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Volume 3 (2010), Number 2 APLIMAT - JOURNAL OF APPLIED MATHEMATICS VOLUME 3 (2010), NUMBER 2 APLIMAT - JOURNAL OF APPLIED MATHEMATICS VOLUME 3 (2010), NUMBER 2 Edited by: Slovak University of Technology in Bratislava Editor - in - Chief: KOVÁČOVÁ Monika (Slovak Republic) Editorial Board: CARKOVS Jevgenijs (Latvia ) CZANNER Gabriela (USA) CZANNER Silvester (Great Britain) DE LA VILLA Augustin (Spain) DOLEŽALOVÁ Jarmila (Czech Republic) FEČKAN Michal (Slovak Republic) FERREIRA M. A. Martins (Portugal) FRANCAVIGLIA Mauro (Italy) KARPÍŠEK Zdeněk (Czech Republic) KOROTOV Sergey (Finland) LORENZI Marcella Giulia (Italy) MESIAR Radko (Slovak Republic) TALAŠOVÁ Jana (Czech Republic) VELICHOVÁ Daniela (Slovak Republic) Editorial Office: Institute of natural sciences, humanities and social sciences Faculty of Mechanical Engineering Slovak University of Technology in Bratislava Námestie slobody 17 812 31 Bratislava Correspodence concerning subscriptions, claims and distribution: F.X. spol s.r.o Azalková 21 821 00 Bratislava [email protected] Frequency: One volume per year consisting of three issues at price of 120 EUR, per volume, including surface mail shipment abroad. Registration number EV 2540/08 Information and instructions for authors are available on the address: http://www.journal.aplimat.com/ Printed by: FX spol s.r.o, Azalková 21, 821 00 Bratislava Copyright © STU 2007-2010, Bratislava All rights reserved. No part may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without prior written permission from the Editorial Board. All contributions published in the Journal were reviewed with open and blind review forms with respect to their scientific contents. APLIMAT - JOURNAL OF APPLIED MATHEMATICS VOLUME 3 (2010), NUMBER 2 DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS MEMORY TERM BARBAGALLO Annamaria, MAUGERI Antonino: 13 FOR DYNAMIC OLIGOPOLISTIC MARKET EQUILIBRIUM PROBLEM BAŠTINEC Jaromír, DIBLÍK Josef, KHUSAINOV Denys, 25 RYVOLOVÁ Alena: STABILITY AND ESTIMATION OF SOLUTIONS OF LINEAR DIFFERENTIAL SYSTEMS WITH CONSTANT COEFFICIENTS OF NEUTRAL TYPE CARKOVS Jevgenijs, PAVLENKO Oksana: AVERAGING, MERGER 35 AND STABILITY OF LINEAR DYNAMICAL SYSTEMS WITH SMALL MARKOV JUMPS DIBLÍK Josef, MORÁVKOVÁ Blanka: REPRESENTATION OF 45 SOLUTIONS OF LINEAR DISCRETE SYSTEMS WITH CONSTANT COEFFICIENTS, A SINGLE DELAY AND WITH IMPULSES SOME GENERALIZATIONS FAJMON Břetislav, ŠMARDA Zdeněk: 53 OF BANACH FIXED POINT THEOREM FARAGÓ István, KOROTOV Sergey, SZABÓ Tamás: 61 NON-NEGATIVITY PRESERVATION OF THE DISCRETE NONSTATIONARY HEAT EQUATION IN 1D AND 2D FILIPE José António, FERREIRA Manuel Alberto M., COELHO 83 M., PEDRO Maria Isabel: CHAOS, ANTI-CHAOS AND RESOURCES: DEALING WITH COMPLEXITY ADOMIAN DECOMPOSITION FILIPPOVA Olga, ŠMARDA Zdeněk: 91 METHOD FOR CERTAIN SINGULAR INITIAL VALUE PROBLEM HLAVIČKOVÁ Irena: BISECTION METHOD FOR FINDING INITIAL 99 DATA GENERATING BOUNDED SOLUTIONS OF DISCRETE EQUATIONS ILAVSKÁ Iveta, NAJMANOVÁ Anna, OLACH Rudolf: 107 OSCILLATION OF NONLINEAR NEUTRAL DIFFERENTIAL SYSTEMS Kecskés Norbert: ON EXISTENCE OF SPECIAL SOLUTIONS OF 113 CERTAIN COUPLED SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS COMPUTER SIMULATIONS OF LINEAR KOLÁŘOVÁ Edita: 119 STOCHASTIC DIFFERENTIAL EQUATIONS MATVEJEVS Andrejs, SADURSKIS Karlis: AUTOREGRESSIVE 127 MODELS OF RISK PREDICTION AND ESTIMATION USING MARKOV CHAIN APPROACH THE STEP METHOD FOR A FUNCTIONAL- MURESAN Anton S.: 135 DIFFERENTIAL EQUATION FROM PRICE THEORY MURESAN Viorica: A FREDHOLM-VOLTERRA INTEGRO- 147 DIFFERENTIAL EQUATION WITH LINEAR MODIFICATION OF THE ARGUMENT THE SOLOW-SWAN GROWTH PŘIBYLOVÁ Lenka, VALENTA Petr: 159 MODEL WITH BOUNDED POPULATION ASYMPTOTIC PROPERTIES OF DELAYED SVOBODA Zdeněk: 167 EXPONENTIAL OF MATRIX VOLTERRA MATRIX INTEGRO-DIFFERENTIAL ŠMARDA Zdeněk: 173 EQUATIONS NEW ASPECTS IN Al ZOUKRA Kristine, SCHMIDT Werner H.: 179 PARAMETER IDENTIFICATION APLIMAT - JOURNAL OF APPLIED MATHEMATICS VOLUME 3 (2010), NUMBER 2 MODELING AND SIMULATION APPLICATION OF NON-EUKLIDIAN KINDLER Eugene, KRIVY Ivan: 185 METRICS IN DISCRETE EVENT SIMULATION STABILITY ANALYSIS OF STATE-SPACE MODELS IN KVAPIL David: 189 MATLAB TALHOFER Václav, HOŠKOVÁ Šárka, KRATOCHVÍL Vlastimil, 199 HOFMANN Alois: MATHEMATICAL MODEL FOR SPATIAL DATA PROPERTIES ASSESSMENT APLIMAT - JOURNAL OF APPLIED MATHEMATICS VOLUME 3 (2010), NUMBER 2 ALGEBRA AND ITS APPLICATIONS CHVALINA Jan, CHVALINOVÁ Ludmila: REALIZABILITY OF THE 211 ENDOMORPHISM MONOID OF A SEMI-CASCADE FORMED BY SOLUTION SPACES OF LINEAR ORDINARY N-TH ORDER DIFFERENTIAL EQUATIONS MYŠKOVÁ Helena: SOLVABILITY CONCEPTS FOR INTERVAL 225 SYSTEMS IN MAX-PLUS ALGEBRA NOVÁK Michal: THE NOTION OF SUBHYPERSTRUCTURE OF ”ENDS 237 LEMMA”–BASED HYPERSTRUCTURES SEIBERT Jaroslav: SOME QUANTITIES RELATED TO THE DISTANCE 249 MATRIX OF A SPECIAL TYPE OF DIGRAPHS. SZALAY István: GIANT BODIES PIECE BY PIECE 272 APLIMAT - JOURNAL OF APPLIED MATHEMATICS LIST OF REVIEWERS Andrade Marina, Professor Auxiliar ISCTE - Lisbon University Institute, Lisboa, Portugal Ayud Sani Muhammed NGO, University of Cape Cost , Accra Barbagallo Annamaria, Dr. University of Catania, Italy University of Economics Prague, Jindřichův Hradec, Czech Bartošová Jitka, RNDr., PhD. Republic Bayaraa Nyamish, Ulaanbaatar, Mongolia Beránek Jaroslav, Doc. RNDr. CSc. Masaryk University, Brno, Czech Republic Brueckler Franka Miriam, DrSc. University of Zagreb, Zagreb, Poland Budíková Marie, RNDr., Dr. Masarykova univerzita, Brno, Czech Republic Budkina Natalja, Dr. math Riga, Latvia Technical university, Riga, Latvia Buy Dmitriy B., PhD. Kyiv Taras Shevchenko National University, Kyiv Conversano Elisa Architettura, Roma, Italy Csatáryová Mária, RNDr., PhD. University of Prešov, Prešov, Slovak Republic Daniele Patrizia, Associate Professor University of Catania, Italy, Slovak University of Technology in Bratislava, Slovak Dobrakovová Jana, Doc., RNDr., CSc. Republic Doležalová Jarmila, Doc., RNDr., CSc. VŠB - TU, Ostrava, Czech Republic Dorociaková Božena, RNDr., PhD. University of Žilina, Žilina, Slovak Republic Doupovec Miroslav, doc. RNDr.. CSc. University of Technology, Brno, Czech Republic Ferreira Manuel Alberto M., Professor ISCTE- Lisbon University Institute , Lisboa, Portugal Catedrático Filipe José António, Prof. Auxiliar ISCTE - Lisbon University Institute, Lisboa, Portugal 9 Francaviglia Mauro, Full