Abstracts

No.	Name	Office	Title of presentation
42.	ALPERS Burkhard	Mechanical Engineering Faculty Aalen University of Applied Sciences Aalen	The new SEFI Mathematics Working Group Curriculum Document	Abstract
32.	ALVAREZ Aurelien	Université d´Orléans, UFR Sciences Bâtiment de mathématiques Orléans cedex 2	Two movies: Dimensions and Chaos	Abstract
58.	BALKO Ludovit	Department of mathematics, Faculty of Mechanical Engineering, Slovak University of Technology Bratislava	Determination of actual mobility of incorrect mechanisms using matrix Lie groups	Abstract
63.	BOCCARDI Beatrice	Esplica-no profit Naples	Students´ creativity in the practices of Adotta Scienza e Arte nella tua classe	Abstract
50.	BOHÁČ Zdeněk	VSB - Technical Universiry of Ostrava Ostrava - Poruba	Problémy studia v prvním ročníku VŠB - TU Ostrava	Abstract
27.	BRUNETTI Federico A	Politecnico di Milano - Scuola del Design Milano	Experience of Three-Dimensional Vision in the Era of Digital Interaction.	Abstract
55.	CAPANNA Alessandra	Dipartimento di Architettura e Progetto Università di Roma "La Sapienza" ROMA	Memories of lost cubes and domes. Auto-similarity in modular contemporary buildings, the persistence of form between math and architecture.	Abstract
9.	DOBRAKOVOVÁ Jana	Institute of Mathematics and Physics SjF STU Bratislava	Implicitné riešenie diferenciálnych rovníc	Abstract
52.	DOLEŽALOVÁ Jarmila	VŠB-TU Ostrava Ostrava - Poruba	Problémy studia v prvním ročníku VŠB-TU Ostrava	Abstract
24.	DOTLACILOVA Petra	Department of Demography, Faculty of Informatics and Statistics, University of Economics in Prague Prague 3	DERAS versus MS EXCEL Solver in Levelling the Life Expectancy at Birth	Abstract
8.	FEČKAN Michal	Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University Bratislava	Dynamic model in advertising	Abstract
18.	FERDIÁNOVÁ Věra	Department of Mathematics, Faculty of Science, University of Ostrava Ostrava	Didactic diagnostics of the educational process concerning basics of mathematics	Abstract
28.	FJODOROVS Jegors	Chair of the Probability Theory and Mathematical Statistics, Riga Technical University Riga	Simulation of Option Prices Using GARCH Processes for Autocorrelated Stock Returns	Abstract
64.	FOLTIN Viktor	Department of Mathematics and Physics, Faculty of Mechanical Engineering, STU Bratislava Bratislava
13.	GABKOVÁ Jana	Institute of Mathematics and Physics SjF STU Bratislava
41.	GEHSBARGS Aleksandrs	Riga Technical University Riga Riga	GARCH model applications. Comparison of stationary solutions of stochastic difference and differential equations.	Abstract
66.	GELATTI Gabriele	c/o maratonda Genova	OBSERVATION OF THE GOLDEN RATIO INSPIRALS OF TRIANGLES AND SQUARES	Abstract
45.	GHEORGHIU Dragos	National University of Arts Doctoral School Bucharest	On the synergy of art, technology, ritual and mathematics. The Bézier curves revisited	Abstract
11.	HALUSKOVÁ Sona	Institute of Mathematics and Physics Slovak University of Technology Bratislava
38.	IORFIDA Vincenzo	Ph.d. School "Archimedes" University of Calabria Rende CS, ITALY	Artistic Aspects of Complex Functions in Algebraic Surfaces	Abstract
35.	JANČAŘÍK Antonín	Charles University in Prague, Faculty of Education Prague 1	Netradiční přístupy k matematické analýze I - Nekonečně malé veličiny	Abstract
33.	KONEČNÁ Petra	Department of Mathematics, Faculty of Science, University of Ostrava Ostrava	Didactic diagnostics of the educational process concerning basics of mathematics	Abstract
61.	KOREN Balazs	Eotvos Lorand University, Budapest Budapest
22.	KORENOVA Lilla	Faculty of Mathematics, Physics and Informatics Bratislava	Kombinované formy vyučovania v školskej matematike (Blended learning in teaching mathematics at primary and secondary school)	Abstract
53.	KREML Pavel	VŠB - TU Ostrava katedra matematiky a DG Ostrava - Poruba	Problémy studia v prvním ročníku VŠB - TU Ostrava	Abstract
23.	KVAPIL David	UNIS Division of Aerospace and Advanced Control Brno	Fault Detection and Isolation Algorithms and Modelling	Abstract
25.	LALATTA COSTERBOSA Cecilia	La Sapienza of Roma Faculty of Design, Visual & Multmedia Communication Rome	Parametric Hybrid Wall: A Responsive Surface for Exhibition Design	Abstract
54.	LAVICZA Zsolt	University of Cambridge Cambridge	Supporting technology enhanced mathematics teaching with development and research	Abstract
62.	LEJA Jozef	Institute of Mathematics and Physics, Faculty of Mechanical Engineering, Slovak University of Technology Bratislava
56.	LORENZI Marcella G	Centro Editoriale e Librario (University Press) University of Calabria Arcavacata di Rende	Memories of lost cubes and domes. Auto-similarity in modular contemporary buildings, the persistence of form between math and architecture.	Abstract
31.	MAGNAGHI-DELFINO Paola	Dipartimento di Matematica del Politecnico di Milano Milano	Galileo Galilei’s Location, Shape and Size of Dante’s Inferno: An Artistic and Educational Project	Abstract
19.	MATVEJEVS Andrejs	Probability Theory and Math. Statistics Dept., DITF, Riga Technical university Riga	Northeast Volatility Winds Effect and it’s Forecasting	Abstract
46.	MURESAN Viorica	Department of Mathematics, Faculty of Automation and Computer Science, Technical University of Cluj-Napoca Cluj-Napoca	A Tonelli-type functional - integral equation, via weakly Picard operators´ technique	Abstract
39.	NAVRÁTIL Vladislav	Faculty of Education, Masaryk University Brno	Plastic Deformation of Cd-Zn Alloys Single Crystals – Some Experimental Problems	Abstract
30.	NORANDO Tullia	Dipartimento di Matematica del Politecnico di Milano Milano	Galileo Galilei’s Location, Shape and Size of Dante’s Inferno: An Artistic and Educational Project	Abstract
3.	NOVOTNÁ Jiřina	Katedra matematiky, Pedagogická fakulta, MU Brno	Chains of Markof and games
34.	NOVOTNÁ Jarmila	Univerzita Karlova v Praze Pedagogická fakulta Praha 1	“Culture of Solving Problems	Abstract
44.	OMACHELOVÁ Milada	ÚMF SjF STU Bratislava
47.	PALČÁK František	Institute of applied mechanics and mechatronics, Faculty of Mechanical Engineering STU Bratislava Nam.slobody 17, 812 31 Bratislava, Slovak republic	Determination of Actual Mobility of Incorrectmechanisms Using Matrix Lie Groups	Abstract
14.	PALLADINO Nicla	Nicla Palladino Frattamaggiore (NA)	Creating New “Mathematically-Sustainable”World: from the Spirograph, a Reverse Path	Abstract
7.	PAUN Marius	Dept. Mathematics and Computer Science Transilvania University of Brasob Brasov	Numbers	Abstract
60.	PIEKARZ Monika	Institute of Mathematics Maria Curie-Skłodowska University Lublin	Partition Problem and Analog Methods	Abstract
59.	PILOUS Derek	Charles University in Prague, Faculty of Education Prague 1 Prague	Sequential and functional approach to limit in education	Abstract
17.	POLA Aija	Probability and Statistics Chair, Riga Technical University Riga	Phase Merger Principle for Nonstationary Impulse Markov Dynamical Systems	Abstract
10.	POLESŇÁK Lukáš	Department of Mathematical Analysis and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University Bratislava	Dynamic model in advertising	Abstract
12.	POTŮČEK Radovan	Department of Mathematics and Physics, Faculty of Military Technology, University of Defence Brno	Two general formulas for the sum of the reduced harmonic series generated by n primes	Abstract
36.	PUCKOVS Andrejs	Riga Technical University Riga	´North-East Volatility Wind´ Effect and its Forecasting	Abstract
15.	RAGUZ Andrija	Zagreb School of Economics and Management Zagreb	A new methodological approach to upgrading the statement of Gross domestic product (GDP) growth rates and implicit GDP deflators	Abstract
26.	RAK Josef	Univerzita Pardubice Fakulta elektrotechniky a informatiky Pardubice	Numerical Solution of a Singular Fredholm Integral Equation of the Second Kind Describing Induction Heating	Abstract
2.	RICHTÁRIKOVÁ Daniela	Institute of Mathematics and Physics SjF STU Bratislava	The role of basic geometrical patterns	Abstract
57.	ROMBOVÁ Zuzana	University of Ostrava, Faculty of Science, Department of Computers Ostrava	Simple Automation of Syntactic Analysis	Abstract
49.	SCHENK Jiří	Department of Computers, Faculty of Science, University of Ostrava Ostrava	Simple automation of syntactic analysis	Abstract
5.	SIVÝ Július	Institute of Mathematics and Physics Faculty of Mechanical Engineering Slovak University of Technology Bratislava
48.	STUPKA Tomáš	Department of Computers, Faculty of Science, University of Ostrava Ostrava	Automated Theorem Proving Systems	Abstract
16.	SUTALO Ivan	Zagreb School of Economics and Management Zagreb	A new methodological approach to upgrading the statement of Gross domestic product (GDP) growth rates and implicit GDP deflators	Abstract
29.	SVOBODA Martin	Faculty of Electical Engineering and Informatics, Department of Mathematics and Physics, University of Pardubice Pardubice	Construction and Statistical Analysis of Zdenek Sýkora’s Lines	Abstract
4.	SZARKOVÁ Dagmar	ÚMF SjF STU Bratislava
21.	TEDESCHINI LALLI Laura	Dipartimento di Architettura Rome	Charts and atlases, a Riemannian onlook at Picasso	Abstract
1.	VELICHOVÁ Daniela	Institute of Mathematics and Physics Bratislava	Some Properties of Minkowski Operators	Abstract
43.	VONDROVÁ Naďa	Charles Univ. in Prague, Faculty of Education Praha 1	Interaktivní tabule v kurzu didaktiky matematiky pro budoucí učitele matematiky	Abstract
65.	WINITZKY DE SPINADEL Vera	FACULTAD DE ARQUITECTURA, DISENIO Y URBANISMO BUENOS AIRES	Generalizaation of the Metallic Means Family	Abstract
6.	ZÁHONOVÁ Viera	Institute of Mathematics and Physics SjF STU Bratislava Bratislava	Implicitné riešenie diferenciálnych rovníc	Abstract
51.	ZAHRÁDKA Jaromír	University of Pardubice Pardubice	Fibonacci Numbers of Graphs Corresponding to a Type of Hexagonal Chains	Abstract
20.	ŠIRŮČKOVÁ Petra	Přírodovědecká fakulta MU Brno	Two Methods of Quadratic Calibration	Abstract
37.	ŠMÍD Jan	Univerzita Karlova v Praze - Pedagogická fakulta, katedra výtvarné výchovy Prague	Leaving of dimension	Abstract
40.	ŽIŽKA David	University of Economics Prague	Fractionally Integrated GARCH Approach to Estimating Financial Time Series	Abstract

