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User:Romeo Mestrovic
Romeo Meštrović Professor of Mathematics (Available at http://sites.google.com/site/romeomestrovic)
C U R R I C U L U M V I T A E
Personal Information Current Addresses
Date of birth: April 28, 1960
Place of birth: Split, Croatia
Citizenship: Montenegro
Office Maritime Faculty Department of Mathematics University of Montenegro Dobrota 36, Kotor Montenegro Telephone: +382 32303188 Fax: +382 32303184 e-mail: romeo@ac.me web page: http://sites.google.com/site/romeomestrovic/
Home Džordža Vašingtona bb, Podgorica Montenegro
Education
Romeo Meštrović, Professor of Mathematics at the Maritime Faculty, University of Montenegro, was born in Split 1960, Croatia. He graduated B.Sc. in Mathematics (Department of Mathematics - Division Algebra and Analysis) in Zagreb, University of Zagreb, Croatia. Romeo Meštrović received his M.Sc. in Mathematics (Complex Analysis and Functional Analysis) in 1996 under the title: On some F-algebras of holomorphic functions and his Ph.D. in Mathematics (Complex Analysis and Functional Analysis) in 1999 under the title: Topological and F-algebras of holomorphic functions at Faculty of Science, Division Mathematical and Computational Sciences, University of Montenegro. As a member of high school team of the former state Yugoslavia, in 1979 he was awarded a third prize in the XXI International Mathematical Olympiad in London. Moreover, he was awarded two first place in Mathematical Olympiads of the former state Yugoslavia in 1978 and 1979. Working Experience
1988-1991, Maritime Faculty, University of Montenegro, Teaching Assistant. 1991-1999, Maritime Faculty, University of Montenegro, Teacher. 1999-2004, Maritime Faculty, University of Montenegro, Assistant Professor. 2001-2002, Department of Mathematics, Faculty of Science, Podgorica, part-time. 2005-2010, Maritime Faculty, University of Montenegro, Associate Professor. 2010- , Maritime Faculty, University of Montenegro, Full Professor.
Research Interests
His main research interests are related to Complex analysis of one variables and Functional analysis. This topics mainly concerned with the investigations of linear topological and functional structure of the Privalov spaces on the unit disk of the complex plane. By studying the linear space structure of these spases and their extensions, he obtained many interesting results with applications. In this topics, he published nine papers in rewieved mathematical journals. Furthermore, his additional research areas are related to Queuing theory and Operations researches in transport and traffic operations. Recently, Romeo Meštrović deals with Combinatorial number theory and Combinatorics. In particular, this concerned with variations of Wolstenholme’s type theorems, Lucas’ type congruences modulo a prime and related combinatorial congruences modulo prime powers. His papers have been published in many scientific journals as well as: Doklady Akademii Nauk (Russian), American Mathematical Monthly, Portugaliae Mathematica, Ars Combinatoria, Acta Sci. Math. (Szeged), Journal of Mathematical Analysis and Applications, Journal of the Korean Mathematical Society etc. He was participated in many international and domestic conferences, symposiums, seminars and congresses related to the mentioned fields of research.
Awards and Honors
Yugoslav high school Mathematical Olympiads:
● Honorable mention, II grade, Titovo Velenje, Slovenia, 1977. ● First place, second prize, III grade, Bečići, Montenegro, 1978. ● First place, first prize, IV grade, Novi Sad, Serbia, 1979.
Bosnian and Herzegovian Mathematics Competitions for high school students: ● First place, first prize, II grade, Livno, 1977. ● Second place, second prize, III grade, Mostar, 1978. ● First place, first prize, IV grade, Foča, 1979.
Third prize in the XXI International Mathematical Olympiad, London, United Kingdom, 1979.
Honorable mention in Balkan Graduate Mathematics Competition, Belgrade, Serbia, 1980.
First prize on World Ocean Forum for the best paper in 2009.
Professional Service
1999-2001, Head of Department of Mathematics and Kibernetics.
2002-2004, Head of Department of Mathematics and Computer Sciences.
2002-2004 and 2008-2010, Head of of Graduate Studies Maritime Management at Maritime Faculty.
2001-2002, Member of a Committee for establishing New Plans and Programs of Graduate Studies Maritime Management at Maritime Faculty.
