17th CONFERENCE ON APPLIED MATHEMATICS APLIMAT 2018 PROCEEDINGS

 

   February 6 - 8, 2018 Bratislava Slovak Republic

 


 

 

 

 

 

 



 

 

 

Language correction of the publication was not performed, language accuracy is the sole responsibility of the contributing authors. Authors are fully responsible for the originality of all ideas presented in their contributions.

All rights reserved. No part of this work may be used or reproduced in any manner whatsoever or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without written permission from the publisher and copyright owner.

 

 

 

 


 

 

 

 

 

Proceedings, 17th Conference on Applied Mathematics – APLIMAT 2018 First edition

 

©

Institute of Mathematics and Physics Faculty of Mechanical Engineering

Slovak University of Technology in Bratislava

Editors: Dagmar Szarková, Daniela Richtáriková, Peter Letavaj, Jana Gabková

Proceedings motif © Daniela Richtáriková

 

Published by:

Slovak University of Technology in Bratislava in publishing house SPEKTRUM STU

 

 

ISBN 978-80-227-4765-3


 

 

 

 

 

Preface

 

This volume contains the papers presented at APLIMAT 2018: The 17th Conference on Applied Mathematics held on February 6 - 8, 2018 in Bratislava, Slovakia.

The purpose of the conference is to promote discussions and interactions between researchers and practitioners focused on cooperation in disciplinary, interdisciplinary and transdisciplinary issues, ideas, concepts, theories, methodologies and applications.

We are particularly interested in fostering the exchange of concepts, research ideas and other results which could contribute to the academic area and also benefit business and the industrial community.

 

 

 

Conference main topics

 

·        Algebra and geometry and their applications

 

·        Differential equations, dynamic systems and their applications

 

·        Mathematics and art, section dedicated to the memory of Mauro Francaviglia

 

·        Modeling and simulation in engineering and scientific computations

 

·        New trends in university mathematics education

 

·        Statistical methods in technical and economic sciences and in practise

 

·        Network science, graphs and combinatorics

 

·        Mathematics and physics in contemporary science and technique

 

 

 

Conference Chair

 

 

VELICHOVÁ Daniela

Slovak Republic

 

Conference Scientific Board

 

 

BAŠTINEC Jaromír

Czech Republic

CARKOVS Jevgeņijs

Latvia

FERREIRA Manuel A. M.

Portugal

JANIGA Ivan

Slovak Republic

LORENZI Marcella G.

Italy

NEHÉZ Martin

Slovak Republic

PĂUN Márius

Romania

TEDESCHINI LALLI Laura

Italy

 

 

 

Additional Reviewers

Baicoianu Alexandra
Bruni Fabio

De Martino Salvatore
Falcolini Corrado
Gabriele Stefano
Iannace Gino

Iltins Ilmars
Jančo Roland
Kozák Vladislav

Křivoňáková Naďa
Madaras Tomáš
Magrone Paola
Marin Marin
Matvejevs Andrejs
Mikeš Josef
Pavlenko Oksana
Rebelos Margareta
Salerno Ginevra
Sangeorzan Livia
Spadafora Giovanna
Vlase Sorin

 

 

 

 

 

 

CONTENTS

 

CONTROL SMOOTHING SPLINES WITH INITIAL CONDITIONS

Asmuss Svetlana and Budkina Natalja

14

ON NORMAL ASSUMPTIONS ON DEMAND FUNCTION AND ITS ELASTICITY.

Barić Pisarović Gordana, Raguž Andrija
and Vojvodić Rosenzweig Višnja

22

TEACHING PROCESS OF AN APPLIED STATISTICS COURSE FOR STUDENTS OF THE ANTROPOLOGY STUDY PROGRAMME AT MASARYK UNIVERSITY

Bendová Veronika and Budíková Marie

32

DALÍ EXPERIENCE: SALVADOR DAL´I AND MATHS.