Number of registered participants: 66

Abstracts of conference Aplimat 2014

ALPERS Burkhard *" The new SEFI Mathematics Working Group Curriculum Document "* - from the section: New trends in mathematical education In September 2013, the third edition of the curriculum document written by SEFI’s (European Society for Engineering Education) Mathematics Working Group appeared, called “A Framework for Mathematics Curricula in Engineering Education”. In the lecture, the main intention and structure of this document will be presented. It is based upon the concept of mathematical competence which was adopted from the Danish KOM project. This concept will be explained and illustrated by providing examples for competence-oriented assignments for students.

ALVAREZ Aurelien *" Two movies: Dimensions and Chaos "* - from the section: Dimensions (www.dimensions-math.org) is a 2-hour movie dedicated to a large audience in order to get some feeling about the fourth dimension. Thanks to the help of many people, it is now available in more than twenty languages. Chaos (www.chaos-math.org) is another 2-hour movie dedicated to a same large audience and which deals with chaos theory and the mathematics behind the famous butterfly effect. The movie is also available in a quite large number of languages and has been online since one year. In this talk, I will take the opportunity to present both films and the way we worked together on that two projects, Étienne Ghys, Jos Leys and myself.

BALKO Ľudovit *" Determination of actual mobility of incorrect mechanisms using matrix Lie groups "* - from the section: Algebra and geometry and their applications BALKO Ľudovít (SK), PALČÁK František (SK): The correct mechanism has geometric constraints, which are enforced according their type and computed mobility is actual. When diameters and configurations of links and geometrical constraints cause their partial or total passivity, then mechanism is incorrect and computed mobility is not actual. In this paper some properties of matrix groups is used for determination of actual mobility of incorrect mechanisms.

