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Optimal control, epidemiology, mathematical models, stability, numerical methods.
Portugal

Biography

Cristiana J. Silva is Assistant Professor at the Department of Mathematics of Iscte – Instituto Universitário de Lisboa, Lisbon, Portugal. She is member of the Center for Research and Development in Mathematics and Applications (CIDMA) of the University of Aveiro, Portugal, since 2010. She was the Coordinator of the Thematic Line Biomathematics of CIDMA, between 2019 and 2022, and responsible for the organization of the seminars of the Systems and Control Group of R&D unit CIDMA, between 2017 and 2022. Between May 2018 and Mars 2022, she was member of the management committee of the COST Action CA16227 and group leader of the WG2 - Structured population models and optimal control, between May 2019 and Mars 2022. She was a Postdoctoral Researcher (FCT grant) at CIDMA, between 2011 and 2018; and Senior Researcher of CIDMA, since 2010. She obtained a B.Sc. in Mathematics from the University of Coimbra in 2003, a M.Sc. in Mathematics from University of Aveiro (UA) in 2005, a Ph.D. in Mathematics (Optimal Control) from UA and University of Orléans (France) in 2010 with the European PhD Label.
Her main research area is optimal control, calculus of variations, optimization (MSC 49); nonlinear control problems; time-delayed systems; mathematical models for infectious diseases; application of optimal control to epidemiology; direct and indirect methods in optimal control; bang-bang controls and regularization procedures.
Cristiana J. Silva co-organized 14 scientific events and gave more than 60 communications in international and national scientific meetings, 4 plenary talks and 2 outreach and dissemination talks. She was PhD co-supervisor of Ana Pedro Lemos-Paião at the Department of Mathematics of University of Aveiro, between September 2016 and December 2019.
Was the Principal investigator of the project "Optimal control and mathematical modelling of COVID-19 pandemic" financed by FCT within the "RESEARCH 4 COVID-19" call. She was member of the project PTDC/EEI-AUT/2933/2014 (TOCCATA), funded by FEDER funds through COMPETE 2020, between 2016 and 2019. Since 2020, she is member of the Editorial Board of the international journals Mathematical and Computational Applications and AIMS Mathematics.
Cristiana J. Silva has been married since 2011 and has 3 sons.

Activities

Employment (9)

ISCTE – Instituto Universitário de Lisboa: Lisbon, PT

2022-09-01 to present | Assistant Professor (Mathematics)
Employment
Source: Self-asserted source
Cristiana J. Silva

Universidade de Aveiro: Aveiro, Aveiro, PT

2020-12-01 to 2022-08-31 | Assistant Researcher (Matemática)
Employment
Source: Self-asserted source
Cristiana J. Silva

Universidade de Aveiro: Aveiro, Aveiro, PT

2019-01-01 to 2020-11-30 | Investigador Doutorado (Nível I) (Matemática)
Employment
Source: Self-asserted source
Cristiana J. Silva

University of Aveiro: Aveiro, PT

2018-09-01 to 2018-12-31 | Assistant Professor (Invited) (Mathematics)
Employment
Source: Self-asserted source
Cristiana J. Silva

Instituto Politécnico de Leiria: Leiria, Leiria, PT

2018-03-01 to 2018-07-31 | Assistant Professor (Invited) (Mathematics)
Employment
Source: Self-asserted source
Cristiana J. Silva

ISLA - Leiria: Leiria, PT

2013-03 to 2014-01 | Professor
Employment
Source: Self-asserted source
Cristiana J. Silva

Instituto Politécnico de Leiria: Leiria, Leiria, PT

2010-09 to 2011-07 | Assistant teacher (Mathematics)
Employment
Source: Self-asserted source
Cristiana J. Silva

Instituto Politécnico do Porto: Porto, Porto, PT

2010-09 to 2011-01 | Assistant teacher (Mathematics)
Employment
Source: Self-asserted source
Cristiana J. Silva