1996, 2005 and 2006, Member of the Serbian and Montenegrin Organizing and Competition Committee of Mathematical Competition for high school students.
2003, 2004, 2005 and 2006, Competition Committee chair of 37th, 38th, 39th and 40th Republic Mathematics Competition for primary and high school students of Montenegro, Podgorica.
2003, 2004, 2005 and 2006, Member of Coordinating Committee for 37th, 38th, 39th and 40th Republic Competition in Natural Sciences, Languages and History for primary and high school students of Montenegro, Podgorica.
2007, Team Leader of Montenegro on 11th Junior Balkan Mathematical Olympiad, Shumen, Bulgaria.
2008, Team Leader of Montenegro on 26th Balkan Mathematical Olympiad, Ohrid, Macedonia.
2006-2011, was proposed problems for third grade of high school and estimated student’s solutions on Mathematical Competitions for primary and high school students of Montenegro, Podgorica, Montenegro.
2000-2007, Member of Editorial Board of Matematičko Računarski Mozaik, Journal for primary school Mathematics and Computation (published fourth times each year), Podgorica, Montenegro, UDK 51 ISSN 1450-9261.
2000-2007, Editor of Advanced Problems Section of Matematičko Računarski Mozaik, Journal for primary school Mathematics and Computation (published fourth times each year), Podgorica, Montenegro, UDK 51 ISSN 1450-9261.
2005- , Member of Forum of University Professors and Researchers of Montenegro.
2009 - , Coordinator of Collaboration between Mathematicul Institute of Serbian Academy of Sciences and Arts at Belgrade and Maritime Faculty at Kotor.
2011, Team Leader of Montenegro on 15th Junior Balkan Mathematical Olympiad, Larnaca, Cyprus.
Courses
Maritime Faculty 1988-1998, Exercises in numerous Mathematical Courses 1991-1999, Mathematics I, Mathematics II. 1996- , Mathematics. 2001-2002, Numerical Analysis. 1999-2003, Probability and Statistics. 2004- , Probability and Statistics for Maritime Studies. 2008- , Mathematical Models of Transport. 2007- , Optimization Maritime Methods. 2009- , Risk Theory. 2007- , Numerous Courses on Postgraduate Studies and Doctoral Studies at Department of Marine Sciences and Department of Maritime Management (related to Analysis, Probability Theory, Queueing Theory, Combinatorial Optimization,...). Department of Mathematics, Faculty of Science, Podgorica 2001-2002, Complex Analysis.
Visiting Positions
Department of Mathematical Analysis at Faculty of Mechanics and Mathematics, M.V. Lomonosov Moscow State University, Moscow, Russia:
October, 1996 November, 1997 June, 1998 December, 1998 June, 2008 April, 2009 Visiting Lectures
Department of Mathematical Analysis at Faculty of Mechanics and Mathematics, M.V. Lomonosov Moscow State University - Seminars under the guidance of Prof.Dr. V. Ivanovich Gavrilov October, 1996 Linear topological properties of the Privalov’s spaces of holomorphic functions in the unit disk. November, 1997 Interpolation in spaces.
June, 1998 On the ideals structure in the algebras .
June, 1998 Asymptotic versions of Szego’s and Helson-Szego’s theorem. December, 1998 Approximative theorems for the classes .
December, 1998 Weakly dense ideals of the rings .
June, 2008 Different Topologies on Privalov Spaces with Applications. April, 2009 Asymptotic analogues of Szego’s theorem and Helson-Szego’s theorem.
Mathematicul Institute of Serbian Academy of Sciences and Arts, Belgrade
May, 2009 Combinatorial congruences modulo a prime
Plenary and Invitation Papers
Park, N.K., Dragović, B. and Meštrović, R., Simulation results by port and container yard type – Case study: Korean terminals, Plenary Paper, 7th International Conference “Research and development in Mechanical industry“, RaDMI 2007, Belgrade, Serbia, September 2007, Conference Proceedings on CD, pp. 625-630.
Dragović, B., Park, N. K., Meštrović, R. and Radmilović, Z, Ports and terminals modeling: New approaches to investigation, Plenary and Invitation Paper, 8th International Conference “Research and development in Mechanical industry“, RaDMI 2008, Užice, Serbia, September 2008, Conference Proceedings on CD, pp. 19-36.
