UNIVERSIDADE ABERTA departamento de ciências e tecnologia secção de matemática RESEARCH REPORT 2012 MARCH 2013 Preface This is the seventh issue of the Research Report produced annually by the Secção de Matemática of the Departamento de Ciências e Tecnologia of the Universidade Aberta. As stated in the previous Research Reports, our goal in producing this document is to enhance the visibility of the research activities of the members of this Secção among our colleagues in the University and our peers in the portuguese and international research communities. This year the Secção continued the monthly research seminar series titled ”Matemática na AbERTA”, to which several members of the Secção have already contributed. The number of members of the Secção decreased to 12, presently all of them are PhD holders. This Report will be permanently available online at the following URL address http://www.uab.pt/web/guest/organizacao/departamentos/dcet/ sm/investigacao. Lisbon, March 6, 2013 The coordinator of the Secção de Matemática Amı́lcar Oliveira 1 Academic degrees awarded in 2012 2 Publications 2.1 2.1.1 Published in 2012 Books or chapters of books, thesis, proceedings, special volumes (authored or edited) Chang-Hwan Im, Kiwoon Kwon, Venky Krishnan, and P. Serranho (eds.)Applied Mathematics in Biomedical Sciences and Engineering, J. Applied Mathematics, (2012). P. Serranho,Matemática Aplicada ao Estudo da Visão, In: J. P. Boavida, R. P. Carpentier, L. Cruz-Filipe, P.S. Gonçalves, E. Grifo, D. Henriques, A. R. Pires (eds.), Números, Cirurgias e Nós de Gravata , IST Press (2012), 207–216. P. Serranho, M. Morgado and R. Bernardes, Optical Coherence Tomography: A Concept Review , In: R. Bernardes, J. Cunha-Vaz (eds.), Optical Coherence Tomography , Biological and Medical Physics, Biomedical Engineering, Springer, (2012), 139–156. T.A. Oliveira, S. Mejza, D. Ferreira, A. Oliveira and L. Grilo (eds.), Book of Abstracts of the 6th Workshop on Statistics, Mathematics and Computation and 3rd Portuguese Polish Workshop on Biometry. Published and printed by: Instituto Politécnico de Tomar, (2012), ISBN: 978-972-9473-62-3. Teresa Oliveira, Amı́lcar Oliveira and Alexandra Pérez-Bonilla, Data Mining and Quality in Service Industry: Review and some applications. Section 1: Services and Decision Making, CRC/Press Taylor & Francis Group: ”Decision Making in Service Industries: A Practical Approach ”. Edited by Javier Faulin; Angel A. Juan; Scott E. Grasman, Rochester Institute of Technology, New York, USA; Michael J. Fry, University of Cincinnati, Ohio, USA, (2012), ISBN 9781439867341. http://www.crcpress.com/product/isbn/9781439867341, Chapter of Book. Sven Trenholm, Angel A. Juan, Jorge Simosa, Amı́lcar Oliveira and Teresa Oliveira (2012), Long-Term Experiences in Mathematics E-Learning in Europe and the USA. Invited Chapter of Book in IGI Global Publisher - Math-ELearning: Teaching Mathematics Online: Emergent Technologies and Methodologies. Chapter 12, pages 238–257. Juan, A.; Huertas, M.; Trenholm, S.; Steegmann, C. (eds.) DOI: 10.4018/978-1-60960-875-0.ch012. http://www.igiglobal.com/viewtitlesample.aspx?id=57942. 2.1.2 Articles in refereed journals and serials F.P. da Costa, M. Grinfeld, M. Langer, N.J. Mottram, and J.T. Pinto, Kickback in Nematic Liquid Crystals, Quart. Appl. Math., 70, (1) (2012), 99–110. 2 F.P da Costa, J.T. Pinto, H.J. van Roessel and R. Sasportes, Scaling Behaviour in a Coagulation-Annihilation Model and Lotka-Volterra Competition Systems, J. Phys. A: Math. Teor., 45, (2012) 285201. D. L. Finkelshtein, Yu. G. Kondratiev and M. J. Oliveira, Glauber dynamics in the continuum via generating functionals evolution, Complex Anal. Oper. Theory, 6 (4) (2012), 923–945. D. L. Finkelshtein, Yu. G. Kondratiev and M. J. Oliveira, Kawasaki dynamics in the continuum via generating functionals evolution, Methods Funct. Anal. Topology, 18 (1) (2012), 55–67. A. Araujo, S. Barbeiro and P. Serranho, Stability of finite difference schemes for complex diffusion processes, SIAM J. Numer. Anal., 50(3), (2012) 1284– 1296. P. Guimarães, P. Rodrigues, P. Serranho and R. Bernardes, 3D Retinal Vascular Network from Optical Coherence Tomography Data, Image Analysis and Recognition, Lecture Notes in Computer Science, Volume 7325/2012, ed. Aurélio Campilho; Mohamed Kamel, ISBN: 978-3-642-31297-7. Berlin, Heidelberg: Springer Berlin Heidelberg, (2012), 339–346. F. Rodrigues, D. Foster,F. Caramelo, P. Serranho, G. Gonçalves, L. Januário and A. Finn, Progressive changes in pneumococcal carriage in children attending daycare in Portugal after 6 years of gradual conjugate vaccine introduction show falls in most residual vaccine serotypes but no net replacement or trends in diversity, Vaccine, 30, 26, (2012), 3951–3956. C. Maduro, P. Serranho, T. Santos, P. Rodrigues, J. Cunha-Vaz and R. Bernardes, OCT Noise Despeckling Using 3D Nonlinear Complex Diffusion Filter, In: Technologies for Medical Sciences. Lecture Notes in Computational Vision and Biomechanics. Jorge, R.; Tavares, J.; Barbosa, M.; Slade, A. (ed). Ed. Springer, 2012, 1, 141–157. Araújo, João and Konieczny, Janusz, A method for finding new sets of axioms for classes of semigroups, Archives for Mathematical Logic, 51 (2012), 461–474. Araújo, João and Kinyon, M., Axioms for unary semigroups via division operations, Communications in Algebra, 40 (02) (2012), 719–737. A. Disterheft, S. Caeiro, M.R. Ramos and U. M.M. Azeiteiro, Environmental Management Systems (EMS) implementation processes and practices in European higher education institutions e Top-down versus participatory approaches, Journal of Cleaner Production, 31 (2012) 80–90. A. Roy and M. Fonseca, Linear Models with Doubly Exchangeable Distributed Errors, Communications in Statistics: Theory and Methods, 41 (2012) 2545– 2569. 