BOCCARDI Beatrice *" Students´ creativity in the practices of Adotta Scienza e Arte nella tua classe "* - from the section: Mathematics and art The first edition of the project Adotta Scienza e Arte nella tua classe (Adopt Science and Art in your class) has been held in the Italian schools in the school year 2012-2013. This paper describes how the popularisation of science through the quotes of famous scientists, annotated and contextualized in the collection of 100 +1 frasi famose sulla scienza (100 +1 famous quotes on science), used by the students as an inspiration for their graphic works on science, may contribute to increasing the curiosity for science, to motivate them and to create a multidisciplinary and creative learning environment. After a brief presentation of some basic facts – where in Italy the project has been implemented, how many students and teachers it has involved – we make an initial assessment of how scientific thinking and the practice of science can help shape the way the new generations see the world. This is done by comparing the quotes chosen by the students with their interpretation s –expressed in their original comments accompanying the graphic creation – and the artworks themselves. The analysis of the classroom practices, the original comments by the students and the graphic works highlight the strong value of the project to define the school as a place for the integration and transmission of knowledge through creativity and for the dissemination of science and scientific culture. Even beyond the school itself, through exhibitions of works, public lectures, etc. Finally, we draw a balance of this first year work and describe the lines of development of the project in the second edition.

BOHÁČ Zdeněk *" Problémy studia v prvním ročníku VŠB - TU Ostrava "* - from the section: New trends in mathematical education BOHÁČ Zdeněk (CZ), DOLEŽALOVÁ Jarmila (CZ), KREML Pavel (CZ): Je všeobecně známou skutečností, že úroveň znalostí studentů z matematiky vykazuje klesající tendenci. Formou dotazníku jsme zjišťovali názory studentů na výuku předmětů garantovaných katedrou matematiky a deskriptivní geometrie v prvním roce studia na VŠB-TUO. Zajímal nás rovněž názor studentů na úroveň jejich vstupních znalostí z matematiky a geometrie i přístup studentů k přednáškám, cvičením a zkouškám.

BRUNETTI Federico A *" Experience of Three-Dimensional Vision in the Era of Digital Interaction. "* - from the section: Mathematics and art EXPERIENCE OF THREE-DIMENSIONAL VISION IN THE ERA OF DIGITAL INTERACTION. NEW DEVICES: OPPORTUNITY AND CHALLEGES FOR APPLIED MATHEMETICS AND VISUAL DESIGN Federico Alberto Brunetti (Italy) Abstract. It will soon be presented to the public a new version of stereoscopic viewers designed for observing files and video projected images through a system of transparent optical prisms which allow the simultaneous perception of the surrounding environment. The real challenge for applied mathematics and visual design it will be to prefigure and how to use and their applications so that new devices can actually enable a deeper 3D visual experience. A specific case study concerns the visualizations of the collisions at the LHC at CERN, selected to verify the traces of the boson theorized by Francois Englert and Peter Higgs, with Robert Brout, who recently received the Nobel Prize for their research. Key words. Digital stereoscopic viewers, augmented reality, virtual vision, science communication, visual design, 3D animation, LHC - CERN, particle Physics, particle collision detector, Higgs boson. Mathematics Subject Classification: Primary Primary AMS01A99; Secondary: 97M80 Arts, music, language, architecture, 1 New generation of digital interactive stereoscopic viewers It will soon be presented to the public a new version of stereoscopic viewers that will update a hardware product already widely distributed, but relatively known only in expert groups. These stereoscopic viewers were designed for viewing files and video projected images through a system of transparent optical prisms - sent by a compact wired remote control comes with internal memory, touchpad and android wi-fi - which allow the simultaneous perception of the surrounding environment. 2 Conceptual references to the interaction with the visual techniques In this context I would underline some preliminary methodological reflections to a possible technical and practical experimentation - which can be coordinated with the appropriate research facilities of educational experimentation-. In particular I would like to point out some factors and conceptual references to the interaction with the visual techniques, that it will allow new visual experience in such apparatus. Several stereoscopic devices have preceded the upcoming technological innovations in three-dimensional viewers, and at least to facilitate its comprehension, each advance must retain the memory of some aspect of the one that of it has preceded it, at least under a typological profile, in order not to be perceived as a foreign object and simply incomprehensible. 3 opportunity and challenge for applied mathematics and for visual design The real challenge for applied mathematics and visual designe it will be to prefigure how to use possible applications of these new devices that can actually enable a deeper 3D visual experience for the observer -and not just an augmented reality of a possible isolated and only passive user- to become a protagonists of new knowledge and real communication (word and idea which etymologically means “shared action”!). 4 Case study: Collisions 3D visualization from LHC-CERN of Geneve A specific case study that we would like to present concerns the visualizations of the particle collisions at the LHC at CERN, selected to verify the traces theorized Higgs boson. It is methodologically an extremely interesting representation path. From a physical phenomenon at the microscopic extreme limits of events in space-time –through the major detectors ATLAS and CMS- the data of the tracks collisions have been recorded, collected and selected: these data obtained from the detectors have been realized in sequences of 3D modeling with chromatic highlights of different types of tracks detected; the modeling of these sequences were visually reproduced in the progressive dynamics of the collisions returned finally in 3D animation. This compex elaboration is an innovative visual product, between science and visual arts, that carries us from the invisible to the infinitesimal space-time the immersive vision of the physical events.

CAPANNA Alessandra *" Memories of lost cubes and domes. Auto-similarity in modular contemporary buildings, the persistence of form between math and architecture. "* - from the section: Mathematics and art CAPANNA Alessandra (I), LORENZI Marcella Giulia (I): After the revolutions of contemporary architecture, and the inventive and daring design experimentations obtained by using, for example, genetic algorithms and computer evolutionary simulations, at the basis of even apparently complex compositions there are simple mathematical rules or forms. In this paper, to be considered as a preliminary study with a preeminent architectural/artistic bias, we will take into consideration a few examples of buildings, in which self-similar, reiterated and even fractal cubes have been used to create very outstanding compositions. A deeper analysis reveals similarities to and influences by very ancient paradigms or iconic symbols and the persistence of form through centuries and different cultures. by A. Capanna & M.G. Lorenzi

DOBRAKOVOVÁ Jana *" Implicitné riešenie diferenciálnych rovníc "* - from the section: New trends in mathematical education DOBRAKOVOVÁ Jana (SR), ZÁHONOVÁ Viera(SR): This paper is devoted to some aspects of teaching ordinary differential equations of the first order, especially properties of their solutions in implicit form and some special tools for visualization of the obtained results, with the aid of the programming system MATHEMATICA.

DOLEŽALOVÁ Jarmila *" Problémy studia v prvním ročníku VŠB-TU Ostrava "* - from the section: New trends in mathematical education BOHÁČ Zdeněk (CZ), DOLEŽALOVÁ Jarmila (CZ), KREML Pavel (CZ): Je všeobecně známou skutečností, že úroveň znalostí studentů z matematiky vykazuje klesající tendenci. Formou dotazníku jsme zjišťovali názory studentů na výuku předmětů garantovaných katedrou matematiky a deskriptivní geometrie v prvním roce studia na VŠB-TUO. Zajímal nás rovněž názor studentů na úroveň jejich vstupních znalostí z matematiky a geometrie i přístup studentů k přednáškám, cvičením a zkouškám.

