| ACHILLES Rüdiger " Intersection numbers and characters of algebraic curves and surfaces, Part II: Computation " Part I (Mirella Manaresi) deals with some invariants of algebraic curves and algebraic surfaces in projective n-space. In Part II examples for the computation of these invariants by using freely available open-source computer algebra systems (Reduce, CoCoA, Macaulay2 and Singular) are given and discussed. |
| AMADEI Daniela " The art of being irrational: √2 and φ in mathematics and architecture " Authors: AMADEI Daniela, FRANCAVIGLIA Mauro, LORENZI Marcella Giulia, TORRE Matteo The great British Physicist William Thomson (Lord Kelvin; 1824-1907) said in one of his Lectures “When we cannot express it through Numbers, our knowledge is poor and unsatisfying”. Although he was probably thinking to scientific progress, Numbers has the strange attitude to contribute to the understanding of a “reality” which is often far from Science. There exist in fact a class of Numbers that since the Antiquity fascinate and make curious human’s mind, leading it to search for symmetries and rules even where these do not exist. Numbers represent the known and the rational for excellence. Nevertheless, from Irrational Numbers of Pythagoreans to the Golden Mean, many are the “mysteries” of Mathematics that have been investigated. Several of these ideas and cultural traditions have a significant influence even on our Society, so that it is interesting to wonder which are their origins and which processes do bring their diffusion. Space is open to a deeper thinking that involves also Art and Architecture. In this paper we shall describe some details of Pythagorean Mathematics, trying to refute the myth that the discovery of Irrationals did in fact challenge their Philosophy. We shall thence deal with the Golden Mean and the Square Root of Two in some pieces of Architecture. Starting from the celebrated book De Architectura libri decem in which Vitruvius exposed the technical knowledge of Greeks and Romans, we shall arrive to analyze the “Tempio Malatestiano” of Leon Battista Alberti (1404-1472), a building that, in spite of being incomplete, shows evident carachteristics of the style and theories developed by Alberti. |
| ANDRADE Marina " Simple maternity search with Bayesian networks " Authors: ANDRADE M., FERREIRA Manuel A. M. DNA profiles are commonly used in forensic identification problems. It was in England, in 1995, that the first DNA profiles databases were built. They gave rise to new challenges concerning the forensic identification. In this paper it is intended to exemplify how to use the analysis of DNA profiles to solve the problem of simple maternity search. For it it is necessary to make use of a probabilistic expert system (PES), in this case an object-oriented Bayesian network (OOBN). |
| BELIBANI Rosalba " The project between art and algorithm " The scientific logic with which the computer requires a certain process leads to the need to distinguish in the approach and in the method the types of process, to reason about the influence that the algorithm could have on the new form, and how it determines the outcome of the project; to see if it exists and where is the boundary or the interrelation between the idea, its process and its appearance. The time of the algorithm is the time of absorption of the vision? In short, whereas the project in the digital dimension can be regarded as a scientifically reasonable undertaking, the fundamental questions of art, its existence, and its purpose, remain undefined. In fact, in principle, the project no longer appears impossible as an Escher’s drawing, but a system with a good degree of rationality, while the idea, in its unreal and technically artistic form, in a position to develop internal representations of the world, it is irrational and emotional. It is once again the paradox of Schrödinger´s cat virtual experiment that summarizes the terms of the long-standing issue on objective reality, or rather on what is independent of our observation. It remains to be determined whether, in the digital representation, we observe what is real or we realize models that properly agree with the idea. The transposition of a digital project follows the preconceived mental model or the logical construction of the algorithm, which is superimposed on the idea, turning it into an unreal vision with an acceptably real chance of being realized, replaces or interacts with the mental prefiguring of the project? |
| BENVENUTI Silvia " The curved line belongs to God»: the use of ruled surfaces in the architecture of Antoni Gaudí. " We introduce the concept of ruled surface and we describe some examples (namely the one-sheeted hyperboloid, the hyperbolic paraboloid, the helicoid and the conoid), illustrating their main technical features. Then, we explain how, where and why (both from the technical and the symbolic point of view) Antoni Gaudí uses such surfaces to get his peculiar architecture, pervaded by curved shapes, which on one hand is the heir of the gothic and traditional Catalan architecture and, on the other hand, anticipates the flavour of the modern topological one. A quick glimpse at the latter concludes the paper. |
| BOCCARDI Beatrice " The undeniable opportunity of famous quotes on science to provide great understanding of the deep thinking of their authors " In this paper we analyse the collection 100 +1 frasi famose sulla scienza (100 +1 famous quotes on science), a support tool for the project Adotta Scienza e Arte nella tua classe (Adopt Science and Art in your class), presented at the Aplimat Conference, Bratislava, 2012, and now under way in the Italian schools. This educational project and for the popularisation of science by Esplica- no profit, Laboratorio per la divulgazione culturale e scientifica nell’era digitale, challenges the students to create graphic works inspired by quotes on science from scientists, writers, artists. 100 +1 frasi famose sulla scienza gathers quotes from the antiquity to the current century, whose original comments highlight their value as stages of scientific thought, and their connections and contrasts with different points of view. Besides an educational tool, the quotes in the collection are a repository of scientific trends and changing patterns. Here we compare how different scientists communicate science and trace the common threads of science dissemination to the general public, to show how the content of this atlas of scientific thought goes beyond the practice for which it was designed. Quotations from famous scientific figures constitute a fil rouge to follow the evolution of science and science communication. Often composed in relation to a specific situation, to the public or to a scientific case, they are a key to investigate the authors’ opinions and sentiments. A study that should be undertaken by historians, philosophers of science and communicators. |
| BOHÁČ Zdeněk " Problematika vyhodnocení evaluačního dotazníku " Autoři: BOHÁČ Zdeněk, DOLEŽALOVÁ Jarmila, KREML Pavel Téměř všechny realizované projekty, zvláště pak projekty financované z grantových projektů, vyžadují evaluaci výsledků. Na příkladu evaluace konkrétního projektu ESF autoři poukazují na úskalí spojená s vyhodnocením evaluačního dotazníku. |
| BROTHÁNKOVÁ Darina " Teaching partial differential equations with Maple " The paper demonstrates the possibilities of teaching mathematics in up-to-date way. Maple is one of the most suitable tools of analyzing, visualizing and solving problems in mathematics. Teaching partial differential equations with help of Maple is much more effective, easier and may be even joyful. |
| BRUNETTI Federico Alberto " Topology and proportion in the drawing of the modern architectural space design. " The Libruary at Parco Sempione in Milano (Ico Parisi, X Triennale di Milano 1954). Geometry and Arts in a environmental experience, between spiral as interior growth dynamic simbol and radial symmetry as covering structure. An analogical didactic re-composition and tracing of a building place. |
