in the various editions. We also talk of: the extension of the project to the Italian schools abroad, the realization of an itinerant exhibition and the print version of the “100 +1 frasi famose sulla scienza” digital collection v.4demo, starting point of the students’ challenge to “draw science”. We also analyze some of the graphic works produced in the first two editions, representing instances of some common processes in the approach to science among the young and its relationship with art. |
| FALCOLINI Corrado " Compounds of Helical Curves: Medieval Tortile Columns " - from the section: Mathematics and art Tortile columns are ubiquitous in cult places, but classical treatises discuss only some specific geometric models. We address medieval columns, which elude this description, and introduce a parametric model mathematically describing a great variety of columns, and their differences. The model is validated through 3D survey. We describe the variety of columns of the Cloister of Saint Paul out of the walls,(A.D.1204-45), in Rome. When a column looks more wrought or torqued, it is obtained by compounding several different helices. |
| FECENKO Jozef " Solving Conditional Probleme of Extreme Functions n Variables with m Conditions - Using Maxima " - from the section: New trends in mathematical education The article describes a method of solving conditional problem of extreme function n variables with m conditions which are in the form of equations. The second order sufficient conditions for mentioned constrained optimization problems are formed in the terms of bordered Hessian matrices. The article additionally presents a computer program in open source system Maxima for solve one from the problems. The program is generally not limited by the number of variables or even the number of conditions. |
| FECHOVÁ Erika " Modernization of Education and Utilization of Mathematical Software Tools in Teaching Natural Science and Technical Subjects " - from the section: New trends in mathematical education At the present technical times we cannot imagine our everyday lives without computing technique. Computer as a fast and efficient means of communication allows communication among people, helps to solve complex tasks and problems, but it is also the source of information from various areas of life. The aim of the paper is to point out the necessity to develop information and communication technologies and need to use software tools in educational process. |
| FERDIÁNOVÁ Věra " Special 3D Models for Monge Projection " - from the section: New trends in mathematical education Teaching Monge projection is not a favorite topic for students. They lack the spatial imagination and have problems with understanding simple tasks. Thus, a few models of simple tasks in Monge projection inspired by KupŁáková [3] have been created. Students can assemble the models during the lesson, which should help them to understand the topic better. |
| FERREIRA Manuel Alb " Results and Applications in Statistical Queuing Theory " - from the section: Statistical methods in technical and economic sciences and in practise A theory of queues overview, single node and in network is presented. Some important results are highlighted. And practical applications, the most of them uncommon but some very well known, using mainly infinite servers nodes are outlined. Key words. Queues, networks of queues, infinite servers nodes, results, applications. |
| FESZTEROVÁ Melánia " Statistics Methods Evaluating the Content of Humus in Soil Based on Environmental and Ecological Relations " - from the section: Statistical methods in technical and economic sciences and in practise The content of soil organic substance in soil depends on environmental and ecological relations. These affect the process of humus creation in the soil in a negative and a positive way. These processes are effected by location, soil type, relief, season, climate, altitude and by the use of soil cover. The article summarizes the influence of land use and vegetation cover on the soil properties of different soil types and deals with the possibilities of using parametric tests in evaluation of humus content based on environmental and ecological relations. |
| FILIPE José Antón " Neuroeconomics and Reinformance Learning. An Exploratory Analysis " - from the section: Statistical methods in technical and economic sciences and in practise In an era in which the study of the brain gets increasingly featured as an analytical tool of economic phenomena, the understanding of the way Neuroeconomics works as a tool for managers, students and other economic agents is now particularly important. There is now a need to have research that allow the clarification of the analytical decision process and the potential of brain study for decision making process of economic agents. Considering this new reality, a study is presented concerning one of the most important issues for the decision maker, which is the reinforcement learning process. Key words. Reinforcement learning, Neuroeconomics, Individual behaviour. Mathematics Subject Classification: 91B06. |
| FLOREA Olivia " Graphical Representation of Implicit Functions in Maple " - from the section: New trends in mathematical education The aim of this paper is to highlight a different approach on functions of many real variables from the point of view of the graphical generation through attractive representations. The main goal is to make mathematics more accessible for engineering students. There were chosen some particular functions that with Maple tools were represented graphically. The impact on students was effective, in the sense that their interest was stimulated to find on their own other particular functions with spectacular representations. |
| FRIEDRICH Václav " Quantitative Methods in Education: Analysis of Eficiency " - from the section: New trends in mathematical education The issue of mathematics anxiety has been discussed for several last decades. Students often come to the universities with negative attitude towards mathematics and quantitative methods. The paper presents the results of research how students react to the education of quantitative oriented subject “Managerial Decision Methods” at the Faculty of Economics, VSB - Technical University in Ostrava. A modified Fennema-Sherman model was used to measure student attitudes and describe their evolution during the education. |
| GABKOVÁ Jana " STEINER´S THEOREM IN PHYSICS AND NUMERICAL MATHEMATICS " - from the section: New trends in mathematical education The aim of this article is to highlight the importance of Interdisciplinary / Cross-Curricular Teaching in mathematics and physics at the Technical University. In the process of solving a simple physics problem we can see benefits of mutual cooperation between mathematics and physics. A maths teacher can incorporate practical tasks into the teaching of numerical mathematics; these are exactly the types of tasks that help students to better understand the need and use of mathematics in other technical disciplines. A physics teacher can answer questions about numerical mathematics and show students step by step solutions “hidden” in software. This way the teachers are preventing isolation of theoretical knowledge and practical activities in student’s minds. |
| GALL Marian " The Need to Implement e-Course to the Basics of University Mathematics Education " - from the section: New trends in mathematical education Mathematics is a key subject on technically-oriented universities. The use of mathematics for solving of scientific-technical problems needs the understanding of the problem, creating its mathematical model, its solving using mathematical methods and finally, the interpretation of obtained mathematical results. This led us to creating of an e-course that shall be useful by improving of secondary school mathematics knowledge necessary to successful technical university studies. Our aim is to increase and unify the mathematics knowledge standard. And to help the students to actively acquire and establish secondary school mathematical knowledge so that they are able to apply it in their later studies, scientific activities and praxis. |
| GELATTI Gabriele " The Golden Ratio in the Most Beautiful Triangle and the Process of Creation of a Work of Art " - from the section: Mathematics and art We show the discovery of an occurrence of the golden ratio in the half-equilateral triangle, as a part of the process of intuition and visualization leading to the creation of a work of art. The process of invention here formulated using mathematical language is substantial part of the same work of art |
| GEMERANOVÁ Mária " Data Approximation Using Lemniscates - Adding One Focus Method with Sequentially Adding Input Points " - from the section: Algebra and geometry and their applications Multifocal lemniscate is a set of points in Euclidean plane, whose product of distances to a finite set of fixed points is a constant. In our work, we look for a set of foci and a corresponding radius value, so that the resulting lemniscate approximates the sequentially adding input data set sufficiently accurate. Our algorithm searches for approximating lemniscate by adding one focus per cycle, appropriately changing the radius value and optimizing parameters of the achieved lemniscate. We also adapt our algorithm to approximate points in real space using 3D lemniscates. |
| GHEORGHIU Dragos " Protogeometry – The Straight Lines as the Basic Unit of Prehistoric Design " - from the section: Mathematics and art A few years ago I decided, together with Professor Mauro Francaviglia, to set up the basis of a new archaeological sub-discipline, i.e., proto-geometry. Unfortunately, faith decided something else. The present work on the line as a unit of protogeometry is dedicated to this special scholar and fiend. The straight line represents the basis of prehistoric and ancient geometry; it is a completely artificial concept, non-biological, and non-geological, with very few examples in nature. But a straight line can be done in many (artificial) ways, the most common being the Egyptian architectural ritual operation of “stretching the cord”. The megalithic alignments could be seen not only as a material positioning, but also as an evocation of an invisible, conceptual principle, which is the straight line. Being interested not only by the experimental tracing of the prehistoric grand designs, but also by the conceptual way this linear patterns were produced and receipted, I tried to use an experiential approach to protogeometry, by employing the instruments of contemporary art, like land-art and installations. Therefore, I traced different linear patterns at a grand scale, reproducing by means of land-art the architectural forms of prehistoric structures (like the walls of a Chalcolithic castro on Monte Vehlo in Portugal), in order to reproduce the cognitive process of tracing and imagining at the same time the line across a slope of 1 km. length. Sometimes I revealed the invisible lines of different rituals by tracing the path of various ceremonies, be they Neolithic (like at Barclodyad Y Gawres, in Wales), or historical (like in the court of the Abrantes Castle in Portugal). The present paper tries then to present the fundamentals of the Euclidian geometry seen through the prism of phenomenology, by reproducing experimentally and experientially some prehistoric and historic patterns with the use of contemporary art. |
