| ANTOŠ Karel " Minimum Spanning Tree Problem " - from the section: Mathematics and art This article provides solutions to certain models of graph theory, where the minimum spanning tree (MST) models are suitable. The principle of the MST problem is the fact that it is necessary to find the model situations for which this method is suitable, to find how to use this method in finding a solution, and finally to compare two methods of looking for the MST, in terms of their different approaches, their complementarity, and their assessment, which of these two methods can find a feasible solution faster in particular cases. A theoretical discussion and a model example are carried out to compare the two methods. |
| ASMUSS Svetlana " On a Problem of Smoothing Histopolation under Additional Restrictions " - from the section: The problem of approximation of a density histogram is considered as the problem of smoothing histopolation with weights under some additional restrictions. The generalization of this problem for Hilbert spaces allows us to investigate this problem, prove the existence of its solutions and suggest the method for their construction. The other possibilities for using the obtained results in the statistical estimation problems are discussed. This work has been supported by the European Social Fund within the project 2013/0024/1DP/1.1.1.2.0/13/APIA/VIAA/045. |
| BÍLÁ Alice " 1.Popularizace vědy - představení matematiky středoškolským studentůmAntonín Jančařík, Alice Bílá2.Limity GeoGebry a jiných softwarů i jejich uživatelů Antonín Jančařík, Alice Bílá " - from the section: New trends in mathematical education bude dodán |
| BÍLKOVÁ Diana " Modern Methods of Parametric Estimation: Estimation Using L-moments and TL-moments " - from the section: Statistical methods in technical and economic sciences and in practise This paper deals with the application of such robust methods of point parameter estimation, as the methods of L-moments and TL-moments on economic data. The study is divided into a theoretical part, in which mathematical and statistical aspects are described, and an analytical part, during which the results of the use of three robust parametric estimation methods are presented. Total 168 income distributions of the years from 1992 to 2007 in the Czech Republic (distribution of net annual income per capita in CZK) were analyzed. |
| BISWAS Haider Ali " Nonlinear Ordinary Differential Equations Applied to Modeling the Epidemic Disease:An Optimal Control Approach " - from the section: Differential equations, dynamic systems and their applications Nonlinear ordinary differential equations (ODEs) in the form of mathematical Modeling play significant role in analyzing the spread of emerging infectious epidemic disease. The nonlinear mechanism of the host-pathogen interactions inside the human body can be investigated and a proper control strategy can be adapted with the help of optimal control techniques in terms of ODEs. In this paper, some applications of optimal control problems in terms of nonlinear ODEs to modeling the human infectious diseases have been addressed and their numerical simulations are presented with graphical illustrations. |
| BOHÁČ Zdeněk " Vybrané aspekty ovlivňující studijní výsledky z matematiky " - from the section: New trends in mathematical education Autoři: BOHÁČ Zdeněk, DOLEŽALOVÁ Jarmila, KREML Pavel Postupně klesající úroveň znalostí z matematiky je problémem, který trápí nejen vyučující matematiky, ale i pedagogy odborných kateder. Příčiny a také názory studentů na tento problém jsme zjišťovali formou anonymního dotazníku. Zajímaly nás vazby mezi úrovní vstupních znalostí matematiky a geometrie, přístupem studentů k přednáškám, cvičením a zkouškám, dobou přípravy na zkoušku a výsledkem první zkoušky z matematiky na vysoké škole. |
| BRANDI Primo " Mathematical Models Games a new approach to innovation in Mathematical Education " - from the section: New trends in mathematical education Mathematics & Real life (M&R) is a project of the Department of Mathematics and Informatics of the University of Perugia which for over twenty years has promoted the dynamic interaction between the real world and mathematics as startup to educational innovation (www.matematicaerealta.it ). M&R´s spirit perfectly agrees with the recommendation (2006/962/EC) of the European Parliament on key competences for lifelong learning which strongly encourages an approach to mathematical education based on mathematical modelling. With the aim of spreading its proposal, M&R organizes many activities devoted to Schools of all levels, from primary to high school. One of the more appreciated is the Mathematical Models Games now in its sixth year, which has involved more than 10.000 young people. This year M&R adds a Creative Relay Race to the individual competition. Participants will become also authors and not just beneficiaries of the event. The materials produced for the competition reveals a significant educational meaning, that will be presented in details. |
| BREIDAKS Juris " The Variance Estimation for the Measures of Change for Multistage Cluster Sampling Designs Using Software R " - from the section: Statistical methods in technical and economic sciences and in practise Since EU-SILC was launched, much attention has been paid to sampling errors. The computation of standard errors for estimates based on EU-SILC faces a number of challenges. In this article, we propose a simple approach for standard error estimation based on basic statistical techniques. The proposed estimator is simple and flexible, now theoretically justified. It can accommodate nearly all the sampling designs and the target indicators used in EU-SILC, regardless of their complexity. The functions vardcros and vardchanges (on the software R base) were made for the proposed approach. |
| BUDÍK Ladislav " Skládání křivek překročení časových řad průtoků SUPERPOSITION OF CUMULATIVE FREQUENCY CURVES OF FLOWS " - from the section: Statistical methods in technical and economic sciences and in practise The author deals with superposition of cumulative frequency curves of flows in junctions in this paper. This is used more common distribution than the LN3 distribution. Than the superposition problem must be solved numerically because of impossibility to obtain the density function. Such estimates are the basical backgrounds for nearly all of hydrological reports produced by Czech Hydrometeorological Institute. |
| BUDÍKOVÁ Marie " Analýza neúspěšnosti bakalářského studia matematiky a aplikované matematiky " - from the section: New trends in mathematical education Autorky se v příspěvku zabývají sledováním vlivu různých faktorů na neúspěšnost studentů bakalářského studia programů Matematika a Aplikovaná matematika na Přírodovědecké fakultě Masarykovy univerzity v Brně v letech 2003 - 2010. V příspěvku jsou podrobně analyzována data o studentech, kteří nastoupili ke studiu v roce 2010, u ostatních ročníků je pak uvedeno celkové shrnutí. Data byla získána z Informačního systému MU a jejich zpracování bylo provedeno v systému STATISTICA Cz 12. |
| BUDKINA Natalja " On a Problem of Smoothing Histopolation under Additional Restrictions " - 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. The generalization of this problem for Hilbert spaces allows us to investigate this problem, prove the existence of its solutions and suggest the method for their construction. The other possibilities for using the obtained results in the statistical estimation problems are discussed. |
| CAPANNA Alessandra " Sound Domes and other Rooms made with Sound. Related Geometries " - from the section: Mathematics and art In the new perspective of considering sound like another building material, the paper illustrates some recent architectural installations conceived as experimental work with spatial-sound characteristics. SoundART and SoundARCHITECTURE are measurable entities in form of augmented-reality installations strictly linked to performing new geometries but also related to a new interpretation of simple, archetypical Euclidean geometry. “Music is not only what we hear and listen, but everything that happens”. George Brecht |