Instituto Politécnico de Leiria: Leiria, Leiria, PT

2006-09 to 2007-02 | Assistant teacher (Mathematics)
Employment
Source: Self-asserted source
Cristiana J. Silva

Education and qualifications (4)

University of Orléans, France: Orléans , FR

2007-03-01 to 2010-10-11 | PhD (Mathematics)
Education
Source: Self-asserted source
Cristiana J. Silva

Universidade de Aveiro: Aveiro, Aveiro, PT

2007-03-01 to 2010-10-11 | PhD (Mathematics)
Education
Source: Self-asserted source
Cristiana J. Silva

Universidade de Aveiro: Aveiro, Aveiro, PT

2003-10 to 2005-06 | Master (Mathematics)
Education
Source: Self-asserted source
Cristiana J. Silva

Universidade de Coimbra Faculdade de Ciencias e Tecnologia: Coimbra, Coimbra, PT

1998-10 to 2003-06 | Licenciate (Mathematics)
Education
Source: Self-asserted source
Cristiana J. Silva

Professional activities (2)

COST Action CA16227: Lisbon, PT

2018-05-01 to present | MC Member and WG Leader
Membership
Source: Self-asserted source
Cristiana J. Silva

Associação Humanitária dos Bombeiros Voluntários da Batalha: Batalha, Leiria, PT

2000 to 2007 | Aspirante de bombeiro
Membership
Source: Self-asserted source
Cristiana J. Silva

Funding (6)

Optimal control fighting against epidemics

2020-12 to present | Contract
Fundação para a Ciência e Tecnologia (FCT) (Lisboa, PT)
GRANT_NUMBER:

CEECIND/00564/2018

Source: Self-asserted source
Cristiana J. Silva

Controlo Ótimo e Modelação Matemática da Pandemia Covid-19: contributos para uma estratégia sistémica de intervenção em saúde na comunidade

2020-06 to 2020-09 | Grant
Fundação para a Ciência e a Tecnologia (Lisboa, PT)
GRANT_NUMBER:

Proj. N. 147

Source: check_circle
CIÊNCIAVITAE

Theory, Applications and Numerics of Optimal Control

2018-05 to 2018-08 | Grant
National Science Foundation (Lisbon, VA, PT)
Part of GRANT_NUMBER:

BPD TOCCATTA UA 2018

Source: Self-asserted source
Cristiana J. Silva

Postdoctoral fellowship

2011-08 to 2018-04 | Grant
Fundação para a Ciência e Tecnologia (Lisboa, PT)
GRANT_NUMBER:

SFRH / BPD / 72061 / 2010

Source: Self-asserted source
Cristiana J. Silva

PhD fellowship

2007-03 to 2010-10 | Grant
Fundação para a Ciência e Tecnologia (Lisboa, PT)
GRANT_NUMBER:

SFRH / BD / 27272 / 2006

Source: Self-asserted source
Cristiana J. Silva

Short term grant for young researchers

2006-02 to 2006-04 | Grant
Fundação Calouste Gulbenkian (Lisboa, PT)
Source: Self-asserted source
Cristiana J. Silva

Works (50 of 59)

Items per page:
Page 1 of 2

Characterization of the Appointment’s Reasons for “P—Psychological” on the ICPC-2 Scale in Primary Health Care Services

Mathematical and Computational Applications
2025-03 | Journal article | Author
Contributors: Filipa Rocha; Cristiana J. Silva; Sofia Pinheiro; Vera Afreixo; Rui Pedro Leitão; Miguel Felgueiras
Source: check_circle
Multidisciplinary Digital Publishing Institute

Analysis of Primary Healthcare Indicators

Mathematical and Computational Applications
2025-01 | Journal article | Author
Contributors: Ana Leonor Saraiva; Cristiana J. Silva; Jorge Cabral; José Pedro Antunes; Paula Rama; Sofia Pinheiro; Vera Afreixo
Source: check_circle
Multidisciplinary Digital Publishing Institute