| GOLDSTEINE Jolanta " CARKOVS Jevgenijs, GOLDSTEINE Jolanta: On Second order Moment Lyapunov Spectrum for Markov Linear Impulse Dynamical Systems " - from the section: Differential equations, dynamic systems and their applications The paper deals with the linear impulse dynamical system with the phase coordinate switched by a homogeneous ergodic compound Poisson type Markov process with moments of jumps dependent of a small positive parameter. The developed method and algorithm is applied to finding of the second order moment Lyapunov spectrum for the initial impulse dynamical system. |
| GRAF Vojtěch " Mathematical Model of Charter Flight Scheduling with Predefined Time Slots " - from the section: Modeling and simulation in engineering and scientific computations Mathematical modelling is a universal tool that can be used to optimize processes arising from different branches of transport. The article deals with a mathematical model that can be used for flight scheduling of a charter air transport company. The mathematical model is tested on the case when several time slots to use an airport are offered to the charter air transport company during the day. |
| GUNČAGA Ján " Geometric Puzzle and Its Application in Primary Mathematics Education " - from the section: New trends in mathematical education The present paper deals with the application of geometric puzzles in primary mathematics education and in the training of future primary education teachers. Geometric puzzles constitute a special type (case) of plane tessellations by means of which one can explain fundamental geometric concepts from the area of isometries in the plane and their characteristics. The aim of the paper is to present concrete examples of the creation of tessellations and didactical approaches in education in the context of training of future teachers with an emphasis on physical and virtual manipulatives. |
| HALUSKOVÁ Soňa " STEINER´S THEOREM IN PHYSICS AND NUMERICAL MATHEMATICS " - from the section: New trends in mathematical education The aim of this article is to highlight the importance of Interdisciplinary / Cross-Curricular Teaching in mathematics and physics at the Technical University. In the process of solving a simple physics problem we can see benefits of mutual cooperation between mathematics and physics. A maths teacher can incorporate practical tasks into the teaching of numerical mathematics; these are exactly the types of tasks that help students to better understand the need and use of mathematics in other technical disciplines. A physics teacher can answer questions about numerical mathematics and show students step by step solutions “hidden” in software. This way the teachers are preventing isolation of theoretical knowledge and practical activities in student’s minds. |
| HECKENBERGEROVA Jana " Introduction to Gnss-Sim Algorithm " - from the section: Statistical methods in technical and economic sciences and in practise The main aim of presented paper is the description of GNSS SIM (GNSS-simplification) algorithm that can decrease size of database of GNSS positions, which is required for discrete GNSS-PIM algorithms. General idea of described algorithm is based on neglecting the data that lie on same linear part of train track. The solution of this problem is based on linear statistical model and test of data linearity. |
| HEDVIČÁKOVÁ Martina " Statistical Analysis of Mobile Platforms Utilization Ineurope " - from the section: Statistical methods in technical and economic sciences and in practise Selling numbers of smart phones and their supplements are rapidly growing worldwide. In Europe More and more people use "smart devices" primarily smartphones and tablets in everyday life. For this reason, there is a dynamic expansion of mobile operating systems and therefore expanding their services. The first part of the paper deals with percentage representation of individual operating systems for mobile devices in the European Union. This paper present unique analysis of mobile platforms (Android, iOS, Symbian OS, Windows phone, Series 40) utilization in different states in Europe. The Android system, which has a dominant position in the whole EU, also has a dominant position in all EU countries except the UK, and by the standard deviations it is noticeable that it has relatively small variations across the EU. The aim of paper is peer analysis used Mobil platform in European states. Peer analysis will base on the principal component analysis and correlation. Results of principal component analysis shows that the states of the former Eastern Bloc have a tendency to fragment the market overage to smaller mobile platforms, unlike the founding members of the EU (Western Europe countries), which usually have one, maximum two dominant mobile platform, namely Android and iOS. From illustrated boxplots it is easy to see differences between Western and Eastern Europe countries, is the comparison of the EU countries. |
| HOFMANN Alois " Development of Applications in the Analysis of the Natural Environment " - from the section: Modeling and simulation in engineering and scientific computations In many situations, we can meet information that is not exactly and clearly defined, either geometrically, or in attributes. In such case it is appropriate to consider applying mechanisms which would take this fact into account. One of the possible solutions is to use fuzzy logic, with the help of which the vagueness can be implemented in the solution and thus provide possibilities of variant solutions in the whole decision-making process. |
| HOJDAROVÁ Marie " Setting the technical state normative for machine element renewal - significant part of technical diagnostics in engineering " - from the section: Modeling and simulation in engineering and scientific computations This paper gives basic functions and general principles for effective applying technical diagnostic, which forms a significant part in the whole system of rules for optimal machine operability protection. Evaluation of the normative for the right time of an element renewal helps to increase economy of the whole machine operation and brings financial savings. |
| HORÁKOVÁ Hana " Estimation of Spring Peak Timing Shift " - from the section: Statistical methods in technical and economic sciences and in practise The goal of the paper is to propose statistical methods for quantifying a size of the shift of spring peak discharge. Two methods were suggested. A non-parametric method that estimates the seasonal cycle by a kernel estimates (by smoothing) and a parametric method where it is assumed that the seasonal cycle is a periodic function, i.e. a linear combination of sine and cosine functions. An argument of the maxima of the estimated seasonal cycle serves as an estimate of location of a peak spring flow. |
| HORSKÝ Richard " Algebra of Linear Filters in Time Series Analysis " - from the section: Nothing The theory of stochastic processes is in modern times inconceivable without functional analysis access. In this theory there are employed some operators. The typical and basic one is the lag operator. Other operators like difference, autoregressive or moving average operators are derived from the lag operator. In Box Jenkins methodology the linear filter is the general operator and the problems of its properties, especially its invertibility, belong to the main topics in this area of science. |
| HOŠKOVÁ-MAYEROVÁ Šárka " Fuzzy Continuous Polygroups " - from the section: Algebra and geometry and their applications We introduce and study fuzzy (quasi) continuous polygroup as a fuzzy polygroup such that its membership function is (quasi) continuous. We also investigate the relationship between the existence of a nontrivial fuzzy (quasi)polygroup and connectness the underlying topological polygroup. |
| HREHOVA Stella " Software Support of Mathematics Teaching " - from the section: New trends in mathematical education The current trend in education is the use of computer support for teaching many subjects. This trend is also applied to teaching of mathematics. In this contribution is described a way how we can use Matlab toolbox - MuPAD in conjunction with the online learning system Moodle. |
| IDA Cristian " On Holomorphic Vector Pseudo-Fields on Affine Complex Bundles " - from the section: Algebra and geometry and their applications In this talk we consider affine holomorphic bundle and we define and discuss the holomorphic vector pseudo-fields on it. More exactly, starting from a given holomorphic vector pseudo-field $Gamma$ on a holomorphic affine bundle $E$ over a complex manifold $M$ we construct an induced holomorphic vector pseudo-field $Gamma^prime$ on a holomorphic affine bundle $E^prime$ over $E$. |
| IVIČIČ Vojtěch " Mathematica Package for Polynomial Hensel´s Lifting " - from the section: Algebra and geometry and their applications In this paper, an algorithm for lifting of a polynomial h_1(x) in Z_p[x] to h_n(x) in Z_p^n[x] is presented and implemented into a package in computing system Mathematica. A number of examples of usage of the algorithm is included. |
| JANÁK Josef " Fractional Brownian Motion " - from the section: Differential equations, dynamic systems and their applications We introduce the concept of scalar fractional Brownian motion, which is an important stochastic process that does not have Markov property. We also recall the definition of stochastic integral of a deterministic function, where the driving process is the (fBm). We introduce the solution to the linear stochastic differential equation driven by (fBm) which is called the fractional Ornstein-Uhlenbeck process. Based on the ergodic type theorems, an estimator of unknown parameter in the stochastic linear oscillator is proposed. |
| JANÁKOVÁ Hana " Two Level Fuzzy Logic for Distributed System " - from the section: Statistical methods in technical and economic sciences and in practise In the application of mathematical sciences in practice we can still meets with a significant discrepancy. On the one hand there is a great accuracy which is the problem mathematically described. On the other hand, there is the excessive complexity of the facts. This is the necessary for the creation of a number of simplifications but this leads to inaccurate mathematical description. Definition of new non-traditional methods of investigation and preparation methodology of a data collection becomes current implemented in the framework of the survey. Nowadays, using fuzzy logic and obtained data can be found in different organizations and also different fields. Transforming surveys values resp. ambiguous vague concepts into the language form of numbers by using fuzzy logic is a possibility as one is able to make decisions based on the non-numeric information. This raises the possibility described by human judgment and decision making formal mathematical way. |
| JANÁKOVÁ / TOMČÍK Hana/Róber " Fuzzy Logic as a Part of Analytic Hierarchy Process (AHP) " - from the section: Statistical methods in technical and economic sciences and in practise The objective of this paper was to present connection of fuzzy logic and the Analytic Hierarchy Process (AHP). AHP is a multi-criteria decision-making tool that has already been used in almost all the situations related with decision-making. Within the article it was analysed how fuzzy logic and fuzzy system could be applied to evaluate the non-numeric results that are necessary for further decision-making procedures via AHP. Fuzzy logic permits to use linguistic expressions and variables which are transformed to the numbers. This application ensured better decision-making process. |