| CARKOVS Jevgenijs " Markov Switched Difference Equations of Investment Risk Analysis " - from the section: Differential equations, dynamic systems and their applications Authors: J. CARKOVS, K. ŠADURSKIS This paper deals with linear difference equations with coefficients dependent on the Markov chain. We derive operator equations for the first and the second moments, which can be used by investors for Markowitz approach to portfolio selection. This results the most convenient for equations with near to constant coefficients. In this case we have succeeded in asymptotic approximation of the above mentioned operator equations by an ordinary difference equations with constant coefficients. Besides we have proved that covariance matrices of solutions can be analyzed as powers of a positive operator in partially ordered Banach space. This permits to formulate the necessary and sufficient mean square stability condition as a spectral problem. The proposed method gives very convenient criterion for ergodic property analysis of GARCH(p,q) processes. Much of our paper is devoted to asymptotic analysis of difference equations subjected to small parameter. For these equation we derive diffusion approximation method and prove that resulting stochastic Ito equation may be used for stationary solution analysis. In order to illustrate of this method availability we analyze the most popular GARCH(1,1) model for portfolio volatility. Our proposal approach permits to develop diffusion approximation for regression model with correlated residuals and to discuss dependence of stationary volatility on correlation coefficient. Some papers relevant to the Plenary lecture: [1] J. Carkovs, J.Stoyanov: Asymptotic methods for stability analysis of Markov dynamical systems with fast variables. – In: From Stochastic Analysis to Mathematical Finance. Festschrift for Professor Albert Shiryaev. Kabanov, Yu. and Liptser, R. (Eds.) Springer-Verlag, Berlin, 2005, pp. 93-110. [2] J. Carkovs: On Diffusion Approximation of Discrete Markov Dynamical Systems. Proceedings of World Academy of Science, Engineering and Technology,Volume 30, July, 2008, 1-6. [3] J. Carkovs, V. Korolyuk: On stochastic stability of Markov evolution associated with impulse Markov dynamic systems. Probability Theory and Mathematical Statistics, 2006, Nr. 75, 60-63. [4] J. Carkovs, V. Jasinsky: Asymptotic methods for stability analysis of linear systems with diffusion coefficients. Theory of Stochastic Processes, 2005, 11(27), Nr. 1-2, 12-23. [5] J. Carkovs, K. Šadurskis: Equilibrium stochastic stability of Markov dynamical systems. Proceedings of the 11 International Conference APLIMAT-2012. Slovak University of Technology, Bratislava, Slovakia, 103-111. |
| CEPPITELLI Rita " An Application of Back´s Theorem to an Ordering of Distributions of Wellbeing. " - from the section: Statistical methods in technical and economic sciences and in practise Back´s Theorem [1] proves the existence of jointly continuous utility functions for a family of closed partial preorder defined on closed subsets of a locally compact, second countable commodity set. In this paper we applied Back´s Theorem to an ordering of distributions of wellbeing when the population varies. The preoders are assumed closed and not necessarily total and they are defined on closed subsets of distributions. In fact, pairs of distributions may not be comparable or their comparison could be not meaningful. In this setting, Back´s Theorem allows us to establish the existence of jointly continuous utility functions, that is, utility functions that depend continuously on the population, the distribution set and the preference relation. Our theorem generalizes Broome´s result [2]. [1] Back, K., Concepts of similarity for utility functions, Journal of Mathematical Economics, 15 (1986), 129-142. [2] Broome, J., Representing an ordering when the population varies, Social Choice and Welfaire, 20 (2003), 243-246. |
| COCCHIARELLA luigi " On the Tribute of Graphic Applications to Geometrical Theories (and vice versa) " - from the section: Mathematics and art It is sometimes hard to decide whether the relationship between theory and application is a top-down or a bottom-up process, not only in science but also in art and techniques, where often math – in our case geometry - seems to arise from applications, like in the case of Survey and Projective Geometry, or to deeply share inspiration with applications, like in the cases of Expressionism and Topology, or of Impressionism and the modern theories in Physics, all the mentioned fields appearing strongly related to their specific cultural contexts. |
| DEMLOVA Marie " Written Tests with Closed Books as a Tool for Assessing Understanding and Competencies Marie Demlová Faculty of Electrical Engineering Czech Technical University in Prague " - from the section: New trends in mathematical education A written test with closed books is one of the mostly used form of a final assessment of a mathematics course. In case the written test is not accompanied by an oral examination, the written test should guarantee that successful passing the test needs from students not only understanding of basic mathematics concepts but also gaining some of mathematical competences (introduced in the Danish KOM project [2] and developed in the new edition of the curriculum document [1]). The talk will bring experience gained at the Faculty of Electrical Engineering in coursed Mathematics 1 (basic calculus), Linear Algebra, and Discrete Mathematics. |
| DOBRUCKÝ Branislav " Harmonic Distortion Determination of Non-Harmonic Waveforms in Impulse Systems Using Theory of Series " - from the section: Modeling and simulation in engineering and scientific computations The novel approach of harmonic distortion determination of non-harmonic wave-forms in Impulse Systems is introducing. The mathematical description of this sys-tem is provided by using of infinite series for analysis and determination of root-mean-square values and harmonic distortion factor of the periodical non-harmonic function. The investigated quantities are output voltages and currents of power electronic converter supplying resistive-inductive or capacitive load. The quantities can be either discrete or continuous ones. Method of calculation based on the theory of numerical series verified by actual examples is presented in the paper. |
| DOLEŽALOVÁ Jarmila " Vybrané aspekty ovlivňující studijní výsledky z matematiky " - from the section: New trends in mathematical education Autoři: BOHÁČ Zdeněk, DOLEŽALOVÁ Jarmila, KREML Pavel Postupně klesající úroveň znalostí z matematiky je problémem, který trápí nejen vyučující matematiky, ale i pedagogy odborných kateder. Příčiny a také názory studentů na tento problém jsme zjišťovali formou anonymního dotazníku. Zajímaly nás vazby mezi úrovní vstupních znalostí matematiky a geometrie, přístupem studentů k přednáškám, cvičením a zkouškám, dobou přípravy na zkoušku a výsledkem první zkoušky z matematiky na vysoké škole. |
| DOTLAČILOVÁ Petra " Polynomial Functions and Smoothing of Mortality Rates: The Czech Republic and Slovakia During Their Independent Development After Their Separation " - from the section: Financial and actuary mathematics In this paper we present the possibility of use of polynomial functions of the 2nd and 3rd order for modelling of mortality in the case of Czech Republic and Slovakia during their independent development after separation in 1993. Mortality significantly affects the length of human life and the approach which is used in this paper clearly show differences between mortality of the Czech and Slovak population. Suitability of used methods is tested by statistical t-tests and at the end we discuss about the circumstances in mortality differences between compared populations. |
| FEČKAN Michal " Dynamics of price and marketing " - from the section: Differential equations, dynamic systems and their applications The goal of the article is to study dynamics of price and marketing. Especially, which price has to be chosen by new company on the market. We will try to find relationships between price and increasing or decreasing of amount of customers new company and competitor company. |
| FERDIÁNOVÁ Věra " Characterizations of Some Special Curves in Four-Dimensional space " - from the section: Algebra and geometry and their applications Data visualization in a two-dimensional or three-dimensional space is not a problem of these days any more owing to using computer graphics. Computers are able to display design and motion of figures on a “two-dimensional” monitor while simultaneously preserving information about the third dimension. There are also stereoscopic methods that are a strong tool for visualizing of figures in a three-dimensional space. Nevertheless, the question is how to do the visualization of figures in a four-dimensional space. If you have a look at this issue from the perspective of physics, the fourth coordinate could represent the time. Alternatively, the fourth dimension can be represented as a colour, height and similar scalar information [1]. İn our case we are going to consider the four-dimensional Euclidean space E^4 being the entry space. One of the objectives is to describe various approaches for how to create visualization in a three-dimensional space without losing any important information on the fourth dimension. The article will introduce examples of displaying using the orthogonal projection and parallel coordinates. It will include both an overview of the curves that are generated by different rotations, for instance by a simple rotation, isoclinic rotation, etc., and determination of their properties. |
| FERRARO Ivana " Math and Art in an Italian post-Futurist contemporary painter " - from the section: Mathematics and art Mathematics and science are sources of inspiration for an Italian post-Futurist contemporary painter, Antonio Oliva. We will present some of his artworks and explain their relations to Mathematics. |
| FERREIRA Manuel Alb " The Hahn-Banach Theorem in Convex Programming " - from the section: Financial and actuary mathematics Separation theorems are the fundamentals of convex programming.They are important consequences of Hahn-Banach theorem. This work begins considering vector spaces, in broad sense, then normed spaces and finally Hilbert spaces. It ends with the application of these results in convex programming, an important tool in operations research,finance, management and economics. |
