Diana Otrocol

### Academic degree:

Ph.D. in Mathematics (2006)

### Current position:

Scientific researcher III at *Tiberiu Popoviciu Institute of Numerical Analysis*

### Domains of research:

- Nonlinear operators and differential equations
- Approximation techniques of the solutions of the delay differential equations
- The study of convergence of iterations of positive and linear operators

(version of September 17, 2020)

**Personal Data**

Date and place of birth | March 1975, Sibiu |

Civil status | Married |

dotrocol[at]ictp.acad.ro, diana.otrocol[at]gmail.com |

**Education and degrees:**

2006 | Ph.D. in Numerical Analysis Babeş-Bolyai University, Cluj-Napoca Thesis: Contributions to the theory of Lotka-Voltera systems with retarted argumentScientific advisor: prof. dr. Petru Blaga |

2001-2002 | Master Studies at Faculty of Mathematics and Computer Science, “Lucian Blaga” University, Sibiu; |

1993-1997 | Faculty of Mathematics and Computer Science, “Babeş-Bolyai” University, section Mathematics, Cluj-Napoca; |

1989-1993 | High-school “Gheorghe Lazăr”, Sibiu, section mathematics-physics; |

**Employment history:**

2011 – present | scientific researcher III at Tiberiu Popoviciu Institute of Numerical Analysis (ICTP), Romanian Academy |

2008 – 2011 | scientific researcher at ICTP |

2006 – 2008 | research assistant at ICTP |

2002 – 2006 | PhD student, Faculty of Mathematics and Computer Science, “Babeş-Bolyai” University, Cluj-Napoca, Romania |

1997 – 2002 | high school teacher |

**Teaching Experience**

- Seminars and laboratories taught at the ”Babeş-Bolyai” University Cluj-Napoca (differential equations and dynamical systems, numerical analysis, probabilities, statistics) 2002-2006.

**Book**

- D. Otrocol,
*Lotka-Volterra Systems with delays*, Editura Presa Universitara Clujeana, 2007 (in Romanian), ISBN 978-973-610-589-0.

**Conferences and workshops:**

- ”
*Integral equations with maxima*”, Academic Days of Cluj-Napoca, June 5-6, 2014, Cluj-Napoca, Romania. - (with V.A. Ilea), ”
*On a functional-integral equation, via Picard operators technique*”, Theodor Angheluta Seminar, The Fourteenth International Conference on Applied Mathematics and Computer Science, August 29-31, 2013, Cluj-Napoca, Romania. - (with V.A. Ilea), ”
*Qualitative properties of functional differential systems*”, 9th International Conference on Applied Mathematics (ICAM9), September 25-28, 2013, Baia Mare, Romania. - (with V.A. Ilea), ”
*On a D.V. Ionescu’s problem for functional-differential equations of second order*”, Fixed Point Theory and its Applications, 10th edition of ICFPTA, July 9-15, 2012, Cluj-Napoca, Romania. - ”
*On the asymptotic equivalence of a differential system with maxima*”, Fixed Point Theory and its Applications, 10th edition of ICFPTA, July 9-15, 2012, Cluj-Napoca, Romania. - ”
*The properties of a solutions of a differential system with maxima*”, Academic Days of Cluj-Napoca, Simpozion “Metode numerice si aproximare”, May 22-25, 2012, Cluj-Napoca, Romania. - (with V.A. Ilea), “
*An iterative method for a functional-differential equation of second order with mixed type argument*”, International Conference on Nonlinear Operators, Differential Equations and Applications (ICNODEA 2011), July 5-8, 2011, Cluj-Napoca, Romania. - (with V.A. Ilea, M.A. Serban, D. Trif), ”
*Step method for some integral equations*”, 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC 2011), September 26-29, 2011, Timisoara, Romania. - ”
*A differential equation with delay from biology*”, International Conference on Nonlinear Operators, Differential Equations and Applications, July 4-8, 2006, Cluj-Napoca. - ”
*Data dependence of the fixed points set for a Lotka-Volterra system*”, International Conference on Numerical Analysis and Approximation Theory (NAAT 2006), July 5-8, 2006, Cluj-Napoca, Romania. - ”
*Numerical solutions of Lotka-Volterra system with delay by spline functions of even degree*”, International Congress of Mathematiciens (ICM 2006), August 22-30, 2006, Madrid. - ”
*Differentiability with respect to delays for a Lotka-Volterra system*”, International Conference on Applied Mathematics, September 21-24, 2006, Baia-Mare, Romania. - ”
*Differentiability with respect to parameters of a differential system with delay*”, Academic Days of Cluj-Napoca, June 26-July 14, 2006, Cluj-Napoca, Romania. - ”
*A numerical method approximating the solution of a Lotka-Volterra system with two delays*”, International Conference on Nonlinear Operators, Differential Equations and Applications, August 24-27, 2004, Cluj-Napoca, Romania.