| JANÁKOVÁ / ZATROCHOVÁ Hana / Mon " The Numerical Methods Used in the Simulation of Economic Processes " - from the section: Statistical methods in technical and economic sciences and in practise Nowadays is a mathematic an integral part of economics. Economical - mathematic methods with IT are becoming increasingly used. Mathematical modelling of economic processes and phenomena takes place gradually in the all sectors. Diversity but also the specificity of individual problems with solving the economic problems by mathematics can be applied as a tool. The need to solve economic challenges and find new solutions still requires the creation of the new procedures and methods. |
| JANCARIK Antonin " Porozumění infinitesimalnímu počtu " - from the section: New trends in mathematical education PRE-SERVICE TEACHERS’ UNDERSTANDING OF INFINITESIMAL CALCULUS The paper presents an analysis of pre-service teachers’ solutions of problems from synthetic geometry in which students were asked to use the basic knowledge of infinitesimal calculus. One of the most serious misconceptions uncovered when analysing the students’ solutions was their misunderstanding of the concept of approach, which is confused with the property of being the nearest element, and also insufficient connection of the concepts of supremum and maximum and deficient ability to apply this relation. |
| JAROŠOVÁ Eva " Process Performance Analysis " - from the section: Statistical methods in technical and economic sciences and in practise The paper deals with quality control and summarizes the steps of performance analysis in the case of an industrial process with varying mean and constant variance. Close attention is paid to the appropriate model identification. Control charts with modified limits, tests of randomness, ARIMA models, tests of normality and Pearson or Johnson curves are used during the analysis. The example of a real industrial process is solved. |
| JELEN Tomasz " Flight Schedule Creating Based on Mathematical Model " - from the section: The article deals with the exact approach convenient for flight schedule creating offering regular airline transportation service. The proposed exact approach is based on linear mathematical model. Out of the specified expected demand linkset the model is designed to select particular subset maximum aircraft fleet utilization. The model results represent optimal connection network at defined time periods. The arithmetical experiments have been carried out on model examples. |
| JELÍNEK Jiří " Application of the Simulation Model of Social Network in Education " - from the section: Modeling and simulation in engineering and scientific computations Social networks are now one of the most studied structures in the area of information and knowledge exchange. Even in the field of education, it is possible to find examples of their formal or informal existence and therefore makes sense to think about their deeper investigation and possible use for understanding the ongoing processes and potentially to support teaching. This contribution shows the application of heuristic multi-agent simulation model of informal social network that exist between students and teacher of the same course, the main purpose of the network is the exchange of knowledge. We will present the particular dynamics of relations development in several model scenarios. |
| JENČURÁKOVÁ Dana " The Statistical Methods for the Management of the Measurement Process " - from the section: Statistical methods in technical and economic sciences and in practise Contribution constitutes the statistical process control of the measurement in the laboratory conditions. Using appropriate statistical methods points to the real state of the measurement process. Presentation of used control charts and other methods highlights the merits of their applications. To supplement the methods with the cumulative sum chart and the Kalman filtering is the consideration on the experience in the regulation of the statistical processes control of the measurement. |
| KALOČÁNY Daniel " The possibilities of effective use of welding processes computation time in numerical simulations by simplifying spatial tasks to planar tasks " - from the section: Modeling and simulation in engineering and scientific computations This paper deals with reducing computation time during numerical simulation of welding processes. Simplification of spatial to planer task causes reduces the number of equations. Welding is defined as a technological process of joining materials by a permanent joint. Specialised software for welding and heat treatment of metals, Visual Weld, was used in the simulations. Visual Weld uses SYSWELD solver, which is based on a finite element method. Keywords: FEM, SYSWELD, welding |
| KASPŘÍKOVÁ Nikola " Calculation of the LTPD Variables Sampling Plans in R Computing Environment " - from the section: Statistical methods in technical and economic sciences and in practise The calculation of the recently proposed LTPD acceptance sampling plans minimizing the mean inspection cost per lot of the process average quality, when the design of the variables sampling plans is based on the exponentially weighted moving average statistic for the known standard deviation case, is addressed. The design of the plans is recalled first. Then the economic efficiency of the plans is discussed and the calculation implemented in an extension package for the R computing environment is shown. |
| KONEČNÁ Petra " Entrance Examination as a Guarantee to Reduce Academic Failurerates and Increase Number of Successful Graduates - Yes Or No? " - from the section: New trends in mathematical education This article reacts to a highly topical issue of the admission procedure process efficiency. Based on the monitoring of the admission procedure strategy, interest in studies and permeation in the first year of study in selected undergraduate Bachelor´s degree programmes, the author has recently been trying to answer the question whether the entrance examination is able to guarantee reduction in academic failure rates and increasing number of successful graduates. The parameters are monitored with respect to mathematical study programmes. |
| KORENOVA Lilla " Digital Technologies in Teaching Mathematics on the Faculty of Education of the Comenius University in Bratislava " - from the section: New trends in mathematical education Digital technologies have made their way not only into our everyday lives, but nowadays they are also commonly used in schools. For future teachers of primary school mathematics, it is important for them to get acknowledged with the possibilities of using these technologies during mathematics lessons. It is also very important to actively use these technologies to achieve effective and active learning in students. In this paper we would like to point out a few examples on how to use technology effectively and their specifications for various topics, teaching methods and forms. |
| KOŤÁTKOVÁ STRÁNSKA Pavla " Data Mining and Analysis of Social Networks and Platforms for Tablets in Europe " - from the section: Statistical methods in technical and economic sciences and in practise Social networks, which have begun to emerge in the last few years, have been rapidly becoming a part of the daily life of people around the world. The number of users for such network grows every year. The number of portable electronic devices, whose major portion consists tables, is now experiencing worldwide growth. The aim of the paper is to introduce the most commonly used social networks and platforms for tablets in Europe, with a focus on the European Union and their analysis. For this purpose, the data-mining technology of K-means for clustering process, correlation and regression analysis will be used. |
| KREJČOVÁ Jana " Analysis of Differences in the Scores of Math Competency Test " - from the section: New trends in mathematical education The paper discusses results of the examinations in mathematics at the College of Polytechnics Jihlava. The aim is focused on the differences between the scores of students of different secondary schools. |
| KREJČOVÁ Jana " Asymptotic Properties of Nonoscillatorysolutions of Neutral Difference Systems " - from the section: Differential equations, dynamic systems and their applications We study nonoscillatory solutions of four-dimensional nonlinear neutral dierence systems. We state asymptotic properties of solutions and we establish su cient conditions for the system to have weak property B. |
| KREMENETSKY Vladislav " Stability of Shallow Mixing Layers With Free Surface and Nonuniform Friction " - from the section: Modeling and simulation in engineering and scientific computations Hydrodynamic stability of shallow mixing layers with free surface is analyzed in the paper. We assume that water depth is different in the main channel and floodplain. The friction coefficient varies in the transverse direction of the flow. Such a situation occurs, for example, in case of floods where resistance force in floodplains and partially vegetated areas is higher than in the main channel. Linear stability problem is solved numerically for different values of the parameters of the problem. It is shown that non-uniform friction stabilizes the flow. In addition, the increase in relative depth in the floodplain also has a stabilizing influence on the flow. |
| KREML Pavel " Is a Large Amount of Study Materials a Benefit? " - from the section: New trends in mathematical education viz. Doležalová |
| KRIVOŇÁKOVÁ Naďa " Logic as a key tool in education " - from the section: New trends in mathematical education Through the years of education in Mediamatics and cultural heritage study program, we had to deal with the perspective questions and set the problems we consider to appear crucial in education of students of humanity-oriented study programs. In this article we highlight the need for critical thinking and logics as key instruments in the logical-mathematical abilities and medial competencies development of students of humanity-oriented-programs. We deliver subjects system (Logics I, Logics II and Argumentation theory) already applied to education process of Faculty of humanity of University of Žilina, Department of Mediamatics and cultural heritage. We highlight the need for logic because of its difference from other sciences by means of fundamentalism of analysed problems. Logic is the only science connecting mathematics, informatics and humanity education. We believe modern logic is only the beginning of the new generation sciences to be asked to combine the science method analytism with the humanity view perception syntheticism. |
| KUBIŠ Milan " Modeling and Synthesis of Control System with Distributed Parameters " - from the section: Modeling and simulation in engineering and scientific computations This article is focused on modeling and design of thermal control of distributed parameters. 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 was simulated control temperature fields of casting mold. Linked softwares 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. |
| LALATTA COSTERBOSA Cecilia " The Smart Greenhouse " - from the section: Mathematics and art The Smart Greenhouse project started from the Parametric Hybrid Wall, presented at Aplimat conference in 2014. You can call Smart a greenhouse when its architectural structure and its the materials lead to improved performances and management of indoor natural conditions. As for the architectural side, the Smart Greenhouse takes advantages of a Responsive Surface that is an architecture able to model its own shape in relation to contextual specific impulses. Regarding the sustainable environment, the structure operates on the irrigation systems making the most use of the materials’ polarization. |