| FJODOROVS Jegors " Estimation of Semi Parametric Markov Models with Frank Copula " - from the section: Statistical methods in technical and economic sciences and in practise The research studies the estimation of a semi parametric stationary Markov models based on Frank copula density function. Described techniques allows us to estimate the parameters of the Frank copula, which has a better fit with compared to a previously selected regression models (estimators of the marginal distribution and the copula parameters are provided). We show how to apply our technique to the financial index S&P 500, or the Standard & Poor´s 500, is an USA stock market index based on the market capitalization of 500 large companies having common stock listed on the NYSE (New York Stock Exchange). Also, using MatLab we made S&P 500 index study - found the best copula fit under our condition, estimated nonlinear parameters and showed an evaluation steps for copula based semi parametric models. |
| FLOREA Olivia " Modelling and Simulation environment for 3D biomechanical systems " - from the section: Modeling and simulation in engineering and scientific computations SimMechanics™ provides a multibody simulation environment for 3D mechanical systems, such as robots, vehicle suspensions, construction equipment, and aircraft landing gear. You model the multibody system using blocks representing bodies, joints, constraints, and force elements, and then SimMechanics formulates and solves the equations of motion for the complete mechanical system. An automatically generated 3D animation lets you visualize the system dynamics. |
| GABKOVÁ Jana " Relationship between of Water jet Cutting Speed and Relevant Quantities Influencing Cutting Quality " - from the section: Statistical methods in technical and economic sciences and in practise Authors: GABKOVÁ J., JANIGA I. Water jet cutting was an exceptional technology in the end of 20th. century, but nowadays it is a highly developed technology. For cutting of any materials (metals, plastics, gum,) were used high-speed Water jets with high pressure 450 MPa in combination with abrasive pieces, which are added to mixing post located before the exit point. The contribution deals with the relationship between cutting speed abrasive Water jet and relevant quantities. Problem solving method is regression analysis, and selection of variables and model building. |
| GEMERANOVÁ Mária " Data Approximation Using Multifocal Lemniscates – Algorithm of Doubling and Removing Lemniscate´s Foci " - 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 input data set sufficiently accurate. Our algorithm searches for approximating lemniscate by doubling and removing its foci, even at the cost of possible increase of local error, appropriately changing the radius value and optimizing parameters of the achieved lemniscate. |
| GFRERRER Anton " Geometric Methods in Robotics " - from the section: Geometric methods have turned out to be quite successful in the field of robotics. In the talk I will exemplarily demonstrate this fact. Among the presented examples are the kinematics of serial and parallel robots, the Schatz mechanism and the complex geometry and kinematics of Mecanum wheels, a wheel type which is frequently used to drive autonomous mobile robots. The applied geometric tools are based on elementary differential geometry, descriptive geometry and the so-called kinematic mappings of W. Blaschke and E. Study. References [1] Gfrerrer, A.: Geometry and Kinematics of the Mecanum Wheel, Computer Aided Geometric Design 25 (2008), p. 784-791. [2] Zsombor-Murray, P. J., Gfrerrer, A.: 3R Wrist Positioning - a Classical Problem and its Geometric Background, Computational Kinematics, A. Kecskemethy and A. Muller (edts.) (2009), p. 175-182. [3] Zsombor-Murray, P. J., Gfrerrer, A.: A Unified Approach to Direct Kinematics of Some Reduced Motion Parallel Manipulators, Journal of Mechanisms and Robotics 2 (021006) (2010), 10 pages, doi:10.1115/1.4001095. |
| GOLDSTEINE Jolanta " Mean square Lyapunov exponents for linear Markov switched difference equations with near to constant coefficients " - from the section: Differential equations, dynamic systems and their applications The paper deals with the system of linear difference equations x(t) in d-dimensional real space with the right part switched by homogeneous ergodic Markov chain y(t) on the compact phase space. Our proven approach permits to derive such a basis matrix that the random process z(t)=B(y(t))x(t) has the same mean square Lyapunov exponent as the solution of the equation x(t) and to propose convenient to application algorithm for asymptotic analysis of the equations with near to constant coefficients. |
| HARASIM Petr " Guaranteed a Posteriori Error Estimates for Obstacle Problem for Elastic Deformation of Membrane " - from the section: Modeling and simulation in engineering and scientific computations We apply functional a posteriori error estimate proposed by S. Repin for numerical solution of obstacle problem for membrane. Numerical solution of the obstacle problem is obtained by the finite element method using bilinear elements. Error of the approximation is estimated by a functional majorant. |
| HECKENBERGEROVA Jana " Algorithm for detection and confirmation of head and shoulders pattern with neckline " - from the section: Statistical methods in technical and economic sciences and in practise Recognition of specific graphical formations such as Flag, Head and Shoulders, Wedge or Triangle in time series of stock prices is an important component of discipline known as technical analysis. These chart patterns are mainly detected by expert visual confirmation long after their occurrence. The aim of presented contribution is description of new revisited automatic detection and confirmation algorithm for Head and Shoulders Pattern (H&SP) with neckline. The detection algorithm is based on statistical estimation of unknown parameter in nonlinear regression model and coefficient of determination evaluation. Confirmation of detection and buying (selling) signals are determinate from stock prices and neckline position in specially chosen trading days. Whole procedure is tested on selected time sections of Dow Jones Industrial Averages, where H&SP is expected to occur. Results of analysis and final discussion, presented in Case Study, show that detection and confirmation of H&SP signalize the fundamental change in trend of stock market prices. |
| HOSKOVA-MAYEROVA Sarka " APPLICATION OF FUZZY MEMBERSHIP FUNCTION IN MATHEMATICAL MODELS FOR ESTIMATION OF VEHICLE TRAFFICABILITY IN TERRAIN " - from the section: Modeling and simulation in engineering and scientific computations The article is the extension of the contribution at conference MEME 2014 at Aveiro, Portugal which was published only in Books of Abstract. The paper deals with verification of complex models of the Cross-Country Movement that were created from standard digital geographic data for typical vehicles being used in the Czech Army. Two variants of mathematical models are considered – crisp set and fuzzy set analysis. The recommendation for appropriate variants is made finally. |
| IDA Cristian " Complex Minkowskian $G$-structures on holomorphic vector bundles " - from the section: Algebra and geometry and their applications For a given holomorphic vector bundle with the type fibre $mathbb{C}^m$ endowed with a complex Minkowski norm, a $G$-structure is defined and called a complex Minkowskian $G$-structure. Several properties of these structures are studied in the present paper, some of them extend to any holomorphic vector bundle the results given by T. Aikou in extit{Complex manifolds modeled on a complex Minkowski space}. J. Math. Kyoto Univ. (JMKYAZ) 35-1 (1995), 85-103, for the holomorphic tangent bundle of a complex manifold. |
| ILTINS Ilmars " Asymptotic Analysis of Non-Parallel Instability of Shallow Mixing Layers with Variable Friction " - from the section: Modeling and simulation in engineering and scientific computations Methods of weakly nonlinear theory are used in the present paper to derive an amplitude evolution equation for the development of instability in a shallow mixing layer. It is assumed that the flow is governed by shallow water equations. Friction term is modeled by means of the Chezy formula where the friction coefficient depends on the transverse coordinate. |
| IORFIDA Vincenzo " Simplicial complexes present in art and arts facilities. " - from the section: Mathematics and art The theory of simplicial complexes arises from the need to classify the many spaces in algebraic topology, complex mathematical and abstract argument. However, some of the techniques used primarily in art for the representation can be applied to different contexts from simple elements to create new objects increasingly multidimensional and complex. Geometric structures that identify a simplicial complex describe the connection structure of the simplessi that generate it. |
| JANCARIK Antonín " Mathematics and Theatre Activities " - from the section: Mathematics and art Theatre activities in mathematics education are an important tool for development of pupils’ comprehension, their motivation and lowering their anxiety and fear of mathematics as too abstract. In this paper, use of theatre activities in teaching mathematics is presented as one of the possible tools that can help teachers make mathematics lessons more enjoyable both for pupils and teachers. Examples of activities suitable for different school level mathematics are presented. |