DOTLACILOVA Petra *" DERAS versus MS EXCEL Solver in Levelling the Life Expectancy at Birth "* - from the section: Financial and actuary mathematics DOTLAČILOVÁ Petra (CZ), ŠIMPACH Ondřej (CZ), LANGHAMROVÁ Jitka (CZ): The article deals with using of MS Excel Solver for demographic calculations. We will focus on the levelling of specific mortality rates for higher ages. The reason is that there is a gradual improvement in mortality. Therefore, it is more and more im-portant to best capture the mortality of oldest persons. In our study, we will focus on levelling specific mortality rates by Gompertz–Makeham (and modified Gom-pertz–Makeham) function. An important part of the article will provide the process for estimating the parameters of mentioned functions using the procedure of MS Excel Solver. Our goal is to present the methodology that we use for estimating pa-rameters of these functions. The procedure will be applied on data about mortality of Czech population. The results will be compared with the estimates, obtained from the software DeRaS, which is used for estimating parameters of selected mod-els used for smoothing specific mortality rates. The aim is to compare the results ob-tained from both procedures. There will be presented the possible consequences of current development of mortality in the conclusion.

FEČKAN Michal *" Dynamic model in advertising "* - from the section: Differential equations, dynamic systems and their applications FEČKAN Michal, POLESŇÁK Lukáš: The goal of the article is to report to the reader something about dynamics in marketing, especially in marketing comunication and advertising. We used and estimated dynamic model with two equation, two variables and one parameter.

FERDIÁNOVÁ Věra *" Didactic diagnostics of the educational process concerning basics of mathematics "* - from the section: New trends in mathematical education FERDIÁNOVÁ Věra (CZ), KONEČNÁ Petra (CZ): Article introduces form, aims and results of the didactic diagnostics of first-grade students´ performance in the cognitive field focusing on the basics of mathematics.

FJODOROVS Jegors *" Simulation of Option Prices Using GARCH Processes for Autocorrelated Stock Returns "* - from the section: Modeling and simulation in engineering and scientific computations In this paper we describe practical example of our studies for an analytical solution for a problem of pricing financial actives with autocorrelated returns. This example is based on option price for Tesla Motors Inc stock. In previous studies we developed a continuous diffusion model for the case of serially correlated stock returns, obtain European call option pricing formula and show that even small levels of predictability due to serial correlation can give substantial deviation from results obtained by Black-Sholes formula and made Monte Carlo simulation for stock volatility. Finally, we showed recalculated option price, based on the simulation result.

GEHSBARGS Aleksandrs *" GARCH model applications. Comparison of stationary solutions of stochastic difference and differential equations. "* - from the section: Financial and actuary mathematics Main results for stochastic diﬀerential equations apply to their stationary solutions. For obvious reasons underlying processes are simulated with stochastic diﬀerence equations. Such equations also have stationary solutions that depend on the time step h. In the current paper relation between statistical features of stationary solutions of stochastic diﬀerence and diﬀerential equations are investigated. Moreover, possible approaches to the choice of time step h are discussed.

GELATTI Gabriele *" OBSERVATION OF THE GOLDEN RATIO INSPIRALS OF TRIANGLES AND SQUARES "* - from the section: Algebra and geometry and their applications In this paper we introduce the notion of L golden gnomon, and some properties of it are observed as applied to the growth of spirals. Spirals of squares and of triangles are especially observed, with relevance of the golden ratio as a geometrical link between the two polygons.

GHEORGHIU Dragos *" On the synergy of art, technology, ritual and mathematics. The Bézier curves revisited "* - from the section: Mathematics and art This paper, dedicated to the memory of Professor Mauro Francaviglia, pleads for a synthesis between art and mathematics, by presenting a set of new data on the Bézier curves, identified on 18th century azulejo from Portugal. As the Portuguese artifacts show, the ritual action of tracing the curves can be considered a cultural universal, its presence being identified after thousands of years span and thousands of kilometers distance in the prehistoric Balkan objects discussed in a previous Aplimat issue. The existence of a mathematical function that copies a vegetal shape across different cultures also infers that Bézier curves are a cultural archetype, neglected until now by the history of art, and whose study would contribute to the understanding of certain mental processes.

IORFIDA Vincenzo *" Artistic Aspects of Complex Functions in Algebraic Surfaces "* - from the section: Mathematics and art The mathematics of the Nineteenth century was characterized by the development of complex analysis, that has also had a significant role in the study of physics. This process was more profitable, in many aspects, than the real analysis. The study of complex functions has been carried out independently, since, according to most of the mathematicians, the problems with complex numbers have emerged from their use in the theory of functions and not in algebra. We will examine some artistic aspects, related to the glamour of modeling of complex numbers whose shapes pass through the cryptography.

JANČAŘÍK Antonín *" Netradiční přístupy k matematické analýze I - Nekonečně malé veličiny "* - from the section: New trends in mathematical education JANČAŘÍK Antonín (CZ), Pilous Derek (CZ): V rámci příspěvku bude představen alternativní přístup k výuce diferenciálního a integrálního počtu pomocí nekonečně malých veličin. Bude poukázáno na historické souvislosti vztahující se k tomuto přístupu a možnosti, které především v oblasti názornosti představuje.

KONEČNÁ Petra *" Didactic diagnostics of the educational process concerning basics of mathematics "* - from the section: New trends in mathematical education FERDIÁNOVÁ Věra (CZ), KONEČNÁ Petra (CZ): Article introduces form, aims and results of the didactic diagnostics of first-grade students´ performance in the cognitive field focusing on the basics of mathematics.

KORENOVA Lilla *" Kombinované formy vyučovania v školskej matematike (Blended learning in teaching mathematics at primary and secondary school) "* - from the section: New trends in mathematical education V posledných rokoch sme svedkami rastúcej tendencie využívania elektronických materiálov učiteľmi matematiky na všetkých stupňoch škôl. E-materiály sú súčasťou nového trendu vo vyučovaní školskej matematiky –blended learningu, teda kombinovanej formy vyučovania spájajúcej fyzické a virtuálne zdroje. V príspevku chceme poukázať na súčasný stav a možnosti využívania blended learnigu vo vyučovaní školskej matematiky a niekoľko ukážok e-materiálov (v prostredí softvéru GeoGebra). Poukážeme aj na možnosti využitia e-materiálov pri rozvíjaní tvorivosti matematicky nadaných žiakov.