| LANGEROVÁ Martina " On Some Semilinear Resonance Problems on Bounded Domain " - from the section: Differential equations, dynamic systems and their applications In this contribution we consider the semilinear problem at resonance. We introduce rather general sufficient condition of Landesman-Lazer type for the existence of a solution in terms of the asymptotic properties of nonlinearity. This condition not only generalizes the classical Landesman-Lazer condition but also implies the existence results for problems with vanishing and oscillating nonlinearities. The research is a joint work with Pavel Drábek. |
| LEJA Jozef " Calculations of the Properties of Atomic Nuclei " - from the section: Modeling and simulation in engineering and scientific computations The paper deals with the calculations of the binding energies of atomic nuclei. The calculations have been performed in the framework of the relativistic mean-field theory. The results obtained for magnesium and silicon isotopes are presented and compared with experimental data. |
| LORENZ Filip " Network Synchronization of Discreet Transport Processes Using a Simulation Model " - from the section: Modeling and simulation in engineering and scientific computations The article deals with the creation of a simulation model which serves to create the coordination bonds between three discreet transport processes. The simulation model was created in the software Witness 2008. The verification and validation of the simulation model was performed using the data obtained from real traffic. The experiment was carried out with a valid model, which allowed the solutions used to create the coordination bonds between particular transport processes. |
| LORENZI Marcella G " Exploring Expo Geometric Exploits " - from the section: Mathematics and art International world fairs are temporary events in which world countries show themselves in a relative narrow space, in buildings constructed on purpose, usually following the main theme of the exposition. These temporary buildings, by their very ephemeral essence, transient, of rapid construction and consumption, express summarily the image of the historical present through a representation of progress and modernity, using the geometry as a means of symbolic abstraction and as materialization of "aesthetic" choices. The different nations participate to the world fairs in order to show their best characteristics, often coinciding with the achievements in the various fields of knowledge, by giving to the architects the task of representing that with amazing pavilions, exploits of imagery and manufacturing competency. From time to time those buildings, became urban icons. Starting from an historical introduction of some of the most famous and relevant, from a geometric point of view, pavilions, we will explore the last world fair architecture. Expo 2015 was held in Milan, Italy, from May 1st to October 31st, 2015, and its main theme was Food for the planet. Although it is noticeable, in this expo just ended, that geometries represent mainly the configuration of the exteriors, some pavilions occur anyway as objects for which the search for the form is addressed starting from strong geometric figures. It may be noted that in some cases the volumes and in others the surfaces determine the external images of the pavilions and in some cases also the character of the interior. We will examine only some of the pavilions - it would occur a book to deal with all – exploring the geometric exploits of this edition of the world fairs. |
| LÖSTER Tomáš " Modification of the Algorithm for 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 that aims to classification of objects into groups called clusters. In the current scientific literature, there are many cluster analysis methods that are used to classify objects into clusters. The aim of this article is to evaluate selected coefficients to determine the optimal number of clusters on real data sets and propose a new algorithm to determine the number of clusters, which aim is to increase the success rate in determining the optimal number of clusters. This algorithm is based on fuzzy clustering. |
| MAGNAGHI DELFINO Paola " Alessandro Mazzucotelli: An Artistic and Educational Project " - from the section: Mathematics and art The authors of the present paper are engaged in interdisciplinary research initiatives of the Effediesse Laboratory of the Politecnico di Milano and, in particular, they are interested to “contamination” projects between scientific thoughts and artistic insights. The mathematical knowledge is applied in drawings with the use of symmetry or the choice of lines and shapes. It is well known that Mathematics plays a very important role from a cultural point of view in the modern world and the students realize that Mathematics is also a powerful tool, rather than being a closed discipline. Mathematical concepts connect new ideas to other ideas learned previously or in other educational experiences, helping to learn concepts used in other disciplines. Within the study of such a context, arises our educational project as a collaboration between the FDS Laboratory and the teachers and students of the fourth class of the high school “Liceo Classico e Linguistico Daniele Crespi” - Busto Arsizio (Lombardy) and the artist and mathematician Adriana Contarini. The project concerns the activity of the artist Alessandro Mazzucotelli, which produced many significant works in Lombardy and, in particular, in Milan and Busto Arsizio, in Art Nouveau style. Look away, see close. The title of the book of a famous art critic can represent the significance of this work. We chose this specific argument because the students could find Mazzucotelli’s artworks in their town and we learned to see it from a different point of view and discover a new approach to the mathematical topics. We chose a “minor” art and an artist, Alessandro Mazzucotelli, because the students could see his artworks in their town or in Milan and we learned to see it from a different point of view and discover a new approach to the mathematical topics. Mazzucotelli was also a great exponent of the arts and crafts that developed both artistically and economically in Lombardy and still survives to the present day, even in Busto Arsizio. The project involved three step. In the first step the students of the whole class were introduced to the study of geometric transformations and, in particular, of symmetry, through lessons that we kept at Politecnico di Milano. Students shared the general thrust of the work and they were divided into three groups. The implementation of our proposal required to the students and the two teachers of mathematics and art make an effort from many points of view. For the subscription of the students in the three groups we divided, we considered their aptitudes and preferences. The first group dedicated to the search of bibliographic sources and documents and created a poster design in Art Nouveau Style, inspired to artworks of Mucha; the second group organized visits to the artworks in Busto Arsizio and in Milan and created a rose window’s design in Art Nouveau Style, inspired to the unique similar artwork of Mazzucotelli. The documental research, in particular that concern the Mazzucotelli’s activity in ISIA, and the organization of the visit in Milan required abilities not usually employed in our schools. The third group planned and performed a print artwork, inspired by the Mazzucotelli’s, at the atelier of Adriana Contarini. The students of this group had a very interesting experience about symmetry, using an etching press. The first step of the students’ work was the choice of the pattern; the students chose a floral pattern with spirals similar to the Mazzucotelli’s design. The students’ choice was justified by the Mazzucotelli’s research of new formal solutions during the period 1902 – 1908. In this years, Mazzucotelli combined floral and zoomorphic elements with abstract structures. In the second step, after the choice of the design project, the students created the matrix or better the module-matrix in plastic material. The students composed the module-matrix, using the two parts together but in different positions related the place occupied in the design project. The colouring was the most important moment and required greater attention to design project. When they colorized the module-matrix, they must always remember that the matrix and the work on paper are like a mirror, so was necessary prepare and colorize the side of the surface that in the mirror symmetry appeared. They colourized the flower (yellow or blue) and the spiral (blue or red) separately using acrylic colours and then they interlaced the two parts. To get the final artwork, the students used the module-matrix four times in four different positions but during the work the sheet of paper was stopped by the roll of the etching press. Obviously the students could change the module-matrix in realizing other artworks and indeed they obtained two different final results. Each group of students worked very well and at the end of the project they shared with all the students of their high school their experience. They show the result of the cooperation of the three groups in an exhibition in “Liceo Daniele Crespi”. Key words. Art Nouveau, Geometry, Transformations, Alessandro Mazzucotelli, Wrought Iron Mathematics Subject Classification: AMS_97M80 Current address Paola MAGNAGHI-DELFINO, Researcher Dipartimento di Matematica, Politecnico di Milano, piazza Leonardo da Vinci 32, 20133 Milano (MI), Italy – tel. +390223994515 - paola.magnaghi@polimi.it Tullia NORANDO, Assistant Professor Dipartimento di Matematica, Politecnico di Milano, piazza Leonardo da Vinci 32, 20133 Milano (MI), Italy – tel. +390223994533 - tullia.norando@polimi.it |
| MALÁ Ivana " On the residual duration of unemployment in the Czech Republic based on finite mixture of lognormal distributions " - from the section: Statistical methods in technical and economic sciences and in practise Unemployment is often used as a measure of the health of the economy and usually the unemployment rate or unemployment duration are used. In the text finite mixtures of lognormal distributions are fitted into interval censored data for the Czech households in 2011 and 2014. The distributions of residual unemployment are analysed through the mean and median residual unemployment duration and compared for both analysed years. All computations are made in R program. |
| MAREK Jaroslav " Investment Funds – Estimation of Appreciation " - from the section: Financial and actuary mathematics The decision to purchase investment fund may be facilitated by the knowledge of appreciation estimate. Funds managed by the investment company ČSOB based on the historical data of DJA are analyzed in this paper. The aim of this paper is to warn about a fact, that future appreciation is greatly influenced by fund rules. Important factors of this analysis are the methods for determining the initial and final prices of fund and investor participation in profit. |
| MARIN Marin " The Initial Boundary Value Problem for Porous Bodies " - from the section: Differential equations, dynamic systems and their applications First, we put down the basic equations and conditions that govern the behavior of porous bodies. Then, by means of some results from theory of equations of evolution we approach the existence and uniqueness of solution for the mixed problem. In the same manner, the continuous dependence of solutions upon initial data and supply terms is also proved. |