3 M. de Carvalho, M. Fonseca, M. Oliveira and J.T. Mexia. A dimension reduction technique for estimation in linear mixed models, Journal of Statistical Computation and Simulation, 82 (2012) 219–226. 2.1.3 Articles in conference proceedings J. Bornales, S. Eleutério, M. J. Oliveira and L. Streit, Fractional Brownian polymers - some first results,, Int. J. Mod. Phys. Conf. Ser. 17 (2012), 54–65. M. J. Oliveira and J. L. Silva, Studies in fractional Poisson measures, Int. J. Mod. Phys. Conf. Ser. 17 (2012), 122–129. Ramos, M. R., Carolino, E., Oliveira, T. and Bicho, M., Two-way MANCOVA: An application to public health, International Conference of Numerical Analysis And Applied Mathematics, ICNAAM 2012. AIP Conference Proceedings, Volume 1479, (2012), pp. 1716–1719. Oliveira, T.A. and Oliveira, A., Ineffectiveness of the FIM in selecting Optimal BIB Designs for testing block effects, in Proceedings of COMPSTAT 2012, pg. 701–722, Limassol, Cyprus, August, 27–31, (2012). ISBN 978-90-73592-322. Oliveira, A., Oliveira, T.A.,and Mejza, S., Joint Regression Analysis and AMMI model applied to oat improvement,, in Proceedings of ICNAAM 2012, Kos Island - Greece, September 19-25, (2012). AIP Conf. Proc. 1479: 1720– 1723. American Institute of Physics, ISBN 978-0-7354-1089-3. Araújo, L.B., Oliveira, M., Dias, C.T., Oliveira, A. and Oliveira, T.A., Tucker3 Method in Biometrical research: Analysis of experiments with three factors, using R, in Proceedings of ICNAAM 2012, Kos Island, Greece, September, 19-25, (2012). AIP Conf. Proc. 1479: 1728–1731. American Institute of Physics, ISBN 978-0-7354-1089-3. M. Fonseca, T. Mathew and R. Zmyslony. Inference for the interclass correlation in familial data using small asymptotics, AIP Conf. Proc. 1479, (2012), 1704–1706. 2.2 Accepted or submitted in 2012 Articles in refereed journals and serials Accepted D. L. Finkelshtein, Yu. G. Kondratiev and M. J. Oliveira, Markov evolutions and hierarchical equations in the continuum. II: multicomponent systems, Rep. Math. Phys. Araújo, João; Cameron, Peter and Mitchell, James D., Max Neunhoffer; The classification of normalizing groups, Journal of Algebra, 373 (2013), 481–490. 4 Araújo, João and Janusz Konieczny, Centralizers in the Full Transformation Semigroup, Semigroup Forum. Araújo, João; Kinyon, M. and Malheiro, António, A characterization of adequate semigroups by forbidden subsemigroups, Proceedings of the Royal Society of Edinburgh Series A. A. Araújo and O. Neto, Limits of tangents of quasi-ordinary hypersurfaces, A. Araújo, O. Neto (accepted, Proceedings of the AMS). A. Berarducci, M. Edmundo and M. Mamino, Discrete subgroups of locally definable groups, Selecta Math. (New Series). M. Edmundo, P. Eleftheriou and L. Prelli, Coverings by open cells, Arch. Math. Logic Seijas-Macias, A. and A. Oliveira, An approach to Distribution of the Product of two normal variables, Discussiones Mathematicae. Submitted Araújo, João and Peter J. Cameron, Two Generalizations of Homogeneity in Groups with Applications to Regular Semigroups, (29 páginas). http://arxiv.org/abs/1204.2195 Araújo, João; Michael Kinyon and R. Padmanabhan, A 2-base for inverse semigroups, (7 páginas). http://arxiv.org/abs/1210.3285 Araújo, João; Bentz, Wolfram and Peter J. Cameron, Groups Synchronizing a Transformation of Non-Uniform Kernel, (14 páginas). http://arxiv.org/abs/1205.0682 Araújo, João; Bentz, Wolfram and Janusz Konieczny, The Commuting Graph of the Symmetric Inverse Semigroup, (29 páginas). http://arxiv.org/abs/1205.1664 Araújo, João; Konieczny, Janusz and Malheiro António, Conjugation in Semigroups, (41 páginas). http://arxiv.org/abs/1301.1568 Araújo, João and Kinyon, Michael; An afternoon with John Howie, http://www.ciul.ul.pt/ mjoao/nongroup/nongroup.html 5 2.2.1 Articles in conference proceedings Accepted Submitted 3 3.1 Research lectures and courses In meetings Araújo, João, Tricks in Semigroup Theory, Workshop on Semigroups (To remember John M. Howie on the occasion of his 76th birthday). Lisbon, Portugal, May 23–25, 2012. (Invited speaker). http://caul.cii.fc.ul.pt/WS2012/ Araújo, João, Are you ready for the revolution? , Semigroups Day, Universidade de Trás os Montes e Alto Douro, january 26, 2012. (Invited speaker). F.P. da Costa, On self-similarity in coagulation-annihilation systems, Minisymposium on Dynamics of Coagulation-Fragmentation Processes, SIAM Conference on Nonlinear Waves and Coherent Structures, Seattle WA, USA, june 2012. F.P. da