**Papers**

- G. Motronea, D. Otrocol, I. Rasa,
*Perov’s theorem applied to systems of equations,*Modern Mathematical Methods,**1**(2023) no. 1, pp. 22-29. - A. Novac, D. Otrocol, D. Popa,
*On Ulam stability of a partial differential operator in Banach spaces*, Mathematics, 11 (2023) no. 11, art. no. 2488, https://doi.org/10.3390/math11112488 - V. Ilea, A. Novac, D. Otrocol, R. Precup,
*Nonlinear alternatives of hybrid type for nonself vector-valued maps and application,*Fixed Point Theory,**24**(2023) no. 1, 221-232, http://doi.org/10.24193/fpt-ro.2023.1.11 - V. Ilea, D. Otrocol, I.A. Rus, M.-A. Serban,
*Applications of fibre contraction principle to some classes of functional integral equations,*Fixed Point Theory, 23 (2022) no. 1, 279-292, http://doi.org/10.24193/fpt-ro.2022.1.18 - V. Ilea, D. Otrocol,
*On a Volterra integral equation with delay, via w-distances*, Mathematics**9**(2021), art. id. 2341, 8 pp., https://doi.org/10.3390/math9182341 - V. Ilea, D. Otrocol,
*Functional differential equations with maxima, via step by**step contraction principle,*Carpathian J. Math.,**37**(2021) no. 2, pp. 195-202, DOI: 10.37193/CJM.2021.02.05 - A. Novac, D. Otrocol, D. Popa,
*Ulam stability of a linear difference equation in locally convex spaces*, Results Math.,**76,**33 (2021). https://doi.org/10.1007/s00025-021-01344-2 - A.M. Acu, A. Maduta, D. Otrocol, I. Raşa,
*Inequalities for information potentials and entropies*, Mathematics 2020, 8(11), 2056; https://doi.org/10.3390/math8112056, IF: 1.747 - V. Ilea, A. Novac, D. Otrocol, R. Precup,
*Solutions with a prescribed interval of positivity for differential systems with nonlocal conditions*, Appl. Math. Comput., 375 (2020), doi: 10.1016/j.amc.2020.125092 - V. Ilea, D. Otrocol,
*Existence and uniqueness of the solution for an integral equation with supremum, via w-distances*, Symmetry 2020, 12, 1554, https://doi.org/10.3390/sym12091554 - V. Ilea, D. Otrocol,
*On the Burton method of progressive contractions for Volterra integral equations*, Fixed Point Theory, 21 (2020) no. 2, 585-594. - T. Cătinaș, D. Otrocol,
*Iterates of Cheney-Sharma type operators on a triangle with curved side*, J. Comp. Anal. Appl., 28 (2020) no. 4, pp. 737-744. - A. Aral, D. Otrocol, I. Raşa,
*On approximation by some Bernstein–Kantorovich exponential-type polynomials*, Periodica Mathematica Hungarica, 79 (2019) 2, pp. 236-254. - A. Măduța, D. Otrocol, I. Rașa,
*Inequalities for indices of coincidence and entropies*, Arxiv:1910.13491, 2019. - D. Otrocol,
*Qualitative properties of solutions for mixed type functional-differential equations with maxima*, Miskolc Mathematical Notes, 20 (2019) no. 2, pp. 1119-1128 - D. Otrocol, M.A. Serban,
*An efficient step method for a system of differential equations with delay*, J. Appl. Anal. Comput.**8**(2018) no. 2, pp. 498-508. - B.C. Dhage, D. Otrocol,
*Dhage iteration method for approximating solutions of nonlinear differential equations with maxima*, Fixed Point Theory,**19**(2018) no. 2, pp. 545-556. - V. Ilea, D. Otrocol,
*Some properties of solutions to a planar system of nonlinear differential equations*, Studia Univ. Babes-Bolyai Math.,**63**(2018) no. 2, pp. 225-234. - D. Otrocol, V. Ilea,
*On the qualitative properties of functional integral equations with abstract Volterra operators*, Res. Fixed Point Theory Appl., vol. 2018 (2018), Article ID 201813, 08