Optimal Control of Microcephaly Under Vertical Transmission of Zika

Axioms
2024-11 | Journal article | Author
Contributors: Dilara Yapışkan; Cristiana J. Silva; Delfim F. M. Torres
Source: check_circle
Multidisciplinary Digital Publishing Institute

An Analytic Method to Determine the Optimal Time for the Induction Phase of Anesthesia

Axioms
2023-09 | Journal article | Author
Contributors: mohamed abdelaziz zaitri; Cristiana J. Silva; Delfim F. M. Torres
Source: check_circle
Multidisciplinary Digital Publishing Institute

Graph Theory Approach to COVID-19 Transmission by Municipalities and Age Groups

Mathematical and Computational Applications
2022-10 | Journal article | Author
Contributors: Pedro Machado; Sofia J. Pinheiro; Vera Afreixo; Cristiana J. Silva; Rui Pedro Leitão
Source: check_circle
Multidisciplinary Digital Publishing Institute

Stability Analysis of Delayed COVID-19 Models

Axioms
2022-08 | Journal article | Author
Contributors: mohamed abdelaziz zaitri; Cristiana J. Silva; Delfim F. M. Torres
Source: check_circle
Multidisciplinary Digital Publishing Institute

Fractional model of COVID-19 applied to Galicia, Spain and Portugal

Chaos, Solitons and Fractals
2021 | Journal article
EID:

2-s2.0-85100151606

Part of ISSN: 09600779
Contributors: Ndaïrou, F.; Area, I.; Nieto, J.J.; Silva, C.J.; Torres, D.F.M.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier

Optimal control of the COVID-19 pandemic: controlled sanitary deconfinement in Portugal

Scientific Reports
2021 | Journal article
EID:

2-s2.0-85101074676

Part of ISSN: 20452322
Contributors: Silva, C.J.; Cruz, C.; Torres, D.F.M.; Muñuzuri, A.P.; Carballosa, A.; Area, I.; Nieto, J.J.; Fonseca-Pinto, R.; Passadouro, R.; Santos, E.S. et al.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier

Global Stability Condition for the Disease-Free Equilibrium Point of Fractional Epidemiological Models

Axioms
2021-09 | Journal article | Author
Contributors: Ricardo Almeida; Natália Martins; Cristiana J. Silva
Source: check_circle
Multidisciplinary Digital Publishing Institute

A New Compartmental Epidemiological Model for COVID-19 with a Case Study of Portugal

Ecological Complexity
2020 | Journal article
EID:

2-s2.0-85096871708

Part of ISSN: 1476945X
Contributors: Lemos-Paião, A.P.; Silva, C.J.; Torres, D.F.M.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier

A survey on sufficient optimality conditions for delayed optimal control problems

Studies in Systems, Decision and Control
2020 | Book chapter
EID:

2-s2.0-85100306512

Part of ISSN: 21984190 21984182
Contributors: Lemos-Paião, A.P.; Silva, C.J.; Torres, D.F.M.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier

Erratum: Modeling and optimal control of HIV/AIDS prevention through PrEP (Discrete Contin. Dyn. SYST. Ser. S (2018) 11: 1 (119-141) DOI: 10.1016/j.physa.2018.10.033)

Discrete and Continuous Dynamical Systems - Series S
2020 | Journal article
EID:

2-s2.0-85088874538

Part of ISSN: 19371179 19371632
Contributors: Silva, C.J.; Torres, D.F.M.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier

On sica models for HIV transmission

Studies in Systems, Decision and Control
2020 | Book chapter
EID:

2-s2.0-85100296257

Part of ISSN: 21984190 21984182
Contributors: Silva, C.J.; Torres, D.F.M.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier

Optimal Control of Aquatic Diseases: A Case Study of Yemen’s Cholera Outbreak

Journal of Optimization Theory and Applications
2020 | Journal article
EID:

2-s2.0-85085313363

Part of ISSN: 15732878 00223239
Contributors: Lemos-Paião, A.P.; Silva, C.J.; Torres, D.F.M.; Venturino, E.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier

Synchronization and Self-organization in Complex Networks for a Tuberculosis Model

Mathematics in Computer Science
2020 | Journal article
EID:

2-s2.0-85083225562

Part of ISSN: 16618289 16618270
Contributors: Silva, C.J.; Cantin, G.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier

A cholera mathematical model with vaccination and the biggest outbreak of world’s history

AIMS Mathematics
2019 | Journal article
EID:

2-s2.0-85066112942

Part of ISSN: 24736988
Contributors: Lemos-Paião, A.P.; Silva, C.J.; Torres, D.F.M.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier

A sufficient optimality condition for delayed state-linear optimal control problems

Discrete and Continuous Dynamical Systems - Series B
2019 | Journal article
EID:

2-s2.0-85063903836

Contributors: Lemos-Paião, A.P.; Silva, C.J.; Torres, D.F.M.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier
grade
Preferred source (of 2)‎

A sufficient optimality condition for non-linear delayed optimal control problems

Pure and Applied Functional Analysis
2019 | Journal article
SOURCE-WORK-ID:

cv-prod-id-717868

Contributors: Silva, Cristiana J.; Ana P. Lemos-Paião; Torres, Delfim F. M.
Source: check_circle
CIÊNCIAVITAE

Influence of the topology on the dynamics of a complex network of HIV/AIDS epidemic models

AIMS Mathematics
2019 | Journal article
Part of ISSN: 2473-6988
Source: Self-asserted source
Cristiana J. Silva
grade
Preferred source (of 2)‎

Stability of a fractional HIV/AIDS model

Mathematics and Computers in Simulation
2019 | Journal article
EID:

2-s2.0-85066146602

Contributors: Silva, C.J.; Torres, D.F.M.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier
grade
Preferred source (of 2)‎

The Portuguese Meeting in Biomathematics

Statistics, Optimization and Information Computing
2019 | Journal article
EID:

2-s2.0-85073253802

Part of ISSN: 23105070 2311004X
Contributors: Torres, D.F.M.; Area, I.; Silva, C.; Silva, C.J.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier

Numerical Optimal Control of HIV Transmission in Octave/MATLAB

Mathematical and Computational Applications
2019-12-19 | Journal article
Part of ISSN: 2297-8747
Source: Self-asserted source
Cristiana J. Silva
grade
Preferred source (of 2)‎

A stochastic analysis of the impact of fluctuations in the environment on pre-exposure prophylaxis for HIV infection

Soft Computing
2019-12-17 | Journal article
Part of ISSN: 1432-7643
Part of ISSN: 1433-7479
Source: Self-asserted source
Cristiana J. Silva
grade
Preferred source (of 2)‎

Optimal control of HIV treatment and immunotherapy combination with state and control delays

Optimal Control Applications and Methods
2019-12-04 | Journal article
Part of ISSN: 0143-2087
Part of ISSN: 1099-1514
Source: Self-asserted source
Cristiana J. Silva
grade
Preferred source (of 2)‎

A Minimal HIV-AIDS Infection Model with General Incidence Rate and Application to Morocco Data

Statistics, Optimization & Information Computing
2019-08-17 | Journal article
SOURCE-WORK-ID:

cv-prod-id-770888

EID:

2-s2.0-85073217928

Contributors: Lotfi, El Mehdi; Mahrouf, Marouane; Maziane, Mehdi; J. Silva, Cristiana; Torres, Delfim F. M.; Yousfi, Noura
Source: check_circle
CIÊNCIAVITAE
grade
Preferred source (of 2)‎

A stochastic SICA epidemic model for HIV transmission

Applied Mathematics Letters
2018 | Journal article
EID:

2-s2.0-85047409047

Contributors: Djordjevic, J.; Silva, C.J.; Torres, D.F.M.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier

Ebola model and optimal control with vaccination constraints

Journal of Industrial and Management Optimization
2018 | Journal article
EID:

2-s2.0-85037541309

Contributors: Area, I.; Ndaïrou, F.; Nieto, J.J.; Silva, C.J.; Torres, D.F.M.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier

Mathematical modeling of Zika disease in pregnant women and newborns with microcephaly in Brazil

Mathematical Methods in the Applied Sciences
2018 | Journal article
EID:

2-s2.0-85055246265

Contributors: Ndaïrou, F.; Area, I.; Nieto, J.J.; Silva, C.J.; Torres, D.F.M.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier

Modeling and optimal control of HIV/AIDS prevention through PrEP

Discrete and Continuous Dynamical Systems - Series S
2018 | Journal article
EID:

2-s2.0-85031017482

Contributors: Silva, C.J.; Torres, D.F.M.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier

Multiobjective optimization to a TB-HIV/AIDS coinfection optimal control problem

Computational and Applied Mathematics
2018 | Journal article
EID:

2-s2.0-85047501784

Contributors: Denysiuk, R.; Silva, C.J.; Torres, D.F.M.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier

Optimal control of a delayed HIV model

Discrete and Continuous Dynamical Systems - Series B
2018 | Journal article
EID:

2-s2.0-85034023646

Contributors: Rodrigues, F.; Silva, C.J.; Torres, D.F.M.; Maurer, H.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier

Stability and optimal control of a delayed HIV model

Mathematical Methods in the Applied Sciences
2018 | Journal article
EID:

2-s2.0-84991717367

Contributors: Rocha, D.; Silva, C.J.; Torres, D.F.M.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier

The effect of immigrant communities coming from higher incidence tuberculosis regions to a host country

Ricerche di Matematica
2018 | Journal article
EID:

2-s2.0-85037743381

Contributors: Rocha, E.M.; Silva, C.J.; Torres, D.F.M.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier

Uniform asymptotic stability of a fractional tuberculosis model

Mathematical Modelling of Natural Phenomena
2018 | Journal article
EID:

2-s2.0-85045217008

Contributors: Wojtak, W.; Silva, C.J.; Torres, D.F.M.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier

Thematic Line BioMathematics

2018-06-01 | Website
SOURCE-WORK-ID:

cv-prod-id-256260

Contributors: Silva, Cristiana J.
Source: check_circle
CIÊNCIAVITAE

A SICA compartmental model in epidemiology with application to HIV/AIDS in Cape Verde

Ecological Complexity
2017 | Journal article
EID:

2-s2.0-85009241654

Contributors: Silva, C.J.; Torres, D.F.M.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier

An epidemic model for cholera with optimal control treatment

Journal of Computational and Applied Mathematics
2017 | Journal article
EID:

2-s2.0-85008205618

Contributors: Lemos-Paião, A.P.; Silva, C.J.; Torres, D.F.M.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier
grade
Preferred source (of 2)‎

Optimal control of a tuberculosis model with state and control delays

Mathematical Biosciences and Engineering
2017 | Journal article
EID:

2-s2.0-85002717979

Contributors: Silva, C.J.; Maurer, H.; Torres, D.F.M.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier

Optimal Spraying in Biological Control of Pests

Mathematical Modelling of Natural Phenomena
2017 | Journal article
EID:

2-s2.0-85020045755

Contributors: Silva, C.J.; Torres, D.F.M.; Venturino, E.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier
grade
Preferred source (of 2)‎

An epidemic model for cholera with treatment through quarantine

16th International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE-2016)
2016-07-04 | Conference paper
SOURCE-WORK-ID:

cv-prod-id-257154

Contributors: Silva, Cristiana J. ; Ana P. Lemos-Paião; Delfim F. M. Torres
Source: check_circle
CIÊNCIAVITAE