Costa, A nonautonomous predator-prey system arising from coagulation theory: is it of any use in biomathematics? Pacific Institute for the Mathematical Sciences—Applied Mathematics Institute Seminar, Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Canada, june 2012. M. J. Oliveira, Glauber dynamics in the continuum: generating functionals approach, International Conference on Particle Systems and PDE’s, Centro de Matemática da Universidade do Minho, Universidade do Minho, december 5–7, 2012. M. J. Oliveira, Glauber dynamics in the continuum: generating functionals approach, II Workshop ”Qualitative Behaviour of Stochastic Systems and Applications”of the ZiF Research Group 2012 ”Stochastic Dynamics: Mathematical Theory and Applications”, Bielefeld, Germany, june 18–22, 2012. M. J. Oliveira, Markov dynamics in the continuum: generating functionals approach, 6th Jagna International Workshop: Mathematical Analysis, Modelling, and Simulation in Interdisciplinary Sciences, Jagna, Philippines, January 4–7, 2012. P. Serranho, Inverse Problems, Medical Imaging and Vision, 2o Encontro Nacional de Bioengenharia, Coimbra, february 2012. P. Serranho, 3D Retinal Vascular Network from OCT data, 6th Workshop on Statistics, Mathematics and Computation and 3rd Portuguese-Polish Workshop on Biometry, Covilhã, july 2012. 6 Guimarães P., Rodrigues P., Bernardes R. and Serranho P., 3D blood vessels segmentation from optical coherence tomography, EVER, Nice, France, october 2012. Rodrigues P., Guimarães P., Bernardes R. and Serranho P., Vascular Network of the Human Macula from OCT , EVER, Nice, France, october 2012. Rodrigues P., Serranho P. and Bernardes R., 3D Nonlinear Complex-Diffusion Filter on GPU , 4th Annual International IEEE-EMBS Conference, august 29 september 01, San Diego, USA, 2012. Guimarães P., Rodrigues P., Serranho P. and Bernardes R., 3D Retinal vascular Network from Optical Coherence Tomography data, 9th annual ICIAR, Aveiro, Portugal, june 2012. Guimarães P., Rodrigues P., Bernardes R. and Serranho P., Vascular Network of the human macula from high-definition OCT, ARVO Annual Meeting, Fort Lauderdale, USA, may 2012. Rodrigues P., Guimarães P., Serranho P. and Bernardes R., 3D Retinal Vascular Network from OCT data, ARVO Annual Meeting, Fort Lauderdale, USA, may 2012. A. Araújo Drawing on the Whole Brain: mathematics and the teaching of art, 4th International Workshop on Mathematical E-Learning - E-MATH 2012, Universidade Aberta, Lisbon, july 5–6, 2012. M.R. Ramos (presenter), E. Carolino, T. Oliveira and M. Bicho. Two-way MANCOVA: An application to public health, ICNAAM 2012: International Conference on Numerical Analysis and Applied Mathematics, Kos, Greece, september 19–25, 2012. B. Fonseca and M.R. Ramos (co-author), Statistical methods in the evaluation of inflammatory parameters in dialysis patients, VI WEMC, Covilhã, july 3–4, 2012. D. Portela and M.R. Ramos (co-author), Structural equation modeling and application to the study of scientific culture in high school students, VI WEMC, Covilhã, july 3–4, 2012. M. Ventura and M.R. Ramos (co-author), Application of Path Analysis to Patient’s Satisfaction with his Doctor , VI WEMC, Covilhã, july 3–4, 2012. M. Fonseca, Inference for the interclass correlation in familial data using small sample asymptotics, ICNAAM’2012, Kos, Greece, september 2012. M. Fonseca, Estimation and hypothesis testing in linear models with doubly exchangeable distributed errors, Joint Meeting of yBIS and jSPE, Caparica, Portugal, july 2012. 7 M. Fonseca, Inference in linear models with doubly exchangeable distributed errors, WEMC2012, Covilhã, Portugal, june 2012. M. Fonseca, Linear models with doubly exchangeable distributed errors, LinStat2012, Bedlewo, Poland, june 2012. T.A. Oliveira, Modelos de Delineamento Experimental com um fator: estudo de ligações e aplicações em várias áreas da Ciência CIIEECA2012 - I Congresso Internacional de Informática e Estatı́stica Experimental e Computacional da Amazônia. ULBRA, Ji-Paraná/RO, Brasil, october 15-20, 2012. T.A. Oliveira, Aplicações e Desafios da Estatı́stica em Ciências da Saúde, CIIEECA2012 - I Congresso Internacional de Informática e Estatı́stica Experimental e Computacional da Amazônia. ULBRA, Ji-Paraná/RO, Brasil, october 15-20, 2012. T.A. Oliveira, A. Oliveira, Estatı́stica, Computação e Ciência: Desafios do Século XXI ( part I e part II). Congresso CIIEECA 2012, 1o Congresso Internacional em Informática, Estatı́stica Experimental e Computacional da Amazónia. Ji-Paraná, Brasil, october 15-20, 2012. (presented by T.A. Oliveira, part I and A. Oliveira, part II) A. Oliveira, T.A. Oliveira, S. Mejza, Joint Regression Analysis and AMMI model applied to oat improvement, ICNAAM 2012, Organized Session 131-BESMART: Biometry and Extremes: Statistical Modelling And R Techniques. Kos Island, Greece, september 19-25, 2012. (presented by A. Oliveira) T.A. Oliveira, A. Oliveira, Ineffectiveness of the FIM in selecting Optimal BIB designs for testing block effects, COMPSTAT 2012, august 27-31, 2012, Limassol - Cyprus. ISBIS session on Information measures and technology. Organized by Christos Kitsos. D. Silva, T.A. Oliveira, Aptidão cardiorespiratória e ı́ndice de massa corporal em alunos do ensino secundário, 6th Workshop on Statistics, Mathematics and Computation and 3rd Portuguese-Polish Workshop on Biometry, Covilhã, july 3-4, 2012. (presented by D. Silva). H. Correia, T.A. Oliveira, Planos em blocos incompletos equilibrados com repetições:Uma aplicação na área da educação. 