Benvenuti Silvia

40

WAGE LEVELS BY REGIONS IN THE CZECH REPUBLIC AND PPP-ADJUSTED WAGES IN SELECTED EUROPEAN AND NON-EUROPEAN COUNTRIES

Bílková Diana

50

BASIC PRINCIPLES OF ORTHOGONAL AXONOMETRY WITH THE USE OF GEOGEBRA

Bímová Daniela and Pirklová Petra

86

PROPERTIES OF REDUCED MEET IDEALS IN LOWER BCK-SEMILATTICES

Bordbar Hashem, Novák Michal, Cristea Irina and Bae Jun Young

97

A MAGIC FORMULA OF NATURE

Brandi Primo and Salvadori Anna

110

THE ABILITY OF PRIMARY SCHOOL PUPILS TO SOLVE COMBINATORIAL TASKS

Břehovský Jiří and Příhonská Jana

127

TALL BUILDINGS IN MILANO. PROPORTIONS AND MORPHOLOGY BETWEEN ANALOGICAL AND DIGITAL DESIGN PROCEDURE. SOME CONSIDERATIONS ABOUT TWO CASE HISTORIES OF CONTEMPORARY CONSTRUCTION SITES: FROM THE XX LEGACY TO THE XXI NEW CENTURY URBAN LANDSCAPE

Brunetti Federico Alberto

137

THE IDEAS’ MACHINE. THE BIG SCIENCE IN SEARCH FOR JOUNG GENERATION CONCEPTS ABOUT IMAGINATION IN PHYSICS. THE EUROPEAN CERN – CMS CHALLENGE ”ARTS & SCIENCE ACROSS ITALY

Brunetti Federico Alberto

154

HYDROLOGICAL AND METEOROLOGICAL DATA AND MODIFICATIONS OF STATISTICAL DISTRIBUTIONS - HEURISTIC APPROACH

Budík Ladislav

165

VIRTUAL RECOMPOSITION AND ANALYSIS OF A SURVEYED MODEL OF THE WOODEN CRUCIFIX OF ST. PETER’S BASILICA

Canciani Marco, Falcolini Corrado and Pastor Altaba Maria

173

ON SUBJECTED TO RAPID RANDOM EXTRACTIONS TWO-SEX POPULATION GROWTH

Carkovs Jevgeņijs and Matvejevs Andrejs

179

ON INTERSPECIFIC COMPETITION OF LOGISTIC POPULATIONS WITH THE ASSUMPTION OF RAPID RANDOM CONTACTS

Carkovs Jevgeņijs and Pavlenko Oksana

189

STOCHASTIC APPROXIMATION PROCEDURE FOR ISOLATED POPULATION IN FAST OSCILLATED RANDOM ENVIRONMENT

Carkovs Jevgeņijs, Sadurskis Karlis and Goldsteine Jolanta

197

MATHEMATICAL MODELS ON MILK, COFFEE AND BEER

Ceppitelli Rita and Marconi Ombretta

205

GOOD KNOWLEDGE OF BASIC MATHEMATICS - A SUCCESSFUL PREREQUISITE TO STUDY IN RIGA TECHNICAL UNIVERSITY

Cernajeva Sarmite, Volodko Inta, Iltina Marija and Iltins Ilmars

217

CONFORMAL MAPPINGS OF RIEMANNIAN MANIFOLDS PRESERVING THE GENERALIZED EINSTEIN TENSOR

Cherevko Yevhen, Berezovski Vladimir and Chepurna Olena

224

GROUPS AND HYPERGROUPS OFARTIFICIAL NEURONS

     Chvalina Jan and Smetana Bedřich

232

AN INNOVATIVE EDUCATIONAL PATH ON MATHEMATICS AND FILM CRITICS FOR THE FLIPPED CLASSROOM

     Civeriati Elisa and Torre Matteo

244

ON THE IDENTITY OF SIGHT(S) IN SOME WESTERN AND EASTERN PROJECTIVE REPRESENTATIONS

     Cocchiarella Luigi

254

DO IMPORTANT NETWORK ACTORS FORM IMPORTANT TIES?