| BUDÍK Ladislav " Odhady parametrů křivek překročení průtoků v nepozorovaných povodích a jejich optimalizace - výsledky " Příspěvek bude navazovat na několik předchozích příspěvků zabývajících se odhady parametrů křivek překročení a jejich zpřesněním metodou optimalizace na data v měřených profilech. Bude se zabývat odhady těchto parametrů pomocí regresních rovnic a jejich kategorizací v GISovém prostředí (v závislosti na geologických a fyzickogeografických podmínkách)¨v závislosti na kvalitě odhadů - relativní nedostatek dat. Tyto odhady jsou nutné pro rozlišení chování jednotlivých povodí a jejich částí. Bude též možné diskutovat první výsledky hromadného zpracování, hodnotit jejich kvalitu a nastínit možnosti dalšího vývoje návazných metod. Spoluautoři - ing. Pavel Kukla, ing. Petr Šercl. |
| BUDÍKOVÁ Marie " Analýza exponenciálního regresního modelu simulačními metodami " Autoři: MAROŠ Bohumil, BUDÍKOVÁ Marie V příspěvku se zabýváme zkoumáním vlastností odhadů regresních parametrů v exponenciálním regresním modelu, jehož hodnoty získáme mnohonásobně opakovanými simulacemi. Parametry v linearizovaném modelu odhadujeme jednak obyčejnou metodou nejmenších čtverců a jednak iterovanou váženou metodou nejmenších čtverců. Kvalitu odhadů posuzujeme mírou odchýlení odhadů od přesných hodnot parametrů a studujeme závislost této míry na variabilitě náhodných odchylek a počtu opakování měření. |
| CAPANNA Alessandra " 1. Tesseract houses. 2. Order and chaos. Norm and form " 1. Author: CAPANNA Alessandra In endeavoring to design a true 4-dimensional house, we must first, as might be expected, concern ourselves with questions of mathematical definition. The foremost among them being: what precisely is a Tesseract or a Hypercube? In mathematics it is easy to define four dimensional geometry. From this point of view it is also quite easy to describe what shape (or shapes) in our real word a Hypercube can assume. In the architect’s imaginary, on the other hand, a tesseract (architecture) could be either a building whose shape looks like one of the infinite configurations the hypercube can assume in its spatial developing; or else, we can try to get and reproduce the core of four dimensional geometry. Living inside a Tesseract can be a very simple way of explaining a complex concept, by means of our limited but developing perceptual skills, or a very complicated way to describe a not so difficult idea, in a narrative sequence of concurrent spatial events. A clever architect in a novel by Robert Heinlein designs a house in the shape of the 3d unfolded vertical tesseract, but it collapses (through the 4th dimension) when an earthquake shakes it into a more stable form. So, if we were Quintus Teal, the "graduate architect" main character of Robert Heinlein’s novel “And He Built a Crooked House”, what kind of folded, reversed, house should we observe and eventually, from that revolutionary event on, could conceive and design? 2. Authors: CAPANNA Alessandra, FRANCAVIGLIA Mauro, LORENZI Marcella Giulia Architecture is always the result of a generative process , carried out on different scale: those peculiar to the city (urban project) and those to the building; or even to the object, if we are in the field of industrial design. “Shape generation” is based on issues of regularity and/or irregularities and it concerns the locking on and the enforcements of laws, principles, rules and exceptions. Architecture is not just a figurative art, and this is easier to understand if you look at the processes of generation of cities: even when it is seemingly spontaneous and unplanned, it highlights evolutionary "natural" processes due to the will and the case. The paper analyzes the layout of different cities, the Pattern Language’s theory by Christopher Alexander - stating that it is beauty of shape and form which rules emerging life and remarking a set of problems and documented solutions for architects - and, as an evolution of those theories, our studies on Makoto Sei Watanabe’s Induction cities. This is a subject that a theoretical mathematician or a computer scientist might call “generative grammar”. So, what does it mean regularity or chaos in the developing of urban form? |
| DALVIT Ester " Braids: a movie to popularise the mathematical theory of braids " We present a movie realised with 3d graphics techniques with the aim of popularising the mathematical theory of braids. This is the result of an interdisciplinary project involving mathematics, computer science, art and science communication. Though art is not the main purpose of the movie, the aesthetic issue is fundamental as a mean of communication with the general public. Braid theory is a relevant subject suitable for popularisation as a key example of mathematics: it puts together different approaches and research is very active in the field. Moreover, it permits to introduce some themes in topology and group theory in an informal way. The movie is freely available at http://matematita.science.unitn.it/braids. |
| DARVAS György " Symmetries In Action! The Experience Workshop Movement In The Education Of Mathematics And Symmetry Studies Through Arts (joint lecture with Dr. Kristóf Fenyvesi)) " The Experience Workshop - Movement for the Experience Centered Education of Mathematics started in 2008 as a collaborative effort of scientists, artists and educators of the Ars Geometrica Conferences. We organize math-art festivals, workshops, exhibitions, trainings and conferences. In our workshops the implemented activities provide the students with unexploited experiences, never met at their school. Symmetry principles are used as a common guide to all these activities. They are, partly, a tool to repetition, to algorithms, to isotropy and isometry, to similitude, and so on, partly, to bridge a link between scientific truth and artistic beauty, between regularity and harmony. Talented students demand such new kind of information that cannot be included in the standard teaching programs. These workshops develop the creative thinking of the students by burdening their left and right cerebral hemispheres more-or less equally balanced. |
| DOBRAKOVOVÁ Jana " Autonomous systems with infinitely many critical points " Authors: DOBRAKOVOVÁ Jana, ZÁHONOVÁ Viera This contribution is devoted to some aspects of teaching autonomous linear differential systems, especially properties of their critical points sets, for some special cases of linear differential systems, by means of the programming system MATHEMATICA. |
| DOLEŽALOVÁ Jarmila " Problematika vyhodnocení evaluačního dotazníku " Autoři: BOHÁČ Zdeněk, DOLEŽALOVÁ Jarmila, KREML Pavel Téměř všechny realizované projekty, zvláště pak projekty financované z grantových projektů, vyžadují evaluaci výsledků. Na příkladu evaluace konkrétního projektu ESF autoři poukazují na úskalí spojená s vyhodnocením evaluačního dotazníku. |
| DRAGOMIRESCU Ioana " Nonclassical polynomials based spectral Galerkin formulation in a swirling flow stability problem " The properties of the spatial instability waves supported by the Batchelor vortex are investigated here using a polynomials based Galerkin technique. The polynomials basis used in the approximation is proposed in order to optimally satisfy the boundary conditions of the two-point boundary value problem governing the linear stability of the flow for the non-axisymmetric modes case. It is shown that the formulation provides fair accuracy and the numerical results are in good agreement with existing ones. The physical parameters influence on the stability domain of the swirling flow is pointed out. |
