Razne magistrske naloge za študente FS

Mentor: doc. dr. Boštjan Gabrovšek

Povezava: https://rsmat.splet.arnes.si/files/2022/10/Teme-za-magisterij.pdf

Nekatere spodnje teme so primerne tudi za študente FS v bolj aplikativni izvedbi.

Številne teme iz
– matrične in operatorske analize,
– optimizacija proizvodnih sistemov z max-plus algebraičnimi metodami (Optimization of manufactoring systems by using max-plus algebraic methods),
– optimizacija in stabilnost transportnih sistemov z max-plus algebraičnimi metodami (Optimization and stability of transport systems by using max-plus algebraic methods)

  • možen tudi dogovor pri izboru teme

Mentor: izr. prof. dr. Aljoša Peperko

Nekaj relevantne literature:

  1. Bernd Heidergott, Geert Jan Olsder, & Jacob van der Woude, Max Plus at Work: Modeling and Analysis of Synchronized Systems: A Course on Max-Plus Algebra and Its Applications, Priceton University Press, 2006.
  2. Rob M.P. Goverde, Bernd Heidergott, Glenn Merlet, Railway Timetable Stability Analysis Using Stochastic Max-Plus Linear Systems
  3. Rob M.P. Goverde, Railway timetable stability analysis using max-plus system theory, Transportation Research Part B 41 (2007) 179–201
  4. R. Sato, Y. Khojasteh-Ghamari, An integrated framework for card-based production control systems, J Intell Manuf (2012), 717- 731.
  5. P. Butkovič Max-linear systems: theory and algorithms, Springer-Verlag, London, 2010.

Teme iz:
– Spektralna teorija za nelinearne max-operatorje in aplikacije (Spectral theory for nonliner max-operators and applications)
– Neenakosti za operatorje in matrike (Inequalities for operators and matrices)
– Posplošeni in skupni spektralni radij množice operatorjev in matrik ter njuni max-algebra verziji (Generalized and joint spectral radius of a set of operators and matrices – and their max-algebra versions)

-možen tudi dogovor pri izboru teme

Mentor: izr. prof. dr. Aljoša Peperko

Nekaj relevantnih publikacij (Some relevant publications):

  1. J. Appell, E. De Pascale, A. Vignoli, Nonlinear Spectral Theory, Walter de Gruyter GmbH and Co. KG, Berlin, 2004, available online
  2. X. Dai, Extremal and Barabanov semi-norms of a semigroup generated by a bounded family of matrices, J. Math. Anal. Appl. 379 (2011) 827-833.
  3. A. Peperko, Bounds on the generalized and the joint spectral radius of Hadamard products of bounded sets of positive operators on sequence spaces, Linear Algebra Appl. 437 (2012), 189–201.
  4. V. Muller, A. Peperko, Generalized spectral radius and its max algebra version, Linear Algebra Appl. 439 (2013), 1006–1016.
  5. A. Peperko, On the max version of the generalized spectral radius theorem, Linear Algebra Appl. 428 (2008), 2312–2318.
  6. M. Kandić, A. Peperko , On the submultiplicativity and subadditivity of the spectral and essential spectral radius, Banach J. Math. Anal., 2016.
  7. V. Muller, A. Peperko, On the spectrum in max-algebra, Lin. Alg. Appl. (2015), 250-266.
  8. Y. A. Abramovich, C. D. Aliprantis, An invitation to operator theory, American Mathematical Society, Providence, 2002.
  9. V.N. Kolokoltsov and V.P. Maslov,Idempotent analysis and its applications, Kluwer Acad. Publ., 1997.
  10. G.L. Litvinov, The Maslov dequantization, idempotent and tropical mathematics: A brief introduction, J. Math. Sci.(N. Y.) 140, no.3 (2007), 426–444, 2005.
  11. G. B. Shpiz, An eigenvector existence theorem in idempotent analysis, Mathematical Notes, 82, 3-4 (2007), 410–417.
  12. L. Pachter and B. Sturmfels (eds.), Algebraic statistics for computational biology, Cambridge Univ. Press, New York, 2005.
  13. .D. Nussbaum, Convexity and log convexity for the spectral radius, Linear Algebra Appl. 73 (1986), 59–122.
  14. B. Lemmens, R.D. Nussbaum, Continuity of the cone spectral radius, 2011.
  15. J. Mallet-Paret and R.D. Nussbaum, Eigenvalues for a class of homogeneous cone maps arising from max-plusoperators, Discrete and Continuous Dynamical Systems, vol 8, num 3 (2002), 519–562.
  16. J. Mallet-Paret and R. D. Nussbaum. Generalizing the Krein-Rutman theorem, measures of noncompactness and the fixed point index, J. Fixed Point Theory and Applications, 7 (2010), 103–143.
  17. V.S. Shulman and Yu.V. Turovskii, Joint spectral radius, operator semigroups and a problem of W.Wojtynski, J. Funct. Anal., 177 (2000), 383–441.