| JANIGA Ivan " Relationship between of Water jet Cutting Speed and Relevant Quantities Influencing Cutting Quality " - from the section: Statistical methods in technical and economic sciences and in practise Authors: GABKOVÁ J., JANIGA I. Water jet cutting was an exceptional technology in the end of 20th. century, but nowadays it is a highly developed technology. For cutting of any materials (metals, plastics, gum,) were used high-speed Water jets with high pressure 450 MPa in combination with abrasive pieces, which are added to mixing post located before the exit point. The contribution deals with the relationship between cutting speed abrasive Water jet and relevant quantities. Problem solving method is regression analysis, and selection of variables and model building. |
| KAŇKA Miloš " Application of Differential Geometry in the Proof of the Fundamental Theorem of Algebra " - from the section: Algebra and geometry and their applications The goal of the submitted paper is the proof of the fundamental theorem of algebra with the use of basic notions of differential geometry, such as singular $n$-dimensional cube, chains of $n$-dimensional cubes, boundary of $n$-dimensional cube, and boundary of this boundary. Specific meaning has the Stokes theorem, which is the main tool in the proof of the fundamental theorem of algebra. All essential notions given in the text are illustrated on concrete comprehensible examples. |
| KERTÉSZ Milan " The role of the stiffly stable integrators in nonlinear dynamic simulations " - from the section: Modeling and simulation in engineering and scientific computations Conducting nonlinear dynamic simulations in the MSC.ADAMS programme requires appropriate knowledge of the mathematical background of algorithms for the numerical solution of a mixed system of DAE. Setting the parameters of solver, such as the proper selection of system formulation or the integration method for these analyses is of utmost importance. This paper illustrates the influence of these parameters on the convergence, computational time, and accuracy of the solution of the numerically unstable (stiff) equations of a dynamic system. |
| KLEPANCOVÁ Michaela " A Geometrical View on the Sum of the Infinite Series " - from the section: New trends in mathematical education As confirmed by several studies and many practicing teachers, in terms of learning process the sum of the infinite series belongs to difficult and problematic concepts. In our opinion, one of the obstacles that students face in relation to the sum of the infinite series is confusion between terms infinite and unbounded. Several visual representations which may help students overcome some difficulties related to this thorough concept are presented in the submitted contribution. |
| KOMÁK Martin " Application of graph theory in designing of spatial workplace layout " - from the section: Modeling and simulation in engineering and scientific computations Every manufacturing company is constantly trying to streamline its production. One of the ways how to minimize the cost of production is advisable to organize workplaces to each other so their location corresponded with material flow. In this article it is proposed a system for appropriate deployment of these workplaces. The solution is based on the triangle method for deployment. This method is modified and its solution is based on graph theory and their representation by matrices. |
| KONEČNÁ Petra " Secondary School Students´ Knowledge Level in the Field of Application Problems in Mathematics and Chemistry " - from the section: Authors: KONEČNÁ P., SOLÁROVÁ M. Current stage of development of the society is referred to as a knowledge society. It means that teachers at all types of schools aim not only at passing knowledge to students but also at encouraging the skills, habits and attitudes. If a teacher wants to develop society via knowledge, he/she needs to insist on students knowing not just mere reproduction of the subject-matter but particularly understanding it well and on creative engagement of the subject-matter into practice; it means the teacher needs to encourage the deep approach to learning. The teacher’s objective should be to work with such tasks that encourage both this approach and the processes related to the approach. It is the reason why he/she should work with the tasks requiring even more complex mental skills as well as with application tasks. In the contribution it will be present results of the research aimed on a determination the level of the cognitive learning processing and the level of applying the acquired knowledge to specific examples from practice. |
| KOZAKOVIČ Radko " Comparative study of different mathematical methods for solving highly nonlinear dynamical engineering problems " - from the section: Modeling and simulation in engineering and scientific computations The common problem in engineering practice is to find simple analytical solution for complex problems. Often the model finding is really problematic. This problem increases if the solution requires including different types of nonlinearities. If the assignment is to solve complex tasks with consideration to time efficiency and to results precision it is impossible to find solution in this form. In general, the difficulty is caused by the mathematical description for examined system which is from mathematical point of view usually system of differential-algebraic equations (DAE). This type of the tasks can be in some cases difficultly solvable. The difficulty of the solution is more affected by the character of equations than by the quantity of them which are frequently highly nonlinear. Despite of it, the solution is possible to find by numerical methods which have many issues in different cases in the engineering practice. |
| KOŤÁTKOVÁ STRÁNSKÁ Pavla " Clustering of Paintings by Using the Fractal Dimension " - from the section: Mathematics and art The paintings and its parts can be characterized by fractal dimension. In this research our attention has been given to find some similarities of paintings by using statistical methods. To reduce the high-dimensional data, the principal component analysis and the hierarchical cluster analysis will be used. We will explore the differences between the result clusters. |
| KREJČOVÁ Jana " Oscillation of fourth-order difference equations " - from the section: Differential equations, dynamic systems and their applications We study the oscillatory and non-oscillatory solutions of nonlinear difference equations. We give the conditions for equations to be oscillatory and a comparison result on the oscillatory behavior of solutions is stated. |
| KREML Pavel " Vybrané aspekty ovlivňující studijní výsledky z matematiky " - from the section: New trends in mathematical education Autoři: BOHÁČ Zdeněk, DOLEŽALOVÁ Jarmila, KREML Pavel Postupně klesající úroveň znalostí z matematiky je problémem, který trápí nejen vyučující matematiky, ale i pedagogy odborných kateder. Příčiny a také názory studentů na tento problém jsme zjišťovali formou anonymního dotazníku. Zajímaly nás vazby mezi úrovní vstupních znalostí matematiky a geometrie, přístupem studentů k přednáškám, cvičením a zkouškám, dobou přípravy na zkoušku a výsledkem první zkoušky z matematiky na vysoké škole. |
| KROUPOVÁ Monika " Analýza neúspěšnosti bakalářského studia matematiky a aplikované matematiky " - from the section: New trends in mathematical education Autorky se v příspěvku zabývají sledováním vlivu různých faktorů na neúspěšnost studentů bakalářského studia programů Matematika a Aplikovaná matematika na Přírodovědecké fakultě Masarykovy univerzity v Brně v letech 2003 - 2010. V příspěvku jsou podrobně analyzována data o studentech, kteří nastoupili ke studiu v roce 2010, u ostatních ročníků je pak uvedeno celkové shrnutí. Data byla získána z Informačního systému MU a jejich zpracování bylo provedeno v systému STATISTICA Cz 12. |
| LALATTA COSTERBOSA Cecilia " Performing Hypercube " - from the section: Mathematics and art By Cecilia Lalatta Costerbosa, Alessandra Mantrici and Valentina Savarese during the Exhibition Design Lab at La Sapienza University of Rome, School of Architecture. The concept of Performing Hypercube is based on three distinct elements: cubic module, sharp edges and organicism. Starting from a rectangular-based chart, six squares, each of 12-metres side, are identified; three of them grow in height defining three adjoining cubic volumes. Such volumes are defined by the outline of the sharp edges which delineate the three extrudes, giving back a sort of skeleton of the structure and then leaving hollow the squared faces. The Performing Hypercube consists into a deformation of the segments which create the outline; furthermore, it replaces the angularity of the vertexes with a fluid line. The ultimate result is the creation of different meshes which dislocate themselves within the three volumes’ inner space, piercing the hollow faces, twisting themselves and intersecting one with the other. This deformation reinterprets the three sides/faces of the cubes from an organic perspective; it creates a sort of suspended texture, which is still intimately linked to the sharp edges of the same cubes. Henceforth, through this oppositional relation, the installation links the geometric and rigid structure of the skeleton with the sinuous forms of the mashes, defining a dynamic exegetical conceptualisation of the cube. |