pp. - V.A. Ilea, D. Otrocol,
*An application of the Picard operator technique to functional integral equations*, J. Nonlinear Convex Anal.,**18**(2017) no. 3, pp. 405-413. - D. Otrocol,
*Hybrid differential equations with maxima via Picard operators theory*, Stud. Univ. Babes-Bolyai Math.**61**(2016), no. 4, 421-428. - D. Otrocol,
*On the asymptotic equivalence of a differential system with maxima*, Rend. Circ. Mat. Palermo, Ser. 2,**65**(2016) no 3, pp. 387-393. - T. Catinas, D. Otrocol, I.A. Rus,
*The iterates of positive linear operators with the set of constant functions as the fixed point set*, Carpathian J. Math.,**32**(2016) no. 2, pp. 165-172. - V. Ilea, D. Otrocol, I. A. Rus,
*Some properties of solutions of the homogeneous nonlinear second order differential equations*, Mathematica, 57 (80) (2015), no 1-2, pp. 38-43 - D. Otrocol, V. Ilea, C. Revnic,
*Addendum to the paper “an iterative method for a functional-differential equation of second order with mixed type argument“, Fixed Point Theory, 14(2013) no. 2, 427-434*, Fixed Point Theory, 16 (2015) no. 1, pp. 191-192. - V.A. Ilea, D. Otrocol,
*Some properties of solutions of a functional-differential equation of second order with delay*, The Scientific World Journal, Volume 2014 (2014), Article ID 878395 - D. Otrocol, V.A. Ilea,
*Qualitative properties of functional differential equation*, Electron. J. Qual. Theory Differ. Equ., 2014, No. 47, 1-8. - D. Otrocol,
*Systems of functional-differential equations with maxima, of mixed type*, Electron. J. Qual. Theory Differ. Equ., 2014, No. 5, 1-9. - T. Cătinaş, D. Otrocol,
*Iterates of multivariate Cheney-Sharma operators*, Journal of Computational Analysis and Applications,15 (2013) no. 7, 1240-1246. - D. Otrocol, V.A. Ilea,
*Ulam stability for a delay differential equation*, Central European Journal of Mathematics, 11 (2013) no. 7, 1296-1303. - D. Otrocol, V.A. Ilea, C. Revnic,
*An iterative method for a functional-differential equation of second order with mixed type argument*, Fixed Point Theory, 14 (2013), no.2, 427-434. - T. Cătinaş, D. Otrocol,
*Iterates of Bernstein type operators on a square with one curved side via contraction principle*, Fixed Point Theory, vol. 14 (2013) no.1, 97-106. - D. Otrocol,
*Properties of the solutions of a system of differential equations with maxima, via weakly Picard operator theory*, Communications in Applied Analysis, 17 (2013), no.1, 99-108. - V. Ilea, D. Otrocol, M.-A. Şerban, D. Trif,
*Integro-differential equation with two time lags*, Fixed Point Theory, 13 (2012), no. 1, pp. 85-97 (pdf file alsohere). - V.A. Ilea, D. Otrocol,
*On a D.V. Ionescu’s problem for functional-differential equations of second order*, Proceedings of the 10th IC-FPTA, 131 – 142, July 9-18, 2012, Cluj-Napoca, Romania (pdf file here). - V. Ilea, D. Otrocol,
*Integro-differential equation with two times modifications*, Carpathian Journal of Math. 27 (2011), no. 2, pp.209-216 (pdf file here). - D. Otrocol,
*Ulam stabilities of differential equation with abstract Volterra operator in a Banach space*, Nonlinear Functional Analysis and Applications, 15, 2010, no. 4, pp. 613-619 (pdf file here). - D. Otrocol, V. Ilea C. Revnic,