| FABBRI Franco " Can ADOTTA SCIENZA E ARTE NELLA TUA CLASSE migrate to Europe? " Adotta Scienza e Arte nella tua classe (Adopt Science and Art in your class) is an educational and popularisation project on the science-art connection addressed to the Italian secondary school. The students are challenged to choose among a hundred commented quotes on science, by physicists, mathematicians and artists, to create a piece of artwork inspired by the interpretation of the selected quote, accompanying it with an original short comment. The project, at its concept stage, was first presented to last year’s Aplimat Conference, Bratislava, 2012, by Esplica– no profit, Laboratorio per la divulgazione culturale e scientifica nell’era digitale. The project is under way in more than 40 Italian schools. It has been selected best project in the section Didattica e Storia della Fisica (Teaching and History of Physics) at the SIF (Italian Society of Physics) Conference, 2012. |
| FENYVESI Kristóf " Symmetries In Action! The Experience Workshop Movement In The Education Of Mathematics And Symmetry Studies Through Arts " Authors: György Darvas, Kristóf Fenyvesi The Experience Workshop – Movement for the Experience Centered Education of Mathematics started in 2008 as a collaborative effort of scientists, artists and educators of the Ars Geometrica Conferences. We organize math-art festivals, workshops, exhibitions, trainings and conferences. In our workshops the implemented activities provide the students with unexploited experiences, never met at their school. Symmetry principles are used as a common guide to all these activities. They are, partly, a tool to repetition, to algorithms, to isotropy and isometry, to similitude, and so on, partly, to bridge a link between scientific truth and artistic beauty, between regularity and harmony. Talented students demand such new kind of information that cannot be included in the standard teaching programs. These workshops develop the creative thinking of the students by burdening their left and right cerebral hemispheres more-or less equally balanced. |
| FERDIÁNOVÁ Věra " Algorithms of Convex Hull for Four-Dimensional Cube " Authors: FERDIÁNOVÁ Věra, ŽÁČEK Jaroslav Visualizing geometric solids in four dimensional Euclidian space is a problem, because recent computers are able to display geometric solids in at most three dimensional space. One possibility is to create a projection of these objects into the Three-dimensional space. We have created a projection of hyper cube and we have found a better convex hull algorithm for this projection. We propose a geometric algorithm based on the Visibility criterion for convex polyhedra [1]. We have tested proposed geometric algorithm on set of isolated vertices, for edges or bodies of our projection |
| FERREIRA Manuel Alberto M. " 1. Infinite servers queue systems computational simulation, 2. The concept of weak convergence in Hilbert spaces " 1. Abstract: For many parameters of interest in the study or application of queuing systems either there are not theoretical results or, existing, they are very complicated what makes their utility doubtful. In this situation it is very common to use simulation methods in order to get useful results. Here a Fortran program to simulate infinite servers queuing systems is presented. Through it, some experiences are performed and the respective results are used to conjecture about some interesting quantities of those systems, mainly about the busy period. 2. Abstract: In order to generalize the Bolzano-Weierstrass Theorem, a weaker notion of convergence is introduced. Then it is discussed in which conditions weak convergence implies convergence. The results presented are in the domain of the real Hilbert spaces. |
| FILIPE José António " Chaos in humanities and social sciences: an approach " Chaos theory has been first used in the applied and natural sciences and just then to the humanities and social sciences. Once introduced, chaos theory got rapidly a developing field. The idea of chaos has been then very significant both for empirical and for theoretical research not just in the applied and natural sciences but also in the humanities and social sciences. Being chaos extremely complex and difficult to be identified in the real world, even using the workable information, it is possible, anyway, up to a certain extent, to find specific mathematical relationships for problems to be solved. In this study some issues are presented in order to work this subject in the humanities and social sciences. |
| FJODOROVS Jegors " Copula Estimation for GARCH (1, 1) Processes " Authors: J.Fjodorovs, An.Matvejevs The possibility of identifying nonlinear time series using nonparametric estimates of the conditional mean and conditional variance were studied in many papers. One of the main problems in these papers is development of time series {x_t, t is from Z } methods of analysis through regression models even without knowing the regression function. The article deals with the estimation of copula-based semi parametric models for GARCH (1, 1) processes with usual kind of information about the distribution law. These models are characterized by conditional heteroscedasticity and have been often used in modelling the variability of statistical data. The basic idea is applied to a local linear regression with squared residuals for finding the unknown function. |
| FLOREA Olivia " The numerical and analytical analysis of some practical problems with high impact in the engineering learning " In this paper are studied some practical problems encountered in the technics. If the systems of differential equations are nonlinear then the numerical analysis using the Matlab software is mandatory. Here is presented a new study of the movement of a projectile in the resistant environement, as well as in the case of an internal mass which vibrates. The harmonic analysis is made with the transfer function. The stability is analysed with the Nyquist and Mihailov criterion. |
| FORBELSKÁ Marie " Using the glm approach for comparing ROC curves " A well accepted measure of accuracy for diagnostic test is the Receiver Operating Characteristic (ROC) curve. Within the generalized linear model (GLM) binary regression framework, ROC curves can be estimated. In studies of classification accuracy, there are often covariates that should be incorporated into the ROC analysis. One nice feature of ROC-GLM method is that it can be easily extended to adjust covariate effects. We illustrate proposed methods on a pancreatic cancer biomarker data set. |
| FRANCAVIGLIA Mauro " The Möbius Band was known to Romans " Although Historians of Mathematics claim that the Möbius strip was somehow introduced in Mathematics rather recently, after work by XVIII Century Geometers, this applies only to the description of its mathematical properties from a formalized viewpoint. The geometric form of the Mobius strip was in fact known long before and it was clear that it had to do with a surface with just one face. Te evidence comes from a IV Century Roman mosaic, in which a Möbius strip is reproduced; the unknown author of the mosaic used this surface to be able to depict a whole Zodiac onto a surface based on a Circle but presenting two half-faces to view. Using a cylinder this was, of course, impossible, so that the artist reverted to the one-faced surface. |
| GABKOVÁ Jana " 1. Použitie softvéru Mathematica® v lineárnom modeli. Using the software Mathematica ® in the linear model . 2. Využitie časovej závislosti procesu vybíjania kondenzátora vo výučbe numerickej matematiky " 1. Autori: GABKOVÁ Jana, JANIGA Ivan Generalized linear model is used to model the functional dependencies, where one variable is a random variable and the second non-random. 2. Autori: Jana GABKOVA, Soňa HALUSKOVÁ Aplikovaná matematika má dôležitú rolu vo vzdelávaní študentov na technickej univerzite. V príspevku uvádzame využitie numerických metód pri spracovaní technického problému. Zamýšľame sa nad posiľnením medzipredmetových vzťahov, diskutujeme o spolupráci učiteľov matematiky a učiteľov „nematematiky“ vo výučbe. V príspevku konkrétne prezentujeme použitie numerických metód pri analýze procesu vybíjania kondenzátora a spätné využitie časovej závislosti procesu vybíjania kondenzátora vo výučbe numerickej matematiky. Neoddeliteľnou súčasťou výučby numerickej matematiky je používanie softvéru Mathematica®. |