6th Workshop on Statistics, Mathematics and Computation and 3rd Portuguese-Polish Workshop on Biometry, Covilhã, july 3-4, 2012. (presented by H. Correia). V. Valente, T.A. Oliveira, Some considerations about models with application to data with hierarchical or multilevel structure. 6th Workshop on Statistics, Mathematics and Computation and 3rd Portuguese-Polish Workshop on Biometry, Covilhã, july 3-4, 2012. (presented by V. Valente). R. Mendes, T.A. Oliveira, Quadrados latinos e planos projetivos: Revisão de problemas clássicos, 6th Workshop on Statistics, Mathematics and Computation and 3rd Portuguese-Polish Workshop on Biometry, Covilhã, july 3-4, 2012. 8 (presented by R. Mendes). T.A. Oliveira, BIB Designs: Joining Experimental Design and Sampling. Invited lecture at the Workshop SEDA2012 - Sampling and Experimental Designs with Applications, Universidade de Évora. Évora, june 26, 2012. T.A. Oliveira, Block Designs: Topics on the Construction Methods and Applications, Invited lecture at the Workshop Statistical Inference in Linear Models, Universidade de Évora. Évora, april 27, 2012. T.A. Oliveira, A. Juan, Costa, A., A. Monteiro, C. Noronha, P. Barroso, Colaboration practices between UAb, UOC and UNED. E-MATH 2012, Lisboa, july 5-6, 2012. A. Oliveira, Estatı́stica Experimental e Simulação usando o Software R, Congresso CIIEECA 2012, 1o Congresso Internacional de Informática, Estatı́stica Experimental e Computacional da Amazónia. Ji-Paraná, Brasil, october 15-20, 2012. A. Seijas-Macias, A. Oliveira, Distribución del Producto de Variables Normales: Estudio Comparativo de los Métodos de Aproximación, E-MATH 2012, Lisboa, july 5-6, 2012, (presented by A. Seijas- Macias). M. Conceição Leal, A. Oliveira, Bootstrap: data speaks for itself, 6thWSMC and 3rdPPWB, Covilhã, july 3-4, 2012. (presented by M. Conceição Leal). A. Seijas-Macias, A. Oliveira, An Approach to Distribution of the Product of Two Normal Variables, 6thWSMC and 3rdPPWB, Covilhã, july 3-4, 2012.(presented by A. Seijas-Macias). bf A. Oliveira, Joint Regression analysis and Computational Issues, Workshop: Statistical Inference in Linear Models, Universidade de Évora, april 27, 2012. 3.2 In sessions of the Matemática na AbERTA seminar Albuquerque, L.G.,Análise Não Standard, Sistemas de Estrutura Variável e Controle Equivalente, Seminário ”Matemática na Aberta”, Universidade Aberta, april 20, 2012. 3.3 In other events F.P. da Costa, Self-similar behaviour in coagulation equations: some results and open problems. Dynamical Systems Seminar, Centro de Matemática da Universidade do Porto, Universidade do Porto, october 2012. P. Serranho, On the Mathematics of Medical Imaging. Mathematics Department Seminar, University of Évora, march 2012. M. Edmundo, Grothendieck six operations on o-minimal sheaves. Differential methods in Arithmetic, Geometry and Algebraic analisys Seminar. Diparti9 mento di Matematica. Università degli Studi di Padova, Italy, january 2012. M. Edmundo, seminar on Invariance of o-minimal sheaf cohomology with definably compact supports, Seconda Università degli Studi di Napoli, Italy, april 2012. Albuquerque, L.G., Smooth models of plane structure variable systems, curso dado na Ecole-symposium ”Réductions de Systtèmes Différentiels et Applications”que decorreu de 18 a 22 de março de 21012 na Universidade Djillali Liabès (Sidi Bel Abbès-Argélia). M.R. Ramos, Modelos e Técnicas Estatı́sticas para a Análise do Risco Ecológico. Lecture in the series of seminars organized by CEMAT- Mathematics Department of Universidade do Minho, Guimarães, december 7, 2012. T.A. Oliveira, Noronha, C. and Barroso, P.Bioestatı́stica e Biometria: Novas perspectivas de Interdisciplinaridade na Universidade Aberta, Seminar E-DCET, Universidade Aberta, Campus do Taguspark, june 20, 2012. T.A. Oliveira, Planos em Blocos Incompletos Equilibrados: Um campo fértil do Planeamento de Experiências, Seminar of CEMAT- organized by ”Departamento de Matemática da Universidade do Minho”, Guimarães, june 22, 2012. T.A. Oliveira, Da Análise de Dados ao Conhecimento: Aplicações e Desafios da Estatı́stica em Medicina, Seminar organized by Center of Mathematics and Information Tecnology, Department of Mathematics, University of Açores, Portugal, march 1-2, 2012 A. Oliveira, Análise Conjunta de Regressões Completada com desenvolvimentos em R. Seminar organized by Department of Mathematics, University of Minho, Guimarães, Portugal, may 11, 2012. A. Oliveira, Estatı́stica, E-learning e Recursos Computacionais, Seminar organized by Center of Mathematics and Information Tecnology, Department of Mathematics, University of Açores, Portugal, march 1-2, 2012. A. Oliveira, R, uma linguagem e um ambiente para análise de dados e gráficos, Workshop Hands-on of DCeT/UAb, Universidade Aberta, Portugal, march 8, 2012. 