Prof. Liptai Kálmán PhD

Professor at Eszterhazy Károly University of Applied Sciences 

Curriculum Vitae

Name

Dr. Kálmán Liptai PhD.

Date of Birth

14 October, 1961.

Studies

  • Gárdonyi GézaGrammer School, Eger (1976-1980)
  • Kossuth Lajos University, Debrecen (1981-1986), teacher of mathematics andphysics
  • Kossuth Lajos University, Debrecen,PhD. Program of Mathematics, Diophantine and constructive number theory, (1993-97)
  • PhD.degree (1997),the title of thesis “Diophantine problems concerning linear recurrences”

Employment and professional experience

  • Gárdonyi Géza Grammer School,Eger (1986-87)
  • Eszterházy Károly College,Department of Mathematics (1987-2003)
  • Eszterházy Károly College, Department of Applied Mathematics (2003- )

Status

  • Professor,Head of the Mathematics and Informatics Institute, head of Department of Applied Mathematics (2003- )
  • Dean of Faculty of Science(2006-)

Research fields

Number theory, diophantine problems, cryptography, recursive sequences,computer algebra

Teaching tasks

Real Analysis,Probability Theory, Calculus, Linear algebra, Computer algebra,Cryptography, Number Theory and Recursive sequences (lectures)

I have taught for 22 years.

Participation of research project

  • OTKAT 020295 (supervisor Professor Péter Kiss)
  • OTKAT 16975 (supervisor Kálmán Győry)
  • OTKAT 032898 (supervisor Ferenc Mátyás) (2005- )

Conference organization

  • Organizer,Number Theory Conference, Eger,1996.
  • Organizer,Fejér-Riesz Conference, Eger, 2005.

Member of

  • the Hungarian Credit Council
  • the Board of János Bolyai Mathematical Society (2004- )
  • the Board of Abacus Foundation, chairman (2003- )
  • the Editorial Board of Annales Mathemaicae at Informaticae
  • the Editorial Board of Teaching Mathematics and Informatics

Fellowship

Békéssy György Postdoctoral Fellowship (2001-2004)

Academic activity

  • Reviewerin Zentralblatt für Mathematik (1998- )
  • Lector

Administrative duties and committees

  • member of the Council of College (2001-2006)
  • member of the Economic Council (2006- )

Lectures

  • Power classes in linear recurrences,Technische Universität, Graz, (1997), (Tempus project)
  • Results concerning linear recurrences,Department of Math. of Jihoceska Univerzita, Ceske Budejovice,(2001), (CEEPUS project)
  • Solutions of diophantine equations,Technische Universität, Graz, (2001) (Tempus project)
  • Pellequations,Scientific Meeting of Dep. of Algebra and Number Theory, KonstantinUniv. Nitra, (2001)
  • On the square roots of triangular numbers,Scientificmeeting, Department of Algebra and Number Theory, Univ. Of Ostrava,Ostrava, (2002)
  • Primality tests,Department of Math. of Jihoceska Univerzita, Ceske Budejovice, (2002)(CEEPUS project)
  • New results on balancing numbers,Department of Algebra and Number Theory, Univ. Of Ostrava, Ostrava, (2006)(Erasmus project)

Fieldtrips

  • Mathematical Institute of Leiden University (Neatherland) (2003)
  • RISC, Linz (Austria) (2005)
  • The 9th Workshop on Elliptic Curve Cryptography, Coppenhagen (Denmark)(2005)
  • ARION fellowship,The teaching profession in transition, Coppenhagen (Denmark), (2005)
  • RISC, Linz (Austria) (2008)

