Research

  • Current research interest
    • Arboristics, acoustic tomography
    • Wood engineering, anizotropic materials
    • Data processing
    • Application of mathematics to selected problems in biology, forestry, urban forestry, material engineering
  • Former reserch interest
    • Qualitative theory of partial and ordinary differential equations, oscillation properties.
    • Qualitative theory of linear and half-linear difference equations.
    • Application of mathematics to selected problems in biology, forestry, urban forestry, material engineering
  • Researcher ID page
  • ORCID 0000-0001-7109-1526
  • Scopus Author ID 6602164820.
  • My profile in university information system and Google Scholar

Current talk

Published research papers

  1. R. Berezjuk, P. Nop, R. Mařík, R. Gracovský, J. Tippner, Towards more accurate grading: non-destructive methods for assessing low-quality sawlogs, Holzforschung – International Journal of the Biology, Chemistry, Physics and Technology of Wood, Volume 39, 2025, ISSN 0018-3830. https://doi.org/10.1515/hf-2025-0039
  2. V. Cristini, J. Tippner, M. Tomšovský, J. Zlámal, R. Mařík, Acoustic tomography outputs in comparison to the properties of degraded wood in beech trees. European journal of wood and wood products. 2022. sv. 80, č. 6, s. 1377–1387. ISSN 0018-3768. https://doi.org/10.1007/s00107-022-01872-w
  3. B. Vojáčková, J. Tippner, P. Horáček, V. Sebera, L. Praus, R. Mařík, M. Brabec, The effect of stem and root-plate defects on the tree response during static loading - Numerical analysis, Urban Forestry & Urban Greening Volume 59, April 2021. online
  4. S. Fišnarová, R. Mařík, Oscillation of second order half-linear neutral differential equations with weaker restrictions on shifted arguments, Mathematica Slovaca, vol. 70 (2020) No.2, 389-400. ISSN 0139-9918. IF.
  5. S. Fišnarová, R. Mařík, Oscillation of neutral second order half-linear differential equations without commutativity in deviating arguments, Mathematica Slovaca, vol. 67 No. 3 (2017), 701–718. ISSN 0139-9918. online, IF=0.346
  6. R. Mařík, On the influence of delay to the strength of oscillation criteria for neutral second order half-linear differential equations, RIMS Kôkyûroku series No. 1959 (2015), 1-14. online
  7. S. Fišnarová, R. Mařík, Modified Riccati technique for half-linear differential equations with delay, Electron. J. Qual. Theory Differ. Equ. 2014, No. 64, 1-14. online, PDF, IF=0.638
  8. R. Mařík, Remarks on the paper by Sun and Meng, Appl. Math. Comput. 174 (2006), Appl. Math. Comput 248 (2014), 309–313. ISSN 0096-3003. online, PDF, doi: 10.1016/j.amc.2014.09.100, IF=1.60
  9. P. Hasil, R. Mařík, M. Veselý, Conditional oscillation of half-linear differential equations with coefficients having mean values, Abstr. Appl. Anal. Volume 2014 (2014), Article ID 258159, 14 pages. online, PDF, IF=1.102
  10. S. Fišnarová, R. Mařík, On eventually positive solutions of quasilinear second order neutral differential equations, Abstr. Appl. Anal. Volume 2014 (2014), Article ID 818732, 11 pages. online, PDF, IF=1.102
  11. S. Fišnarová, R. Mařík, Oscillation criteria for neutral second-order half-linear differential equations with applications to Euler type equations, Bound. Value Probl. 2014:83 (2014), 1-14. online, PDF,IF=0.92
  12. S. Fišnarová, R. Mařík, Oscillation of half-linear differential equations with delay, Abstr. Appl. Anal. Volume 2013 (2013), Article ID 583147, 6 pages. online, PDF, IF=1.102
  13. O. Došlý, S. Fišnarová, R. Mařík, Power comparison theorems in half-linear oscillation theory, J. Math. Anal. Appl. (2013) vol. 401, No. 2, pp. 611-619. ISSN 0022-247X. online, doi: 10.1016/j.jmaa.2012.12.029, PDF, IF=1.001
  14. S. Fišnarová, R. Mařík, Local estimates for modified Riccati equation in theory of half-linear differential equation, Electron. J. Qual. Theory Differ. Equ. 2012, No. 63, 1-15. online, MathScinet, PDF, IF=0.74
  15. R. Mařík, Coupled intervals for discrete p-degree functional, Adv. Difference Equ., 2012:100. doi: 10.1186/1687-1847-2012-100, online, PDF, IF=0.85
  16. R. Mařík, Summation comparison theorems for half-linear second order difference equations on finite interval, Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis (2011) 59, No. 7, pp 245-248. ISSN 1211-8516. online, PDF