    Coroničová Hurajová Jana and Madaras Tomáš

260

NOTES TO THE PROBLEMS WITH FIGURES AT SCHOOL MATHEMATICS

    Csachová Lucia and Jurečková Mária

270

NETWORK FLOWS AS A TOOL FOR SOLVING LOCATION - SCHEDULING PROBLEM TO OPTIMIZE CHARGING INFRASTRUCTURE FOR ELECTRIC VEHICLES

    Czimmermann Peter, Buzna Ľuboš and Koháni Michal

280

NEW TRENDS IN TEACHING FUNCTIONS AT UNIVERSITY LEVEL

    Dillingerová Monika and Vankúš Peter

290

OUR EXPERIENCE WITH THE INVOLVEMENT OF STUDENTS IN THE CREATION OF STUDY MATERIALS

Dlouha Dagmar and Hamrikova Radka

301

MODELLING OF MATRIX SYSTEM WITH FICTITIOUS INTERLINK FUNCTION USING INSTANTANEOUS STATE CALCULATION

Dobrucký Branislav, Chernoyarov Oleg, Marčoková Mariana and Štefanec Pavol

309

THE ROLE OF RTU STUDENTS’ SURVEY IN ENSURING THE QUALITY OF MATHEMATICS STUDIES

Dzenite Ilona, Cernajeva Sarmite and Matvejevs Aleksandrs

316

B3/S23 DESCENDING A STAIRCASE NO. 2

Feijs Loe

326

CONSTRUCTIONS OF A SQUARE AND A REGULAR PENTAGON ONLY WITH A COMPASS

Ferdiánová Věra and Branny Michael

338

FINANCIALLY DEPENDENT PENSIONS FUNDS MAINTENANCE APPROACH THROUGH BROWNIAN MOTION PROCESSES

Ferreira Manuel Alberto M.

348

STUDY OF A COLLECTION OF SERVICE TIME DISTRIBUTIONS AND IMPACT  IN  THE  RESPECTIVE  M/G/¥  SYSTEM  BUSYPERIOD PARAMETERS

Ferreira Manuel Alberto M. and Filipe José António

356

THE ALEXANDER MOSAIC AND THE HOUSE OF FAUN (POMPEII VI 12, 1-8) GEOMETRY PROPORTIONS AND ART OF COMPOSITION

Ferro Luisa

365

EVALUATION OF THE QUALITATIVE PARAMETERS OF HUMUS AND SELECTED HEAVY METALS CONTENT

Feszterová Melánia, Hudec Michal, Porubcová Lýdia and Noga Henryk

377

CRYSTAL, MOLECULAR AND ELECTRONIC PROPERTIES OF (E)-1-((5-BROMO-[2,2-BITHIOPHEN]-5-YL) METHYLENE)-2-(PERFLUOROPHENYL) HYDRAZINE

Fronc Marek, Sivý Július, Bortňák Dušan, Végh Daniel and Králik Marián

390

REALISING SOME TYPES WHILE OMITTING OTHERS

Glivická Jana

397

A NOTE ON THE PROBLEM OF PRISONERS AND HATS

Glivický Petr

402

STOCHASTIC ANALYSIS OF POPULATION DYNAMICS SUBJECT TO CHANGES AT THE RANDOM TIME MOMENTS

Goldšteine Jolanta, Pola Aija and Šadurskis Kārlis

412

CREATING AN INTERACTION WITH CELLULAR AUTOMATA FOR SCIENCE ANDTECHNOLOGY MUSEUMS

Haude Lucas

420

PORTFOLIO OPTIMIZATION FOR RISK AVERSE AND RISKSEEKING INVESTOR

Heckenbergerová Jana and Šild Petr

434

GRAPHLET COUNTING

Hočevar Tomaž

442

SERLIO´S, GUARINI´S AND MEYER´S CONSTRUCTIONS OF OVALS IN ARCHITECTURE

Holešová Michaela

450

THE GENERALIZED SOLUTION TO A LINEAR OPERATOR EQUATION. THE CASE OF FINITE DIMENSION

Horský Richard

460

THE ACOUSTICS OF THE VANVITELLIANAHUNTING LODGE

Iannace Gino and Trematerra Amelia

468

THE ACOUSTICS OF THE LONGOBARD CHURCH OF SANTA SOFIA IN BENEVENTO.