Dragović, B., Park, N. K, Meštrović, R., Kim, J. Y. and Mihaljević, N., Modeling and optimization of container terminals operations, Plenary and Invitation Paper, 9th International Conference “Research and development in Mechanical industry“, RaDMI 2009, Vrnjačka Banja, Serbia, September 2009, Conference Proceedings, Vol. 1, pp. 28-41.
Selected Congresses and Conferences
R. Meštrović, On some F-algebras of holomorphic functions, 9th Congress of Yugoslav Mathematicians, Petrovac, Montenegro, September 1995. R. Meštrović, Multipliers and linear functionals for the classes , International Kurepa’s Symposium, Belgrade, Serbia, May 1996, Book of abstracts, p. 69. R. Meštrović and Ž. Pavićević, The logarithmic version of Szego’s theorem, International Conference GF-96, Novi Sad, Serbia, August/September 1996, Appendix of Abstracts, p. 4. R. Meštrović, Interpolation theorems for the classes , 4th International Symposium on Mathematical Analysis and its Applications, Arandjelovac, Serbia, May 1997, Book of abstracts, p. 51. R. Meštrović, Topologies on some F-algebras of holomorphic functions, International Congress of Mathematicians, Berlin, Germany, August 1998, Book of abstracts, p. 141. R. Meštrović, Weakly dense ideals in some F-algebras of holomorphic functions, 3rd European Congress of Mathematics, Barcelona, Spain, August 2000, List of Posters, p. 133. R. Meštrović, Topologies on some generalized Orlicz spaces, 10th Congress of Yugoslav Mathematicians, Belgrade, Serbia, October 2000, Book of abstracts, p. 56. R. Meštrović, Invariant subspaces of some spaces of holomorphic functions, 5th International Symposium on Mathematical Analysis and its Applications, Niška Banja, Serbia, October 2002, Book of abstracts, p. 17. R. Meštrović, Multipliers of a class of de Branges spaces, 11th Congress of Mathematicians of Serbia and Montenegro, Petrovac, Montenegro, September/October, 2004, Book of abstracts, pp. 36-37. R. Meštrović, B. Dragović, S. Simić and Z. Radmilović: An analysis of the berth and container cranes allocation in port, 4th International Congress on Maritime Technological Innovations and Research, Barcelona, Spain, 2004, pp. 417-428. R. Meštrović and Ž. Pavićević, Weak Outer Functions for Privalov Spaces of Holomorphic Functions on the Disk, International Conference: Extremal Problems in Complex and Real Analysis, Moscow, Russia, May 2007. R. Meštrović and Ž. Pavićević, Universal multipliers of a class of de Branges spaces, 5th European Congress of Mathematics, Amsterdam, Holland, July 2008, Poster Session, Poster number 08.18. www.5ecm2.nl R. Meštrović, A characterization of primes and prime powers, 12th Serbian Mathematical Congress, Novi Sad, Serbia, August/September 2008, Book of Abstracts, p. 16.
Research Projects
Member of Research Projects founded by Ministry of Education and Science of Montenegro - Sector for Science and University
Jan. 2000 – Jan. 2001. “Problemi linearne i nelinearne analize”, Project Leader: Žarko Pavićević. July 2005 - July 2007. “Analiza s primjenama”, Project Leader: Žarko Pavićević. Sep. 2007 – Sep. 2010. “Kompleksna analiza”, Project Leader: Žarko Pavićević. Dec. 2008 – Dec. 2011. “Istraživanje optimalnog povezivanja pomorskih i kontinentalnih transportnih sistema - Case study: Valorizacija intermodalnosti crnogorskih potencijala (Brodarstva-Luka-Drumskog/Željezničkog/Vazdušnog transporta)”, Project Leader: Branislav Dragović.
Postgraduate students
● Žarko Sokolov, in progress, M.Sc. Thesis, Maritime Faculty, 2011, Kotor. ● Jasmina Koleb, in progress, M.Sc. Thesis, Maritime Faculty, 2011, Kotor.
