FQM377: Differential Equations. Control Theory. Orthogonal Polynomials

Submitted by francisco.grimaldi on Mon, 08/31/2020 - 19:57
Size of the team
number of researchers number of supporting staff number of PhD students
Composition of Joint Unit of Research, if relevant

The research group was created in 2014 and is currently made up of eight PhD in Mathematics, investigating about the following research lines: models of random matrices and orthogonal polynomials; control theory; symmetries of differential equations, both ordinary and partial differential equations; and integrability of  distributions.

Some of the members of the group have extensive teaching and research experience, recently incorporating two doctors, whose doctoral theses, led by group members, collect the latest advances in some of the group's research lines.

Among the five members of the group who can get six-year terms of investigation, they accumulate a total of sixteen six-year terms recognized by CENAI. The research activity of the group has generated 143 publications in JCR indexes scientific journals, 30 book chapters from prestigious publishers, 11 books and more than 100 contributions to congresses, mostly international.

The members of the group have jointly directed 16 doctoral theses and numerous final and master's degree works in Mathematics. As a whole, the group has been the beneficiary of a total of 40 grants and R + D + i projects. Currently, there are two projects currently financed by the Ministry of Science and Innovation, Innovation and Universities through the State Program for Generation of Knowledge and Scientific and Technological Strengthening of the R + D + i System, (projects PGC2018-101514-B-I00 and PGC2018-094898-B-I00) in which group members participate as co-principal investigator or as part of the research team.

PI name
PI bio

ORCID ID 0000-0003-4478-4524

She finished her degree in Mathematics at the University of Salamanca on 07/24/1995 and on October 16, 1995 She was hired as a full-time Associate Professor at the University of Cádiz (UCA). This contract ended on 12/25/1997, after obtaining a position as Associate Professor of the University School. Since 05/05/2004 she is a tenured Professor at the University. During these years she taught subjects in the area of Mathematical Analysis, mainly in the Bachelor and Master degrees in Mathematics at the UCA. She has participated in 37 courses and seminars of improvement, innovation and teacher improvement, being the principal investigator of an innovation project awarded on 03/07/2013 and a member of five others. She supervised 6 last-year degree students’ projects and 12 master thesis in Mathematics.
Secretary of  the Mathematics department,  from 12/23/2012 until 01/16/2020. Since 01/10/2012 She is coordinator of master projects in Mathematics ; member of the corresponding commission of the Faculty of Sciences since 03/19/2013; member of the academic commission of the Doctoral Program in Mathematics since 03/25/2019; member of the  the quality assurance commission of the Doctoral Program in Mathematics since 12/01/2016.  
Her research activity began with the completion of the courses of the Pure and Applied Mathematical PhD program at the University of Salamanca, which ended in 1997. That same year, she defended the first Bachelor's Thesis of the Department of Mathematics at the UCA, under the supervision of Dr. Juan Luis Romero. It was the beginning of her research activity in the theory of groups of symmetries in the study of differential equations. She defended my doctoral thesis, also directed by Dr. Romero, on 03/24/2000 at the University of Salamanca. It introduces the concept of λ-symmetry (or C∞-symmetries), giving rise to a new research line with a great internationally impact since its inception. Since then, She has published a total of 55 papers, 37 in journals published in the JCR / SCI, 2 papers in non-indexed journals, and 18 contributions in books, including contributions to congresses published in prestigious editorials and all of them with external evaluation. Part of these results have been presented in 51 international conferences.
As a result of the research activity, 3 periods of six years have been granted by the National Commission for the Evaluation of the Research Activity, (CENAI) corresponding to the periods 1996-2001, 2002-2007 and 2008-2013. She has been part of several scientific teams with 11 projects funded by competitive calls of regional or national scope since 1999. She was a member of the PAIDI Research Group FQM-201 from 08/19/1997 until 12/17/2013, date in which she joined the Research Group PAIDI FQM-377, being the responsible since 04/19/2018. Since 2015, She has participated as a researcher in 8 collaboration contracts (OTRI) between companies and the University of Cádiz. She is currently one of the two main researchers of the national project PGC2018-101514-B-I00.
She is organized and taught formative activities on λ-symmetries in the Doctorate in Mathematics during the last four academic years and She has supervised two doctoral theses on the subject. Both students are beneficiaries of highly competitive grants (FPU15 / 02872 and UCA-AUIP agreement).

Contact person and e-mail
Contact person
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Short description of research profile

Integrability of Distributions
Random Matrix Models. Orthogonal Polynomials
Differential Equations Through Symmetry
Control Theory

Research area

Representative publications

1. New optical solitons of Kundu-Eckhaus equation via λ-symmetry José Mendoza, Concepción Muriel y José Ramírez Chaos, Solitons and Fractals   (2020) Vol: 136. Pgs: 109786-109792
2. A new method to obtain either first- or second-order reductions for parametric polynomial ODEs José Ramírez, Juan Luis Romero y Concepción Muriel Journal of Computational and Applied Mathematics. 2019. Vol: 358. Págs: 146--162    
3. Exact general solution and first integrals of a remarkable static Euler-Bernoulli beam equation Adrián Ruiz, Concepción Muriel y José Ramírez Communications in Nonlinear Science and Numerical Simulation. 2019. Vol: 69.Pgs: 261-269
4. Gravitational lensing by eigenvalue distributions of random matrix models Martínez-Alonso, Luis; Medina-Reus, Elena Blanca Classical and Quantum Gravity. 2018. Vol: 35. Núm: 09500. Págs: 095009-1--095009-25
5. Stabilization of switched linear systems by using projections Pérez-Martínez, María Del Carmen; Benítez-Trujillo, Francisco; García-Gutiérrez, Juan Bosco Journal of Computational and Applied Mathematics. 2017.Vol: 318.  Pgs. 117-123.  

Link to extended list of publication

Technology Expertise

Symmetries,  λ-symmetries, exact solutions, reductions, linearization, first integrals and new techniques to solving partial differential equations and ordinary differential equations. Solvable structures and integrability of distributions.  

Characterization of eigenvalue distributions in the Penner and Gross-Witten-Wadia models, phase transitions and electrostatic interpretation. Applications to the determination of the position of the images in gravitational lensing. Existence of separatrices in cosmological models.

Control Theory, switched systems, stabilization and control of these systems, design of stabilizing switching laws and research about conditions under which the stabilization is assured. Development of theory of switched systems applied to real models.