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Natália Martins, PhD in Mathematics (2006, University of Aveiro, Portugal), is an Associate Professor in the Department of Mathematics at the University of Aveiro (UA), Portugal. She works in the Department of Mathematics of UA since 1992 and was Vice-Director of the department from 2008 to 2019. She was also a member of the Pedagogical Council of UA from 2009 to 2016, where she was elected Vice-President, a position she held for more than 5 years, between 2011 and 2016. Since 2022 she is the scientific coordinator of the group "System and Control group" of the research unit CIDMA (Center for Research & Development in Mathematics and Applications), a research team hosted at the Department of Mathematics of the University of Aveiro. Her research interests include Time Scale Calculus, Fractional Calculus, Calculus of Variations and Optimal Control Theory. She is author of more than 50 papers in international journals, conference papers and book chapters. Natália Martins belongs to the Editorial Board of Fractal and Fractional, Axioms, and International Journal of Dynamical Systems and Differential Equations. She has presented 17 invited talks and 34 talks at international conferences and organized 22 scientific events in Portugal, Cape Verde, Morocco, France, Greece, Austria, and Italy. Moreover, she has successfully supervised 2 PhD students in Mathematics. Additionally, she was a member of the European projects MELES (More Entrepreneurial Life at European Schools), ABC-MELES (Academic Business Coach), and MELES-BOT (BOT-Learning as a modern teaching method of GEN Z), in the area of Entrepreneurship, Innovation and Leadership. From 03/2021 to 02/2023 she was the local coordinator at the University of Aveiro of the project e-CLOSE (A model for Interactive (A) Synchronous Learning in Online STEM Education), financed by the ERASMUS + program. She is currently a member of the European project ENTREACTION! (EntreAction: An Innovative Case-to-videostory Approach in Entrepreneurial Education).
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Identification

Personal identification

Full name
Natália da Costa Martins

Citation names

  • Martins, Natália

Author identifiers

Ciência ID
521D-6BFD-BDAE
ORCID iD
0000-0003-3535-3909

Knowledge fields

  • Exact Sciences - Mathematics

Languages

Language Speaking Reading Writing Listening Peer-review
English Upper intermediate (B2) Upper intermediate (B2) Upper intermediate (B2) Upper intermediate (B2) Upper intermediate (B2)
Spanish; Castilian Upper intermediate (B2) Advanced (C1) Intermediate (B1) Advanced (C1) Upper intermediate (B2)
Portuguese (Mother tongue)
Education
Degree Classification
2006
Concluded
 Nonstandard Analysis in Ordinary Differential Equations and in Critical Point Theory (Doutoramento)
Universidade de Aveiro, Portugal
"Análise Não-Standard em Equações Diferenciais Ordinárias e na Teoria dos Pontos Críticos" (THESIS/DISSERTATION)
 Aprovado
1992
Concluded
 Licenciatura em Ensino de Matemática (Licenciatura)
Universidade de Aveiro, Portugal
"n/a" (THESIS/DISSERTATION)
 15
Affiliation

Teaching in Higher Education

Category
Host institution 		Employer
2021/03/01 - Current Associate Professor (University Teacher) Universidade de Aveiro, Portugal
Universidade de Aveiro, Portugal
2006/04/07 - Current Assistant Professor (University Teacher) Universidade de Aveiro, Portugal
1997/07/01 - 2006/04/06 Assistant (University Teacher) Universidade de Aveiro, Portugal
1992/10/01 - 1997/07/01 Trainee Assistant (University Teacher) Universidade de Aveiro, Portugal
Projects

Grant

Designation Funders
2017/09 - 2020/06 ABC-MELES2.0-- "Academic Business Coaching"
2017-1-PL01-KA203-038541
 European Commission
2014/09 - 2017/08 More Entrepreneurial Life at European Schools
2014-1-PL01-KA203-003501
 European Commission