| GELATTI Gabriele " A geometrical connection between √2 and √5: the Pythagorean triangle 3-4-5 and the golden section. " The Pythagorean triangle with proportion 3 – 4 – 5 is generated by an elementary geometrical relationship between √2 and √5, thus finding its relation with the golden section. MSC classification number: 51M04 |
| HABIBALLA Hashim " Character recognition through fuzzy logic analysis " Authors: Vilem NOVAK and Hashim HABIBALLA The article shows application of unique method for recognition of characters. The method is based on fuzzy predicate logic with evaluated syntax. It present both basics of theory and implementation - freeware tool for usage of the method. We show also brief results of experiments and also results of current industrial application. |
| HALUSKOVÁ Soňa " Využitie časovej závislosti procesu vybíjania kondenzátora vo výučbe numerickej matematiky " Autori: Jana GABKOVA, Soňa HALUSKOVÁ Aplikovaná matematika má dôležitú rolu vo vzdelávaní študentov na technickej univerzite. V príspevku uvádzame využitie numerických metód pri spracovaní technického problému. Zamýšľame sa nad posiľnením medzipredmetových vzťahov, diskutujeme o spolupráci učiteľov matematiky a učiteľov „nematematiky“ vo výučbe. V príspevku konkrétne prezentujeme použitie numerických metód pri analýze procesu vybíjania kondenzátora a spätné využitie časovej závislosti procesu vybíjania kondenzátora vo výučbe numerickej matematiky. Neoddeliteľnou súčasťou výučby numerickej matematiky je používanie softvéru Mathematica®. |
| HAVELKOVÁ Veronika " Geogebra Applets in Teaching General Chemistry: Chemical Kinetics and Termochemistry " Authors: ADAMEC Martin, HAVELKOVÁ Veronika The paper introduces five interactive applets created in GeoGebra environment for use in teaching general chemistry at bachelor level of teacher-training study program. Four applets were created to illustrate the meaning of reaction rate (chemical kinetics) and one applet to illustrate principles of calorimetry (thermochemistry). |
| IDA Cristian " Some remarks about 1-differentiable cohomology of Sasakian manifolds " Authors: Cristian Ida and Sabin Merchesan In this paper we study some aspects concerning to relative cohomology, Poincaré Lemma, basic cohomology in the context of 1-differentiable cohomology of Sasakian manifolds. |
| IORFIDA Vincenzo " Fractal Images from Electric "Short-Circuits" " We present a description of fractal 3-dimensional images that are generated in electromagnetic and electromechanical devices when a "short circuit" happens. We shortly discuss the relations of this phenomenon with Quantum Theory and Fractals à la Mandelbrot. These images have a nice artistic interpretation, that we comment also in relation with new trends in Art coming from XX Century Physics and Positivism. |
| JANČAŘÍK Antonín " The role of computers in pre-service teacher training – are our graduates ready fot the challenge? " Authors: Antonín JANČAŘIK, Jarmila NOVOTNÁ Introduction of computers to mathematics education is a worldwide trend touching all levels and types of schools. Although development of ICT is rapid and first-class, its introduction to schools often faces many difficulties. Teachers and their training play a significant role in this process. The aim of this paper is to show some aspects that make obstacles to more extensive and effective use of computers in teaching, namely in the area of pre-service mathematics teacher training. |
| JANIGA Ivan " Použitie softvéru Mathematica® v lineárnom modeli. Using the software Mathematica ® in the linear model " Autori: GABKOVÁ Jana, JANIGA Ivan Generalized linear model is used to model the functional dependencies, where one variable is a random variable and the second non-random. |
| JAROŠOVÁ Eva " Analysis of the central composite experiment with pseudoreplications " The statistical model of a response surface relating density of pine wood pellets to four technological factors is built based on data obtained through a central composite design. Canonical analysis is used to find the stationary point and as the resulting point is a saddle point, the optimal setting is determined by means of ridge analysis. Because several pellets are produced at each treatment, a corresponding covariance structure of data must be considered. When the usual method based on averages is used, degrees of freedom of the test statistic distribution must be modified and the prediction interval for response determined with regard to two variance components. |
| KONEČNÁ Petra " Assessment of the concept of undergraduate teacher training presentation of the evaluation results " The paper deals with the presentation of the development and of existing concept of teacher training studies in the field of natural sciences at the University of Ostrava in 2012. This work aims at comparison of this concept with the results of undergraduate students evaluation. In the sections which deal with the structure of the field of study, didactics and practical training are the results enriched with specifics of training teachers of mathematics. |
| KONFRŠT Zdeněk " 1. Linear regressions on panel data " 1. The research report estimates the effects of annual inflation, interest rate and growth rate of three economies on their equity indexes. We have selected economies of USA, Japan and China. Due to difficult to find a ready panel data, these panel data were compiled from various sources. The prepared panel data were linearly regressed, calculated and reported. |
| KOVÁČOVÁ Monika " First overview to Modelling techniques for Intra-tumor heterogeneity and its implication in recurrence of hepatocellular carcinoma " The medical strategies targeting hepatocellular carcinoma (HCC) are often hindered by tumor recurrence that may be as high as 75% in a 5-year period. A part explanation of this dismal figure is due to different etiologies responsible for underlying liver damage facilitating the onset of HCC, and resulting in mutations in variety of genes and molecular pathways of which only few are targetable. Strategic advances in molecular therapy of HCC based on a good understanding of inter-tumor molecular heterogeneity have precipitated into the development of Sorafenib, the first small molecule inhibitor of MAP kinase pathway in viral-induced hepatocellular carcinoma. We will develop and present in this article some techniques on how heterogeneity measurement should be provide in hepatocellular carcinoma data. We will present first implementation of probabilistic model to estimate the frequency at which mutation occur in a population cells. Also some problems as a loss of heterozygosity (LOH) at the mutation will be discussed to elicit prior beliefs about genotype of cells with the mutation. Probabilistic model of allelic counts will be present in this paper. |
| KREML Pavel " Problematika vyhodnocení evaluačního dotazníku " Autoři: BOHÁČ Zdeněk, DOLEŽALOVÁ Jarmila, KREML Pavel Téměř všechny realizované projekty, zvláště pak projekty financované z grantových projektů, vyžadují evaluaci výsledků. Na příkladu evaluace konkrétního projektu ESF autoři poukazují na úskalí spojená s vyhodnocením evaluačního dotazníku. |
| LORENZI Marcella Giulia " “TRAVELING WITH ALBERT” art and scienceevent inspired by Einstein’s life and theory " Arts can make possible a synergic dialogue between Science and society in different ways: from visual Arts and Music, passing through Theatre and Cinema, to the newest hybrid forms of media Arts, the language of emotion can intermingle the rigor of Science with the aim of diffusing Culture, from educational projects, to initiatives involving the general public. There are various possible relationships among them, as witnessed by a variety of specific cases. In particular, as an example, in this paper we will analyze in which way a play (“Traveling with Albert”) inspired by Albert Einstein’s true life and Science was created and represented on stage. Set approximately in 1895, when the young Albert Einstein is living in Pavia, Italy, and beginning to cultivate his interests in Mathematics and Physics, “Travelling With Albert” is written by Edoardo Erba, one of the best Italian playwrights. A cycle of public lectures on Science and Art precedes the shows, that will be accompanied by an e-book, following the aim to involve the audience in the cultural topics dealt with. |