Stability and Optimal Control of a Delayed HIV Model

16th International Conference on Computational and Mathematical Methods in Science and Engineering (CMMSE-2016)
2016-07-04 | Conference paper
SOURCE-WORK-ID:

cv-prod-id-257152

Contributors: Silva, Cristiana J. ; D. Rocha; Delfim F. M. Torres
Source: check_circle
CIÊNCIAVITAE

A TB-HIV/AIDS coinfection model and optimal control treatment

Discrete and Continuous Dynamical Systems- Series A
2015 | Journal article
EID:

2-s2.0-84926618599

Contributors: Silva, C.J.; Torres, D.F.M.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier
grade
Preferred source (of 2)‎

Multiobjective approach to optimal control for a tuberculosis model

Optimization Methods and Software
2015 | Journal article
EID:

2-s2.0-84940451914

Contributors: Denysiuk, R.; Silva, C.J.; Torres, D.F.M.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier
grade
Preferred source (of 2)‎

Cost-Effectiveness Analysis of Optimal Control Measures for Tuberculosis

Bulletin of Mathematical Biology
2014 | Journal article
EID:

2-s2.0-84919398031

Contributors: Rodrigues, P.; Silva, C.J.; Torres, D.F.M.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier

Modeling TB-HIV syndemic and treatment

Journal of Applied Mathematics
2014 | Journal article
EID:

2-s2.0-84904685759

Contributors: Silva, C.J.; Torres, D.F.M.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier

Optimal control for a tuberculosis model with reinfection and post-exposure interventions

Mathematical Biosciences
2013 | Journal article
EID:

2-s2.0-84881227998

Contributors: Silva, C.J.; Torres, D.F.M.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier

Optimal control strategies for reducing the number of active infected individuals with tuberculosis

SIAM Conference on Control and Its Applications 2013
2013 | Conference paper
EID:

2-s2.0-84919351821

Contributors: Rodrigues, P.; Silva, C.J.; Torres, D.F.M.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier
grade
Preferred source (of 2)‎

An optimal control approach to malaria prevention via insecticide-treated nets

The Cape Verde International Days on Mathematics 2013
2013-04-22 | Conference paper
SOURCE-WORK-ID:

cv-prod-id-257234

Contributors: Silva, Cristiana J. ; Delfim F. M. Torres
Source: check_circle
CIÊNCIAVITAE

Optimal control strategies for tuberculosis treatment: A case study in Angola

Numerical Algebra, Control and Optimization
2012 | Journal article
EID:

2-s2.0-84892398225

Contributors: Silva, C.J.; Torres, D.F.M.
Source: Self-asserted source
Cristiana J. Silva via Scopus - Elsevier
grade
Preferred source (of 2)‎

Optimal control applied to tuberculosis models

The IEA-EEF European Congress of Epidemiology 2012: Epidemiology for a Fair and Healthy Society
2012-09-05 | Conference paper
SOURCE-WORK-ID:

cv-prod-id-257241

Contributors: Silva, Cristiana J. ; Delfim F. M. Torres
Source: check_circle
CIÊNCIAVITAE
Items per page:
Page 1 of 2

Peer review (16 reviews for 13 publications/grants)

Review activity for Acta biotheoretica. (1)
Review activity for Advances in difference equations. (2)
Review activity for Bulletin of mathematical biology. (1)
Review activity for Communications in nonlinear science & numerical simulation (1)
Review activity for International journal of dynamics and control. (2)
Review activity for Journal of optimization theory and applications. (2)
Review activity for Journal of the Egyptian Mathematical Society. (1)
Review activity for Matemática aplicada e computacional (1)
Review activity for PloS one. (1)
Review activity for SN Business & Economics. (1)
Review activity for The European physical journal plus. (1)
Review activity for The European physical journal. Special topics. (1)
Review activity for Tạp chí toán học (1)