Contract

Designation Funders
2022/09/01 - 2025/06/30 EntreAction: An Innovative Case-to-videostory Approach in Entrepreneurial Education
2022-1-BG01-KA220-HED-000086899
Researcher
Erasmus
Ongoing
2020/09/01 - 2023/06/30 BOT-Learning as a modern teaching method of GEN Z
2020-1-PL01-KA203-081777
Researcher
Erasmus
Concluded
2021/03/01 - 2023/02/28 A model for Interactive (A)Synchronous Learning in Online STEM Education
2020-1-PL01-KA226-HE-096239
Researcher
Erasmus Plus
Concluded
2019/01/01 - 2019/12/31 Centro de Investigação e Desenvolvimento em Matemática e Aplicações
UID/MAT/04106/2019
UID/MAT/04106/2013
Universidade de Aveiro, Portugal

Universidade de Aveiro Centro de Investigação e Desenvolvimento em Matemática e Aplicações, Portugal
Fundação para a Ciência e a Tecnologia
Concluded
2011/01/01 - 2013/12/31 Projecto Estratégico - UI 4106 - 2011-2012
PEst-C/MAT/UI4106/2011
PEst-OE/MAT/UI4106/2014
Universidade de Aveiro, Portugal

Universidade de Aveiro Centro de Investigação e Desenvolvimento em Matemática e Aplicações, Portugal
Fundação para a Ciência e a Tecnologia
Concluded
Outputs