Iannace Gino and Trematerra Amelia

479

PARAMETER ESTIMATION FOR SCALAR STOCHASTIC DIFFERENTIAL EQUATION OFSECOND ORDER

Janák Josef

487

RESPONSE DEVICES IN TERTIARY EDUCATION

Jančařík Antonín

500

GAGE STUDIES FOR VARIABLES AVERAGE AND RANGE METHOD

Janiga Ivan

507

MEASUREMENT SYSTEM STUDIES USING ANOVA

Janiga Ivan

516

GENERALIZED LINEAR MODEL WITH SOFTWARE MATHEMATICA

Janiga Ivan and Gabková Jana

525

DESTRUCTIVE R&R STUDY - EVALUATION PROBLEMS

Jarošová Eva

535

LIENHARD INTERPOLATION METHOD, ITS GENERALISATIONAND ADDITION

Kaňka Miloš

545

DATA SCIENCE AND STATISTICS WITH PYTHON

Kaspříková Nikola

558

MAPPINGS OF SPACES WITH AFFINE CONNECTION

Kiosak Volodymyr, Lesechko Olexandr and Savchenko Olexander

563

VISUALIZATION OF MATHEMATICAL CONCEPTS IN TEACHING LINEAR AND VECTOR ALGEBRA TO FIRST-YEAR ENGINEERING STUDENTS

Koliskina Valentina and Iltina Marija

570

THE LEAVE-ONE-OUT MAXIMUM LIKELIHOOD METHOD FOR THE PRISESTLEY-CHAO ESTIMATOR OF CONDITIONAL DENSITY

Konečná Kateřina

577

STUDENTS’ AUTOEVALUATION IN THE FIRST YEAR OF SCIENCE STUDY FIELDS ESPECIALLY IN MATHEMATICS(COMPLEX ANALYSIS)

Konečná Petra and Habiballa Hashim

590

AUGMENTED REALITY IN MATHEMATICS EDUCATION FOR PRE-SERVICE TEACHERS IN PRIMARY LEVEL

Koreňová Lilla and Gunčaga Ján

597

THE USAGE OF MOBILE DEVICES IN THE STUDENTS’ MATHEMATICS LEARNING

Koreňová Lilla and Veress-Bágyi Ibolya

606

THE THREE-MEASURABLE PROBLEM CHANGE OF COORDINATES FUNCTIONS OF FLOATER SUSPENDED IN ACOUSTIC ENVIRONMENT

Korobiichuk Igor, Karachun Volodimir, Mel’nick Viktorij, Asaftei Olena and Szewczyk Roman

621

VERIFYING THE AUTHENTICITY OF THE ACCOUNTING DATA USING THE BENFORD’S ALGORITHM

Košťálek Josef and Koťátková Stránská Pavla

632

REGULARITY CRITERION FOR LOCAL IN TIME EXISTENCE OF STRONG SOLUTIONS TO THE NAVIER-STOKES EQUATIONS WITH NAVIER’S TYPE BOUNDARY CONDITIONS

Kučera Petr, Píšová Jitka and Vacková Petra

638

NATURE INSPIRED ARCHITECTURES AND JEWELS PARAMETRIC DESIGN

Lorenzi Marcella Giulia and Schiavello Francesco

648

COMPARISON OF RESULTS IN DETERMINING THE OPTIMAL NUMBER OF CLUSTERS IN CLUSTER ANALYSIS

Löster Tomáš

662

TWO NUMERICAL APPROACHES TO THE NON-LINEAR LEAST-SQUARES METHOD VIA PRACTICAL EXAMPLES

Ludvík Pavel and Morávková Zuzana

670

GRAVITATIONAL MUSIC

Luminet Jean-Pierre

679

GEOMETRICAL ANALYSIS OF A DESIGN ARTWORK COFFEE TABLE DESIGNED BY THE ARCHITECT AUGUSTO MAGNAGHI-DELFINO

Magnaghi-Delfino Paola and Norando Tullia

686

TOWARDS A DIFFUSED (OPEN AIR) MUSEUM IN THE HISTORICAL CENTER OF ROME. UNIVERSITY THIRD MISSION INVOLVING ART, ARCHITECTURE, MATHEMATICS

Magrone Paola, Brancaleoni Fabio, Carlini Alessandra, Falcolini Corrado, Gargano Maurizio and Tedeschini Lalli Laura

698

WHEN TURIN CAME TO ROME: A WALK IN THE PRATI DISTRICT AND ITS SYMMETRIES

Magrone Paola, Scirocchi Antonio, Tedeschini Lalli Laura and Tricarico Daniele

708

HANKEL TRANSFORM AND FREE VIBRATION OF
A LARGE CIRCULAR MEMBRANE
.