| MATVEJEVS Andrejs " CARKOVS Jevgenijs, MATVEJEVS Andrejs: Stochastic Stability Of Pipeline Induced By Pulsed Fluid Flow " - from the section: Differential equations, dynamic systems and their applications The paper deals with linearized partial diferential equation for analysis of the transverse oscillations of a pipeline section under an action of pulse fl uid flow. Assuming the mathematical model of fl uid-caused longitudinal force in cosine form with the Brownian phase and applying the stochastic modifi cation of the second Lyapunov method we analyze a phase variance affect the pipeline section stability. |
| MELE Giampiero " Geometrical Analysis for Lecce’s Roman Theatre and Amphitheatre Drawing " - from the section: Mathematics and art The signs of the Romans in the city of Lupiae, currently Lecce, are many and among them the most noteworthy is the Roman Theatre. The monument has been accidentally discovered during the excavations for the foundations of a house in 1929 and it is located at a short distance from another landmark of the Roman Lecce: the amphitheatre. The plan of the theater seems set to a nine-sided polygon, which is not common, and that involves many difficulties on a practical level, in relation to draw architecture plans baased on polygon although known since the antiquity, can not be drawn with a ruler and compass without approximation. The paper presents an approximate construction of the nonagon respect to a considerable simplicity to draw it in a way that makes feasible even the use of this polygon to construct the plan of a real building. The chance of utilizing the latest threedimensional technology for the detection of the ruins was an opportunity to study the model of the obtained survey and to compare the surveyed plans with the instructions in “De Architectura” by Vitruvius. It shows a particular use of the nonagon for the design of its iconography. Moreover the analysis of the second monument, the amphitheatre, was an opportunity to master on its oval construaction in plan Here we propose a reasoning based on the perimeter of the outer oval of the amphitheater. Proceeding out of successive approximations we achieve the measures of the span of the external arches, of the cavea and of the bleachers. The oval drawn starting from the square is particularly useful in order to simplify the calculation of the perimeter of the building. The emerging solution is that one leading the caput magister operis to adopt integers by successive approximations This study aims to compare the hypothesis obtained from the analysis of the metrological survey with the rules explained in the work of Vitruvio to underline similarities and differences between theory and practice. It also aims to present how the geometry, with its forms, and the arithmetic, with calculus and approximations, contribute to the definition of the measures of the drawing in plan of two of the most common types of Roman buildings at the time of the empire. |
| MINCULETE Nicusor " About the Bounds of Several Statistical Indicators " - from the section: Statistical methods in technical and economic sciences and in practise In this paper we present some properties of bounds of the variance, the standard deviation, the coefficient of variation and of the covariance related to discrete random variables in finite case. |
| MISKOLCZI Martina " Multistate Life Tables and Projection with Four-Attributes (Gender, Age, Education Level, Marital Status) – Methodology " - from the section: Statistical methods in technical and economic sciences and in practise The article introduced methodology of multistate life tables and multistate projection for four attributes – gender, age, education level and marital status. Before estimating particular transition probabilities and calculate projection for the case of the Czech Republic, it is necessary to identify the most crucial and relevant issues that need to be described and solved in order to achieve outcomes of the high quality. Mainly, it is the problem of "normalization" each year calculation when applying specific rates that represent trends in fertility, mortality, marriage, divorce, imigration, emmigration and education. |
| MORAOVÁ Hana " Rysy situace vhodné pro výuku matematiky metodou CLIL (Content and Language Integrated Learning) " - from the section: New trends in mathematical education The paper focuses on teaching mathematics through CLIL (Content and Language Integrated Learning), a method growing importance in the increasingly global world. In the theoretical part the authors discuss the famous four Cs’ of CLIL and try to link it to Brousseau’s Theory of Didactical Situations looking for the properties of a well developed CLIL lesson in both perspectives. In the following part they propose types of tasks, problems and lessons that can be used when teaching mathematics through CLIL. They also analyse problems posed by future teachers in compulsory CLIL seminar and show their strengths, potential and possible shortcomings. The paper is of importance to math educators as well as pre- and in-service teachers as it shows how to use the CLIL method efficiently and for the benefit of learners. |
| MOŠNA František " Graphs in Everyday Life " - from the section: Algebra and geometry and their applications Applications of mathematics seem to be very efficient tool for improvement of pupils´ attitude to this subject. In the paper, two simple examples using graph theory are offered. The first one shows the application of graph theory for putting up a schedule at school. The second one concerns one card game. Problem solving of such tasks from every-day life can motivate the students and attract them to mathematics. |
| NAŠTICKÁ Zuzana " Blending Experiential Mathematics Learning and Clil to Teach Fundamentals of Orthographic Projections " - from the section: New trends in mathematical education Various non-traditional educational approaches have become popular in mathematics classes, such as Experiential Learning (EL), useful in vocational schools, and Content and Language Integrated Learning (CLIL) in bilingual classes. In this paper we present an analysis of three identical lessons with altogether 59 secondary comprehensive school students in which both EL and CLIL were used for teaching fundamentals of multiview orthographic projections. The paper summarizes results of content analysis of student drawings and related statistical analysis of student errors in the drawings. |
| NEHÉZ Martin " Analysis of the Randomized Algorithm for Clique Problems " - from the section: In this paper, we address two modifications of the clique problem: the Maximum Clique Problem and the k-Clique Problem, respectively. We provide a simple randomized algorithm whose modifications are able to solve both of the above problems. The essential part of this paper contains a probabilistic analysis of the algorithm. Moreover, its behavior is compared to other known algorithms and its overall performance is discussed. |
| NORANDO Tullia " Alessandro Mazzucotelli: An Artistic and Educational Project " - from the section: Mathematics and art The authors of the present paper are engaged in interdisciplinary research initiatives of the Effediesse Laboratory of the Politecnico di Milano and, in particular, they are interested to “contamination” projects between scientific thoughts and artistic insights. The mathematical knowledge is applied in drawings with the use of symmetry or the choice of lines and shapes. It is well known that Mathematics plays a very important role from a cultural point of view in the modern world and the students realize that Mathematics is also a powerful tool, rather than being a closed discipline. Mathematical concepts connect new ideas to other ideas learned previously or in other educational experiences, helping to learn concepts used in other disciplines. Within the study of such a context, arises our educational project as a collaboration between the FDS Laboratory and the teachers and students of the fourth class of the high school “Liceo Classico e Linguistico Daniele Crespi” - Busto Arsizio (Lombardy) and the artist and mathematician Adriana Contarini. The project concerns the activity of the artist Alessandro Mazzucotelli, which produced many significant works in Lombardy and, in particular, in Milan and Busto Arsizio, in Art Nouveau style. Look away, see close. The title of the book of a famous art critic can represent the significance of this work. We chose this specific argument because the students could find Mazzucotelli’s artworks in their town and we learned to see it from a different point of view and discover a new approach to the mathematical topics. We chose a “minor” art and an artist, Alessandro Mazzucotelli, because the students could see his artworks in their town or in Milan and we learned to see it from a different point of view and discover a new approach to the mathematical topics. Mazzucotelli was also a great exponent of the arts and crafts that developed both artistically and economically in Lombardy and still survives to the present day, even in Busto Arsizio. The project involved three step. In the first step the students of the whole class were introduced to the study of geometric transformations and, in particular, of symmetry, through lessons that we kept at Politecnico di Milano. Students shared the general thrust of the work and they were divided into three groups. The implementation of our proposal required to the students and the two teachers of mathematics and art make an effort from many points of view. For the subscription of the students in the three groups we divided, we considered their aptitudes and preferences. The first group dedicated to the search of bibliographic sources and documents and created a poster design in Art Nouveau Style, inspired to artworks of Mucha; the second group organized visits to the artworks in Busto Arsizio and in Milan and created a rose window’s design in Art Nouveau Style, inspired to the unique similar artwork of Mazzucotelli. The documental research, in particular that concern the Mazzucotelli’s activity in ISIA, and the organization of the visit in Milan required abilities not usually employed in our schools. The third group planned and performed a print artwork, inspired by the Mazzucotelli’s, at the atelier of Adriana Contarini. The students of this group had a very interesting experience about symmetry, using an etching press. The first step of the students’ work was the choice of the pattern; the students chose a floral pattern with spirals similar to the Mazzucotelli’s design. The students’ choice was justified by the Mazzucotelli’s research of new formal solutions during the period 1902 – 1908. In this years, Mazzucotelli combined floral and zoomorphic elements with abstract structures. In the second step, after the choice of the design project, the students created the matrix or better the module-matrix in plastic material. The students composed the module-matrix, using the two parts together but in different positions related the place occupied in the design project. The colouring was the most important moment and required greater attention to design project. When they colorized the module-matrix, they must always remember that the matrix and the work on paper are like a mirror, so was necessary prepare and colorize the side of the surface that in the mirror symmetry appeared. They colourized the flower (yellow or blue) and the spiral (blue or red) separately using acrylic colours and then they interlaced the two parts. To get the final artwork, the students used the module-matrix four times in four different positions but during the work the sheet of paper was stopped by the roll of the etching press. Obviously the students could change the module-matrix in realizing other artworks and indeed they obtained two different final results. Each group of students worked very well and at the end of the project they shared with all the students of their high school their experience. They show the result of the cooperation of the three groups in an exhibition in “Liceo Daniele Crespi”. Key words. Art Nouveau, Geometry, Transformations, Alessandro Mazzucotelli, Wrought Iron Mathematics Subject Classification: AMS_97M80 Current address Paola MAGNAGHI-DELFINO, Researcher Dipartimento di Matematica, Politecnico di Milano, piazza Leonardo da Vinci 32, 20133 Milano (MI), Italy – tel. +390223994515 - paola.magnaghi@polimi.it Tullia NORANDO, Assistant Professor Dipartimento di Matematica, Politecnico di Milano, piazza Leonardo da Vinci 32, 20133 Milano (MI), Italy – tel. +390223994533 - tullia.norando@polimi.it |