  17. S. Fišnarová, R. Mařík, On Constants in Nonoscillation Criteria for Half-Linear Differential Equations, Abstr. Appl. Anal. 2011. (2011), č. 638271, s. 1-15. ISSN 1085-3375.
    online, doi: 10.1155/2011/638271, PDF, IF=1.442
  18. S. Fišnarová, R. Mařík, Half-linear ODE and modified Riccati equation: Comparison theorems, integral characterization of principal solution, Nonlinear Anal., vol. 74 (2011), issue 17, pages 6427-6433. online, PDF, IF=1.279
  19. O. Došlý, S. Fišnarová, R. Mařík, Comparison theorems for Riccati inequalities arising in the theory of PDE’s with p-Laplacian, Electron. J. Differential Equations, No. 53. (2011), 1-9. online, PDF
  20. R. Mařík, A remark on connection between conjugacy of half-linear differential equation and equation with mixed nonlinearities, Appl. Math. Lett. 24 (2011), 93-96. online, doi: 10.1016/j.aml.2010.08.024, PDF, IF=0.978
  21. S. Fišnarová, R. Mařík, Generalized Picone and Riccati inequalities for half-linear differential operators with arbitrary elliptic matrices, Electron. J. Differential Equations 2010. vol. 2010, 111, p. 1-13. ISSN 1072-6691. online, PDF
  22. R. Mařík, Conjugacy criteria for half-linear ODE in theory of PDE with generalized p-Laplacian and mixed powers, Nonlinear Anal. Vol. 73 (2010), No. 2, 500-509. online, doi: 10.1016/j.na.2010.03.045, IF=1.487
  23. R. Mařík, Ordinary differential equations in the oscillation theory of partial half-linear differential equation, J. Math. Anal. Appl. 2008. sv. 338, č. 338, s. 194-208. online, doi: 10.1016/j.jmaa.2007.05.015, IF=1.046 (2008)
  24. L. Baráková, R. Mařík, An age-structured model of cannibalism, Electron. J. Differential Equations, Vol. 2006(2006), No. 106, 1-11. online, PDF
  25. R. Mařík, Interval-type oscillation criteria for half-linear PDE with damping, Appl. Appl. Math., Vol. 1 (2006), No 1, 1-10. online, PDF at publisher, PDF preprint
  26. R. Mařík, Discrete singular functionals, Arch. Math. (Brno), Vol. 41 (2005), No. 3, 339-347. online
  27. R. Mařík, Oscillation of the half-linear PDE in general exterior domains—the variational approach, Nonlinear Anal. 60/3 (2005), 485-489. online, doi: 10.1016/j.na.2004.08.038, IF=0.519
  28. R. Mařík, Asymptotic estimates for PDE with p-Laplacian and damping, Electron. J. Qual. Theory Differ. Equ., No. 5. (2005), 1-6. online, PDF
  29. R. Mařík, Integral averages and oscillation of half-linear PDE, Appl. Math. Comp., Vol. 150 (2004), Issue 1, 69-87. online, doi: 10.1016/S0096-3003(03)00198-X
  30. R. Mařík, Riccati-type inequality and oscillation of half-linear PDE with damping, Electron. J. Differential Equations, Vol. 2004(2004), No. 11, 1-17. online, PDF
  31. R. Mařík, Positive solutions of inequality with p-Laplacian in exterior domains, Mathematica Bohemica, Vol. 127 (2002), No. 4, 597-604. online, PDF
  32. R. Mařík, Oscillation criteria for a class of nonlinear partial differential equations, Electron. J. Differential Equations, Vol. 2002(2002), No. 28, 1-10. online, PDF
  33. R. Mařík, Comparison theorems for half-linear second order difference equations, Arch. Math (Brno) 36 (2000), Proceedings of CDDE 2000 issue, 513-518. online
  34. R. Mařík, A half-linear differential equation and corresponding variational problem, Nonlinear Anal. 45/2 (2001), 203-211. online, PDF, IF=0.406
  35. R. Mařík, Focal points of half-linear second order differential equations, Diff. Eqs. Dyn. Syst. vol. 8. No. 2, (2000), 111-124. PDF preprint
  36. R. Mařík, Oscillation criteria for PDE with p-Laplacian via the Riccati technique, J. Math. Anal. Appl. 248 (2000), 290-308. online, PDF, IF=0.431
  37. R. Mařík, Hartman-Wintner type theorem for PDE with p-Laplacian, Electron. J. Differential Equations Proc. 6th Coll. QTDE 2000, No. 18, 1-7. online, PDF
  38. O. Došlý, R. Mařík, Nonexistence of the positive solutions of partial differential equations with p-Laplacian, Acta Math. Hungar. 90 (1-2) (2001), 89-107. PDF, IF=0.184
  39. R. Mařík, Oscillation criteria for Schroedinger PDE, Adv. Math. Sci. Appl. No. 2, Vol. 10 (2000), 495-511. PDF preprint
  40. R. Mařík, Nonnegativity of functionals corresponding to the second order half-linear differential equation, Arch. Math (Brno) 35 (1999), 155-164. online
  41. R. Mařík, On p-degree functionals with one free end point, Proc. Int. Sci. Conf. Math. Žilina (1998), 183-188. PDF preprint