*An iterative method for a functional-differential equation with mixed type argument*, Fixed Point Theory, vol. 11 (2010) no. 2, 327-336 (pdf file also here). - V.A. Ilea, D. Otrocol,
*On a D.V. Ionescu’s problem for functional-differential equations*, Fixed Point Theory 10 (2009), no. 1, 125-140 (pdf file also here). - D. Otrocol, I.A. Rus,
*Functional-differential equations with “maxima” via weakly Picard operators theory*, Bull. Math. Soc. Sci. Math. Roumanie, 51(99) 2008, no. 3, 253-261 (pdf file also here). - D. Otrocol, I.A. Rus,
*Functional-differential equations with maxima of mixed type*, Fixed Point Theory 9 (2008), no. 1, 207-220 (pdf file here). - D. Otrocol,
*A differential equation with delay from biology*, J. Appl. Math. & Informatics Vol. 26(2008), no. 5-6, pp. 1037 – 1048 (pdf file here). - Ş. M. Şoltuz, D. Otrocol,
*Classical results via Mann-Ishikawa iteration*, Rev. Anal. Numér. Théor. Approx., 36 (2007), no. 2, 195-199 (pdf file also here). - Ş. M. Şoltuz, D. Otrocol,
*The convergence of Mann iteration with delay*, Mathematical Sciences Research, 2007, Vol. 11, no. 3, pp. 390-393 (pdf file here). - D. Otrocol,
*Differentiability with respect to delays for a Lotka-Volterra system*, Creative Math. and Inf., 2007, Vol. 16, pp. 36-41 (tech. rep. here). *D. Otrocol, Smooth dependence on paramters for a differential equation with delay from population dynamics*, 2007 International Conference on Engineering and Mathematics, Bilbao, July 9-11, 2007, pp. 3-10.- D. Otrocol,
*Data dependence of the fixed points set for a Lotka-Volterra system*, Proceedings of the International Conference on Numerical Analysis and Approximation Theory, Cluj-Napoca, Romania, July 5-8, 331-336, 2006 (pdf file here). - D. Otrocol,
*Differentiability with respect to a parameter for a Lotka-Volterra system with delays, via step method*, Rev. Anal. Numér. Théor. Approx., 35 (2006), no. 1, 83-86 (pdf file here). - D. Otrocol,
*Iterative functional-differential system with retarded argument*, Rev. Anal. Numér. Théor. Approx., 35 (2006), no. 2, 147-160 (pdf file alsohere). - D. Otrocol,
*Numerical solutions of Lotka-Volterra system with delay by spline functions of even degree*, Studia Univ. Babeş-Bolyai, Mathematica, Vol 51, no. 4, 167-180, 2006 (pdf file here). - D. Otrocol,
*Data dependence for the solution of a Lotka-Volterra system with two delays*, Mathematica, Tome 48(71), No. 1 (2006), 61-68 (pdf file here). - D. Otrocol,
*Smooth dependence on parameters for some Lotka-Volterra system with delays*, Analele Universităţii din Timişoara, Seria Matematică-Informatică, Vol. XLIII, fasc. 1, 2005, 109-114 (pdf file also here). - D. Otrocol,
*A numerical method approximating the solution of a Lotka-Volterra system with two delays*, Studia Univ. Babeş-Bolyai, Mathematica, Vol L. No.1, 2005, 99-110(pdf file here). - D. Otrocol,
*Lotka-Volterra system with two delays, via weakly Picard operators*, Nonlinear Analysis Forum, 10 (2), pp. 193-199, 2005 (pdf file here).