| MAGLI Giulio " Geometry and astronomy in the project of ancient straight roads: " Many ancient cultures planned and constructed long, straight roads, sometimes taking an uttermost care of their “going straight”. In many cases, interesting geometrical and astronomical methods were applied to gain an astonishing accuracy. As it turns out, this “desire of going straight” was not always due to practical purposes but rather to symbolical, cosmological motivations. Sometimes, the very existence of the roads was connected mainly to such motivations. We discuss here some key examples and present the recent results we have obtained about the project of the masterpiece of the Roman roads, Via Appia, |
| MANARESI Mirella " Intersection numbers and characters of algebraic curves and surfaces Part I: Theory " It will be discussed how the algebraic algorithmic approach to intersection theory of Stückrad and Vogel can be used to relate several invariants of algebraic curves and algebraic surfaces in projective n-space. The computational aspects will be treated in Part II by Rüdiger Achilles. |
| MATVEJEVS Andrejs " Copula Estimation for GARCH (1, 1) Processes " Authors: J.Fjodorovs, An.Matvejevs The possibility of identifying nonlinear time series using nonparametric estimates of the conditional mean and conditional variance were studied in many papers. One of the main problems in these papers is development of time series {x_t, t is from Z } methods of analysis through regression models even without knowing the regression function. The article deals with the estimation of copula-based semi parametric models for GARCH (1, 1) processes with usual kind of information about the distribution law. These models are characterized by conditional heteroscedasticity and have been often used in modelling the variability of statistical data. The basic idea is applied to a local linear regression with squared residuals for finding the unknown function. |
| MEJZNAR Jakub " Automatic head and shoulders pattern recognition using nonlinear statistical modelling " Chart Pattern recognition is one of the keystone of Technical Analysis, discipline that concentrates all methods of market development evaluation. Graphical formations such as Head and Shoulders, Flag or Triangle are usually detected only visually by experts long after their appearance. The aim of presented contribution is introduction of new automatic algorithm for Head and Shoulders Pattern (HaSP) detection. The algorithm is based on nonlinear function approximation and statistical estimation of unknown parameters. Whole procedure is tested in Case Study consisting long time series of Dow Jones average indexes. In the end, the successfulness of different market strategies is tested by statistical analysis of percentage profit. Results show that pattern appearance does not have significant effect on prices development. |
| MESIAR Radko " COPULAS - a tool for modeling the dependence structure of random vectors. Theory and applications. " Copulas were introduced in 1959 by Sklar as a tool to capture the stochastic dependence structure of random vectors. We present the theoretical background of copulas and several classes of copulas and construction methods for copulas, including the latest results in the area, both for 2-dimensional case and general d-dimensional case. Then we sketch some applications. |
| MICHELINI Marisa " Magnetic field flux in understanding electromagnetism " Electromagnetic phenomena offer an ideal theoretical framework in which students could address the investigation of the physical reality by means of the use of multivariable abstract elements of synthesis. The role played by the flux of the magnetic field in that description is pivotal but at the same time its interpretation represents an important learning knot that students had to face. To explore this physical quantity, a Real Time Laboratorial activity was developed and proposed to Italian high school students in the framework of the development of vertical Inquired Based Learning path in which the formal nature of the magnetic field flux is constructed step by step from the observation of simple hands-on experimental activities and developed thought the use of the real time sensor to reach the interpretation of the electromagnetic induction. The core activities of the investigation of the magnetic field flux is described looking to the experimental explorations and discussions done with students concerning core concepts as the the constancy of magnetic field flux along a flux tubes, the measure of the field along field lines and in each flux tubes individuating the relation between the magnetic field and the distance between the lines, the identification of the vector ature of the magnetic field distinguishing this entity from a the forces. In particular the visualization by means of a flux tubes representation of the magnetic field which is built from the field line representation in a framework in which the role of experiment founded the formal role of the entity and the formal representation and the critical analysis of them provide new more refined interpretative tools that could be applied in different, more general, contexts. The experimental apparatus and its characteristics will be addressed and the analysis of the learning outcomes and reasoning that this learning activity promotes in students mind will be presented and discussed. Data presented from students referred to four different activities held with different groups of high school students: 1) 5th class of experimental scientific lyceum, 2) 5th class of scientific lyceum; 3) 5th class of a classic lyceum; 4) a selection of the Italian best student coming from all of the 4th and 5th classes of all the Italian high schools. From it, looking in particular to the role of the development of the angle of attach proposed, it represent a crucial step in which pupils recognize the presence of a constant of the system that is related to a multivariable abstract entity as the flux. In this way the role of the rigor and the inner coherence adopted in the learning path allow students to address the exploration of the phenomenology and its analysis in a systematic way constructing the formal representation of the physical entity involved. |
| MURESAN Viorica " Ulam stability of a functional-integral equation with linear modification of the argument " In this paper we study Ulam stability for a functional-integral equa-tion with linear modi…cation of the argument by using some results given by I.A. Rus in the paper: Remarks on Ulam stablity of the operatorial equations, Fixed Point Theory, 10(2009), no. 2, 305-320. |
| MYŠKOVÁ Helena " 1. Interval eigenvectors of circulant-Hankel matrices in fuzzy algebra. 2. Robustness of circulant-hankel matrices in fuzzy algebra " 1. Fuzzy algebra is an algebraic structure in which classical addition and multiplication are replaced by and *, where a b = max{a,b}, a * b = min{a,b}. A vector x is an eigenvector of a matrix A if A * x = x. An interval vector X and the possible and universal eigenvectors are deffined. A necessary and sufficient condition for the possible and universal eigenvectors of a circulant-Hankel matrix are proved and several examples are given. 2. Fuzzy algebra is an algebraic structure in which classical addition and multiplication are replaced by and *, where ab = max{a,b}, a * b = min{a,b}. A vector x is an eigenvector of a matrix A if A * x = x. Robust matrices over fuzzy algebra are studied. The possible and universal robustness of interval matrices are deffined. The necessary and sucient conditions for the possible and universal robustness of interval circulant-Hankel matrices are given. |