Other publications

  1. Oscillation theory of partial differential equations with p-Laplacian, Mendel university (2008) 103 pages. Folia. ISBN 978-80-7375-215-6. PDF

Textbooks

  1. Differential and difference equations (Diferenciální a diferenční rovnice), textbook in Czech, Mendel University Brno (2004), 79 pages.
  2. Differential equations and autonomous systems (Diferenciální rovnice a autonomní systémy), textbook in Czech, Mendel University Brno (2009).PDF

Electronic textbooks in English

  1. Robert Mařík’s eReadings on Mathematics (in English, supported by the grant 18/2006 of FRVŠ)

Other publications

  1. Half-linear differential equations, PhD. thesis, Masaryk Univ. Brno (2000), 72 pages.
  2. Bessel functions, thesis, Masaryk Univ. Brno (1997), in Czech.
  3. Tvorba interaktivních pdf testů pomocí programu AcroTeX. Department of Mathematics Report Series. 2005. No. 13, p. 111-114. In Czech.
  4. Pojďte pane, budeme si hrát (… s PDF). Mařík, Robert - Tihlaříková, Miroslava, In Proceedings of 7th International Conference APLIMAT 2008 - Part IV Open source Software in Research and Education. Bratislava: Department of Mathematics, Faculty of Mechanical Engineering, Slovak University of Technology, 2008, s. 63-73.
  5. Vkládání JavaScriptů pdfLaTeXem prakticky. Zpravodaj Československého sdružení uživatelů TeXu. 2007. sv. 2, č. 2, s. 72-83.
  6. LaTeX packages jeopardy, fancytooltips, mfpic4ode, OCGtools
  7. OpenSource versus proprietární software ve výuce a tvorbě výukových materiálů, Sborník 6. ročníku konference o elektronické podpoře výuky SCO 2009, s. 99-104.
  8. Oslí okénka v PDF, Zpravodaj Československého sdružení uživatelů TeXu. 2009. sv. 19, č. 1-2, s. 7-13.
  9. Mathematical Assistant on Web - skládanka ze svobodných matematických programů, In Otvorený softvér vo vzdelávaní, výskume a v IT riešeniach. s. 61-68. online.
  10. Support for differential equations in Sage
  11. Matematický program Sage, Matematika - fyzika - informatika 20 No. 2 (2010), 119-127.