KREML Pavel *" Problémy studia v prvním ročníku VŠB - TU Ostrava "* - from the section: New trends in mathematical education BOHÁČ Zdeněk (CZ), DOLEŽALOVÁ Jarmila (CZ), KREML Pavel (CZ): Je všeobecně známou skutečností, že úroveň znalostí studentů z matematiky vykazuje klesající tendenci. Formou dotazníku jsme zjišťovali názory studentů na výuku předmětů garantovaných katedrou matematiky a deskriptivní geometrie v prvním roce studia na VŠB-TUO. Zajímal nás rovněž názor studentů na úroveň jejich vstupních znalostí z matematiky a geometrie i přístup studentů k přednáškám, cvičením a zkouškám.

KVAPIL David *" Fault Detection and Isolation Algorithms and Modelling "* - from the section: Modeling and simulation in engineering and scientific computations KVAPIL David(CZ), WEISMAN Andrej (SK): Fault detection and isolation (FDI) is very important for enhancing the safety and reliability of aircraft systems. Several mathematical methods and algorithms useful for processing and operation evaluating in engine control systems are presented in this article. The role of FDI in System Health Monitoring (SHM) issues and Data-Driven approach is reminded. Residual-based modeling and analysis is considered. Control chart approach and state estimator using Kalman filtering is presented and modelled. Perturbed system with implemented dummy fault is simulated and analyzed, all simulations are created in MATLAB.

LALATTA COSTERBOSA Cecilia *" Parametric Hybrid Wall: A Responsive Surface for Exhibition Design "* - from the section: Modeling and simulation in engineering and scientific computations A Responsive Surface is an architecture able to model its own shape in relation to contextual specific impulses. The surface shapes itself differently depending on the stimuli which are related to a spectrum of variables classified as sensors. The deformation of the surface happens subsequently to the received impulse: the dynamism of these structures is then the result of the interaction between the end-user, who acts upon the sensors, and the surface, which modifies its own shape after having been subjected to the stimuli of the sensors. Parametric Hybrid Wall not only presents these preliminary characteristics, hence resulting to be a responsive surface, but also it outlines a further process which combines the planning parametric approach with specific instruments for Open Source and Low Cost modelling and prototyping.

LAVICZA Zsolt *" Supporting technology enhanced mathematics teaching with development and research "* - from the section: New trends in mathematical education Technology is increasingly becoming an important part of mathematics teaching and learning in the 21st Century. There are numerous attempts to integrate technology into education systems, but without serious development and research the success of these attempts have been limited. Recently, we started a project in Hungary to develop high-quality teaching and learning materials and work with 800 schools and 2500 teachers. The project involves extensive development and evaluation parts to ensure the quality of the work. The developed materials and the software framework are based on GeoGebra (http://geogebra.org), which an open-source, dynamic mathematics software used by more than 20million students and teachers around the world. In our project we aim to involve and collaborate with as many experts and researchers as possible from around the world. We plan to base our work on previously successful projects, collect ideas from the GeoGebra community, and invite colleagues to work with us. We hope that this project could be a test bed for future projects and trialing ground for different ideas. In our talk, we will outline GeoGebra as a software, its community, the directions for software development, and our aims for research and evaluation.

LORENZI Marcella G *" Memories of lost cubes and domes. Auto-similarity in modular contemporary buildings, the persistence of form between math and architecture. "* - from the section: Mathematics and art CAPANNA Alessandra (I), LORENZI Marcella Giulia (I): After the revolutions of contemporary architecture, and the inventive and daring design experimentations obtained by using, for example, genetic algorithms and computer evolutionary simulations, at the basis of even apparently complex compositions there are simple mathematical rules or forms. In this paper, to be considered as a preliminary study with a preeminent architectural/artistic bias, we will take into consideration a few examples of buildings, in which self-similar, reiterated and even fractal cubes have been used to create very outstanding compositions. A deeper analysis reveals similarities to and influences by very ancient paradigms or iconic symbols and the persistence of form through centuries and different cultures.

MAGNAGHI-DELFINO Paola *" Galileo Galilei’s Location, Shape and Size of Dante’s Inferno: An Artistic and Educational Project "* - from the section: Mathematics and art ANGELINI Alessandra (I), MAGNAGHI-DELFINO Paola (I), NORANDO Tullia (I): Mathematics and Art have a long historical relationship, which goes as far back as the ancient Greeks. It suffices to think, for instance, to their use of the golden ratio, regarded as an aesthetically pleasing canon and incorporated into the design of many monuments and temples. With the Renaissance we can see a rebirth of Classical (Greek and Roman) culture and ideas, and among them the study of Mathematics as a relevant subject needed to understand the nature and the arts. Two major reasons drove Renaissance artists towards the pursuit of Mathematics. Firstly, painters needed to figure out how to depict three-dimensional scenes on a two-dimensional canvas. Secondly, philosophers and artists alike were convinced that Mathematics was the true essence of the physical world so that the entire universe, including the arts, could be explained in geometrical terms. For instance, Galileo Galilei in his Il Saggiatore wrote that “[The universe] is written in the language of Mathematics, and its characters are triangles, circles, and other geometric figures.” Thus, there is a close relation between Mathematics and Fine Arts during the Renaissance: mathematical knowledge is applied in drawings and paintings with the use of symmetry, producing ratios and proportions. Within the study of such a context arises the artistic and educational project “Galileo: location, shape and size of Dante’s Inferno” as a collaboration between the FDS Laboratory for Mathematical Education and Science Communication at the Department of Mathematics of the Politecnico di Milano and Accademia di Belle Arti di Brera. The project is inspired by the first of two lectures held by Galileo Galilei at the Accademia Fiorentina in 1588. These lectures were commissioned by the Accademia to solve a literary controversy concerning the interpretation of Dante’s Inferno. In these lessons Galileo took the opportunity to show his mathematical abilities combined with his strong background in Humanities. His ultimate aim was to show that Mathematics is not merely useful from a technical point of view, but can also give a contribution to nobler cultural debates, thus acquiring an intellectual status comparable to that of the Humanities. When giving his lectures Galileo probably used drawings to explain how to map Dante’s Inferno, because of “ la difficoltà del suggetto che non patisce esser con la penna facilmente esplicato” (the difficulty of the subject which does not admit of easy explication in writing). Galileo’s manuscript survives and is catalogued in the Filza Rinucciniana 21 of the Biblioteca Nazionale di Firenze, but the drawings are lost. The project here presented included an accurate analysis of Galileo’s work and was meant as an opportunity for the students of Graphic to investigate the relationship between geometric representation and artistic interpretation. They made scale drawings of the Inferno, by using different paper media and drawing techniques of their choice. Later they produced original art works resulting from a personal artistic interpretation of the subject, free of pure scientific representation. The results reflect various artistic and creative sensibilities: drawings, paintings, engravings. The students’ works were gathered, accompanied by short sentences associated with the selected quotes of Inferno and displayed on the exhibition that was held at Politecnico di Milano (May 2012). After the works were exhibited at the Museo Dantesco of Ravenna (September 2013) and at the Bergamo Science Fesstival (XI Edition, October 2013).