Publications

  1. Polynomials with special coefficients, Annales Mathematicae et Informaticae, 37 (2010), 101-106. (with F. Mátyás, F. Filip and J. T. Tóth)
  2. On the best estimations for dispersions of special ratio block sequences, Annales Mathematicae et Informaticae, 37 (2010), 85-93. (with F. Mátyás, F. Filip and J. T. Tóth)
  3. Balancing with Fibonacci Powers, Fibonacci Quarterly, (accepted) (with A. Behera, G. K. Panda and L. Szalay)
  4. About (a,b)-type balancing numbers, Publ. Math. Debrecen, 77/3-4 (2010), 485-498. (with T. Kovács and P. Olajos)
  5. On the shifted product of binary recurrences, Journal of Integer Sequences, Vol. 13. (2010), article 10.6.1. (with Omar Khadir and L. Szalay)
  6. On generalized balancing sequences, Fibonacci Quarterly 48 No.2, (2010), 121–128. (with A. Bérzes and I. Pink)
  7. Generalized balancing numbers, Indag. Math. N.S. 20 (2009), 87-100. (with F. Luca, Á. Pintér and L. Szalay László)
  8. Cryptographycal protocols in the Egerfood Information System, Annales Mathematicae et Informaticae, 34 (2007), 61–70. (with G. Kusper and T. Radványi)
  9. Lucas balancing numbers, Acta Math. Univ. Ostrav 14, No 1. (2006) 43-47.
  10. On prime divisors of remarkable sequences, Annales Mathematicae et Informaticae, 33 (2006) 45-56. (with F. Filip and J. T. Tóth)
  11. Power classes of recurrence sequences, Publ. Math. Debrecen, 65/3-4 (2004), 421-428. (with L. Szalay)
  12. Fibonacci balancing numbers, Fibonacci Quarterly, 42 (2004), 330-340.
  13. Kiss and the linear recursive sequences, Acta Acad. Paed. Agriensis Sect. Mat., 30 (2003), 7-22. (with F. Mátyás)
  14. Results concerning perfect powers in linear recurrences, Acta Matematica (Nitra) 4 (2000), 47-56.
  15. On polynomial values of the product of the sum and the product of the terms of linear recurrence sequences, Acta Acad. Paed. Agriensis, Sect. Math., 27 (2000), 9-19.
  16. Solution of diophantine equations by second order linear recurrences, Ann. Univ. Sci. Budapest, Eötvös, XVIII. (1999), 109-114. (with P. Kiss)
  17. On polynomial values of the product of the terms of linear recurrence sequences, Acta Acad. Paed. Agriensis Sect. Mat., 26 (1999), 19-23.
  18. On products of the terms of linear recurrences, Proceedings of the International Number Theory Conference , W. de Gruyter GmbH and Co., (1998) 101-106. (with B. Brindza and L. Szalay).
  19. On a Diophantine equation, Discus. Math., 18 (1998) 49-59.
  20. An application of a theorem of Thue, Discus. Math., 18 (1998) 111-120.
  21. On a three dimensional aproximation problem, Applications of Fibonacci Numbers, Volume 7 (1998), 265-270.
  22. Pure powers in recurrence sequences, Acta Acad. Paed. Agriensis, Sect. Mat., 24 (1997), 35-40. (with T. Tómács)
  23. Points on the plane whose coordinates are terms of recursive sequences, Publ. Math. Debrecen 49/1-2 (1996), 177-182.
  24. An approximation problem concerning linear recurrences, Acta Acad. Paed. Agriensis, Sect. Mat., 23. (1995-96), 11-15.
  25. Közös elemek másodrendű rekurzív sorozatokban, Acta Acad. Paed. Agriensis, Sect. Mat., 22 (1994), 47-54.
  26. Pell egyenletek megoldása lineáris rekurzív sorozatok segítségével, Acta Acad. Paed. Agriensis, Sect. Mat., 21 (1993), 15-26.

Lecture notes

  1. Analízis feladatgyűjtemény, EKF Líceum Kiadó, (2005)
  2. Liptai-Mátyás-Rados-Sashalminé-Szepessy-Tómács-Zay: Matematika nem matematika szakos hallgatóknak (Analízis fejezet), EKF Líceum Kiadó, (2000)

