Institute of Mathematics and Computer Sciences
1. Dr. habil. Blahota István
Name of the Institute: Institute of Mathematics and Computer Sciences
Name of the researcher(s) and research group: Dr. habil. István Blahota
Research area and keywords of research: Dyadic harmonic analysis and applications
Research objectives: Approximation theory with respect to series based on systems formed by piecewise constant functions as Walsh and Vilenkin systems, the characters of 2-adic integers and representative product systems.
Description and results of research: Approximation theory with respect to series based on systems formed by piecewise constant functions as Walsh and Vilenkin systems, the characters of 2-adic integers and representative product systems. These systems have a wide applications in areas ranging from the field of communication to the area of systems and control as well as digital signal processing. Recently, we apply Walsh-Fourier series to solve differential equations numerically and to analyse seasonal time series. The website of the group: http://zeus.nyf.hu/~dyadic/.
Research partners from other institutions: The research team is in close contact with ELTE, IK, Department of Numerical Analysis (Toledo, R.), DE, Department of Analysis (Gát, G.), Department of Mathematics and EKCU, Institute of Mathematics and Computer Sciences (Nagy, K.).
The research team has extensive international contacts, which has resulted in nearly 30 publications with foreign authors. International connections: Ushangi Goginava (Ivane Javakhishvili Tbilisi State University, Georgia), Giorgi Tephnadze (The University of Georgia, Tbilisi, Georgia), Nacima Memic (University of Sarajevo, Sarajevo, Bosnia and Herzegovina), Radomir Stankovic (University of Nis, Serbia), Mohamed Salim (United Arab Emirates University, Al Ain, UAEU), Lars-Erik Persson (Luleå University of Technology, Luleå, Sweden). Most of the above-mentioned scientists were invited to the University of Nyíregyháza on several occasions.
Other information: Project: "International research in dyadic analysis and related topics, solutions in the digital world" (2012-2014), TÁMOP-4.2.2.A-11/1 /KONV-2012-0051. (https://daproject.nyf.hu/)
Publications (max. 5):
1) Blahota, I. and Gát, G., Norm summability of Nörlund logarithmic means on unbounded Vilenkin groups, Analysis in Theory and Applications, 24, 2008, 1-17.
2) Blahota, I., On a norm inequality with respect to Vilenkin-like systems, Acta Mathematica Hungarica 89 (1-2), 2000, 15-27.
3) Blahota, I. and Gát, G., Almost everywhere convergence of Marcinkiewicz means of Fourier series on the group of 2-adic integers, Studia Mathematica, 191, 2009, 215-222.
4) Blahota, I., Persson L.E. and Tephnadze G., Two-sided estimates of the Lebesgue constants with respect to Vilenkin systems and applications, Glasgow Mathematical Journal 60 (1), 2018, 17-34.
5) Blahota, I. and Nagy, K., Approximation by Marcinkiewicz-type matrix transform of Vilenkin-Fourier series, Mediterranean Journal of Mathematics 19 (4), 2022, 165.
2. Dr. Falucskai János
Name of the Institute: Institute of Mathematics and Computer Sciences
Name of the researcher(s) and research group: Dr. János Falucskai
Research area and keywords of research: Quasi codes
Research objectives: Investigation of decipherability of codes. We defined "quasi codes", which is a new interpretation of codes: a code word is the set of sequances of symbols.
Description and results of research: Investigation of decipherability of codes. We defined "quasi codes", which is a new interpretation of codes: a code word is the set of sequances of symbols.
Publications (max. 5):
1) Borics, G., Várbíró, G., Falucskai, J., Végvári, Zs., T‐Krasznai, E., Görgényi, J., B‐Béres, V., Lerf, V., A two‐dimensional morphospace for cyanobacteria and microalgae: Morphological diversity, evolutionary relatedness and size constraints, Freshwater Biology, 68 (1), 2023, 115-126.
2) Falucskai, J., A novel test for unique decipherability of codes, Publicationes Mathematicae Debrecen, 78 (3-4), 2011, 535-541.
3) Falucskai, J., On the k-reversibility of finite automata, Annales Mathematicae et Informaticae, 36 (1), 2009, 71-75.
4) Falucskai, J., On equivalence of two tests for codes, Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, 24 (2), 2008, 249-256.
5) Falucskai, J. On a test for codes, Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, 22 (1), (2006), 121-125.