Conferences

  1. Equadiff 9, Brno, August 1997
  2. Int. Scientific Conference of Mathematics, Zilina (SL), July 1998 - Half-linear differential equation and corresponding $p$-degree functional.
  3. Workshop on Qualitative Theory of Differential Equations, Brno, September 1998 - Half-linear differential equation and corresponding $p$-degree functional.
  4.  1. seminar of Center of Applied Mathematics, Plzen, May 1999 - Oscillation criteria for Schroedinger PDE.
  5. Boruvka Mathematical Symposium, Valtice, June 1999 poster - Oscillation criteria for Schroedinger PDE.
  6.   6. Colloq. Qual. Theory of Diff. Eqs., Szeged (HU), August 1999 - Oscillation criteria for Schroedinger PDE.
  7. 3-rd World Congress of Nonlinear Analysts - WCNA, Catania (IT), July
    1. Oscillation criteria for equations with p-Laplacian.
  8. Colloqium of Differential and Difference Equations - CDDE, Brno, September 2000. Focal points of half-linear difference equations.
  9. Colloqium of Differential and Difference Equations - CDDE, Brno, September 2002. Integral averages and oscillation of half-linear PDE.
  10. Equadiff 11, Bratislava, August 2005, Riccati technique for half-linear PDE.
  11. Colloqium of Differential and Difference Equations - CDDE, Brno, September 2006, An age-structured model of cannibalism.
  12.   8. Colloq. Qual. Theory of Diff. Eqs., Szeged (HU), June 2007 - Ordinary differential equations in the oscillation theory of partial half-linear differential equation.
  13. Conference on Differential and Difference Equations and Applications 2008 (CDDEA 2008) Strečno, Slovak Republic, June 23 - 27, 2008, Oscillation of half-linear partial differential equation.
  14. Equadiff 12, Brno, July 2009, Oscillation of PDE with p-Laplacian.
  15. International Conference on Difference Equations and Applications (ICDEA09) - October 19 - October 23, 2009, Estoril, Portugal.
  16. Conference on Differential and Difference Equations and Applications, Rajecké Teplice, Slovak Republic, June 21 - 25, 2010, Conjugacy criteria for half-linear ODE in theory of PDE with generalized p-Laplacian and mixed powers
  17. Colloquium on Differential Equations and Integration Theory, October 14 – 17, 2010, Křtiny, Czech Republic, Picone type inequality for half-linear differential operators with anisotropic p-Laplacian
  18.   9. Colloq. Qual. Theory of Diff. Eqs., Szeged (HU), June 2011 Principal solutions of half-linear equation: yet another integral characterization
  19. International Conference on Difference Equations and Applications (ICDEA09) - July 2011, Trois Rivieres, Canada, Half-linear difference equations and the discrete $p$-degree functional.
  20. Conference on Differential and Difference Equations and Applications, Terchova, Slovak Republic, On constants in nonoscillation criteria for half-linear differential equations, June 2012
  21. Equadiff 13, Riccati technique for half-linear delay differential equation, Prague, Czech Republic, Summer 2013
  22. DFDE 2014 - The Seventh International Conference on Differential and Functional Differential Equations, Riccati equation method for second order neutral half-linear equations, Moscow, Russia, August 2014
  23. International Workshop on Differential Equations in Osaka 2014 Riccati differential equation and its generalizations: a real treasure in oscillation and comparison theory of second order linear and half-linear differential equations, Japan, Osaka, November 2014.
  24. Qualitative theory of ordinary differential equations in real domains and its applications, Oscillation and nonoscillation criteria for half-linear differential equations: exploring ”terra incognita” and the hunt for better oscillation constants, Research Institute for Mathematical Sciences (RIMS) Kyoto University, Kyoto, Japan, November 2014.
  25. The 67th SWST International Convention, Portorož, Slovenia 2024. Acoustic tomography for standing trees
  26. 7-th International Conference “WOOD TECHNOLOGY & PRODUCT DESIGN”. Resistograph meets tomograph Faculty of Design and Technologies of Furniture and Interior, Ss. Cyril and Methodius University in Skopje, Republic of North Macedonia.

Conferences focused on education

  1. Using compuers in teaching mathematics (in Czech), České Budějovice, November 2005, Využití systému LaTeX ve výuce matematiky.
  2. Using computers in teaching mathematics (in Czech), České Budějovice, November 2007, LaTeXem hravě.
  3. Aplimat 2008, February 2008, Bratislava, Pojďte pane, budeme si hrát (… s PDF).
  4. SCO (Sharable Content Objects) 2008, June 2008, Brno, Systém pro online výpočty v prostředí WWW
  5. Aplimat 2009, February 2009, Bratislava Mathematical Assistant on Web.
  6. SCO (Sharable Content Objects) 2009, June 2009, Brno, OpenSource versus proprietární software ve výuce a tvorbě výukových materiálů

Talks on seminars

  1. Seminar of differential equations, Masaryk Univ. Brno, fall 1998 and spring 1999, Nonnegativity of p-degree functionals and Oscillation properties of the partial differential equations of elliptic type, Czech
  2. Mathematical Institute at Hungarian Academy of Sciences: Budapest, April 1999 - 2 talks
  3. Seminar of differential equations, Masaryk Univ. Brno, Riccati transformation in the oscillation theory of PDE - radially nonsymetric criteria, 28.04.2003, in Czech
  4. Seminář katedry matematiky Ped. F. MU v Brně, Tvorba interaktivních matematických kvízů (ukázky, možnosti, návody a zkušenosti s programem AcroTeX), 16.11.2005, in Czech
  5. Seminar of differential equations, Masaryk Univ. Brno, Oscilační kriteria pro parciální diferenciální rovnice s p-Laplaciánem, 7.4.2008, in Czech
  6. Seminář katedry matematiky Ped. F. MU v Brně, Symbolické výpočty online, 22.10.2008, in Czech
  7. Odborný seminář z cyklu Aplikace matematických metod, Ekonomická fakulta VŠB v Ostravě, Proprietární versus OpenSource software ve výuce matematiky, 26.3.2009, in Czech
  8. Seminar of differential equations, Masaryk Univ. Brno, Oscillation criteria for half-linear neutral differential equation, 28.04.2014, in Czech

Presentations/prezentace

  1. Některé mé prezentace jsou dostupné zde

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