4 Research posters M. R. Ramos, A. P. Garcia, S. Caeiro, P. Costa, T. Repolho, I. Cunha; M. H. Costa, Assessing sediment quality and comparisons in ecological risk framework, VI International Workshop on Spatio-Temporal Modelling (METMA VI) - Universidade do Minho, Guimarães, Azurém, 12-14 september 2012. E. Henning and A. Oliveira, Avaliação do Desempenho dos testes de Normalidade do Pacote Nortest do R, Congresso CLAIO/SBPO 2012, Rio de Janeiro, 10 Brasil, september 24-28, 2012. Araújo, L.B., Oliveira, M., Dias, C.T., A. Oliveira and T.A. Oliveira, Tucker3 Method in Biometrical research: Analysis of experiments with three factors, using R, ICNAAM 2012, Kos Island, Greece, september 19–25 2012. A. Oliveira and T.A. Oliveira, On analyzing finite mixture models, COMPSTAT 2012, Limassol - Cyprus, august 27–31, 2012. Conceição Leal, M. and A. Oliveira, Process Capability Analysis: an application to the orders management, 6thWSMC and 3rdPPWB, Covilhã, july 3–4, 2012. Lopes da Silva, D.J. and A. Oliveira, Análise estatı́stica da evolução da performance motora na exibilidade ao longo do ensino secundário - Comparação Rapazes vs Raparigas, 6thWSMC and 3rdPPWB, Covilhã, july 3–4, 2012. C. Noronha, T.A. Oliveira, Crossover Designs: Revisão e desafios, 6th Workshop on Statistics, Mathematics and Computation and 3rd Portuguese-Polish Workshop on Biometry, Covilhã, july 3-4, 2012. A. Monteiro, T.A. Oliveira, A. Juan, Aplicação de Técnicas Estatı́sticas e Probabilı́sticas no Desenvolvimento e Análise de Algoritmos de Optimização Combinatória na Área da Bioinformática, 6th Workshop on Statistics, Mathematics and Computation and 3rd Portuguese-Polish Workshop on Biometry, Covilhã, july 3-4, 2012. C. Roçadas, T.A. Oliveira, J. T. Mexia, Isomorphism of Marcov Chains: Application to a Customer Population, 6th Workshop on Statistics, Mathematics and Computation and 3rd Portuguese-Polish Workshop on Biometry, Covilhã, july 3-4, 2012. C. Ferreira, T. A. Oliveira, J. Pereira, Modelo de regressão logı́stica multivariada - Uma ferramenta na área da medicina, 6th Workshop on Statistics, Mathematics and Computation and 3rd Portuguese-Polish Workshop on Biometry, Covilhã, july 3-4, 2012. 5 Research visits to other institutions As a fellow of the ZiF Research Group 2012 ”Stochastic Dynamics: Mathematical Theory and Applications”(May 15–September 30, 2012), M. J. Oliveira visited the Center for Interdisciplinary Research ZiF, Bielefeld (Germany), june 3–30, 2012. T. A. Oliveira visit under ERASMUS mission to TEI-ATHENS, Greece, june 11–18, 2012. 11 6 Research meetings and courses attended A. Araújo, 4th International Workshop on Mathematical E-Learning - EMATH 2012 , Universidade Aberta, Lisbon, july 5–6, 2012. M. R. Ramos, T.A. Oliveira and A. Oliveira ICNAAM 2012: International Conference on Numerical Analysis and Applied Mathematics, Kos, (Greece), september 19–25, 2012. M. R. Ramos, 6th International Workshop on Spatio-Temporal Modelling (METMA VI) - Universidade do Minho, Guimarães, Azurém, september 12– 14, 2012. M. R. Ramos, T.A. Oliveira, A. Oliveira 6th Workshop on Statistics, Mathematics and Computation and 3rd Portuguese Polish Workshop on Biometry, organized by Universidade Aberta in Colaboration with Universidade da Beira Interior, Covilhã, july 3–4, 2012. T.A. Oliveira and A. Oliveira CIIEECA2012 - I Congresso Internacional de Informática e Estatı́stica Experimental e Computacional da Amazônia, JiParaná, Brasil, october 15–20, 2012. T.A. Oliveira and A. Oliveira COMPSTAT 2012 , Limassol, Cyprus, august 27–31, 2012. 7 Organization of research courses, meetings and seminars F.P. da Costa together with L. Barreira, P. Girão, P.G. Henriques, J. Matias, J.P. Matos, W. Oliva (chairman), H. Oliveira, and J.T. Pinto, was an organizer ot the 4th IST-IME Meeting: Ordinary and Partial Differential Equations and Related Topics; Honoring the 60th Birthday of Luı́s T. Magalhães and Carlos Rocha, Instituto Superior Técnico, Lisbon, september 2012. Mário Edmundo together with Sandra Alves (U. Porto and LIACC, Portugal), Reinhard Kahle (U. Nova de Lisboa and CENTRIA, Portugal), Imme van den Berg (U. Évora and CIMA, Portugal) was organizer of Days in Logic 2012. Universidade de Évora, Portugal. 06 - 08/02/2012. Mário Edmundo together with Tamara Servi (CMAF, Portugal), Janak Ramakrishnan (CMAF, Portugal) was organizer of the Workshop O-minimal preparation theorems (after van den Dries and Speissegger). Instituto para a Investigação Interdisciplinar da Universidade de Lisboa, Portugal. 28-29/02/2012. Mário Edmundo was organizer of Seminários de Teoria de Modelos do CMAF (Centro de Matemática e Aplicações Fundamentais), Universidade de Lisboa, Portugal. 