Prof. University of Calabria, Calabria, Italy Franců Jan, prof. RNDr., CSc. University of Technology, Brno, Czech Republic Fulier Jozef, prof. RNDr. CSc. UKF Nitra, Slovak Republic Habiballa Hashim, RNDr., PaedDr., PhD. University of Ostrava, Ostrava, Czech Republic Hennyeyová Klára, doc. Ing. CSc. Slovak University of Agriculture, Nitra, Slovak Republic Hinterleitner Irena, PhD. University of Technology, Brno, Czech Republic Hošková Šárka, Doc. RNDr., PhD. University of Defence, Brno, Czech Republic Hunka Frantisek, Doc. (Assoc. Prof) University of Ostrava, Ostrava, Czech Republic Chvosteková Martina, Mgr. Slovak Academy of Science, Bratislava, Slovak Republic Jan Chvalina, Prof. DrSc. University of Technology, Brno, Czech Republic Janková Mária, Mgr. Slovak Academy of science, Bratislava, Slovak Republic Jukic Ljerka University of Osijek, Osijek, Croatia Slovak University of Technology in Bratislava, Slovak Kalina Martin, Doc. RNDr., CSc. Republic Kapička Vratislav, Prof. RNDr., DrSc. Masaryk university, Brno, Czech Republic Klobucar Antoaneta, University in Osijek, Osijek, Croatia Klůfa Jindřich, prof. RNDr., CSc. University of Economics, Prague, Czech Republic Slovak University of Technology in Bratislava, Slovak Kováčová Monika, Mgr., PhD. Republic M. Bel University Banská Bystrica, Poprad, Slovak Kulčár Ladislav, Doc. RNDr. CSc. Republic Brno, Czech Republic University of Technology, Brno, Kureš Miroslav, Assoc. Prof. Czech Republic Kvasz Ladislav, Doc. PhD. (Assoc. Prof) University Komenskeho, Bratislava, Slovak Republic Lopes Ana Paula, PhD. Polytechnic Institute of Oporto – IPP, Oporto, Portugal Marcella Giulia Lorenzi, prof. Università della Calabria, Calabria, Italy 10 Technical University of Cluj- Napoca, Cluj-Napoca, Lungu Nicolae, Prof. Romania Majstorović Snježana J.J.Strossmayer University, Osijek, Croatia Mendel University in Brno, Czech Republic, Brno, Czech Mařík Robert, doc. PhD. Republic Matvejevs Andrejs, Ing., DrSc. Riga, Latvia Technical university, Riga, Latvia Michálek Jiří, RNDr, CSc. Czech Academy of Sciences, Prague, Czech Republic Mikeš Josef, Prof. RNDr., DrSc. Palacky University, Olomouc Czech Republic Myšková Helena, RNDr., PhD. Technical University of Košice, Košice Nemoga Karol, doc. RNDr., PhD. Slovak Academy of Sciences, Bratislava, Slovak Republic Mathematical Institute of the Academy, Brno, Czech Neuman František, Prof., RNDr., DrSc. Republic Slovak University of Technology in Bratislava, Slovak Omachelová Milada, Mgr., PhD Republic Paun Marius, Prof. Dr. Transilvania University of Brasov, Brasov, Romania Pavlenko Oksana, Dr. math Riga, Latvia Technical university, Riga, Latvia Plavka Ján Technical University Košice, Košice, Slovak Republic Plch Roman, RNDr., PhD. Masaryk University, Brno, Czech Republic Pokorný Michal, Prof. University of Zilina, Zilina, Slovak Republic Potůček Radovan, RNDr., PhD. University of Defense, Brno, Czech Republic University of Hradec Králové, Hradec Králové, Czech Půlpán Zdeněk, Prof., RNDr., PhD.r., CSc. Republic Račková Pavlína, PhD.r., PhD. University of Defense, Brno, Czech Republic Rus Ioan A., Professor Babes-Bolyai University, Cluj-Napoca,
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