| NOVOTNÁ Jarmila " STEM a projektové vyučování " - from the section: New trends in mathematical education The paper focuses on the use of projects in STEM education. The paper first introduces inquiry-based learning and project-based education. Then the authors present a detailed classification of projects in school education. This classification comes out of classification of projects in general and of characteristics of STEM. Four main areas are identified as essential for assessment and classification of STEM projects. The proposed classification will be used in research of implementation of project-based education as one of the efficient methods of STEM education. |
| PAUN Marius " On Holomorphic Vector Pseudo-Fields on Affine Complex Bundles " - from the section: Algebra and geometry and their applications In this talk we consider affine holomorphic bundle and we define and discuss the holomorphic vector pseudo-fields on it. More exactly, starting from a given holomorphic vector pseudo-field $Gamma$ on a holomorphic affine bundle $E$ over a complex manifold $M$ we construct an induced holomorphic vector pseudo-field $Gamma^prime$ on a holomorphic affine bundle $E^prime$ over $E$. |
| PAVLENKO Oksana " CARKOVS Jevge nijs and PAVLENKO Oksana: On Reducibilty of the Covariancesemigroup for Markov Linear Dynamical Systems by 2-Moment Lyapunov Spectrumsubspace " - from the section: Differential equations, dynamic systems and their applications The paper deals with impulse linear dynamical system composed of linear differential and difference equations with coe fficients analytically dependent on small positive parameter and homogeneous ergodic Poison type process. We construct such the basis in the space of constant matrices that permits to reduce the above semigroup to matrix exponent and prove that the mean square Lyapunov spectrum for the initial system consists of the Lyapunov spectrum for this exponent. |
| PILOUS Derek " Critical Problems in 2015 Entrance Exams at Faculty of Education, Charles University in Prague " - from the section: New trends in mathematical education Results of college entrance exam multiple-choice type mathematical test are interpreted using knowledge of frequent mistakes made by first-year students. |
| PIVOŇKA Tomáš " Title Rationality and the Link with Permanent Income Theory " - from the section: Statistical methods in technical and economic sciences and in practise Rational choice and consumer behaviour mean how consumers balance their selection of goods and services to achieve their object of interest and satisfy their needs. Submitted paper compares theories of consumer`s rationality and deals with the rationality and permanent income theory in the Visegrad Countries. Data were selected from the Eurostat Database that collects information from EU-SILC. Another aim of the paper is to present the development of mean and median income in the Czech Republic. Examining rationality from the view of income is very important, because the level of income affects the level of affordable goods and services. Keywords: Rationality, Permanent income, Visegrad Countries |
| POLCEROVÁ Marie " New approach to teaching of differential equations in application tasks " - from the section: New trends in mathematical education This contribution deals with a new approach to teaching how to solve application tasks from physical chemistry and chemical engineering in computer aided teaching of mathematics at Faculty of Chemistry of the Brno University of Technology. These application tasks require solving separable and first order differential equations. The contribution focuses on method of teaching of the solution which has to be used by students while solving individually assigned task, evaluation of these tasks and experience gained. |
| POLEC Jaroslav " Fuzzy Segmentation for Texture Aware Image Error Concealment " - from the section: Algebra and geometry and their applications We propose a fast technique for concealment of transmission errors in images. Corrupted regions are restored by texture extrapolation from the surrounding regions logically associated through image segmentation. Hardly segmentable parts of the image with unsharp edges or gradients are the main problem producing artefacts in the result. Therefore, we propose to use a fuzzy segmentation where segments include soft edges and are allowed to overlap. |
| POTŮČEK Radovan " The sum of the series of reciprocals of the quadratic polynomials with double non-positive integer root " - from the section: Modeling and simulation in engineering and scientific computations This contribution, which is a follow-up to author´s paper dealing with the sums of the series of reciprocals of some quadratic polynomials, deals with the series of reciprocals of the quadratic polynomials with double non-positive integer root. The formula for the sum of this kind of series expressed by means of harmonic numbers are derived and verified by several examples evaluated using the basic programming language of the computer algebra system Maple 16. There are stated two another formulas using an improper integral and generalized harmonic numbers, too. This contribution can be an inspiration for teachers of mathematics who are teaching the topic Infinite series or as a subject matter for work with talented students. |
| POZDÍLKOVÁ Alena " Data Mining and Analysis of Social Networks and Platforms for Tablets in Europe " - from the section: Statistical methods in technical and economic sciences and in practise Social networks, which have begun to emerge in the last few years, have been rapidly becoming a part of the daily life of people around the world. The number of users for such network grows every year. The number of portable electronic devices, whose major portion consists tables, is now experiencing worldwide growth. The aim of the paper is to introduce the most commonly used social networks and platforms for tablets in Europe, with a focus on the European Union and their analysis. For this purpose, the data-mining technology of K-means for clustering process, correlation and regression analysis will be used. |
| RICHTÁRIKOVÁ Daniela " Supporting Methods in Mathematics Effectiveness of Mathematics Workshops " - from the section: New trends in mathematical education The paper presents overview of supporting methods in Mathematics facilitating the transition of high school graduates to technical university studies, which have been introduced at Faculty of Mechanical Engineering STU in Bratislava during the last 25 years. The special consideration is given to Mathematics Workshops, originally proposed at our department, and to the results of pedagogical research applied in the process of introducing this authentic supportive form of education. |
| RICHTÁRIKOVÁ Daniela " Present and Futureo Geometry / International Slovak – Czech Conference on Geometry and Graphics " - from the section: Algebra and geometry and their applications The paper presents the information about Visegrad fund project facilitating meeting of researchers and teachers from different European universities, secondary schools, and research institutions who discussed development, current situation, and new trends in Geometry and Graphics in research and education at the International Conference on Geometry and Graphics held in September 2015 in Slovak Republic. |
| RIEČANOVÁ Izabela " Rigid piston simulations of acoustic space based on Finite volume method " - from the section: Modeling and simulation in engineering and scientific computations The main goal of the paper is to contribute to the area of acoustical simulations. Authors deal with the approach of numerical methods, particularly the Finite volume method. The boundary conditions used are of Robin type, and they include rigid piston on one side of the domain, and changing boundary conditions on other sides. Further the numerical solution of one case is compared with the analytical one. Joined work with Angela Handlovičová and Nicolaas Bernardus Roozen |
| RIHOVA Elena " On parametric method to estimate the optional number of clusters " - from the section: Statistical methods in technical and economic sciences and in practise Nowadays there are many fuzzy clustering algorithms. One of their fundamental and yet satisfactorily unsolved problem is to determine the optimal number of clusters, which has a deterministic effect on the clustering results. In this paper, factors determining the number of clusters in the existing fuzzy clustering are researched and their advantages and disadvantages are examined. We analyze behavior of two types of coefficient for determining the proper number of clusters (the first one is a silhouette statistic and the second one is a statistic based on membership degrees) and design a modification. |
| RUMANOVÁ Lucia " Fostering Creativity in Geometry Through the Lesson Problem with Using Communication in Classroom " - from the section: New trends in mathematical education In the school is a lot of creative students who are able to combine their knowledge, imagination and inspiration in a problem solving. The creativity in their solutions is evident when they have an opportunity to find and use their own solving methods. The paper presents results of an activity which was focused on the creativity and also on a communication in the geometry. |