Publications

Book
  1. Calculus of Variations, Optimal Control, and Mathematical Biology A Themed Issue Dedicated to Professor Delfim F. M. Torres on the Occasion of His 50th Birthday. 2023.
    10.3390/books978-3-0365-6857-7
Book chapter
  1. Martins, Natália. "An Optimal Control Approach to Herglotz Variational Problems". 2015.
    10.1007/978-3-319-20352-2_7
Conference paper
  1. Natália Martins. "Distributed-order fractional variational problems with arbitrary kernels and generalized Lagrangians". 2023.
    10.1063/5.0162301
  2. Ricardo Almeida; Ewa Girejko; Luis Machado; Agnieszka B. Malinowska; Natalia Martins. "Multi-agent systems with memories under DoS attacks". 2022.
    10.1109/icarcv57592.2022.10004364
  3. Martins, Natália. "Noether's theorem for higher-order variational problems of Herglotz type". 2015.
    10.3934/proc.2015.990
  4. Cruz, A.M.C.B.D.; Martins, N.; Torres, D.F.M.. "A Symmetric Nörlund Sum with Application to Inequalities". 2013.
    10.1007/978-1-4614-7333-6_44
  5. da Cruz, A.M.C.B.; Martins, N.; Torres, D.F.M.. "A Symmetric Quantum Calculus". 2013.
    10.1007/978-1-4614-7333-6_29
Journal article
  1. Almeida, Ricardo; Girejko, Ewa; Luis Machado; Malinowska, Agnieszka B.; Martins, Natália. "Evacuation by leader-follower model with bounded confidence and predictive mechanisms". Archives of Control Sciences (2023): http://dx.doi.org/10.24425/acs.2021.138695.
    10.24425/acs.2021.138695
  2. Iouliia Skliarova; Inês Meireles; Tatiana Tchemisova; Isabel Cação; Natália Martins. "Teachers’ Appreciation of Benefits and Shortcomings of Online and Blended Higher STEM Education". Education Sciences (2023): https://doi.org/10.3390/educsci13040338.
    10.3390/educsci13040338
  3. Adelaide Freitas; Helena Sofia Rodrigues; Natália Martins; Adela Iutis; Michael A. Robert; Demian Herrera; Manuel Colomé-Hidalgo. "Multiplicative Mixed-Effects Modelling of Dengue Incidence: An Analysis of the 2019 Outbreak in the Dominican Republic". Axioms (2023): https://doi.org/10.3390/axioms12020150.
    10.3390/axioms12020150
  4. Natália Martins; Ricardo Almeida; Cristiana J. Silva; Moulay Rchid Sidi Ammi. "Editorial for the Special Issue of Axioms “Calculus of Variations, Optimal Control and Mathematical Biology: A Themed Issue Dedicated to Professor Delfim F. M. Torres on the Occasion of His 50th Birthday”". Axioms (2023): https://doi.org/10.3390/axioms12020110.
    10.3390/axioms12020110
  5. Fátima Cruz; Ricardo Almeida; Natália Martins. "Herglotz Variational Problems Involving Distributed-Order Fractional Derivatives with Arbitrary Smooth Kernels". Fractal and Fractional (2022): https://doi.org/10.3390/fractalfract6120731.
    10.3390/fractalfract6120731
  6. Iouliia Skliarova; Inês Meireles; Natália Martins; Tatiana Tchemisova; Isabel Cação. "Enriching Traditional Higher STEM Education with Online Teaching and Learning Practices: Students’ Perspective". Education Sciences (2022): https://doi.org/10.3390/educsci12110806.
    10.3390/educsci12110806
  7. Natália Martins. "A non-standard class of variational problems of Herglotz type". Discrete and Continuous Dynamical Systems - S 15 3 (2022): 573-573. http://dx.doi.org/10.3934/dcdss.2021152.
    10.3934/dcdss.2021152
  8. Ricardo Almeida; Natália Martins; Cristiana J. Silva. "Global Stability Condition for the Disease-Free Equilibrium Point of Fractional Epidemiological Models". Axioms 10 4 (2021): 238-238. https://doi.org/10.3390/axioms10040238.
    10.3390/axioms10040238
  9. Adela Iutis; Helena Sofia Rodrigues; Freitas, Adelaide; Martins, Natália. "A preliminary analysis of weekly dengue incidence rate in the Dominican Republic during 2019". Journal of Statistics on Health Decision (2021): vol. 3 n.º 1 (2021):-Statistics on Health. https://proa.ua.pt/index.php/jshd/article/view/24685.
    10.34624/JSHD.V3I1.24685