Malacká Zuzana

717

COMPARISON OF HOME TEAM ADVANTAGE IN ENGLISH AND SPANISHFOOTBALL LEAGUES

Marek Patrice and Vávra František

724

NETWORK MODEL INSPIRED BY THE REAL DATA - FUNCTIONAL BRAIN NETWORKS

Markošová Mária

733

SQUARE AND TRIANGULAR MATRICES IN MAGNAGHI-TERZAGHI’S ARCHITECTURES

Mele Giampiero and Capanna Alessandra

744

SOME ALGEBRAIC PROPERTIES OF TENSORS

Mikeš Josef

756

USE OF STRUCTURAL DYNAMIC MODIFICATION TO REDUCING VIBRATION LEVEL

Musil Miloš, Havelka René, Havelka Ferdinand and Mihelová Silvia

761

COMPARING EEG SIGNALS AND EMOTIONS PROVOKED BY IMAGES WITH DIFFERENT AESTHETIC VARIABLES USING EMOTIVE INSIGHT AND NEUROSKY MINDWAVE

Nedvědová Marie and Marek Jaroslav

777

ACTIVE-LEARNING TECHNIQUES IN MATH COURSES IN ENGINEERING DEGREES: THE PURSUIT FOR A NEW ENGINEER PROFILE

Nicola Susana, Mendonça Jorge and Pinto Carla

786

APPLICATION OF SHAPE DISTRIBUTIONS TO COMPARE TRIANGULAR MESHES

Pajerová Nikola and Linkeová Ivana

795

MODELING AND SYNTHESIS OF CONTROL THE PROCESS OF CASTING

Palenčár Jakub, Kubiš Milan and Palenčár Rudolf

803

WEAK PROPERTY B AND PROPERTY B OF SYSTEM OF FOUR NONLINEAR DIFFERENCE EQUATIONS

Pasáčková Jana

813

PARALLEL ILLUMINATION IN GEOGEBRA

Pirklová Petra and Bímová Daniela

821

IMPROVING THE SENSITIVITY OF TRACTOGRAPHY USING MICROSTRUCTURE MODELING AND PSEUDO-INVERSION

Piskořová Zuzana, Baštinec Jaromír and Labounek René

832

COMPARATIVE STUDY OF SEVEN METHODS FOR ESTIMATING THE WEIBULL DISTRIBUTION PARAMETERS FOR WIND SPEED IN BRATISLAVA - MLYNSKÁ DOLINA