| LETNANOVA Elena " Pythagoras Ratios in the Musical Piece "Alice Was Getting Very Tired..." by Slovak Composer Juraj Beneš " - from the section: Mathematics and art The mathematical ratios 2:1, 3:4, etc. which were found by Pythagoras by mere chance became the basic intervals and perfect consonances not only the Greek music of Antiquity but continued to inspire the mankind in the early Christian, Romanesque, Gothic, and Renaissance times, until the present. The presented composition will demonstrate the struggle of perfect ratios with the imperfect, dissonant ratios which create the dynamics in our peception. |
| LORENZI Marcella G " Math and Art in an Italian post-Futurist contemporary painter " - from the section: Mathematics and art Mathematics and science are sources of inspiration for an Italian post-Futurist contemporary painter, Antonio Oliva. We will present some of his artworks and explain their relations to Mathematics. |
| LÖSTER Tomáš " The Evaluation of CHF Coefficient in Determining the Number of Clusters Using Mahalanobis Distance Measure " - from the section: Statistical methods in technical and economic sciences and in practise The aim of this paper is to evaluate the CHF coefficient, which is often used to determine the number of clusters. There will be used 20 artificially created files for clustering. Conditions are, that the clusters must be touched or partially overlapped. These generated files are created under the same conditions in order to consider the objective results. Based on the analyses we found, that the CHF coefficient using Mahalanobis distance measure is successful for determining the number of clusters together with Ward´s method (70 %) and the average distance method (80 %). |
| MAGNAGHI-DELFINO Paola " Luca Pacioli´s Alphabeto Dignissimo Antiquo " - from the section: Mathematics and art The authors 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. They are particularly interested in the Renaissance mathematicians that combine the classical mathematical knowledge with the humanistic culture and the artistic sensibility. Mathematics and Art have a long historical relationship that goes as far back as the ancient Greek. It suffices to think for example to their use of the Golden Ratio, regarded as an aesthetically pleasing canon. The Humanists of the Renaissance believed that their mission was to revive the magnificence of the classical age, such as that of Latin literature and of Roman architecture and statuary. In particular, in the first decades of the fifteenth century, elaborate lettering which resembles the ancient Roman capital letters began to appear in stone inscriptions. Later, with the discovery and the study of previously unknown ancient inscriptions and an improved historical sensitivity, many artists, craftsmen and architects demanded the lettering style to remain consistent with the classical style as much as possible. Many Renaissance scholars thus proposed various lettering styles, associated both to a geometrical construction and to a theoretical approach. A synthesis of Mathematics, Architecture and Lettering occurs in an encyclopaedic text written by Luca Pacioli. Luca Pacioli, born in Borgo Sansepolcro (Tuscany) in 1455, was a Mathematician, friend of the greatest artists of his time and skilful populariser of Mathematics. He published several works on Mathematics, among which the best known are Summa de arithmetica, geometria, proportioni et proportionalità and De Divina Proportione. Between 1496 and 1498, Luca Pacioli was in Milan at the court of Ludovico Sforza, in the same time Leonardo da Vinci was in Milan. In this time he worked on De Divina Proportione that consists of three distinct manuscripts. The first part, Compendio Divina Proportione, studies and describes the Golden Ratio from a mathematical point of view and studies polygons. The work also discusses the use of perspective by painters such as Piero della Francesca, Melozzo da Forlì and Marco Palmezzano. The second part discusses the ideas of Vitruvius on the application of Mathematics in Architecture. The third part, Libellus in tres partiales tractatus divisus, is mainly an Italian translation of Piero della Francesca´s Latin writings De quinque corporibus regularibus (On the Five Regular Solids) and offers some mathematical examples. The book contains illustrations based on drawings by Leonardo da Vinci. On June 1509 the first printed edition was released in Venice by Paganinus de Paganinis. The clarity of the written material and Leonardo´s diagrams gave the book popularity beyond mathematical circles. Since then, the book has been reprinted several times. We can trace Leonardo´s influence in some parts of the text and there is no doubt that he drew the figures which illustrate the 1509 edition: Pacioli says so more than once. In the book we found particularly interesting examination of woodcuts in which Luca builds his Alphabeto Dignissimo Antiquo and we had proposals for reproducing some characters, chosen on which that reveal the nature of constructive principles. In order to better understand the geometry of the characters and the originality of the work of Pacioli, we compared his letters with those of other Renaissance authors. We felt that this beautiful alphabet needed to be known to students and in general to non-specialists in the history of lettering. To this aim we present here an accurate replica of some letters of Pacioli´s alphabet with the program GeoGebra, following the author´s original instructions which are, however, not always complete. Key words. Art, Geometry, Geometrical Shapes, Luca Pacioli Mathematics Subject Classification: AMS_01A40 |
| MAGRONE Paola " Form and Art of Closed Crease Origami " - from the section: Mathematics and art We show some origami models appeared for the first time as student projects in Bauhaus around 1930. The same models are studied today by mathematicians and structural engineers for its geometric and mechanical properties and not yet completely understood. A brief discussion on origami axioms will introduce origami geometry. |
| MAREK Jaroslav " CLUSTERING OF PAINTINGS Clustering of paintings by using of the fractal dimension " - from the section: Mathematics and art The paintings and its parts can be characterized by fractal dimension. In this research our attention has been given to find some similarities of paintings by using statistical methods. To reduce the high-dimensional data, the principal component analysis and the hierarchical cluster analysis will be used. |
| MATVEJEVS Andrejs " On Stochastic Resonance in Pipeline, Induced By Pulsed Fluid Flow " - from the section: Differential equations, dynamic systems and their applications This paper deals with stability analysis of elastic pipes containing water flow. The velocity of the water flow is perturbed harmonically with random rush of phase. Applying diffusion approximation approach to analysis of Markov dynamical systems we derive the Lyapunov index for the pipe shapes. We have proved that for the pipe safekeeping examination is not sufficient only to make analysis of the first shape dynamics but also we should examine the Lyapunov index for the shapes of more large numbers. |
| MINCULETE Nicusor " Several Bounds for Some Statistical Indicators " - from the section: Statistical methods in technical and economic sciences and in practise In the introduction we will present several notions related to several statistical indicators for discrete random variables in finite case; these have been presented in some Statistics books. In the present paper we will obtain some properties of bounds of the variance, the standard deviation, the coefficient of variation and of the covariance. |
| MORAOVÁ Hana " Non-Mathematical Aspects of Mathematics Textbooks – What Are the Values and Who Is Responsible for Them " - from the section: New trends in mathematical education The paper presents results of text and picture analysis of a set of mathematics textbooks for primary schools written by a team of two authors. The analysis is supplemented by in-depth interviews with the main author and with the editor from the publishing house. The author of the paper tries to find an answer to the question what values are implicitly handed over to the younger generation and who is responsible for their selection into the textbooks. The findings suggest that cultural values are “accidental” rather than deliberate and none of the parties involved feels any obligation to pay any special attention to them. |
| MOŠNA František " Riemann integral - possibilities of definition " - from the section: New trends in mathematical education Riemann integral can be defined by several ways. We offer one possible simplification of Riemann definition which is suitable also for line integrals, double integrals or integrals in higher dimensions or other types. This introduction is quite simple, general and illustrative, and so suitable for students from didactic point of view. |