  10. Fátima Cruz; Ricardo Almeida; Natália Martins. "Variational Problems with Time Delay and Higher-Order Distributed-Order Fractional Derivatives with Arbitrary Kernels". Mathematics 9 14 (2021): 1665-1665. https://doi.org/10.3390/math9141665.
    10.3390/math9141665
  11. Ricardo Almeida; Natália Martins. "New Variational Problems with an Action Depending on Generalized Fractional Derivatives, the Free Endpoint Conditions, and a Real Parameter". Symmetry 13 4 (2021): 592-592. https://doi.org/10.3390/sym13040592.
    10.3390/sym13040592
  12. Ricardo Almeida; Natália Martins. "A Generalization of a Fractional Variational Problem with Dependence on the Boundaries and a Real Parameter". Fractal and Fractional 5 1 (2021): 24-24. https://doi.org/10.3390/fractalfract5010024.
    10.3390/fractalfract5010024
  13. Almeida, Ricardo; Martins, Natália. "Fractional variational principle of Herglotz for a new class of problems with dependence on the boundaries and a real parameter". Journal of Mathematical Physics 61 10 (2020): 102701. http://dx.doi.org/10.1063/5.0021373.
    Published • 10.1063/5.0021373
  14. Martins, Natália. "Variational and Optimal Control Approaches for the Second-Order Herglotz Problem on Spheres". Journal of Optimization Theory and Applications (2019): http://dx.doi.org/10.1007/s10957-018-1424-0.
    10.1007/s10957-018-1424-0
  15. Martins, Natália; Almeida, Ricardo; Cruz, Artur Miguel; Martins, Natália; Monteiro, Maria Teresa. "An epidemiological MSEIR model described by the Caputo fractional derivative". International Journal of Dynamics and Control (2019): http://dx.doi.org/10.1007/s40435-018-0492-1.
    10.1007/s40435-018-0492-1
  16. Ricardo Almeida; Ewa Girejko; Luís Machado; Agnieszka B. Malinowska; Natália Martins; Almeida, Ricardo; Girejko, Ewa; et al. "Application of predictive control to the Hegselmann-Krause model". Mathematical Methods in the Applied Sciences 41 18 (2018): 9191-9202. https://doi.org/10.1002/mma.5132.
    10.1002/mma.5132
  17. Choquet, C.; Martins, N.; Sidi Ammi, M.R.; Tilioua, M.; Torres, D.F.M.; Torres, Delfim; Tilioua, Mouhcine; et al. "Preface". Discrete and Continuous Dynamical Systems - Series S 11 1 (2018): i-ii. http://www.scopus.com/inward/record.url?eid=2-s2.0-85031032122&partnerID=MN8TOARS.
    10.3934/dcdss.201801i
  18. Santos, S.P.S.; Martins, N.; Torres, D.F.M.. "Noether currents for higher-order variational problems of Herglotz type with time delay". Discrete and Continuous Dynamical Systems - Series S 11 1 (2018): 91-102. http://www.scopus.com/inward/record.url?eid=2-s2.0-85030991099&partnerID=MN8TOARS.
    10.3934/dcdss.2018006
  19. Brito da Cruz, A.M.C.; Martins, Natália. "General quantum variational calculus". (2018): http://hdl.handle.net/10773/24187.
    10.19139/soic.v6i1.467
  20. Torres, D. F. M.; Almeida, R.; Malinowska, A. B.; Martins, Natália; Sidi Ammi, M. R.. "Introduction: new trends on dynamical systems and differential equations". (2018): http://hdl.handle.net/10773/24511.
  21. Martins, Natália; Malinowska, Agnieszka B.; Machado, Luís; Girejko, Ewa; Girejko, E.; Machado, L.; Malinowska, A.B.; Martins, N.. "On consensus in the Cucker--Smale type model on isolated time scales". Discrete and Continuous Dynamical Systems - Series S 11 1 (2017): 77-89. http://hdl.handle.net/10773/24540.
    10.3934/dcdss.2018005
  22. Girejko, E.; Machado, L.; Malinowska, A.B.; Martins, N.; Girejko, Ewa; Machado, Luís; Malinowska, Agnieszka B.; Martins, Natália. "Krause's model of opinion dynamics on isolated time scales". Mathematical Methods in the Applied Sciences 39 18 (2016): 5302-5314. http://www.scopus.com/inward/record.url?eid=2-s2.0-84961839686&partnerID=MN8TOARS.
    10.1002/mma.3916
  23. Santos, Simão P. S.; Martins, Natália; Torres, Delfim F.M.. "Higher-order variational problems of Herglotz type with time delay". (2016): http://hdl.handle.net/10773/16669.