Specialist papers: ● Filip Soković, Jedan pristup istraživanju modela teorije redova čekanja u pomorstvu, Maritime Faculty, Kotor, 2009. ● Zorica Kraljević, Modeliranje mrežnog saobraćaja sa primjenom Markovljevih procesa, Maritime Faculty, Kotor, 2010. ● Ivana Radulović, O pojmu vjerovatnoće blokiranja u teoriji redova čekanja, Maritime Faculty, Kotor, 2010. ● Ana Vukićević, Analiza diskretnog vremena sistema reda čekanja G(X)/D/1-S sa primjenama, Maritime Faculty, Kotor, 2010. ● Svetlana Ratković, Ekstremne vrijednosti funkcije više promjenljivih s primjenama, Maritime Faculty, Kotor, 2010. ● Andrea Samardžić, Obične diferencijalne jednačine s primjenama, Maritime Faculty, Kotor, 2010. ● Ivana Todorović, Transportni zadatak linearnog programiranja s primjenama, Maritime Faculty, Kotor, 2011. ● Jovanka Radović, Elementi teorije rizika sa primjenom u pomorskom transportu, Maritime Faculty, Kotor, 2011. ● Jovan Žižić, Araliza teorije rizika sa aplikacijama u modeliranju lučkih operacija, Maritime Faculty, Kotor, 2011. ● Ljiljana Marković, Simplex metoda sa primjenom u rješavanju transportnih problema, Maritime Faculty, Kotor, 2011. ● Veselin Vujanović, Matematičko modeliranje jednokanalnih i višekanalnih redova čekanja, Maritime Faculty, Kotor, 2011. ● Miloš Trivić, Modeli teorije redova čekanja sa osvrtom na intenzitet protoka klijenata, Maritime Faculty, Kotor, 2011. ● Ana Bukilica, Simulacioni softveri redova čekanja, Maritime Faculty, Kotor, 2011. ● Bojana Vujošević, Povećanje efikasnosti sistema redova čekanja u funkciji uzajamnog odnosa kanala opsluživanja , Maritime Faculty, Kotor, 2011. ● Ivana Stanković, Transportni zadatak linearnog programiranja s primjenama, Maritime Faculty, Kotor, 2011.
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WORKS OF ROMEO MESTROVIC
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BOOKS
1. R. Meštrović and Ž. Pavićević, Privalov Spaces on the Unit Disk (research monograph), Department of Mathematics, Faculty of Science, University of Montenegro, Podgorica, 2009, ISBN 978-9940-551-00-1, pages 142. 2. S. Šaranović and R. Meštrović, A Collection of Solved Problems and Sample Qualifying Exams for Mathematics, Maritime Faculty, Kotor, 2001.
PUBLISHED PAPERS AND PREPRINTS
(CLASSIFIED BY TOPICS A, B, C and D)
A) F-spaces of holomorphic functions in the unit disk - Privalov’s spaces and related Hardy-Orlicz classes (2010 MSC: 46J15, 46J20, 30H05, 30D55, 46E15, 46 E22, 46E30, 47B35)
1. R. Meštrović and Ž. Pavićević, Remarks on some classes of holomorphic functions, Math. Montisnigri 6 (1996), 27-37. 2. R. Meštrović, A characterization of a subclass of the Smirnov class, Math. Montisnigri 7 (1996), 29-34. 3. R. Meštrović, Ideals in some rings of Nevanlinna-Smirnov type, Math. Montisnigri 8 (1997), 127-135. 4. R. Meštrović and Ž. Pavićević, The logarithmic analogue of Szego’s theorem, Acta Sci. Math. (Szeged), 64 (1998), 97-102. 5. R. Meštrović, Ž. Pavićević and N. Labudović, Remarks on generalized Hardy algebras, Math. Montisnigri 11 (1999), 25-42. 6. R. Meštrović and A. V. Subbotin, Multipliers and linear functionals in Privalov’s spaces of holomorphic functions in the disk, Dokl. Akad. Nauk, 365, No. 4 (1999), 452-454 (Russian). 7. R. Meštrović, O konvergenciji Taylorovih redova u nekim klasama analitičkih funkcija, Zbornik Fakulteta za pomorstvo Kotor, 20 (2003), 361-374. 8. R. Meštrović and Ž. Pavićević, Topologies on some subclasses of the Smirnov class, Acta Sci. Math. (Szeged), 69 (2003), 99-108. 9. R. Meštrović, The failure of the Hahn Banach properties in Privalov spaces of holomorphic functions, Math. Montisnigri 17 (2004), 27-36. 10. R. Meštrović and Ž. Pavićević, A note on common range of a class of co-analytic Toeplitz operators, Portugal. Math. (N.S.), Vol. 66, Fasc. 2 (2009), 147-158. www.ems-ph.org 11. R. Meštrović and Ž. Pavićević, Weakly dense ideals in Privalov spaces of holomorphic functions, J. Korean Math. Soc., 48 (2011), 397-420. www.kms.or.kr