Pobočíková Ivana, Sedliačková Zuzana and Šimon Ján

840

THE SUM OF THE SERIES OF RECIPROCALS OF THE QUADRATIC POLYNOMIALS WITH INTEGER ROOTS

Potůček Radovan

853

TEMPERAMENT THEORY AND STATISTICAL ANALYSIS OF TEMPERAMENTAL DEPENDENCE ON OTHER FACTORS – EMPIRICAL STUDY

Pozdílková Alena and Hedvičáková Martina

861

SPATIAL LAG MODEL FOR APARTMENT PRICES IN PARDUBICE REGION

Pozdílková Alena and Marek Jaroslav

867

NOTES ON ITERATIVE CLOSEST POINT ALGORITHM

Prochazkova Jana and Martisek Dalibor

876

NUMERICAL SOLUTION OF A SPECIAL SINGULAR INTEGRAL EQUATION OF THE SECOND KIND

Rak Josef

885

AN APPLICATION OF BELL POLYNOMIALS IN NUMERICAL SOLVING OF NONLINEARDIFFERENTIAL EQUATIONS

Rebenda Josef

891

SINUSOID CHARACTERISTICS IN APPLETS

Richtarikova  Daniela

901

FUZZY C-MEANS CLUSTERING. TECHNIQUE AND EVALUATING RESULTS

Rihova Elena and Malec Miloslav

908

RUBRICS AS SELF-ASSESSMENT TOOL OF MATHEMATICAL EDUCATION

Šabíková Henrieta, Judinová Lenka and Čeretková Soňa

918

NORMALIZATION TECHNIQUES FOR UNIVARIATE BIOSTATISTICS ANALYSIS

Šedivá Blanka, Pelantová Helena and Bugáňová Martina

925

ON THE HOSOYA INDEX FOR THE MOLECULAR GRAPHS OF HELICENES

Seibert Jaroslav and Zahrádka Jaromír

933

STOCHASTIC EXTRAPOLATION OF MORTALITY RATES IN THE CZECH REPUBLIC WITH AN IMPACT ON PROBABILITY AND NUMBER OF SURVIVING

Šimpach Ondřej and Dotlačilová Petra

943

MODELS USED IN FUZZY LINEAR REGRESSION

Škrabánek Pavel and Marek Jaroslav

955

SECONDARY MATHEMATICS MISCONCEPTION AS
A MAIN OBSTACLE
IN SOLVING HIGHER MATHEMATICS PROBLEMS

Slavíčková Mária and Vargová Michaela

965

COOPERATION IN TEACHING AND LEARNING ANALYTIC GEOMETRY

Šovčíková Petronela

972

CYCLIC PERMUTATIONS: CROSSING NUMBERS OF THE JOIN PRODUCTS OF GRAPHS

Staš Michal

979

TWO METHODS FOR ESTIMATING NUMBER OF INTERACTING VEHICLES

Szabová Zuzana and Krbálek Milan

988

LINES ON COMPLETE INTERSECTION OF TWO QUADRICS IN P4

Tereňová Zuzana

999

FORCED DUFFING EQUATION WITH A NON-STRICTLY MONOTONIC POTENTIAL

Tomiczek Petr

1007

TRAJAN’S COLUMN: MATH, ART AND CRYPTOGRAPHY

Torre Matteo

1016

POSSIBLE COMPARISON BETWEEN TWO TIME SERIES

Ťoupal Tomáš and Šedivá Blanka

1025

QUALITY COMPARISON BETWEEN HYBRID REGULARIZED EXPONENTIAL FORGETTING ALGORITHM WITH ALTERNATIVE COVARIANCE MATRIX AND SELECTED STANDARD LONG-RUN ON-LINE IDENTIFICATION METHODS OF INDUSTRIAL SYSTEMS.

Vachálek Ján, Melicher Markus, Vašek Pavol, Šišmišová Dana and Volenský Tomáš

1036

PROTOTYPES IN PLANIMETRICS

Václavíková Zuzana

1047

THE ROLE OF VISUALISATION IN SOLID GEOMETRY PROBLEM SOLVING

Vágová Renáta and Kmeťová Mária

1054

COMPUTATIONAL OPTIMIZATION OF MATERICAL CHOICE FOR THERMAL CONTAINERS OF ADVANCED BUILDINGS

Vala Jiří

1065

GEOGEBRA AND LOGARITHMIC SPIRAL IN EDUCATIONAL PROCESS

Vallo Dusan and Duris Viliam

1076

CREATIVE USE OF MATHEMATICAL STRATEGIES IN PROOFS IN UNDERGRADUATE CALCULUS

Varga Marek and Naštická Zuzana

1083

SURFACE MEASURES REVISITED - ON THE BOUNDARIES OF MATHEMATICS AND ART

Velichova Daniela

1090

THEATRE, LOVE AND GRAPHS

Zawiślak Stanislaw, Kopeć Jerzy

1100

GENERAL THEORY OF RETAIL GRAVITATION FIELD

Zeithamer Tomáš R. and Pospíšil Jiří

1112

 

 

 

 

 

 

 

 

 

 

 

 

 

First Edition Bratislava 2018

ISBN 978-80-227-4765-3