  24. Abrunheiro, Lígia; Machado, Luís; Martins, Natália. "The Herglotz variational problem on spheres and its optimal control approach". (2016): http://hdl.handle.net/10773/15635.
  25. Almeida, R.; Martins, N.; Almeida, Ricardo; Martins, Natália. "Variational problems for Hölderian functions with free terminal point". Mathematical Methods in the Applied Sciences 38 6 (2015): 1059-1069. http://www.scopus.com/inward/record.url?eid=2-s2.0-84925361531&partnerID=MN8TOARS.
    10.1002/mma.3128
  26. Brito da Cruz, A.M.C.; Martins, N.; Torres, D.F.M.. "The Diamond Integral on Time Scales". Bulletin of the Malaysian Mathematical Sciences Society 38 4 (2015): 1453-1462. http://www.scopus.com/inward/record.url?eid=2-s2.0-84941096448&partnerID=MN8TOARS.
    10.1007/s40840-014-0096-7
  27. Santos, S.P.S.; Martins, N.; Torres, D.F.M.. "Variational problems of Herglotz type with time delay: DuBois-Reymond condition and Noether's first theorem". Discrete and Continuous Dynamical Systems- Series A 35 9 (2015): 4593-4610. http://www.scopus.com/inward/record.url?eid=2-s2.0-84926636605&partnerID=MN8TOARS.
    10.3934/dcds.2015.35.4593
  28. Martins, Natália. "Existence results for fractional q-difference equations of order a ¿] 2, 3 [ with three-point boundary conditions". Communications in Nonlinear Science and Numerical Simulation (2014): http://www.scopus.com/inward/record.url?eid=2-s2.0-84887398569&partnerID=MN8TOARS.
    10.1016/j.cnsns.2013.10.018
  29. Santos, S.P.S.; Martins, N.; Torres, D.F.M.. "Higher-Order Variational Problems of Herglotz Type". Vietnam Journal of Mathematics 42 4 (2014): 409-419. http://www.scopus.com/inward/record.url?eid=2-s2.0-84926624400&partnerID=MN8TOARS.
    10.1007/s10013-013-0048-9
  30. Delfim F. M. Torres; Biswa N. Datta; Gastão S. F. Frederico; Natália Martins; Alexander J. Zaslavski. "The Cape Verde International Days on Mathematics 2013". Conference Papers in Mathematics (2013): https://doi.org/10.1155/2013/673818.
    10.1155/2013/673818
  31. Brito Da Cruz, A.M.C.; Martins, N.; Torres, D.F.M.. "Symmetric differentiation on time scales". Applied Mathematics Letters 26 2 (2013): 264-269. http://www.scopus.com/inward/record.url?eid=2-s2.0-84867889527&partnerID=MN8TOARS.
    10.1016/j.aml.2012.09.005
  32. Malinowska, A.B.; Martins, N.. "Generalized transversality conditions for the Hahn quantum variational calculus". Optimization 62 3 (2013): 323-344. http://www.scopus.com/inward/record.url?eid=2-s2.0-84874474708&partnerID=MN8TOARS.
    10.1080/02331934.2011.579967
  33. Brito da Cruzv, A.M.C.; Martins, N.; Torres, D.F.M.. "Hahn's symmetric quantum variational calculus". Numerical Algebra, Control and Optimization 3 1 (2013): 77-94. http://www.scopus.com/inward/record.url?eid=2-s2.0-84892611238&partnerID=MN8TOARS.
    10.3934/naco.2013.3.77
  34. Malinowska, A.B.; Martins, N.. "The second noether theorem on time scales". Abstract and Applied Analysis 2013 (2013): http://www.scopus.com/inward/record.url?eid=2-s2.0-84893761554&partnerID=MN8TOARS.
    10.1155/2013/675127
  35. Brito Da Cruz, A.M.C.; Martins, N.; Torres, D.F.M.. "Higher-order Hahn's quantum variational calculus". Nonlinear Analysis, Theory, Methods and Applications 75 3 (2012): 1147-1157. http://www.scopus.com/inward/record.url?eid=2-s2.0-82155164176&partnerID=MN8TOARS.
    10.1016/j.na.2011.01.015
  36. Martins, N.; Torres, D.F.M.. "Necessary Optimality Conditions for Higher-Order Infinite Horizon Variational Problems on Time Scales". Journal of Optimization Theory and Applications 155 2 (2012): 453-476. http://www.scopus.com/inward/record.url?eid=2-s2.0-84869126412&partnerID=MN8TOARS.
    10.1007/s10957-012-0065-y
  37. Martins, N.; Torres, D.F.M.. "Higher-order infinite horizon variational problems in discrete quantum calculus". Computers and Mathematics with Applications 64 7 (2012): 2166-2175. http://www.scopus.com/inward/record.url?eid=2-s2.0-84866123825&partnerID=MN8TOARS.