B) Combinatorial number theory and Combinatorics (2010 MSC: 11A07, 11A25, 11A51, 05A10, 05A17, 05A19, 11B65, 11B68) 12. R. Meštrović, A note on the congruence , American Mathematical Monthly, Vol. 116, no. 1 (2009) 75-77. www.maa.org/pubs/monthly.html . 13. R. Meštrović, An inductive proof of a result about Bulgarian Solitaire, Ars Combinatoria, 95 (2010), 65-70. www.bkocay.cs.umanitoba.ca/arscombinatoria . 14. R. Meštrović, An extension of the identity by Sury and related congruences, accepted for publication in Bulletin of the Australian Mathematical Society, 13 pages. 15. R. Meštrović, A note on the congruence , accepted for publication in Czechoslovak Mathematical Journal, 6 pages. 16. R. Meštrović, On the mod determination of , submitted. 17. R. Meštrović, Congruences for Wolstenholme primes, submitted. 18. R. Meštrović, An extension of Babbage’s criterion for primality, submitted.. 19. R. Meštrović, Congruences involving the Fermat quotient, submitted. 20. R. Meštrović, An elementary proof of a congruence by Skula and Granville, submitted. 21. R. Meštrović, An extension of a congruence by Kohnen, submitted.
C) Inequalities (Inequalities for sums, series and inequalities in the complex plane) (2010 MSC: 26D15, 30A10, 46B10, 46B20)
22. R. Meštrović and D. Kalaj, A Converse of Minkowski’s Type Inequalities, J. of Ineq. and Appl., Vol. 2010 Article ID 461215, 9 pages. 23. D. Kalaj and R. Meštrović, Isoperimetric type inequalities for harmonic functions, J. Math. Anal. Appl., 373 (2011), 439-448. 24. R. Meštrović, An Extension of Clarkson’s Inequalities, submitted.
D) Queuing theory (MSC 2010: 05A10, 05A17, 05A19, 11A07, 11B65, 11B68)
25. B. Dragović, R. Meštrović, S. Simić and V. Maraš, An analysis of the berth and QCs combinations in containerports, Tehnika 51 (2004), 105-112. 26. Z. Radmilović, B. Dragović and R. Meštrović, Optimal Number and Capacity of Servers in Queueing Systems, International Journal of Information and Management Sciences, 16 (2005), 1-16. 27. Park, N. K, Dragović, B., Meštrović, R. and Kim, J. Y., Simulation and analysis of container terminals operations – Case study: Korean ports, Modelling and Optimization in the Machines Building Field, Vol. 3, no. 4 (2007), 171-180. 28. B. Dragović, N. Đ. Zrnić, N. K. Park and R. Meštrović, Mathematical models of multi-server queuing system for dynamic performance evaluation in port, Mathematical Problems in Engineering, article in press.
Manuscripts in preparation
29. R. Meštrović, Variations of Lucas’ Theorem modulo prime powers. 30. R. Meštrović, Wolstenholme’s type congruences. 31. R. Meštrović, M. Riesz Theorem for a large class of functions. 32. R. Meštrović, An induction proof of a result about Bulgarian Solitaire. 33. R. Meštrović, Determination of the cardinality of some collections of subsets of the set {1,2,…,k} with k > 1. 34. R. Meštrović, A generalization of Carlitz’s congruence. 35. R. Meštrović, An extension of a Pan’s generalization of Carlitz’s congruence. 36. R. Meštrović, A simple combinatorial criterion for primality. 37. R. Meštrović, Interpolation in Privalov spaces on the unit disk of C. 38. R. Meštrović, F- algebras of holomorphic functions.
Unpublished manusripts
39. R. Meštrović, Linear topological structure of Privalov’s spaces of holomorphic
functions in the disk the unit disk, 25 pages.
40. R. Meštrović, Minkowski-Clarkson’s type inequalities, 5 pages.