12 Mário Edmundo together with Fernando Ferreira (U. Lisboa, Portugal) was organizer of Seminários de Lógica Matemática do CMAF (Centro de Matemática e Aplicações Fundamentais), Universidade de Lisboa, Portugal. T.A. Oliveira was chairman and together with Adérito Marcos, A. Oliveira, Célia Nunes, Dário Ferreira, Luis Grilo, Rafael Sasportes, M. R. Ramos and Sandra Ferreira was an organizer of the 6th Workshop on Statistics, Mathematics and Computation and 3rd Portuguese-Polish Workshop on Biometry, july 3–4, 2012, University of Beira Interior, Covilhã. http://www.sites.google.com/site/wsmc2012/ 7.1 Matemática na AbERTA seminars A. Oliveira was the organizer of the monthly seminar Matemática na AbERTA, at Universidade Aberta, Portugal, from january until december 2012. José Gomes Requeijo(FCT/UNL), Controlo Estatı́stico do Processo aplicado a uma grande diversidade de caracterı́sticas, january 13, 2012. Miguel Casquilho, (IST/UTL), Computação cientı́fica na Internet, um campo pouco explorado, february 3, 2012. Célia Nunes (DM/UBI) Como escolher o tamanho da amostra? march 30, 2012. Sandra Ferreira (DM/UBI), Regressão Linear Simples e Regressão Linear Múltipla, march 30, 2012. Dário Ferreira (DM/UBI), Regressão Logı́stica, march 30, 2012. Luı́s Gonzaga (DCeT/UAb), Análise Não Standard e Sistemas de Estrutura Variável, april 20, 2012. Rosemary Bailey (Queen Mary, University of London), Conflicts between optimality criteria for block designs with low replication, april 20, 2012. João Teixeira Pinto (IST/UTL), The dynamics of some predador-prey models, may 17, 2012. Mário J. Edmundo (DCeT/UAb), Invariância da cohomologia o-minimal, june 27, 2012. Stanislaw Mejza (Poznan University of Life Sciences, Poland), Analyzing genotypeby-environment interaction using curvilinear regression, july 6, 2012. Iran Abreu Mendes (UFRN/Brasil), Arte, Matemática e Educação Matemática, october 26, 2012. Marina Andrade (ISCTE/Instituto Universitário de Lisboa), Bayesian Networks in Civil and Criminal Identification and Other Forensic Problems, november 26, 13 2012. 7.2 Other events F.P. da Costa (chairman), A. Oliveira, and T. Oliveira, together with A. Costa, Ma .A. Huertas, and A.A. Juan, were organizers of the 4th International Workshop on Mathematical E-Learning (E-MATH 2012), Universidade Aberta, Lisbon, july 5–6, 2012. M. R. Ramos was member of the Scientific Committee of the 6th WSMC Workshop on Statistics, Mathematics and Computation, organized by Universidade Aberta in Colaboration with Universidade da Beira Interior, Covilhã, july 3–4, 2012. M. R. Ramos organized a session for the 4th WSMC - Workshop on Statistics, Mathematics and Computation, organized by Universidade Aberta in Colaboration with Universidade da Beira Interior, Covilhã, july 3–4, 2012. M. R. Ramos was member of the organizing team of the series of e-DCeT seminars, organized by the Deparment of Sciences and Technology (DCET) of Universidade Aberta. T.A. Oliveira and A. Oliveira was members of scientific committee of 42th Biometrical Colloquium, University of Life Sciences, Poznan, Poland, september 2012. T.A. Oliveira organized a symposium ”Statistical Modelling and Data Analysis: Biometry and Extremes”, ICNAAM2012- 10th International Conference of Numerical Analysis and Applied Mathematics, Kos, Greece, september 19–25, 2012. T.A. Oliveira organized a session in 6th Workshop on Statistics, Mathematics and Computation and 3rd Portuguese-Polish Workshop on Biometry, University of Beira Interior, Covilhã, july 3–4, 2012. A. Oliveira organized a session in 6th Workshop on Statistics, Mathematics and Computation and 3rd Portuguese-Polish Workshop on Biometry, University of Beira Interior, Covilhã, july 3–4, 2012. T.A. Oliveira and A. Oliveira organized the course: ”Introdução à Estatı́stica com aplicações computacionais em R- Revisão de noções teóricas”in Congresso CIIEECA 2012, 1o Congresso Internacional de Informática, Estatı́stica Experimental e Computacional da Amazónia. Ji-Paraná, Brasil, october 15–20, 2012. (4 hours) T.A. Oliveira and A. Oliveira organized the course: ”Técnicas de Inferência Estatı́stica com aplicações computacionais em R- conceitos gerais”in Congresso CIIEECA 2012, 1o Congresso Internacional de Informática, Estatı́stica Experimental e Computacional da Amazónia. Ji-Paraná, Brasil, october 15–20, 2012. 14 (12 hours) T.A. Oliveira and A. Oliveira organized the course: ”Análise de Regressão e correlação com aplicações computacionais em R - metodologias de modelação de dados”in Congresso CIIEECA 2012, 1o Congresso Internacional de Informática, Estatı́stica Experimental e Computacional da Amazónia. Ji-Paraná, Brasil, october 15–20, 2012. (12 hours) 8 8.1 Research grants and funded projects Coordinated by Secção de Matemática members P. Serranho, 3D retinal vascular network from Optical Coherence Tomography data, FCT Project (PTDC/SAU-ENB/111139/2009), QREN, FEDER and Program Compete. 2011-2014. Mário Edmundo, FCT project PTDC/MAT/122844/2010 (Applications and extensions of o-minimality). 01/02/2012 - 31/01/2014. Mário Edmundo, FCT project PTDC/MAT/101740/2008 (O-minimality and definably compact groups). 01/02/2010 - 31/01/2012. 