3. Grünwald Richárd, Molnár Gábor Marcell
Name of the Institute: Institute of Mathematics and Computer Sciences
Name of the researcher(s) and research group: Gábor Marcell Molnár, Richárd Grünwald
Research area and keywords of research: Functional equations and inequalities
Research objectives: Additive functions, derivations, theory of means.
Description and results of research: Necessary and sufficient conditions for an additive/Leibniz-type function to be a derivation, characterization of the equality problem of generalized Bajraktarević means and of the invariance equation of the arithmetic mean with respect to generalized Bajraktarević means, local and global comparison of nonsymmetric generalized Bajraktarević means. Convex and concave sequences and their applications
Research partners from other institutions: The supervisor of both researchers is Prof. Dr. Zsolt Páles
Publications (max. 5):
1) Molnár, G.M. and Páles, Zs., On convex and concave sequences and their applications, Mathematical Inequalities & Applications 25 (3), 2022, 727-750.
2) Molnár, G.M. and Páles, Zs., An extension of the Rådström cancellation theorem to cornets, Semigroup Forum 102, 2021, 765-793.
3) Grünwald, R. and Páles, Zs., On derivations with respect to finite sets of smooth functions, Acta Mathematica Hungarica 154 (2), 2018, 530-544.
4) Grünwald, R. and Páles, Zs., On the equality problem of generalized Bajraktarević means, Aequationes Mathematicae 94 (4), 2020, 651-677.
5) Grünwald, R. and Páles, Zs., On the invariance of the arithmetic mean with respect to generalized Bajraktarević means, Acta Mathematica Hungarica, 166 (2), 2022, 594-613.
4. Dr. Iszály Ferenc Zalán
Name of the Institute: Institute of Mathematics and Computer Sciences
Name of the researcher(s) and research group: Member of IFLA (International Federation of Library Associations and Institutions) Member of MKE
Research area and keywords of research: Library Innovation, Web 2.0 services, University, Startup
Research objectives: Library Innovation systems (UnInLib)
Description and results of research: The UnInLib project is designed to create the ‘Library Innovation Ecosystem’. Its main goal is to implement and apply a new, closed Web 2.0 service system, primarily for national and international university libraries - that facilitates the creation, development and implementation of innovation, startup ideas and inventions for university students, lecturers, graduates and professionals in dual trainings. The centre of the UnInLib is the Web Innovation Library Knowledge Base (WIKT) software system, a new library portal with a structure similar to Linkedin and Facebook. The WIKT system provides all the necessary information to start and run a successful innovative business such as Startup Information, Online Courses, Startup Problems Database, Ideas Database, Professionals Database, Connecting Professionals, Creating New Startups, or Providing Conditions for Online and Offline Meetings. The GenILib subsystem of UnInLib supports the innovation efforts of public libraries in numerous areas, with key functions such as value preservation, value creation, co-working spaces in libraries, exhibitions, online scholarships, skill-enhancing competitions, forums, blogs, online reviews, rankings, the organization of modern e-transportation tools in a library environment and library tourism.
Publications (max. 5):
1) Iszály, F.Z., A könyvtárak új innovációs elektronikus szolgáltatási rendszere: Az UnInLib innovációs könyvtári projekt, a könyvtári innováció egy lehetséges iránya, Tudományos és Műszaki Tájékoztatás, 13188, 2022.
2) Iszály, F.Z., A könyvtárak új innovációs elektronikus szolgáltatási rendszere. - G06Q 50/00, Benyújtás éve (szabadalom): 2020.
3) Keerthana, C.H., Manjula, Devi T.H., De Silva, L. M.M. et. al., New Web 2.0 Services at University Libraries, Proceedings of 40th IRF International Conference, Bengaluru, India: Interdisciplinary Research Foundation (IRF), 2018, 58-64.
4) Iszály, F.Z. and Tanyiné, K.A., Digitális alkalmazások. elektronikus tananyag MOOC keretrendszerben, Nyíregyházi Egyetem, 2018.
5) Iszály, F.Z., Electronic library services in Hungary and in the USA, Libellarium Journal For The History Of Writing, Books and Memory Institutions 10 (1), 2017, 93-114.
5. Tanyiné Dr. Kocsis Anikó
Name of the Institute: Institute of Matematics and Computer Sciences
Name of the researcher(s) and research group: Anikó Tanyiné Dr. Kocsis
Research area and keywords of research: Digital competence development in a secondary-higher education environment
Research objectives: Digital Competencies, Digital Competence Development, Information Retrieval, Business Information Retrieval, Dangers of the Internet and Social Networking, Coaching, Using of coaching to reduce burnout.