MATVEJEVS Andrejs *" Northeast Volatility Winds Effect and it’s Forecasting "* - from the section: Financial and actuary mathematics Andrejs Puckovs (Latvia), Andrejs Matvejevs (Latvia): This paper describes volatility forecasting approach applicable for stock indexes, allowing to reveal the instability of financial time series initially. This approach is based on time series (signal) decomposition into components by using wavelet filtering with subsequent volatility evolution research in time of each signal component. According to research, a slight increase in volatility in the low-frequency components of the signal leads to significant disturbances in high-frequency components destine entire signal volatility growth.

MURESAN Viorica *" A Tonelli-type functional - integral equation, via weakly Picard operators´ technique "* - from the section: Differential equations, dynamic systems and their applications In the paper we consider a Tonelli-type functional - integral quation with linear modifications of the arguments in a Banach space. By using weakly Picard operators´ technique we obtain existence, data dependence and comparison results for the solution.

NAVRÁTIL Vladislav *" Plastic Deformation of Cd-Zn Alloys Single Crystals – Some Experimental Problems "* - from the section: Modeling and simulation in engineering and scientific computations NAVRÁTIL Vladislav (ČR), NOVOTNÁ Jiřina (ČR): The character of plastic deformation is a sensitive function of such variables as temperature, the strain rate of deformation, the past history of the sample, crystal size and other parameters. It is purpose of the present work to examine the reproducibility of measurements of some basic parameters, characterized plastic flow of metals, depending on stress, temperature and concentration of impurities. Our investigations proved that the stress dependence of activation area and stress sensitivity parameter does not depend on such subjective and objective conditions as adding or removing stress increment, or the strain rate at which the increment or decreasing stress is realized.

NORANDO Tullia *" Galileo Galilei’s Location, Shape and Size of Dante’s Inferno: An Artistic and Educational Project "* - from the section: Mathematics and art ANGELINI Alessandra (I), MAGNAGHI-DELFINO Paola (I), NORANDO Tullia (I): Mathematics and Art have a long historical relationship, which goes as far back as the ancient Greeks. It suffices to think, for instance, to their use of the golden ratio, regarded as an aesthetically pleasing canon and incorporated into the design of many monuments and temples. With the Renaissance we can see a rebirth of Classical (Greek and Roman) culture and ideas, and among them the study of Mathematics as a relevant subject needed to understand the nature and the arts. Two major reasons drove Renaissance artists towards the pursuit of Mathematics. Firstly, painters needed to figure out how to depict three-dimensional scenes on a two-dimensional canvas. Secondly, philosophers and artists alike were convinced that Mathematics was the true essence of the physical world so that the entire universe, including the arts, could be explained in geometrical terms. For instance, Galileo Galilei in his Il Saggiatore wrote that “[The universe] is written in the language of Mathematics, and its characters are triangles, circles, and other geometric figures.” Thus, there is a close relation between Mathematics and Fine Arts during the Renaissance: mathematical knowledge is applied in drawings and paintings with the use of symmetry, producing ratios and proportions. Within the study of such a context arises the artistic and educational project “Galileo: location, shape and size of Dante’s Inferno” as a collaboration between the FDS Laboratory for Mathematical Education and Science Communication at the Department of Mathematics of the Politecnico di Milano and Accademia di Belle Arti di Brera. The project is inspired by the first of two lectures held by Galileo Galilei at the Accademia Fiorentina in 1588. These lectures were commissioned by the Accademia to solve a literary controversy concerning the interpretation of Dante’s Inferno. In these lessons Galileo took the opportunity to show his mathematical abilities combined with his strong background in Humanities. His ultimate aim was to show that Mathematics is not merely useful from a technical point of view, but can also give a contribution to nobler cultural debates, thus acquiring an intellectual status comparable to that of the Humanities. When giving his lectures Galileo probably used drawings to explain how to map Dante’s Inferno, because of “ la difficoltà del suggetto che non patisce esser con la penna facilmente esplicato” (the difficulty of the subject which does not admit of easy explication in writing). Galileo’s manuscript survives and is catalogued in the Filza Rinucciniana 21 of the Biblioteca Nazionale di Firenze, but the drawings are lost. The project here presented included an accurate analysis of Galileo’s work and was meant as an opportunity for the students of Graphic to investigate the relationship between geometric representation and artistic interpretation. They made scale drawings of the Inferno, by using different paper media and drawing techniques of their choice. Later they produced original art works resulting from a personal artistic interpretation of the subject, free of pure scientific representation. The results reflect various artistic and creative sensibilities: drawings, paintings, engravings. The students’ works were gathered, accompanied by short sentences associated with the selected quotes of Inferno and displayed on the exhibition that was held at Politecnico di Milano (May 2012). After the works were exhibited at the Museo Dantesco of Ravenna (September 2013) and at the Bergamo Science Festival (XI Edition, October 2013).

NOVOTNÁ Jarmila *" “Culture of Solving Problems "* - from the section: New trends in mathematical education EISENMANN Petr (CZ), NOVOTNÁ Jarmila (CZ), PŘIBYL Jiří (CZ): In the paper, Culture of Solving Problems – a tool for evaluating pupil problem solving in mathematics – is presented and analyzed. The Culture of Problem Solving consists of four components: Intelligence, Creativity, Reading texts with comprehension (tested by psychological tests), and Ability to use the existing knowledge (tested by solution of a set of mathematical problems). The results gained using the tool are sometimes very surprising. Deviations from the standard results can only be explained with the help of interviews with the pupils’ teachers of mathematics. Some of the possible explanations for these deviations are also illustrated in the paper.

PALČÁK František *" Determination of Actual Mobility of Incorrectmechanisms Using Matrix Lie Groups "* - from the section: Algebra and geometry and their applications Balko Ľudovít (SR), PALČÁK František (SR): The correct mechanism has geometric constraints, which are enforced according their type and computed mobility is actual. When diameters and configurations of links and geometrical constraints cause their partial or total passivity, then mechanism is incorrect and computed mobility is not actual. In this paper some properties of matrix Lie groups is used for determination of actual mobility of incorrect mechanisms.

PALLADINO Nicla *" Creating New “Mathematically-Sustainable”World: from the Spirograph, a Reverse Path "* - from the section: Mathematics and art Palladino Nicla (I), Pastena Nicolina (I): The approach to the subject of mathematic learning, represents, in the pedagogical-educational field, a problematic situation. Nowadays we attend to an heated discussion on the character of the basic mathematical concepts, on the analytical-critical succession between processes and objects. The purpose of these notes is to recover and to value the contribution of the autopoiesis theory in the characterization of the mathematical domain going beyond the mere reiteration, inspecting and testing new and generative paths of ideas. In this mechanism we would insert the use of the spirograph as a disturbing, uncertain element able to nourish the “mind-system”.