| RUSEK Martin " Chemical Calculations: A Neccessary Evil or an Important Part of Chemistry Education? " - from the section: The biggest STEM intersection between Chemistry and Mathematics lies in chemical calculations. Despite calculations in elementary and secondary school Chemistry are mostly based on elementary mathematic principles and they are also a part of word problems in Mathematics lessons, students usually struggle with them. In some schools, the calculations also serve as a good testing tool since correcting such student works is quite easy for a teacher. This paper is based on a questionnaire survey focused on students’ attitudes towards chemical calculations. The survey was conducted at the beginning of a new school year in 2012, therefore the results show these students’ attitudes in the form they were created at elementary schools. Following a general questionnaire about students’ attitudes towards Chemistry, a list of Chemistry topics from a Chemistry textbook following the general chemical curriculum of the Czech Republic was used. Students’ attitudes towards the topic of chemical calculations were regarded as its importance, difficulty and the amount of time spent on the topic in education. Out the last two the motivational potential has been calculated as a product of the students given difficulty and the amount of time given to the topic. These were measured separately for the particular topics with the use of a four-point Likert scale e.g. the most difficult, difficult, simple, very simple. The students (N=595) have been chosen randomly from all secondary schools in the Middle-bohemian region. First, five schools from these categories have been chosen: grammar school, lyceum, chemistry-oriented vocational school, non-chemistry oriented vocational school, apprentice school. Second, one class of first grade students has been selected from these groups (study programmes) for the questionnaire survey. Statistically significant difference among groups of these students based on the type of secondary school they attend were found. The students, overall describe the topic as difficult and demotivating. Only chemistry-oriented school students consider the topic important, the rest of the students unimportant. Grammar school students are the only ones who identify the motivational potential slightly positive, the rest of the students slightly (or) negative. The authors of the paper argue that not only incomprehensibility of calculations but also the students’ inability to think about the problems from interdisciplinary point of view play a vital role. Also the practicalness (measure as perceived importance) of the topic is being discussed. Some authors focusing on this problem suggest a change of the word problem into more meaningful. Here, however, they introduce proposals of seemingly practical problems which are also impractical as sweetness of tea or salinity of water for cooking pasta is a matter of spoons into water and not percentage. Such problems only pretend to be practical. Another approach of authors trying to support students in learning chemical calculations aims at particular problems according to their complexity. From this reason also the mathematical knowledge point of view is taken into account in this paper. At the end, the authors argue that the position as well as conception of chemical calculations as a school topic needs to be reconsidered in order not to deepen students negative attitudes towards Chemistry. |
| SALVADORI Anna " Mirrors, Lens and Megic Effectsmathematics to Discover the Real Life " - from the section: New trends in mathematical education Mathematics&Real life in a national project of the Department of Mathematics and Informatics of the University of Perugia, which promotes the interaction between real world and Mathematics as a driver for didactical innovation. We present here the journey of light ([1-5]) as a prototype of didactical approach which combines mathematical knowledge and skills with the understanding of natural phenomena, the evolution of history and scientific thought and modern technology. |
| SAMKOVÁ Libuše " Developing views of proof of future primary school teachers " - from the section: New trends in mathematical education In our contribution we focus on the possibility to develop views of proof of future primary school teachers during a university course on arithmetic conducted in inquiry-based manner. We present our classroom interventions aiming to route future primary school teachers towards secure methods of validation and non-empirical argumentation. |
| SIVÝ Július " Crystal, Molecular and Electronic Structure of N,N-bis(4-Methylphenyl) Malonamide Hemihydrate " - from the section: SIVÝ Július, (SK), VRÁBEL Viktor, (SK), KRÁLIK Marián, (SK), GOWDA Thimme B., (IND): In the structure of the title compound, C17H18N2O2 • 0.5H2O, the two aromatic rings form a dihedral angle of 89.4 (4)°. Each amide group is almost coplanar with the adjacent phenyl ring, making dihedral angles of 5.2 (6)° and 4.9 (6)°. The water molecule lies on a twofold rotation axis. In the crystal, intermolecular N–H・・・O and O–H・・・O hydrogen bonds link the molecules into a three-dimensional network. Calculation of the NBO analyses (DFT/B3LYP/6-311G) were performed. |
| SLAVÍK Antonín " Mixing Problems with Many Tanks and other Diffusion-Type Equations " - from the section: Differential equations, dynamic systems and their applications In the first part of the talk, we revisit the classical calculus problem of describing the flow of a chemical in a system of tanks connected by pipes. For various configurations involving an arbitrary number of tanks, we show that the corresponding linear system of differential equations can be solved analytically. We also analyze the asymptotic behavior of solutions for a general closed system of tanks. The topic is accessible to undergraduate students and displays a nice interplay between differential equations, linear algebra, and graph theory. In some cases, the system of equations that arises from the above-mentioned mixing problem corresponds to the spatial discretization of the one-dimensional diffusion equation. In the second part of the talk, we provide a survey of a recent research on dynamic diffusion-type equations with discrete space and continuous, discrete, or mixed time. Discrete-space equations are interesting from the viewpoint of numerical mathematics, but also show up directly in applications. The results that will be presented were obtained in collaboration with Petr Stehlík (University of West Bohemia, Pilsen). |
| SMETANOVÁ Dana " On Lepagean Equivalents and Multisymplectic Forms " - from the section: Algebra and geometry and their applications The paper is devoted the case of the Lepagean and the multisymplectic forms whose coming from first order Lagrangian. Contrary to standard aproach we find new class of multisymplectic forms which depends not only given Lagrangian but ``free' functions. This problem is usefull in variational theories and physical problems. |
| SOTAK Vladimir " Innovative Trends in Education of Safety Specialists at Selected Higher Schools " - from the section: Statistical methods in technical and economic sciences and in practise In this contribution we present the design of a new educational model in the area of Occupational Safety and Health (OSH) while taking into consideration specifications of the abovementioned field. Efficiency of the newly proposed approach in the preparation of future safety specialists was also experimentally verified. The outcomes of our experiment were evaluated via non-parametrical statistical methods. The research was taking place between 2011-2014 and its aim was to propose an optimal model of education in the OSH area through the analysis of current state in the field. |
| SZARVAS Martin " FEA analysis of epoxy granite structure based on image processing using Matlab " - from the section: Modeling and simulation in engineering and scientific computations The applied algorithm developed in MatLab using Image Processing Toolbox was used to determine mechanical behavior of epoxy granite (polymer concrete) microstructure. Numerical simulation based on processed digital image with classified objects for different material models utilizes automatic finite element mesh generator. Boundary and initial conditions for finite element analysis have been applied according to past laboratory measurement conditions. |
| TALHOFER Václav " Verification Tests of Mathematical Model of Passage Through Terrain " - from the section: Modeling and simulation in engineering and scientific computations At conference APLIMAT 2015, the authors of this paper presented a mathematical model for assessment of possibility of passage through terrain for military vehicles. This model was based on the physical model of passage through terrain, in which behavior of vehicles on terrain obstacles is described and verified. Based on this behavior, a complex physical model of movement of vehicles in real terrain was developed. The said publication described the creation of a mathematical and information model. In 2014 the research team of “Development of expert workplace focused on the analysis of impact of environment to activities of military forces” project, solved at University of Defense in Brno, realized first complex verification of the model in practical tests in real terrain. The aim of the tests was to verify complex behavior of the whole model in a real environment, in which units of the Czech Army are or can be located. The basic aim of the tests was primarily to find out, to which extent the modelling results with the help of the above-mentioned physical, mathematical and information models are usable in the real deployment in decision-making processes in the systems of commanding and controlling (C2I). The basic aim was completed with several secondary aims that were supposed to specify partial coefficients of drivers` general abilities and their skills to drive in difficult conditions at night, as well as further specify the coefficient of meteorological conditions. The aim was also the quality check of the underlying geographic data with the help of independent terrain measuring. |
| TEICHMANN Dušan " A Model for Design of Public Transport Network with Predefined Route Headways " - from the section: Modeling and simulation in engineering and scientific computations The presented article deals with the problem of planning public transport networks. The problem is solved by means of linear programming methods. Results got by solving the original mathematical models often require consequent corrections in order to put the results in practice. Problems may arise if we want to keep regular headways on a route (time intervals between the consecutive connections of the route). The headway can be calculated on the basis of the cycle time of the route and the number of the vehicles that are assigned to the route. The presented model differs in the fact that the model takes into account only feasible values of the headway on the route. Vehicles are allocated according to the feasible headways; their values are predetermined. The total number of the vehicles assigned to the routes forms the optimization criterion. The model is created for transport companies having a heterogeneous vehicle fleet. The heterogeneous vehicle fleet is the fleet consisting of different kinds of the vehicles (for example buses and trams). Moreover, individual vehicles of the same kind can differ in their capacity. The presented mathematical model takes into account both of these facts. |
| TORRE Matteo " WHICH WAS BORN FIRST, ART OR SCIENCE? FROM ROCK PAINTINGS TO FEYNMAN DIAGRAMS " - from the section: Mathematics and art The birth of science and art is hard to define by a date or a specific event, but since the beginning of civilization these two creative activities of man are closely linked. Art has always used scientific achievements, think of the rock paintings or the subsequent alchemical technics used to produce pigments, science since the XIX century has influenced the artists who, through their works, have contributed to science. |
| TURŇA Ľubomír " Manifestation of Memory Properties and Selective and Dynamic Behaviorof the Technical and Social Environment " - from the section: Differential equations, dynamic systems and their applications This paper focuses on the analysis of two problems: enviroment depletion and impact of enclosed options environment. Any activity in any environment or device, the environment changes, even impaired, whether it wears direct abrasive manner or possibly saturation of options owning to loss or exhaust consumed, by its limitations in capacity, often produces waste and changes the environment. The environment maintains changes of a their properties as a result of these processes store in its "memory", as a result of something changing its quality and thus able to use the surroundings. The contribution aims to analyze on a simple model of the process and determine the conditions change of environment characteristics using the parameter of the model. Results of the analysis of biological species coexistence in their various relationships, such as cooperation, competition, antinomy are within mathematical ecology known for almost a century. The same mathematical apparatus of evolution equations, but the complexity of nonlinear dynamical systems, within the synergistic approach used for monitoring the coexistence of inanimate entities, for example: in particle physics theories, in the behavior of gases and thermodynamics, quantum generator, in the theory of management and so on. The contribution follows the use of mathematical tools, for example: in the area of information technology, eventually and the analysis of interacting stakeholders and groups in the socio-economic environment. |