| MURESAN Viorica " An Approximation Integration Method for the Solution of a Differential Equation with Linear Modification of the Argument " - from the section: Differential equations, dynamic systems and their applications In the paper we consider a Cauchy problem for a differential equation with linear modification of the argument. In the conditions of an existence and uniqueness theorem, we give an algorithm to approximate the solution. We use Picard operators´ technique([3]), Bernstein operators([1]) and the same procedure as that used by O. Arama in the paper [2]. References: [1] Agratini O., Approximation by linear operators, Presa Universitara Clujeana Cluj-Napoca, 2000 (In Romanian) [2] Arama O., Properties concerning monotonicity of the sequence of polinomials of interpolation of S.N.Bernstein and their application to the study of approximation of functions, Studii si Cercetari de Matematica, Acad. R.P.R., Filiala Cluj, 8(1957), 195-210 (In Romanian) [3] Rus I. A., Picard operators and applications, Scientiae Mathematicae Japonicae, 58(2003), No.1, 191-219 |
| NAGY-KONDOR Rita " Determination and Solution of the Motion of Equation of a Pneumatic Drive Vehicle " - from the section: Autors: SZÍKI Gusztáv Áron, JUHÁSZ György, NAGY-KONDOR Rita, JUHÁSZ Botond As a part of a several-year long development process, applying our computerized measuring system, we determined the basic characteristics of the engine of a pneumatic driven mobile. Utilizing the above characteristics and also the Maple13.0 software we established and solved the equation of motion of the vehicle and determined its velocity- and covered distance-time functions. The dependence of the above kinematic functions on the technical parameters were analysed by the GeoGebra 4.4 software. Applying this software the optimal parameters of the drive can be determined indirectly. |
| NORANDO Tullia " Luca Pacioli´s Alphabeto Dignissimo Antiquoa Geometrical Reconstruction " - from the section: Mathematics and art The authors 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. They are particularly interested in the Renaissance mathematicians that combine the classical mathematical knowledge with the humanistic culture and the artistic sensibility. Mathematics and Art have a long historical relationship that goes as far back as the ancient Greek. It suffices to think for example to their use of the Golden Ratio, regarded as an aesthetically pleasing canon. The Humanists of the Renaissance believed that their mission was to revive the magnificence of the classical age, such as that of Latin literature and of Roman architecture and statuary. In particular, in the first decades of the fifteenth century, elaborate lettering which resembles the ancient Roman capital letters began to appear in stone inscriptions. Later, with the discovery and the study of previously unknown ancient inscriptions and an improved historical sensitivity, many artists, craftsmen and architects demanded the lettering style to remain consistent with the classical style as much as possible. Many Renaissance scholars thus proposed various lettering styles, associated both to a geometrical construction and to a theoretical approach. A synthesis of Mathematics, Architecture and Lettering occurs in an encyclopaedic text written by Luca Pacioli. Luca Pacioli, born in Borgo Sansepolcro (Tuscany) in 1455, was a Mathematician, friend of the greatest artists of his time and skilful populariser of Mathematics. He published several works on Mathematics, among which the best known are Summa de arithmetica, geometria, proportioni et proportionalità and De Divina Proportione. Between 1496 and 1498, Luca Pacioli was in Milan at the court of Ludovico Sforza, in the same time Leonardo da Vinci was in Milan. In this time he worked on De Divina Proportione that consists of three distinct manuscripts. The first part, Compendio Divina Proportione, studies and describes the Golden Ratio from a mathematical point of view and studies polygons. The work also discusses the use of perspective by painters such as Piero della Francesca, Melozzo da Forlì and Marco Palmezzano. The second part discusses the ideas of Vitruvius on the application of Mathematics in Architecture. The third part, Libellus in tres partiales tractatus divisus, is mainly an Italian translation of Piero della Francesca´s Latin writings De quinque corporibus regularibus (On the Five Regular Solids) and offers some mathematical examples. The book contains illustrations based on drawings by Leonardo da Vinci. On June 1509 the first printed edition was released in Venice by Paganinus de Paganinis. The clarity of the written material and Leonardo´s diagrams gave the book popularity beyond mathematical circles. Since then, the book has been reprinted several times. We can trace Leonardo´s influence in some parts of the text and there is no doubt that he drew the figures which illustrate the 1509 edition: Pacioli says so more than once. In the book we found particularly interesting examination of woodcuts in which Luca builds his Alphabeto Dignissimo Antiquo and we had proposals for reproducing some characters, chosen on which that reveal the nature of constructive principles. In order to better understand the geometry of the characters and the originality of the work of Pacioli, we compared his letters with those of other Renaissance authors. We felt that this beautiful alphabet needed to be known to students and in general to non-specialists in the history of lettering. To this aim we present here an accurate replica of some letters of Pacioli´s alphabet with the program GeoGebra, following the author´s original instructions which are, however, not always complete. |
| PALLADINO Nicla " From Art to Geometry: Aesthetic and Beauty in the Learning Process " - from the section: Mathematics and art The choice to conceive an educational path on operational strategies that develop to the establishment of mathematical knowledge intended, not only from the technical-operational point of view but also as complex and articulated activity of the human thought (beauty and ecstasy in the synergic effect between reality and fantasy) has been made taking into consideration careful considerations on ability of the mind to deduce conjectures, retract or verify them in a frame of reference not strictly attributable to rationality as form of mathematical expression (in general and of geometrical expression in particular) for excellence. The knowledge comes mainly as element of mediation between two types of thinking: convergent thinking, founded on experience, and divergent thinking that, going beyond the boundaries of reality, is placed in the perceptive, intuitive, creative dimension. The main functions of drawing are to stimulate creativity and to construct individual imagines of reality. When we draw lines that create geometric shapes, for example, we are looking trough the eyes of the mind beyond the simple specified form, attributing a series of geometries, dynamic tensions, proportions to it. In summary there is a close continuous dynamic interaction between what is graphically symbolized in the geometrical shape we see and what constantly changes and is imprinted as image in our mind. A synergic and dynamic connection between what is drawn on paper and what is formed and changes in our mind begins. It is a special capacity of humans to see, in the complexity of shapes that surround them, the essential structures that constitute the shapes and interpret them in connection with their individual and subjective abilities. We see through our eyes, but we discern and know full well these images through our brain. The continuous interaction between idea and design allows, in summary, the materialization of the form in its essence. Starting from images of artistic artefacts from the collections of some of the most important museums in the world, we observed that the inner geometric shapes used for the decoration are all referable to the same type of curve now called hypocycloid. During the centuries, famous mathematicians were interested on alternative methods for generate hypocycloids and some of their methods are very interesting to recreate through interactive geometry software. It is possible to use our dissertation as a starting point to conceive a geometric laboratory that, drawing inspiration from artistic works, get to create geometric shapes provided with fascinating symmetries. In particular, we describe as example the construction of the envelope of the Simson-Wallace line starting from a square, through Cabrì. We think that combining in the learning process some historical notes, that highlight the continuous evolution of the mathematics, and suggestions aroused by the beauty of artistic objects and shapes can stimulate the interest and the learning of simple or complex concepts, within the geometry. |
| PAUN Marius " Teaching Mathematics " - from the section: Mathematics and art Doing mathematics is primary a competition with yourself to find the roots of the science. Teaching mathematics is a struggle to make these roots understandable and in this reason we have to go back to the beginnings when mathematics and art were one. An old story, a piece of art, some music will help the student to easily understand some quite difficult mathematical notions. |