PAUN Marius *" Numbers "* - from the section: Mathematics and art Pythagoras saw numbers in everything and he was right. Our Universe lays in 80 octaves of vibrations and countless secrets. Every vibration is a number.

PIEKARZ Monika *" Partition Problem and Analog Methods "* - from the section: Modeling and simulation in engineering and scientific computations Jerzy Mycka (PL), Monika Piekarz (PL), Wojciech Rosa (PL): In this paper we test non-standard methods of dealing with one of the most famous NP-problems - namely with the partition problem. We employ elements of analog computation in two ways: first by use of the specific analog device, second by use of numerical analysis. We compare times of computation for some examples and reliability of obtained answers. We provide some estimations of bounds guaranteeing the proper answer of the mentioned methods. (by J. Mycka, M. Piekarz, W. Rosa)

PILOUS Derek *" Sequential and functional approach to limit in education "* - from the section: New trends in mathematical education This article compares two ways by which notion of limit is commonly introduced, through sequences and through functions, by educationally relevant criteria. It focuses on sequential approach and shows how we can obtain results commonly associated with limit of composition of functions theorem.

POLA Aija *" Phase Merger Principle for Nonstationary Impulse Markov Dynamical Systems "* - from the section: Differential equations, dynamic systems and their applications CARKOVS Jevgenijs (LV), POLA Aija (LV): The paper deals with impulse type non-stationary dynamical systems fast switched by step Markov process having {it m} invariant measures. We have derived more simple Markov dynamical system in a form of ordinary differential equation with right part switched by merger homogeneous Markov process with $m$ states and have proved that for sufficiently fast switching this dynamical system approximates initial system.}

POLESŇÁK Lukáš *" Dynamic model in advertising "* - from the section: Differential equations, dynamic systems and their applications FEČKAN Michal, POLESŇÁK Lukáš: The goal of the article is to report to the reader something about dynamics in marketing, especially in marketing comunication and advertising. We used and estimated dynamic model with two equation, two variables and one parameter.

POTŮČEK Radovan *" Two general formulas for the sum of the reduced harmonic series generated by n primes "* - from the section: Modeling and simulation in engineering and scientific computations This contribution is a follow-up to author´s papers dealing with sums of the reduced harmonic series generated by two, three, and four primes. These sums were determined analytically and computed by using CAS Maple. In this contribution two general formulas for the sum of the reduced harmonic series generated by n primes (and more generally also by n natural numbers) are derived and proved by mathematical induction. These series so belong to such special types of convergent infinite series, as geometric and telescoping series, which sums can be easy calculated by means of a simple formula.

PUCKOVS Andrejs *" ´North-East Volatility Wind´ Effect and its Forecasting "* - from the section: Statistical methods in technical and economic sciences and in practise Andrejs Puckovs (Latvia), Andrejs Matvejevs (Latvia): This paper describes volatility forecasting approach applicable for stock indexes, allowing to reveal the instability of financial time series initially. This approach is based on time series (signal) decomposition into components by using wavelet filtering with subse- quent volatility evolution research in time of each signal component. According to research, a slight increase in volatility in the low-frequency components of the signal leads to signif-icant disturbances in high-frequency components destine entire signal volatility growth.

RAGUZ Andrija *" A new methodological approach to upgrading the statement of Gross domestic product (GDP) growth rates and implicit GDP deflators "* - from the section: Statistical methods in technical and economic sciences and in practise Njavro Mato (HR), Raguž Andrija (HR), Sutalo Ivan (HR): The purpose of this paper is to present a new methodological approach to upgrading the statement of Gross domestic product (GDP) growth rates and implicit GDP deflators. We construct Lloyd-Moulton-Törnqvist-Fisher (LMTF) model which improves GDP price-volume decomposition. LMTF supported Fisher index is also built. Our approach preserves the product test identity. We obtain some empirical results which show that LMTF supported Fisher index can be considered as "ideal" in the practical applications.

RAK Josef *" Numerical Solution of a Singular Fredholm Integral Equation of the Second Kind Describing Induction Heating "* - from the section: Modeling and simulation in engineering and scientific computations Problem of induction heating can be described by an integral equation of the second kind. Its numerical solution is based on collocation and Nyström methods. The idea of collocation methods is to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree). The Nyström methods are based on approximation of the integral in equation by numerical integration rule. The main aim is to show and compare both methods.

RICHTÁRIKOVÁ Daniela *" The role of basic geometrical patterns "* - from the section: Mathematics and art The role of basic geometrical patterns

ROMBOVÁ Zuzana *" Simple Automation of Syntactic Analysis "* - from the section: Modeling and simulation in engineering and scientific computations SCHENK Jiří (CZ), ROMBOVÁ Zuzana (CZ): This article is focused first on the lexical analysis and then on the syntactic analysis and the processes connected to both of them. Also the way of creating simple generators for the analyzers with a given grammar is shown.

SCHENK Jiří *" Simple automation of syntactic analysis "* - from the section: Modeling and simulation in engineering and scientific computations SCHENK Jiří (CZ), ROMBOVÁ Zuzana (CZ): This article is focused first on the lexical analysis and then on the syntactic analysis and the processes connected to both of them. Also the way of creating simple generators for the analyzers with a given grammar is shown.

STUPKA Tomáš *" Automated Theorem Proving Systems "* - from the section: Modeling and simulation in engineering and scientific computations This article describes the process of theorem proving and number of independent experiments of theorem provers that were run in order to evaluate the most appropriate implementation for automated theorem proving.

SUTALO Ivan *" A new methodological approach to upgrading the statement of Gross domestic product (GDP) growth rates and implicit GDP deflators "* - from the section: Statistical methods in technical and economic sciences and in practise Njavro Mato (HR), Raguž Andrija (HR), Sutalo Ivan (HR): The purpose of this paper is to present a new methodological approach to upgrading the statement of Gross domestic product (GDP) growth rates and implicit GDP deflators. We construct Lloyd-Moulton-Törnqvist-Fisher (LMTF) model which improves GDP price-volume decomposition. LMTF supported Fisher index is also built. Our approach preserves the product test identity. We obtain some empirical results which show that LMTF supported Fisher index can be considered as "ideal" in the practical applications.

SVOBODA Martin *" Construction and Statistical Analysis of Zdenek Sýkora’s Lines "* - from the section: Mathematics and art SVOBODA Martin (CZ), MAREK Jaroslav (CZ): Czech painter Zdenek Sýkora (1920 – 2011) is one of first painters who started using the random variables as a tool for artistic production. He used a dice for choosing parameters of curves. Later he used a computer for simulation of those parameters. In this article a construction of his Lines (arcs) based on solution of one geometric problem is shown. Then we propose regression models for detection of arcs. The main goal is to find estimators of unknown parameters of arcs and determine random numbers formulating Zdenek Sýkora’s painting Lines No. 145.