| VAGASKÁ Alena " The Application of Mathematical and Statistical Methods in Technical Practice " - from the section: Statistical methods in technical and economic sciences and in practise The paper deals with the application of mathematical and statistical methods to identify and analyse factors acting during the process of aluminium anodic oxidation at defined current density of 1 Adm-2. The influence of input chemical and physical factors and their interaction on the resulting layer thickness has been investigated in order to determine the theoretical speed of layer creation. Based on the Design of Experiments methodology the set of 26 experimental runs was carried out, data were analysed and prediction model was developed. |
| VALLO Dušan " Using Geometry Software GeoGebra in Solution of Stereometric Problem " - from the section: New trends in mathematical education In this paper we concerned with didactical aspects of mathematical teaching via dynamic geometry software support. Our findings are based in the theory of didactical constructivism and there are demostated at a sample of the solution of the real-life problem. |
| VARGA Marek " Multiple proofs " - from the section: In mathematics as a science proofs play an irreplaceable role – they serve for verification of our propositions. In school mathematics proofs fulfil several other functions – deeper explanation of theorems, deduction of formulas, development of thinking and problem-solving strategies etc. We believe that it is not right to lessen the amount of proofs in school mathematics. Quite the contrary, learners should be exposed to multiple proofs of single propositions so that they can choose the most comprehensible for them. In this paper we demonstrate the idea through computation of the limit of sequence . |
| VARGOVÁ Michaela " Visualization of Functions of Two Variables by Anaglyphs " - from the section: New trends in mathematical education Paper presented practical examples of utilising anaglyphic projection in support of student better comprehension and visualisation of functions of two variables. For comparison, the projection of surface to flat is connected to each anaglyph. |
| VELICHOVÁ Daniela " Minkowski combinations of free-form curves " - from the section: Algebra and geometry and their applications Some of intrinsic geometric properties of curves generated as Minkowski summative or multiplicative combinations of various types of free-form curve segments will be presented. Illustrations of particularly interested forms will be presented and some form modelling principles will be discussed. |
| VISKOTOVÁ Lenka " Annuity Due and Ordinary Annuity using Linear Difference Equations and CAS " - from the section: Financial and actuary mathematics The contribution presents the way how to apply linear difference equations in the field of financial mathematics. We focus on calculating the future value and the present value of annuities when we distinguish two basic types of annuities - an annuity due and an ordinary annuity. We also demonstrate derivations of formulas and computations of corresponding examples with using two computer algebra systems (online service Wolfram|Alpha and Maple software). |
| VISNYAI Tomas " Convergence of Series Along the Sets From Ideals " - from the section: Algebra and geometry and their applications In the year 1986 R. Estrada and R. P. Kanwal published a sucient condition for convergence of series with positive terms, where they used the notion of zero asymptotic density of set. In this paper we generalize their result by using the notion of admissible ideal for the sets of indexes. We give some examples of ideals for which the analogy of above result holds and for which no. |
| VITÉZOVÁ Zuzana " Blending Experiential Mathematics Learning and Clil to Teach Fundamentals of Orthographic Projections " - from the section: New trends in mathematical education Various non-traditional educational approaches have become popular in mathematics classes, such as Experiential Learning (EL), useful in vocational schools, and Content and Language Integrated Learning (CLIL) in bilingual classes. In this paper we present an analysis of three identical lessons with altogether 59 secondary comprehensive school students in which both EL and CLIL were used for teaching fundamentals of multiview orthographic projections. The paper summarizes results of content analysis of student drawings and related statistical analysis of student errors in the drawings. |
| VOŠTINÁR Patrik " Mobile Applications – a Tool for Teachers, Pupils and Their Families " - from the section: New trends in mathematical education In the current school environment, tablets and mobile telephones are gradually becoming standard integral teaching aids. Although terms such as the “informatisation of education” may be increasingly encountered, we should not forget, though, about the use of information-communication technologies in mathematics. The aim of education informatisation is to increase the effectiveness of the teaching process, whereby a pupil is not only passively receiving information, but is also taking an active part in the teaching process. Even though our school is currently undergoing a process of modernisation, the use of modern technologies may still not be considered as standard practice in the field of mathematics. In this article an application of geometric shapes is described which may be used as a tool in the teaching process. |
| VYSOKÁ Jana " Analysis of Attitude of Students Towards Mathematics and Physics " - from the section: New trends in mathematical education This paper describes the results of a research, which was conducted at two schools. With the use of a questionnaire there were investigated attitudes of the students of two different forms of study towards mathematics and physics. The survey was deliberately targeted at two different groups of students, students of economics and technology studying a combined form of study and students of teacher training study programmes studying the full-time form of study and it was particularly focused on the detection of the following facts: whether the two subjects, mathematics and physics, are interesting for the students and whether the students are aware of using their mathematical and physical knowledge in their field of study and in everyday life. Subsequently the aim of this paper was to analyse the discovered results. |
| WINITZKY DE SPINADEL Vera Marth " Mathematics & Artistic Design " - from the section: Mathematics and art Since the first artistic human manifestations, Mathematics has been one of the basic tools used in the production of many designs, with the main aim of obtaining more harmonic and aesthetic results. At present, the computer systems used in artistic fields, such as drawing with the help of sophisticated methods or producing different types of images, have indicated the importance of computer graphics to explain from hyperbolic spaces, fractal structures and chaos up to the more general topologic transformations. |
| ZEITHAMER Tomáš " Methodology of Theoretical Physics in Economics: " - from the section: New trends in mathematical education We assume that non-satiation axioms are general economic axioms which are associated with the genetic essence of life existing in any part of the Universe. Scalar model of retail gravitation is generalized in the three-dimensional vector model of retail gravitation for the geoid. The potential of retail gravitation is introduced along with the vector of an intensity of retail gravitation. |
| ŠIMPACH Ondřej " Smoothing of Mortality Curve: The Usage of Moving Averages and Gompertz-Makeham Function in the Case of the Czech Republic " - from the section: Financial and actuary mathematics Our paper discusses the possibilities of levelling the age-specific death rates of the Czech population using different lengths of moving averages and the Gompertz-Makeham (G-M) function. Moving average is a technique that belongs between the simpler one, G-M function between the most used approaches for levelling of mortality curves at higher ages. These approaches are very useful in the conditions of the Czech Republic. The lengths of moving averages were used according to Czech literature and empirical studies and finally set to 3, 9 and 19 values with different weights. The best results of smoothing by moving averages is achieved with the use of moving averages of 19 values, on the other hand we lose most initial observations. The G-M functions were estimated in STATA software and results are different e.g. in comparison with 19 values length moving averages. Results from this study will be used for future research to implement this technique into extrapolation script that will be able to smooth the values and then extrapolate them to the highest ages (110 years or above). |
| ŽDÍMALOVÁ Mária " Mathematics in Architecture, Design and Structure Engineering " - from the section: Mathematics and art Abstract. In this paper we would like to introduce the concept of teaching mathematics on universities focused on architecture, design and structure engineering. We present the topics from mathematics suitable for graduate students on bachelor and engineering degree for the students of architecture, landscape architecture, design, and civil engineering. We introduce a concept of project teaching and an international webpage covering multidisciplinary teaching of mathematics in architecture and design with the aim to join international universities. |
| ŽILKOVÁ Katarína " Axial Symmetry in Pre-Primary and Primary Teachers Education " - from the section: New trends in mathematical education The paper deals with the problems of geometrical education of students, who study pre-primary and primary pedagogy. The low level of the knowledge about geometric transformations in the plane and their properties does not allow the students to understand the importance of their practical applications that they will realize in their practice with preschool children. Traditional geometric tasks and exercises are not motivating for the students. A more effective way of teaching geometric transformations is, for example, the creation of real or virtual models, dynamic and interactive models. In this paper, we present some examples of geometric problems that are based on reality of teaching process, emphasizing their geometric nature. |
| ŘIHOVÁ Dana " Annuity Due and Ordinary Annuity Using Linear Difference Equations and CAS " - from the section: Financial and actuary mathematics The contribution presents the way how to apply linear difference equations in the field of financial mathematics. We focus on calculating the future value and the present value of annuities when we distinguish two basic types of annuities - an annuity due and an ordinary annuity. We also demonstrate derivations of formulas and computations of corresponding examples with using two computer algebra systems (online service Wolfram|Alpha and Maple software). |
Number of registered papers: 148 |
Last change: 4.02.2016 19:11:02 |