    10.1016/j.camwa.2011.12.006
  38. Brito Da Cruz, A.M.C.; Martins, N.. "The q-symmetric variational calculus". Computers and Mathematics with Applications 64 7 (2012): 2241-2250. http://www.scopus.com/inward/record.url?eid=2-s2.0-84866111690&partnerID=MN8TOARS.
    10.1016/j.camwa.2012.01.076
  39. Bartosiewicz, Z.; Martins, N.; Torres, D.F.M.. "The second Euler-Lagrange equation of variational calculus on time scales". European Journal of Control 17 1 (2011): 9-18. http://www.scopus.com/inward/record.url?eid=2-s2.0-79951562167&partnerID=MN8TOARS.
    10.3166/ejc.17.9-18
  40. Martins, N.; Torres, D.F.M.. "Generalizing the variational theory on time scales to include the delta indefinite integral". Computers and Mathematics with Applications 61 9 (2011): 2424-2435. http://www.scopus.com/inward/record.url?eid=2-s2.0-79955479977&partnerID=MN8TOARS.
    10.1016/j.camwa.2011.02.022
  41. Malinowska, A.B.; Martins, N.; Torres, D.F.M.. "Transversality conditions for infinite horizon variational problems on time scales". Optimization Letters 5 1 (2011): 41-53. http://www.scopus.com/inward/record.url?eid=2-s2.0-78650756398&partnerID=MN8TOARS.
    10.1007/s11590-010-0189-7
  42. Natália Martins; Delfim F.M. Torres. "Necessary conditions for linear noncooperative N-player delta differential games on time scales". Discussiones Mathematicae. Differential Inclusions, Control and Optimization (2011): http://dx.doi.org/10.7151/dmdico.1126.
    10.7151/dmdico.1126
  43. Martins, N.; Torres, D.F.M.. "Noether's symmetry theorem for nabla problems of the calculus of variations". Applied Mathematics Letters 23 12 (2010): 1432-1438. http://www.scopus.com/inward/record.url?eid=2-s2.0-77957579664&partnerID=MN8TOARS.
    10.1016/j.aml.2010.07.013
  44. Martins, N.. "Mountain pass theorems without Palais-Smale conditions". Journal of Mathematical Sciences 161 6 (2009): 783-791. http://www.scopus.com/inward/record.url?eid=2-s2.0-70350337083&partnerID=MN8TOARS.
    10.1007/s10958-009-9599-4
  45. Martins, N.; Torres, D.F.M.. "Calculus of variations on time scales with nabla derivatives". Nonlinear Analysis, Theory, Methods and Applications 71 12 (2009): http://www.scopus.com/inward/record.url?eid=2-s2.0-72149132561&partnerID=MN8TOARS.
    10.1016/j.na.2008.11.035
  46. Martins, N.; Neves, V.. "Nonstandard Palais-Smale conditions". The Strength of Nonstandard Analysis (2007): 271-285. http://www.scopus.com/inward/record.url?eid=2-s2.0-84887879259&partnerID=MN8TOARS.
    10.1007/978-3-211-49905-4_19
  47. Martins, N.; Neves, V.. "Nonstandard discrete derivatives and existence theorems for ODE". Rendiconti del Seminario Matematico 63 4 (2005): 383-396. http://www.scopus.com/inward/record.url?eid=2-s2.0-33751504862&partnerID=MN8TOARS.
Journal issue
  1. Martins, Natália; Almeida, Ricardo; Silva, Cristiana J.. "Special Issue: "Calculus of Variations, Optimal Control, and Mathematical Biology: A Themed Issue Dedicated to Professor Delfim F. M. Torres on the Occasion of His 50th Birthday"". Axioms (2022): https://www.mdpi.com/journal/axioms/special_issues/delfim.
Activities

Supervision

Thesis Title
Role 		Degree Subject (Type)
Institution / Organization
2019 - Current Optimality conditions for variational problems involving distributed order fractional derivatives
Supervisor
 PhD (PhD)
Universidade de Aveiro, Portugal
2017 - 2018 Cálculo das variações de Herglotz
Supervisor of Claudio Tendai
Master (Master)
Universidade de Aveiro, Portugal
2013 - 2017 Calculus of variations of Herglotz type
Supervisor of Simão Pedro da Silva Santos
 PhD (PhD)
Universidade de Aveiro, Portugal
2009 - 2012 Symmetric Quantum Calculus
Co-supervisor of Artur Miguel Capêllo Brito da Cruz
 PhD (PhD)
Universidade de Aveiro, Portugal