| NAVRÁTIL Vladislav " Poznámka k projektové výuce matematiky a fyziky " Autoři: SVOBODOVÁ Jindřiška, NOVOTNÁ Jiřina, NAVRÁTIL Vladislav In present times characterised by decreasing interest of young generation in physics and chemistry, plays an important role motivation. It concerns all pupils, including gifted ones. Our contribution can be an inspiration for project work in physics and chemistry. It deals with surface tension of liquids (surface energy of solids). |
| NEAGU Mircea " On the symmetry group of the n-dimensional Berwald-Moór metric " Authors: Hengameh Raeisi-Dehkordi, Mircea Neagu In this paper we parametrize the symmetry group of the n-dimensional Berwald-Moór metric. Some properties of this Lie group are studied, and its corresponding Lie algebra is computed. |
| NOVOTNÁ Jiřina " Poznámka k projektové výuce matematiky a fyziky " Autoři: SVOBODOVÁ Jindřiška, NOVOTNÁ Jiřina, NAVRÁTIL Vladislav In present times characterised by decreasing interest of young generation in physics and chemistry, plays an important role motivation. It concerns all pupils, including gifted ones. Our contribution can be an inspiration for project work in physics and chemistry. It deals with surface tension of liquids (surface energy of solids). |
| OMACHELOVÁ Milada " Vplyv času na osvojovanie poznatkov v predmete Základy štatistickej analýzy " V tomto článku sa budeme zaoberať experimentom, ktorý sme uskutočnili v rámci vyučovania v predmete Základy štatistickej analýzy vyučovanom v zimnom semestri v 2. ročníku bakalárskeho štúdia na SjF STU v Bratislave v akademickom roku 2012-2013. V rámci experimentu sme skúmali, ako vplýva časový interval, ktorý uplynul od posledného opakovania učiva pod vedením pedagóga do písania kontrolnej práce zameranej na prebrané učivo, na celkový bodový výsledok dosiahnutý v písomnej práci. Pri analýze sme použili číselné a grafické metódy spracovania dát pomocou programu STATGRAFIC Centurion. |
| PAUN Marius " Dynamic painting using cellular automaton " The purpose of this paper is to produce a cellular automaton in order to obtain a dynamic painting on a given domain D. A regular hexagonal lattice is superimposed over the domain and a model depending on l parameters (l>6) is supposed to be known. Using an application of linear algebra one constructs the transition rule defining the influence function of the active cell over its system of vicinities. |
| POLA Aija " Asymptotic methods for stability analysis of Markov evolution families based on diffusion approximation of slow motion " Authors: CARKOVS Jevgeŋijs, POLA Aija Asymptotic method for stability analysis of linear di erential equations with matrix-function frequently switched by fast random evolution and ergodic Markov process is presented. The proposed method is based on di usion approximation of linear slow motion and random evolution family applying averaging procedure with respect to time and the invariant measure of the Markov process. It is proved that exponential p-stability of the resulting linear stochastic equation non-dependent on time and switched Markov process is sucient for exponential p-stability of the initial random system. |
| POTŮČEK Radovan " Bounds and sums of reduced harmonic series formed by zero and two another digits computed by means of the CAS Maple " This contribution deals with harmonic series and especially with one of reduced harmonic series -- the reduced harmonic series formed by zero and two another digits. The lower bounds and the upper one´s of sums of all these thirty-six reduced harmonic series are derived. Furthermore sums of these thirty-six infinite series are approximative computed and the errors of the computations are estimated. This paper, as an example of scientific computations in the CAS Maple, can be an inspiration for teachers of mathematics whose are teaching the topic Infinite series or as a subject matter for work with talented students. |
| PUCKOVS Andrejs " Fractal Brownian Motion Analysis Using Continuous Wavelet Transform " Authors: PUČKOVS Andrejs, MATVEJEVS Andrejs This article is dedicated for Fractal Brownian process analysis using Continuous Wavelet Transform (Direct and Inverse). Wavelet Analysis of stochastic processes is very important for financial time series analysis, risk estimation and financial time series forecasting. Wavelet Analysis is very precious for scalability analysis, because of its ability to analyze the signal (process) in scaling and shifting dimensions. In current research, Fractal Brownian motion is analyzed using Direct and Inverse Continuous Wavelet Transform, wavelet coefficients probability density function is estimated, wavelet coefficients lower and upper bounds are calculated using Mexican hat mother wavelet function. At the end estimation results are illustrated. |
| PURCARU Monica Ana Paraschiva " On the Groups of Transformations of Semisymmetric Conformal Metrical N-Linear Connections on a Hamilton Space of order k " In the present paper we introduce the concepts of conformal metrical d-structure and of conformal metrical N-linear connection with respect to the conformal metrical d-structure, corresponding to an 1-form on Hamilton space of order k; k>=2. We determine the set of all conformal metrical N-linear connections corresponding to the same nonlinear connection and we find important examples and particular cases. We find the transformations group of these connections. We study the role of the torsion d-tensor fields $T^i_{jk}, S^i_{jk}$ and $S^{jk}_i$ in this theory, especially to determination of the set of all semisymmetric conformal metrical N-linear connections with respect to the conformal metrical d-structure, corresponding to the same nonlinear connection N. We give the transformations group of these connections and other two important groups. Finally we fi nd their remarkable invariants. |
| RICHTÁRIKOVÁ Daniela " Power of Geometry in Compositions of Gustav Klimt " The paper deals with geometric aspects presented in the artwork of Gustav Klimt. It mainly focuses on geometry of composition and considerable usage of elementary geometric patterns. The latter one was reflected in the last year contribution “The patterns that last”, pointing out the origin and symbolical meaning explanation of used geometric figures. The former one is discussed in details here within three selected artworks. The paper presents also the factors of influence, and significance upon foreshadowing the birth and origins of abstract art. |
| ROEGNER Katherine " Reforming Mathematics Courses for Engineering Students in the 1st Semester " Several projects at the Technical University Berlin are centered around helping engineering students learn mathematics. The need for such measures is based upon the traditionally low success rates in the course “Linear Algebra for Engineers” with only 34% of all enrolled students passing at the end of the semester. In this contribution, key aspects of two of these projects are explained. The first major reform (“TuMult” Project) came with the introduction of multimedia in tutorials using the MUMIE (MUltimedia Mathematics Education for Engineers). The MUMIE is an open-source learning and teaching platform that can be used flexibly in STEM courses. This educational tool has been applied to the first-semester course „Lineare Algebra for Engineers“ at the Technical University Berlin, which is offered as a blended-learning course to over 3500 students per year. The basic goal of the didactical concept developed especially for this course is that the students are supported in their transition from school to university mathematics. |
| SPINADEL W. de Vera " Mathematics and artistic design " Paper brings ideas on how mathematics serves as an essential language of artistic design, bringing many interesting ideas on forms and shapes. Artists use these theoretical models and creating their pieces of art, they make real models of respective mathematical entities. Minimal surfaces and their sculptures, hyperbolic spaces and tessellations, and fractal art and colouring algorithms are discussed. |