8.2 Participated by Secção de Matemática members M. J. Oliveira, research project funded by FCT, Portugal, under contract PTDC/MAT/100983/2008. M. J. Oliveira, research project co-funded by FCT/MCTES and COMPETE - Programa Operacional Factores de Competitividade, under contract FCT/1560/25/1/2012/S. P. Serranho, Optical Modelling of the Human Retina in Health and Disease: from structure to function, FCT Project (PTDC/SAU-ENB/119132/2010), QREN, FEDER and Program Compete, 2012-2015. P. Serranho, Evaluation of blood-retinal barrier functional alterations by optical coherence tomography, FCT Project (PTDC/SAU-BEB/103151/2008), QREN, FEDER and Program Compete, 2010-2013. P. Serranho, Analysis and Numerical Methods for Direct and Inverse Problems in Mathematical Mechanics, FCT Project (PTDC/MAT/105475/2008), QREN, FEDER and Program Compete, 2010-2012. M. Fonseca, Population and Empire: Demography and the statistical processes in the Portuguese overseas, 1776-1875, PTDC/3697/2012. T.A. Oliveira, Fundação Nacional para a Ciência e Tecnologia, Portugal FCT under the project Pest-OE/MAT/UI0006/2011. 15 A. Oliveira, Fundação Nacional para a Ciência e Tecnologia, Portugal - FCT under the project Pest-OE/MAT/UI0006/2011. 9 9.1 Participation in academic juries PhD theses T.A. Oliveira was member of the jury of Osvaldo Dias Lopes da Silva at Universidade dos Açores, february, 2012. 9.2 MSc theses P. Serranho was member of the jury of Rui Miguel Morgado Venâncio in the context of his masters thesis in Biomedical Engineering ”Retinal Vascular Network from Color Fundus Photography: a SVM Classification Approach”at the University of Coimbra. João Araújo was member of the jury of Ana Sofia Silva, Faculdade de Ciências da Universidade de Lisboa. (Master’s), november 21, 2012. João Araújo was member of the jury of José Duarte, Universidade Aberta, may 28, 2012.(As Master’s supervisor). Mário Edmundo was Presidente of júri of José Manuel da Costa, Mestrado em Estatı́stica, Matemática e Computação, Universidade Aberta, 2012. M. Rosário Ramos was member (thesis advisor) of the jury of Bruno Pinheiro Faria, at Universidade Aberta, january 2012. M. Rosário Ramos was member (thesis co-advisor) of the jury of Cristina Cassis, at Universidade Aberta, may 2012. M. Rosário Ramos was member (thesis advisor) of the jury of Anabela Jorge Costa, at Universidade Aberta, july 2012. M. Rosário Ramos was member (thesis advisor) of the jury of Juan Vicente Bógalo Román, at UNED, Madrid, Spain, october 2012. M. Rosário Ramos was president of the jury of Ricardo Mendes, at Universidade Aberta, november 2012. M. Rosário Ramos was member (thesis advisor) of the jury of Bruno Gabriel Fonseca, at Universidade Aberta, november 2012. M. Rosário Ramos was member (thesis advisor) of the jury of Mónica Ventura, at Universidade Aberta, december 2012. 16 A. Oliveira was member (president of the jury) of Bruno Fernando Pinheiro Faria, at Universidade Aberta, january 2012. A. Oliveira was member (president of the jury) of Helga Carina Batista Martins Correia, at Universidade Aberta, july 2012. A. Oliveira was member of the jury of Diogo Miguel da Fonseca Ferreira, at Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, july 2012. A. Oliveira was member of the jury of João Pedro Mira Salgado, at Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, november 2012. T.A. Oliveira was member of the jury (thesis advisor) of Ricardo Mendes at Universidade Aberta, november 2012. T.A. Oliveira was member of the jury (thesis advisor) of Helga Carina Baptista Martins Correia at Universidade Aberta, july, 2012. T.A. Oliveira was member (president of the jury) of Bruno Gabriel Antunes Fonseca at Universidade Aberta, november 2012. T.A. Oliveira was member (president of the jury) of Anabela da Silva Jorge da Costa at Universidade Aberta, july, 2012. 10 10.1 Research supervision Postdoc João Araújo, supervised Andreas Distler, (Center of Algebra University of Lisbon). Mário Edmundo supervised the research of Luca Prelli (PhD in Mathematics, University of Padova, Italy, and University of Paris 6, France 2006). Marie Curie Intra-European Fellowships (IEF) (FP7-PEOPLE-2010-IEF). CMAF (Centro de Matemática e Aplicações Fundamentais), Universidade de Lisboa, Portugal. 01/12/2012 - . . . . Mário Edmundo supervised the research of Marcello Mamino (PhD in Mathematics, Scuola Normale Superiore di Pisa, Italy, 2010). FCT Post-doctorial Research Fellow. CMAF (Centro de Matemática e Aplicações Fundamentais), Universidade de Lisboa, Portugal. 01/04/2011 - . . . . Co-advisor: Gustavo Granja (Instituto Superior Técnico, Universidade Técnica de Lisboa, Portugal). Mário Edmundo supervised the research of Tamara Servi (PhD in Mathematics, Scuola Normale Superiore di Pisa, Italy, 2007). FCT Post-doctorial Research Fellow. CMAF (Centro de Matemática e Aplicações Fundamentais), 17 Universidade de Lisboa, Portugal. 01/07/2008 - . . . . Mário Edmundo supervised the research of Alexander Usvyatsov (PhD in Mathematics, The Hebrew University in Jerusalem, Israel, 2006). FCT Postdoctorial Research Fellow. CMAF (Centro de Matemática e Aplicações Fundamentais), Universidade de Lisboa, Portugal. 01/07/2007 - . . . . Mário Edmundo supervised the research of Janak Ramakrishnan (PhD in Mathematics, University of California, Berkeley, USA, 2008.) FCT Post-doctorial Research Fellow. CMAF (Centro de Matemática e Aplicações Fundamentais), Universidade de Lisboa, Portugal. 