| POLESŇÁK Lukáš " Dynamics of price and marketing " - from the section: Differential equations, dynamic systems and their applications The goal of the article is to study dynamics of price and marketing. Especially, which price has to be chosen by new company on the market. We will try to find relationships between price and increasing or decreasing of amount of customers new company and competitor company. |
| POTŮČEK Radovan " Sum of generalized alternating harmonic series with four periodically repeated numerators " - from the section: Modeling and simulation in engineering and scientific computations This contribution deals with the generalized convergent harmonic series with four periodically repeated numerators and it is a follow-up to author’s papers dealing with the generalized alternating harmonic series with two and three periodically repeated numerators. It is derived the only value of the last numerator for which this series converges. Then the formula for the sum of this series is analytically derived. Finally, the obtained analytical results are numerically verified by using the computer algebra system Maple 15. |
| POZDÍLKOVÁ Alena " Comparison of the Business Accounts in The Czech Republic " - from the section: Statistical methods in technical and economic sciences and in practise With increasing competition in the banking market, banks are looking for new clients via packages and tailor-made services. The target group also includes entrepreneurs, i.e. legal entities as well as individuals. The aim of the paper is a comparison of the offers of 12 business accounts intended for entrepreneurs and small businesses with no restriction on the type of the client and the company´s turnover. The comparison of various business accounts is performed by the height of the bank fees, benefits offered, availability of bank machines and quality of smartbanking using multi-criteria evaluation of the alternatives. |
| PUCKOVS Andrejs " Volatility forecasting by using Wavelet based Neural Network with Exogenous Input " - from the section: Differential equations, dynamic systems and their applications In current research financial time series forecasting is done for world volatility (implied volatility) indexes. In current research a wavelet decomposition is used together with Neural Networks for financial time series volatility forecasting on mid-term investment horizons. This is very important for investment risk control which can be used by financial institutions. Volatility forecasting is made in two steps. In the first wavelet decomposition is done by using Direct and Inverse Discrete Wavelet Transform with second order Daubechies mother wavelet function. Decomposed parts of the signal are used for subsequent (historical) volatility estimates. Further volatility estimates of decomposed signal are used as input for Neural Networks, which are making implied volatility forecasts. In the second step Implied Volatility data are preprocessed and feed the output of the Neural Network. For research is used Neural Network with NARX (Nonlinear Autoregressive Neural Network with Exogenous Input) with one hidden layer. After training realised by Levenberg-Marquart training algorithm results are tested on additional data. Wavelet based Neural Networks are showing good results for implied volatility (volatility indexes) forecasts. In current researc VIX index forecasts are realized based on historical VIX index and S&P500 data. (may be revieved) |
| PŘIBYL Jiří " Heuristic Strategy Introduction of an Auxiliary Element " - from the section: New trends in mathematical education The paper describes a heuristic strategy for problem solving called Introduction of an Auxiliary Element. The strategy is described and illustrated by several problems. Moreover, the paper presents conclusions of an experiment in which pupils were for the period of four months exposed to the solution of problems using the strategy Introduction of an Auxiliary Element. This experiment was conducted in six schools in the Czech Republic with the total of 158 pupils aged 14-15. The experiments show that mastery of the strategy had positive impact on the pupils’ attitude to problem solving. |
| RAK Josef " Simulation of Convergence of Nyström Method with Singularity Subtraction in Integral Equation of the Second Kind " - from the section: Modeling and simulation in engineering and scientific computations This paper deals with the numerical solution of a singular integral equation of the second kind with a special singular kernel function. The numerical solution in this paper is based on the Nystrom method. The Nystrom method is based on approximation of the integral in equation by numerical integration rule. The speed of convergence of the Nyström method is compared with an alternative method. |
| RIEČANOVÁ Izabela " Finite Volume Method Scheme for the Solution of Helmholtz Equation " - from the section: Differential equations, dynamic systems and their applications The presented paper shows the approach by the Finite volume method to the solution of the Helmholtz equation. This equation arises in various fields of physics including acoustics. Its solving by numerical methods could lead to new contributions into the area of acoustical simulations. Article describes the particular numerical method and presents the results of our first experiments. |
| SALVADORI Anna " Linearity´s magic circle " - from the section: New trends in mathematical education The recommendation (2006/962/EC) of the European Parliament on key competences for lifelong learning encourages an education based on mathematical modeling. This often requires a radical renewal of teaching practice. Mathematics & Real life (M&R), a project of the Department of Mathematics and Informatics of the University of Perugia which promotes the dynamic interaction between the real world and mathematics as startup to educational innovation, makes available to the Schools the know-how acquired in over 20 years of didactical experimentation (www.matematicaerealta.it). One of the more appreciated educational paths suggested by M&R is Linearity´s magic circle which involves students of 12-17 years old. The path, leading from the proportionality to logarithms, involves key knowledge as linear equations, arithmetical and geometrical progressions, exponential functions. As usual in M&R proposal, it evolves into an ascending helix between real life situations and mathematical concepts. The didactical plane will be presented into details. |
| SKRIPKOVA Lucia " On fundamental solution for neutral differential equations with a delay " - from the section: Differential equations, dynamic systems and their applications We are concerning with the study of linear systems of neutral differential equations with a delay. Fundamental solution of the corresponding matrix equation is stated assuming the linear parts to be given by pairwise permutable matrices. Some of its properties are proved, including an exponential estimation of the norm. Solution of a nonhomogeneous initial value problem is represented using this matrix polynomial of a time-dependent degree. |
| SMETANOVÁ Dana " The second order Lagrangians - regularity problem " - from the section: Algebra and geometry and their applications The aim of the paper is to apply some recent results on regularization of Lagrangians to the case of second order Lagrangians corresponding to 3rd order Euler-Lagrange equations. The case of the second order Lagrangians afinne and non-affine in second derivatives is studied. Its related 3rd order Hamiltonian systems and geometrical correspondence between solutions of Hamilton and Euler-Lagrange equations are found. |
| SZÍKI Gusztáv Á. " Determination and Solution of the Motion of Equation of a Pneumatic Drive Vehicle " - from the section: As a part of a several-year long development process, applying our computerized measuring system, we determined the basic characteristics of the engine of a pneumatic driven mobile. Utilizing the above characteristics and also the Maple13.0 software we established and solved the equation of motion of the vehicle and determined its velocity- and covered distance-time functions. The dependence of the above kinematic functions on the technical parameters were analysed by the GeoGebra 4.4 software. Applying this software the optimal parameters of the drive can be determined indirectly. |
| TEDESCHINI LALLI Laura " Earpoints: Timescales in Listening " - from the section: Our act of listening incorporates an ability to decode signals in real time and extract several time-scales. We will review timescales intrinsic to spatial hearing. |
| TORRE Matteo " From Quantum Physics to Piero Manzoni: the new role of the observer " - from the section: Mathematics and art Quantum mechanics has returned to the viewer a key role in the realization of the experiment, role it had lost in the context of classical physics. Almost the same years, the viewer of artwork acquires a key role, even going so far to be himself an artwork or to decide until it´s both. The article outlines a parallel between the operation of measure in the quantum mechanics experiments and the works of the Italian artist Piero Manzoni, creator of the famous and irreverent Artist´s Shit. |