TEDESCHINI LALLI Laura *" Charts and atlases, a Riemannian onlook at Picasso "* - from the section: Mathematics and art Simultaneity of points of view is a habit for today´s mathematicians. A poly-centric onlook seems to characterize both our ways of imagining geometry, as in Riemannian geometry, and has characterized much of the visual culture of the twentieth century. We will review two paintings of Picasso in detail, drawing details seen from the same point of view in local charts, and then assembling the charts in a global atlas to reconstruct the immersed object. This talk is dedicated to Mauro Francaviglia, who encouraged this research with stimulating questions.

VELICHOVÁ Daniela *" Some Properties of Minkowski Operators "* - from the section: Mathematics and art Few results of investigations concerning properties of differentiable manifolds generated as images of smooth manifolds under various Minkowski operators will be presented. Some of these properties are inherited from the original manifolds that are operands in the Minkowski operators, others appear due to the properties of the generating principles themselves.

VONDROVÁ Naďa *" Interaktivní tabule v kurzu didaktiky matematiky pro budoucí učitele matematiky "* - from the section: New trends in mathematical education VONDROVÁ Naďa (CZ), JANČAŘÍK Antonín (CZ): V roce 2013 byla PedF UK v Praze příjemcem projektu FRVŠ, jehož hlavním cílem bylo vybudovat a rozšířit stávající technologické zázemí pro využívání moderních informačních a komunikačních technologií v přípravě budoucích učitelů matematiky a učitelů 1. stupně základní školy. Vybudované technické zázemí bylo využito v řadě předmětů, jejichž obsah a způsob prezentace látky byly přizpůsobeny novým možnostem. Článek se zabývá jedním z těchto předmětů, a sice didaktikou matematiky, a na několika příkladech z tohoto kurzu ilustruje, jakým způsobem se studenti seznamují s potenciálem interaktivní tabule pro jejich budoucí výuku na školách. Ilustrace se týkají mj. tvorby a didaktického hodnocení prezentací pro interaktivní tabule a apletů a elektronických učebnic. Příklady dokumentují, jak je ve zmíněném kurzu interaktivní tabule využívána nejen jako prostředek vyučování, ale také jako prostředek učení. Stručně jsou zmíněny některé výzkumy týkající se využití interaktivní tabule na základních a středních školách.

WINITZKY DE SPINADEL Vera *" Generalizaation of the Metallic Means Family "* - from the section: Mathematics and art As it is well known, the MMF is divided into two subfamilies: 1) the PPMMF (Purely Periodic Continued Fraction Expansion; 2) the PMMF.(Periodic Continued Fraction Expansion) In the first case we have all the positive quadratic irrationals, that are solutions of equations of the type x2- px – 1 = 0, where p is a natural number. All of them have a purely periodic continued fraction expansion of the type x = [n,n,...], n € N. If n = 1the solution is the well known Golden Mean ∅=1,618…. In the second case, we consider the solutions of equations of the type x2 - x – q = 0, where q € N. And all have a periodic (not purely) continued fraction expansion.Applying George Odom,s idea of looking for the Golden Mean in n-polygons and polytopes, we begun analyzing the sequence of ratios obtained in considering spaces of higher dimenaiona and taking p and q as real numbers.

ZÁHONOVÁ Viera *" Implicitné riešenie diferenciálnych rovníc "* - from the section: DOBRAKOVOVÁ Jana (SR), ZÁHONOVÁ Viera(SR): This paper is devoted to some aspects of teaching ordinary differential equations of the first order, especially properties of their solutions in implicit form and some special tools for visualization of the obtained results, with the aid of the programming system MATHEMATICA.

ZAHRÁDKA Jaromír *" Fibonacci Numbers of Graphs Corresponding to a Type of Hexagonal Chains "* - from the section: Algebra and geometry and their applications SEIBERT Jaroslav (CZ), ZAHRÁDKA Jaromír (CZ): The concept of the Fibonacci number of an undirected graph, refers to the number of subsets of such that no two vertices in are adjacent. In this contribution a variant of the decomposition theorem is derived. The Fibonacci numbers of graphs corresponding to one type of hexagonal chains are calculated by using the decomposition formula. Searching of the Fibonacci numbers of certain classes of graphs leads to difference equations or their systems. The Fibonacci number of hexagonal chain with linearly annelated hexagons is found as a function of the number of hexagons in the chain.

ŠIRŮČKOVÁ Petra *" Two Methods of Quadratic Calibration "* - from the section: Statistical methods in technical and economic sciences and in practise Calibration is a set of tasks which gives relationship between the reference device and the calibrated device (if some special conditions are realized). This relationship is described by the calibration function and represented by the calibration curve. In the contribution we assume that the calibration curve is a parabola. So we focus on the quadratic calibration. We use the maximum likelihood method and method based on linearized errors-in-variables model and Kenward-Rogers type approximation for obtaining the calibration curve. Both method will be presented and compared. Calibration process can be divided into two parts: 1) creation of the calibration model (calibration of the device), 2) application (use) of the calibration model (measuring by calibrated device). In the contribution we estimate parameters of the calibration function and their confidence region by both above mentioned methods and we also show the use of the calibration curve in the measuring process. At the conclusion both methods will be compared in a small simulation study. Programs used for the simulation study are programmed in software Matlab.

ŠMÍD Jan *" Leaving of dimension "* - from the section: Mathematics and art Šmíd Jan (CZ), Jančařík Antonín (CZ): Příspěvek na téma „Opuštění dimenze“ řeší téma dimenze a rozměru jako fenoménu prostoru a času v matematické a umělecké (výtvarné) oblasti, zabývá se možnostmi a způsoby „opouštění dimenzích“ v různém chápání zvolené problematiky a navrhuje způsoby, kterými danou problematiku definovat pro možnosti aplikace do didaktiky i živé výuky matematiky a výtvarné výchovy.

ŽIŽKA David *" Fractionally Integrated GARCH Approach to Estimating Financial Time Series "* - from the section: Statistical methods in technical and economic sciences and in practise This paper investigates application of the fractionally integrated generalized autoregressive conditional heteroscedastic (FIGARCH) models. Fractionally integrated models are used mainly for describing the observed persistence in the volatility of a time series. FIGARCH models are long memory models for volatility and allow to be a better candidate than other conditional heteroscedastic models for modeling volatility in exchange rates, stock market returns and option prices. The application of a FIGARCH model to exchange rate data is discussed in experimental part. Finally, the results and further possibilities of analysis are discussed.