| STEFANEL Alberto " How students link quantum concept and formalism " Authors: MICHELINI Marisa, SANTI Lorenzo, STEFANEL Alberto Quantum Mechanic is the theory of reference for the modern description of the world and therefore it is important to include its basic concepts in the physics curricula starting from the upper secondary school. Its formalism assumes an interpretive role, which gives rise to the physical meaning of entities and quantities. Literature shows that research based innovative proposals focused on the fundamental concepts activate a quantum vision of phenomena, at the same time documenting areas of learning knots for students. In particular the physical meaning of the formal quantum constructs emerges as a problematic area both for secondary and college students. To give a contribution to the ways in which student’s link formalism and quantum concept, a study was performed with 17 students of a 13 grade class of an Italian secondary school. An experimentation was performed involving students in the exploration of an educational path based on the Dirac approach to the basic concepts of the quantum theory in the phenomenology of light polarization, developed and valued in a long time research program. The data about how students approach the formalism was collected by inquiry based worksheets and a posttest. A research finding is the individuation of four modalities activated by students approaching the quantum formal constructs, among which the geometrical one plays a relevant role in bridging phenomenology to the concepts and their formal representation. |
| TOMICZEK Petr " Entrance test from mathematics at the University of West Bohemia " In this paper we present the entrance test from the mathematics at the University of West Bohemia. This test is held annually since 2006. Firstly we describe the entrance test and summarize the aggregate results of students. Secondly we compare the obtained data about input mathematical knowledge of a student with subsequent student outcomes achieved in the course of his/her studies. We relate the results of the entrance examination to successful completion of mathematical subjects included in the first year of study. |
| TOMICZKOVÁ Světlana " Using GeoGebra in Teaching Descriptive Geometry: Challenges and Opportunities " Authors: LÁVIČKA Miroslav, TOMICZKOVÁ Světlana In the past, descriptive geometry played a more important role at secondary schols and technical universities. It was a subject in which students were learning and developing their geometric thinking, considerations and creativity. Nevertheless, the classical conception of the descriptive geometry as a simple first step towards technical drawings and documents is exceeded now and one can find several attempts how to make this old and traditional geometric field more attractive and mainly useful for the generation of engineers of the 21st century. In this paper, we discuss using variational and dynamic geometry software in teaching high-level geometry in courses for students in mechanical engineering programs. |
| TORRE Matteo " On the notion of time: guidelines for a didactical path for the higher secondary school " The great Physicist, Nobel Prize Feynmann, said that Time is what happens when nothing else happens. The notion of Time is pervasive and makes an integrating part of the way under which we feel “reality”. Notwithstanding our permanent and primordial investigation about Time, many of its fascinating mysteries are still unresolved. The history of the notion of Time is the result of the entanglement of several histories, from Astronomy to Physics, to Biology, Psychology, from the Religions to Technology. But also in Art, in Music and in Philosophy. What is really Time..? Future and Past are real as the Present..? Did Time exist before the Big-Bang..? Which logical formalisms are adequate to model the role that Time plays in our reasoning..? This paper illustrates the guidelines of a possible didactical path about the notion of Time, explicitly thought for the Higher Secondary School (age 14-19). It was experimented by the Author within the II Level Master IDIFO3 on a sample of 39 students of the last two years of courses. We also present some ideas that the notion of Time stimulates both at the didactical and pedagogical level. The topic will be investigated under a scientific perspective, joining historical aspects together with ideas of great scientists, both from an artistic and philosophical viewpoint (relying on opinions and works by experts) as well as from an historical viewpoint (through the evolution of human thought about Time within the history of the cultural evolution of mankind). The goal is to understand one of the most fascinating and mysterious themes of the whole history of Humanity. |
| TÜRKOĞLU Mustafa Deniz " Generalized Einstein tensor for L-Weyl Spaces " Authors: Fatma ÖZDEMIR, Mustafa Deniz TÜRKOĞLU In this work, we introduce nearly-Kahlerian and almost L-structures on Weyl spaces Wn and examine some curvature properties of these spaces. Also, we define Einstein L-Weyl spaces and the generalized Einstein tensor in L-Weyl spaces. Moreover, we give a necessary and sufficient condition for an Einstein L-Weyl space (ELW) to be Einstein Weyl. |
| VELICHOVÁ Daniela " 1. Minkowski triples 2. Concept of Invariance " 1. Few ideas about generalization of Minkowski sum and product of point sets will be presented in the paper. Minkowski triples of curves are studied, as Minkowski sum linear combinations, Minkowski product combinations and Minkowski mixed combinations of three curves. 2. Paper brings ideas about invrinace as a concet applied in creative processes in maths and art for design of a piece of art or similarly for introduction of a new concept or theory in maths. |
| VERCELLATI Stefano " Magnetic field flux in understanding electromagnetism " Electromagnetic phenomena offer an ideal theoretical framework in which students could address the investigation of the physical reality by means of the use of multivariable abstract elements of synthesis. The role played by the flux of the magnetic field in that description is pivotal but at the same time its interpretation represents an important learning knot that students had to face. To explore this physical quantity, a Real Time Laboratorial activity was developed and proposed to Italian high school students in the framework of the development of vertical Inquired Based Learning path in which the formal nature of the magnetic field flux is constructed step by step from the observation of simple hands-on experimental activities and developed thought the use of the real time sensor to reach the interpretation of the electromagnetic induction. The core activities of the investigation of the magnetic field flux is described looking to the experimental explorations and discussions done with students concerning core concepts as the the constancy of magnetic field flux along a flux tubes, the measure of the field along field lines and in each flux tubes individuating the relation between the magnetic field and the distance between the lines, the identification of the vector ature of the magnetic field distinguishing this entity from a the forces. In particular the visualization by means of a flux tubes representation of the magnetic field which is built from the field line representation in a framework in which the role of experiment founded the formal role of the entity and the formal representation and the critical analysis of them provide new more refined interpretative tools that could be applied in different, more general, contexts. The experimental apparatus and its characteristics will be addressed and the analysis of the learning outcomes and reasoning that this learning activity promotes in students mind will be presented and discussed. Data presented from students referred to four different activities held with different groups of high school students: 1) 5th class of experimental scientific lyceum, 2) 5th class of scientific lyceum; 3) 5th class of a classic lyceum; 4) a selection of the Italian best student coming from all of the 4th and 5th classes of all the Italian high schools. From it, looking in particular to the role of the development of the angle of attach proposed, it represent a crucial step in which pupils recognize the presence of a constant of the system that is related to a multivariable abstract entity as the flux. In this way the role of the rigor and the inner coherence adopted in the learning path allow students to address the exploration of the phenomenology and its analysis in a systematic way constructing the formal representationof the physical entity involved. |