| VAGASKÁ Alena " The Application of Mathematical and Statistical Methods to Determine the Critical Temperature of the Electrolyte During the Anodizing Process " - from the section: Statistical methods in technical and economic sciences and in practise Abstract. The paper deals with the application of mathematical and statistical methods to identify and analyse factors acting during the process of aluminium anodic oxidation. The influence of the input chemical factors (amount of sulphuric acid, concentration of aluminium cations in the electrolyte) and physical factors (the electrolyte temperature, duration of oxidation) on the resulting layer thickness has been investigated at defined current density of 3 A.dm-2. The experiment was based on the Design of Experiments methodology. Príspevok sa zaoberá aplikáciou matematicko-štatistických metód pri identifikácií a analýze faktorov pôsobiacich v procese anodickej oxidácie hliníka. Experiment, realizovaný na základe metodiky DoE (Design of Experiments), sleduje v rámci 26 samostatných pokusov vplyv chemických faktorov (množstvo kyseliny sírovej, koncentrácia hliníkových katiónov v elektrolyte) a fyzikálnych faktorov (teplota elektrolytu, doba anodickej oxidácie) na výslednú hrúbku vytváranej oxidovej vrstvy pri konštantnej anodickej prúdovej hustote 3 A.dm-2. |
| VARGA Marek " Notes To Proofs " - from the section: New trends in mathematical education Any mathematical theory consists of a system of logically bound definitions, theorems and their proofs. As a result of mathematics lessons reduction, argumentation and verification of mathematical propositions are often omitted at primary and secondary schools. Consequently, knowledge of proofs, or argumentation competence, is not necessarily required in mathematics exams at universities anymore. In the submitted contribution we attempt to suggest how it might be possible to preserve mathematical proofs in mathematics instruction. |
| VELICHOVÁ Daniela " Minkowski Point Set Algebra " - from the section: Algebra and geometry and their applications Minkowski set operations defined on point sets in arbitrary geometric space can be used for introduction of an algebra structures with specific properties valid on point sets as basic elements. Some of the basic notions and concepts of such Minkowski point set algebras are derived and applied as modelling tool for generating differentiable manifolds in geometric spaces of arbitrary dimension. |
| VÖRÖS László " Spatial Reconstructions of Picturesbased on Penrose Shapes " - from the section: Mathematics and art The Reuterswärd-Penrose triangle and the Penrose staircase establish the geometrical foundation of impossible pictures and several works of art created by the application of 2D images of cubes touching each other by faces. These are often impossible to reconstruct in space. We can build spatial reconstructions of these pictures with help of 3D models of the 6D cube and of lower dimensional parts derived from those. This paper describes how to transform these spatial shapes to get the same pictures by oblique parallel or central projections. |
| ZÁHONOVÁ Viera " Influence of Students’ High School Mathematics Knowledge on Their Success in Subject Mathematics I " - from the section: New trends in mathematical education Reforms in educational system have a considerable influence on mathematics knowledge of high school graduates. This situation has negative effect on students’ success in Mathematics I at the Faculty of Mechanical Engineering of STU in Bratislava. In this article, the results of an entrance test from high school mathematics since academic year 2008/09 are presented. Success in Mathematics I is also presented and it is compared with the results of entrance test. |
| ZAHRÁDKA Jaromír " On the Acyclic Polynomial of the Linear Chain of Hexagons " - from the section: Algebra and geometry and their applications will be added |
| ŠADURSKIS Karlis " Markov Switched Difference Equations of Investment Risk Analysis " - from the section: Differential equations, dynamic systems and their applications Authors: J. CARKOVS, K. ŠADURSKIS This paper deals with linear difference equations with coefficients dependent on the Markov chain. We derive operator equations for the first and the second moments, which can be used by investors for Markowitz approach to portfolio selection. This results the most convenient for equations with near to constant coefficients. In this case we have succeeded in asymptotic approximation of the above mentioned operator equations by an ordinary difference equations with constant coefficients. Besides we have proved that covariance matrices of solutions can be analyzed as powers of a positive operator in partially ordered Banach space. This permits to formulate the necessary and sufficient mean square stability condition as a spectral problem. The proposed method gives very convenient criterion for ergodic property analysis of GARCH(p,q) processes. Much of our paper is devoted to asymptotic analysis of difference equations subjected to small parameter. For these equation we derive diffusion approximation method and prove that resulting stochastic Ito equation may be used for stationary solution analysis. In order to illustrate of this method availability we analyze the most popular GARCH(1,1) model for portfolio volatility. Our proposal approach permits to develop diffusion approximation for regression model with correlated residuals and to discuss dependence of stationary volatility on correlation coefficient. Some papers relevant to the Plenary lecture: [1] J. Carkovs, J.Stoyanov: Asymptotic methods for stability analysis of Markov dynamical systems with fast variables. – In: From Stochastic Analysis to Mathematical Finance. Festschrift for Professor Albert Shiryaev. Kabanov, Yu. and Liptser, R. (Eds.) Springer-Verlag, Berlin, 2005, pp. 93-110. [2] J. Carkovs: On Diffusion Approximation of Discrete Markov Dynamical Systems. Proceedings of World Academy of Science, Engineering and Technology,Volume 30, July, 2008, 1-6. [3] J. Carkovs, V. Korolyuk: On stochastic stability of Markov evolution associated with impulse Markov dynamic systems. Probability Theory and Mathematical Statistics, 2006, Nr. 75, 60-63. [4] J. Carkovs, V. Jasinsky: Asymptotic methods for stability analysis of linear systems with diffusion coefficients. Theory of Stochastic Processes, 2005, 11(27), Nr. 1-2, 12-23. [5] J. Carkovs, K. Šadurskis: Equilibrium stochastic stability of Markov dynamical systems. Proceedings of the 11 International Conference APLIMAT-2012. Slovak University of Technology, Bratislava, Slovakia, 103-111. |
| ŠIMPACH Ondřej " Polynomial Functions and Smoothing of Mortality Rates: The Czech Republic and Slovakia During Their Independent Development After Their Separation " - from the section: Financial and actuary mathematics In this paper we present the possibility of use of polynomial functions of the 2nd and 3rd order for modelling of mortality in the case of Czech Republic and Slovakia during their independent development after separation in 1993. Mortality significantly affects the length of human life and the approach which is used in this paper clearly show differences between mortality of the Czech and Slovak population. Suitability of used methods is tested by statistical t-tests and at the end we discuss about the circumstances in mortality differences between compared populations. |
| ŠOOŠ Ľubomír " Dynamic Analysis Spindel-Bearings System (Sbs) of the Headstock Machine Tools " - from the section: Authors: ŠOOŠ Ľubomír, KOVÁČ Pavel, MATÚŠ Miloš, KRIŽAN Peter, BENIAK Juraj The quality of machine tools is critical in determining their productivity and the accuracy of the finished work piece. While static analysis of SBS describes spindle behaviour in a static mode, dynamic analysis describes SBS behaviour under real conditions and so the real operational state is better represented. It is very important to know the dynamic characteristics, especially in high-speed headstocks. It is important to ensure that the operational revolving frequencies do not fall within the resonant zone. When this happens, the vibration amplitude of the spindle is considerably increased, and the spindle´s total stiffness falls to unacceptable levels. |
| ŽDÍMALOVÁ Mária " Graph Cutts in Image Processing " - from the section: Modeling and simulation in engineering and scientific computations In the contribution we discuss an application of min-cut algorithms on graphs for problems segmentation of images. Segmentation, as many problems in image processing can be formulated as a minimization problem. Graph cuts can work as a powerful energy minimization tool producing in some cases globally optimal solutions. We concern on Ford-Fulkerson algorithm and its slight modification Edmonds-Karp algorithms for finding the maximal flow in a directed weighted graph. It holds that the maximal flow corresponds to minimal cut, thus the maximal flow leads to minimal cuts, enabling to find a semi-automatic segmentation of an two-dimensional image obtained in a polynomial time. The image is considered as a graph for which we find the maximal flow. The segmentation of an image is then determined by this cut, which enables us to partition the image into pixels of an object and pixels of a background, while the user is expected to determine the typical pixels of the background and the object interactively. |
Number of registered papers: 98 |
Last change: 21.02.2015 22:23:14 |