Publications (max. 5):
1) Iszály, F.Z. and Tanyiné, K.A., Digitális alkalmazások. elektronikus tananyag MOOC keretrendszerben, Nyíregyházi Egyetem, 2018.
2) Tanyiné K.A., Coaching alkalmazása a kiégés csökkentésére. - In: Rusinné, Fedor Anita; Tóth, Dalma; Zakor-Broda, Rita (szerk.): XIV. Nemzetközi Nyíregyházi Doktorandusz és Posztdoktori Konferencia: Absztraktkötet, Nyíregyháza: Debreceni Egyetem Egészségtudományi Kar, 167 (72), 2022.
3) Tanyiné K.A., Az internet és a közösségi oldalak veszélyei, a megelőzés lehetőségei az általános és középiskolások körében. - In: János, István (szerk.): Tradíció és innováció ötvözete a Nyíregyházi Egyetemen. Nyíregyháza: Nyíregyházi Egyetem 614, 2022, 461-476.
4) Tanyiné K.A., A pedagógiai szakirodalom online forrásai. - In: Schmercz, István (szerk.): Értékteremtő tudomány, A Magyar Tudomány Napja alkalmából 2019. november 13-án rendezett tudományos konferencia anyaga, Nyíregyháza. Szent Atanáz Görögkatolikus Hittudományi Főiskola, 217, 2020, 205-217.
6. Dr. Vályi Sándor
Name of the Institute: Institute of Mathematics and Computer Sciences
Name of the researcher(s) and research group: Sándor Zoltán Vályi, Research Group in Computer Science
Research area and keywords of research: Interval-valued computing
Research objectives: A new massively parallel computing paradigm
Description and results of research: We have developed a new, massively parallel computing paradigm, whose basic data units are finite unions of subintervals of [0,1). (Publication 1.) We have given some interesting computations within this paradigm. Publication 2.) We have established a connection of a class of interval-valued computations to the complexity class NP. (Publication 3.) Recently, we are seeking connections to other new computing paradigms. (Publication 4.) In (Publication 5.) we have finished our research into logic in relativity theory.
Research partners from other institutions: Nagy, B.. East Mediterran University in Famagusta, Cyprus
Publications (max. 5):
1) Nagy, B. and Vályi, S., Interval-valued computations and their connection with PSPACE, Theoretical Computer Science, 394 (3) 2008, 208-222.
2) Nagy, B. and Vályi, S., Prime factorization by interval-valued computing, Publicationes Mathematicae Debrecen, 79 (3-4) 2011, 539-551.
3) Nagy, B. and Vályi, S., A Shift-free Characterization of NP within Interval-valued Computing, Fundamenta Informaticae, 155 (1-2), 2017, 187-207.
4) Nagy, B. and Vályi, S., Circular Interval-valued Computers and Simulation of (Red-green) Turing Machines, Fundamenta Informaticae, 181 (2-3), 2021, 213-238.
5) Vályi, S., On the axiomatizability of some first-order spatio-temporal theories, Synthese, 192 (7), 2015, 2293-2309.
7. Dr. Vattamány Szabolcs
Name of the Institute: Institute of Mathematics and Computer Sciences
Name of the researcher(s) and research group: Dr. Szabolcs Vattamány
Research area and keywords of research: Spray geometry, Finsler geometry, Projective change, Metrizability
Publications (max. 5):
1) Szilasi, J. and Vattamány, Sz., On the projective geometry of sprays, Differ. Geom. Appl. 12, 2000, 183-208.
2) Vattamány, Sz., Projection onto the indicatrix bundle of a Finsler manifold, Publ. Math. Debrecen 58, 2001, 193-221.
3) Vattamány, Sz. and Vince, Cs., Two-dimensional Landsberg manifolds with vanishing Douglas tensor, Annales Univ. Sci. Budapest 44, 2001, 11-26.
4) Szilasi J. and Vattamány Sz., On the Finsler metrizabilities of spray manifolds, Periodica Mathematica Hungarica 44, 2002, 81-100.
5) Vattamány, Sz. and Vince Cs., On a new geometrical derivation of two-dimensional Finsler manifolds with constant main scalar, Periodica Mathematica Hungarica 48, 2004