| ZÁBOJNÍKOVÁ Eva " E-learning. Yesterday, today and tomorrow " Yesterday. E-learning as a new form of teaching has already been a tradition for decades. The focus of e-learning has moved from the area of technological equipment and multimedia side to teaching process itself. Today. Development and implementation of e-learning course as a support for linear algebra study of mathematics at undergraduate level of study of regional technical college faculty. Tomorrow. Discussion on the portal Elearningeuropa 12th November – 30th November 2012: A world map of Open Educational Resources initiatives: Can the global OER community design and build it together? |
| ZÁHONOVÁ Viera " Autonomous systems with infinitely many critical points " Authors: DOBRAKOVOVÁ Jana, ZÁHONOVÁ Viera This contribution is devoted to some aspects of teaching autonomous linear differential systems, especially properties of their critical points sets, for some special cases of linear differential systems, by means of the programming system MATHEMATICA. |
| ZAHRÁDKA Jaromír " An extension of the wiener polynomial and the wiener index for the square of graphs " Authors: SEIBERT Jaroslav, ZAHRÁDKA Jaromír The first topological index based on the distances of vertices in a graph was defined by chemist H, Wiener in 1947. Many authors tried to find some extensions of this topological invariant during the last twenty years. Most of the new topological indices have applications in various arises as chemistry, biochemistry, physics, computer sciences and so on. These indices and related polynomials were determined for some classes of simple graphs. In this contribution we calculate the generalized Wiener indices and polynomials for the square of certain types of graphs. |
| ZUCCARINI Giacomo " Exploring university student ideas on the relationship between formal aspects and physical meanings in quantum mechanics " Authors: MICHELINI Marisa, STEFANEL Alberto, ZUCCARINI Giacomo Research on university student understanding of quantum mechanics (QM) has shown the fragmented nature of student mental models and the existence of deep and persistent difficulties to make sense of quantum formalism. Learning problems are often tied to a lack of recognition or misinterpretation of physical meaning of theoretical entities, especially of quantum state formal representation. Nevertheless there hasn´t been much research on ideas ascribed by student to basic properties of state vector and wavefunction (WF), to their role in the theory and to their physical meaning. In order to explore student way of thinking and connections they make between formalism and concepts, we studied a questionnaire and an interview protocol. As research calibration stage, a case study was designed including a written questionnaire followed by semi-structured interviews to be administered to 3rd year physics students who are being exposed to QM university course. The questionnaire consists of four open qualitative essay questions concerning 1) valid WFs, 2) stochastic character of quantum state, 3) complex nature of its representations, 4) WF as a description of the state at a single instant. Each of them is divided into sub-questions. Individual interviews focus on both on a pre-structured grid and on the discussion of questionnaire answers. On the base of case study results, a structured questionnaire is designed to explore how students link quantum formalism to concepts both in general terms and in the application context of specific problems. A grid for a multiple perspectives exploration of ideas is the basis of the 21 items on three levels: cultural, qualitative-conceptual and formal. For each element of the grid, one or more items are designed in order to cross investigate the selected aspects. |
| ŠABO Michal " On Relervancy Transformation Operators " The notion of Relevancy Transformation Operator (RET operator) was introduced by R.R. Yager (2001) as an appropriate operator for fuzzy modeling inference process. The properties and possibilities of construction of RET operators are studied. |
| ŠADURSKIS Kārlis " Covariance semigroup for delayed geometric brownian motion " Authors: CARKOVS Jevgenijs, ŠADURSKIS, Kārlis The paper proposes algorithm for time asymptotic analysis of stochastic linear functional differential equations. An approach is based on extension of the deffned by deterministic part of this equation resolving semigroup to linear operator semigroup in the space of countable additive symmetric measures. The weak infinitesimal operator of this semigroup helps to nd such Lyapunov-Krasovsky type quadratic functional that gives a necessary and sufficient asymptotic stability condition for the equation defined by selected deterministic part of analyzed stochastic equation. Furthermore, we have got a stochastic process, usable for Ito stochastic differential, by substituting the solution of the analyzed stochastic equation as an argument of this quadratic functional. This property permits to derive an analogue of Ito formula for the above mentioned stochastic process and to discuss equilibrium asymptotic stochastic stability conditions for initial stochastic functional differential equation. As an example, we have deduced necessary and sufficient condition for mean square decrease of stochastic exponent given by Ito type scalar equation with delay. |
| ŠEDIVÁ Blanka " Entrance test from mathematics at the University of West Bohemia " prispevek společně s kolegou Petrem Tomiczek a Michalem Frieslem |
| ŽÁČEK Martin " Reasoning in Fuzzy Graph-based Clausal Form Logic " Authors: Martin Žáček, Rostislav Miarka This paper follows the work of T. Richards specialization Clausal Form Logic (CFL) formal system of the first order logic. The paper presents also the way of using graph-based clausal form statements in the frame of fuzzy semantic networks. The goal of our research is to follow the direction towards graph-based clausal form knowledge representation shaped by Richards and build up a fuzzy graph-based formal system. The new formal system Fuzzy Graph-based Clausal Form Logic (FGCFL) has its own graph-based language with the expressivity similar to that one of CFL and enriched Fuzzy logic (implementation of fuzzy logic increases expressivity). The idea of the FGCFL graph-based approach is also useful in the frame of the fuzzy RDF model especially in its graph version. |
| ŽIŽKA David " GARCH Forecasting performance depending on different distribution assumptions " This paper investigates impact of different distribution assumptions to predictions linear volatility GARCH model. Firstly, daily returns from Czech financial market were fitted by volatility models GARCH (1, 1) based on six different error distribution assumptions. These fitted models based on different distributions were used to out-of-sample predictions. Finally, the results were compared by predictive power measurements and shown that utilizing a leptokurtic and a skewed error distribution leads to significant improvements in variance forecasts compared to using traditional assumption of the normal distribution. |
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Number of registered papers: 78 |
Last change: 28.06.2013 13:36:35 |