Conferencies

 
  1. On balancing numbers, Number Theory and its Applications, Debrecen, 2010. október 4-8.
  2. About (a, b)-type balancing numbers, The Fourteenth International Conference on Fibonacci Numbers and Their Applications, Morelia (Mexikó), 2010. július 5-9.)
  3. Generalized balancing numbers, I. International Scientific Conference, Komarno (Slovakia), 2009. szeptember 7-8.
  4. Remarks on public key cryptography, International conference on information (ICI 19) (Learning innovation in higher education), (Kuala Lumpur, Malaysia), 2009. augusztus 12-13.
  5. Diophantine equations and balancing numbers, Thirteenth International Conference On Fibonacci Numbers and Their Applications, Patras (Görögország) 2008. július 7-11.
  6. Generalized balancing numbers, Numbers, functions, equations ’08, De La Motte Castle, Noszvaj, 2008. június 15-21.
  7. Remarks on balancing numbers, Journées Arithmétiques, Edinburgh (Skócia), 2007. július 2-6.
  8. Generalized balancing numbers, 17th Czech and Slovak International Conference on Number Theory, Malenovice (Csehország) 2005. szeptember 5-10.
  9. Általánosított balansz számok, Soproni Számelméleti Napok, 2004. október 8-9.
  10. The products and the sums of the terms of linear recurrences, V. Polish, Slovak and Czech Conference on Number Theory, Terchová (Szlovákia), 2004. június 14-18.
  11. Generalized balancing numbers, Nyitrai Matematikai Konferencia, Nyitra, 2003. október 16-17.
  12. Balancing numbers, XVI. Slovak and Czeh International Number Theory Conference, Pozsony, 2003. június 30-tól július 4.
  13. Balancing numbers, Kiss Péter Emlékkonferencia, Eger, 2002. november 22-23.
  14. Relations between Pell equations and linear recurrences, International Number Theory Conference, Eger, 2000. november 8-10.
  15. Results concerning perfect powers in linear recurrences, Ninth International Conference on Fibonacci Numbers and their Application, Luxembourg, 2000. július 17-21.
  16. Perfect powers in linear recurrences, Nemzetközi Számelméleti Konferencia, Nyitra, 1999. október 10-13.
  17. On products of the terms of linear recurrences, Conference on Number Theory, Eger, 1996. július 29-augusztus 2.
  18. On a three dimensional approximation problem, Seventh International Conference on Fibonacci Numbers and their Application, Graz, 1996. július 15-19.
  19. On a diophantine problem, Kovács-Környei Nemzetközi Emlékkonferencia, Mátraháza, 1995. március 16-18.

Lectures

  1. Public key cryptography, Satakunta University of Applied Sciences, Pori, (Finnország), 2010. szeptember 19-23. (Erasmus ösztöndíj)
  2. History of Balancing numbers, Department of Mathematics, National Institute of Technology, Rourkela (India), 2009. november 15-30. (Magyar Ösztöndíjbizottság)
  3. New results on balancing numbers, Department of Algebra and Number Theory, Univ. Of Ostrava, Ostrava, 2006. február 7-14. (Erasmus ösztöndíj)
  4. Primality tests, Department of Math. of Jihoceska Univerzita, Ceske Budejovice, 2002. november 10-től december 6. (CEEPUS ösztöndíj)
  5. On the square roots of triangular numbers, Scientific meeting, Department of Algebra and Number Theory, Univ. Of Ostrava, Ostrava, 2002. április 15-18.
  6. Pell equations, Scientific Meeting of Dep. of Algebra and Number Theory, Konstantin Univ. Nitra, 2001. október 23-25.
  7. Solutions of diophantine equations, Technische Universität, Graz, 2001. július 2-5. (Tempus scholarship)
  8. Results concerning linear recurrences, Department of Math. of Jihoceska Univerzita, Ceske Budejovice, 2001. április 8- május 3. (CEEPUS ösztöndíj)
  9. Power classes in linear recurrences, Technische Universität, Graz, 1997. december 1-8. (Tempus ösztöndíj)

Monographies

  1. Mathematical Institute Leiden University (Hollandia) 2003. december 1-6.
  2. RISC, Linz (Ausztria) 2005. május 29-31.
  3. The 9th Workshop on Elliptic Curve Cryptography, Koppenhága (Dánia), 2005. szeptember 17-21.
  4. ARION ösztöndíj, The teaching profession in transition, Koppenhága (Dánia), 2005. október 9-13.
  5. RISC, Linz (Ausztria) 2008. február
  6. JoMiTe program meetings, Barcelona (Spanyolország) 2008. február 4-7.
  7. JoMiTe program meetings, Tartu (Észtország) 2009. március 2-6.