01/10/2010 - 30/09/2012. Mário Edmundo supervised the research of Ayhan Gunaydin (PhD in Mathematics, University of Illinois at Urbana-Champaign, USA, 2008). FCT Postdoctorial Research Fellow. CMAF (Centro de Matemática e Aplicações Fundamentais), Universidade de Lisboa, Portugal. 01/09/2009 - 30/08/2012. 10.2 PhD M. Rosário Ramos is supervisor in collaboration with Hilario Navarro Veguillas of the research activities of Juan Vicente Bógalo Román, UNED-Universidad Nacional de Educación a Distancia, Spain, started in december 2012. T.A. Oliveira is supervisor of the research activities of Vitor Manuel Fernandes Valente in the context of his PhD thesis in Mathematics (Statistical Modeling) at the Universidade Aberta. T.A. Oliveira is supervisor in collaboration with A. Oliveira of the research activities of Ricardo Fernando Ferreira Carneiro Pereira in the context of his PhD thesis in Mathematics (Design of Experiments) at the Universidade Aberta. T.A. Oliveira is supervisor in collaboration with Maria do Rosário Alves de Almeida of the research activities of Luı́s Manuel Santa Mansos in the context of his PhD thesis in Management at the Universidade Aberta. A. Oliveira is supervisor in collaboration with Tomás Prieto, of the research of José António Macias Seijas in the context of his PhD in Mathematics, UNEDUniversidade Nacional de Ensino a Distância, Spain. A. Oliveira is supervisor in collaboration with Maria do Rosário Almeida of the research activities of João Pereira in the context of his PhD thesis in Management at the Universidade Aberta. A. Oliveira is supervisor in collaboration with Maria do Rosário Almeida of the research activities of Pedro Gomes in the context of his PhD thesis in Management at the Universidade Aberta. 18 10.3 MSc F.P. da Costa and R. Ramos supervised the research activities of Denise Candeias at Universidade Aberta. P. Serranho supervised the research activities of Rui Miguel Morgado Venâncio in the context of his masters thesis in Biomedical engineering at the University of Coimbra. P. Serranho is supervising the research activities of Marlon Oliveira in the context of his masters thesis in Statistics, Mathematics and Computation at Universidade Aberta. J. Araújo supervised the research of Fernanda Miranda (MEMeC). Mário Edmundo supervised the research of António Pedro Raimundo (Mestrado em Estatı́stica, Matemática e Computação). Universidade Aberta, Portugal. 01/10/2012 - . . . . Co-advisor: Marcelllo Mamino (CMAF - Universidade de Lisboa). Mário Edmundo supervised the research of Maria do Rosário Inácio (Mestrado em Estatı́stica, Matemática e Computação). Universidade Aberta, Portugal. 01/10/2012 - . . . . Co-advisor: Gilda Maria Saraiva Dias Ferreira (CMAF Universidade de Lisboa). Mário Edmundo supervised the research of Luı́s Manuel da Silva Augusto (Mestrado em Estatı́stica, Matemática e Computação). Universidade Aberta, Portugal. 01/10/2012 - . . . . Co-advisor: Reinhard Kahle (Universidade Nova de Lisboa). M. Rosário Ramos co-supervised the research activities of Estela Gomes, of the Master in Pedagogy of eLearning at Universidade Aberta, ongoing. M. Rosário Ramos supervised the research activities of Juan Vicente Bógalo Román, Master in Matemáticas Avanzadas of UNED- Universidad Nacional de Educación a Distancia - Madrid, Spain, concluded in october 2012. M. Rosário Ramos supervised the research activities of Bruno Pinheiro Faria, of the Master in Statistics, Mathematics and Computation at Universidade Aberta, concluded in january 2012. M. Rosário Ramos was co-supervisor of the research activities of Cristina Cassis, of the Master in Educational Management and Administration at Universidade Aberta, concluded in may 2012. M. Rosário Ramos supervised the research activities of Anabela Jorge Costa, of the Master in Statistics, Mathematics and Computation at Universidade Aberta, concluded in july 2012. 19 M. Rosário Ramos supervised the research activities of Bruno Gabriel Fonseca, of the Master in Statistics, Mathematics and Computation at Universidade Aberta, concluded in november 2012. M. Rosário Ramos supervised the research activities of Mónica Ventura, of the Master in Statistics, Mathematics and Computation at Universidade Aberta, concluded in december 2012. M. Rosário Ramos supervised the research activities of Dina Duarte Cabrita, of the Master in Statistics, Mathematics and Computation at Universidade Aberta, submitted. M. Rosário Ramos supervised the research activities of Domingas Portela, of the Master in Statistics, Mathematics and Computation at Universidade Aberta, submitted. M. Rosário Ramos was co-supervisor of the research activities of Hermı́nia Falcão, of the Master in Educational Management and Administration at Universidade Aberta, submitted. M. Rosário Ramos was co-supervisor of the research activities of Eurico Valente, of the Master in Educational Management and Administration at Universidade Aberta, submitted. M. Rosário Ramos was co-supervisor of the research activities of Luisa Fernandes, of the Master in Educational Management and Administration of Universidade Aberta, submitted. T.A. Oliveira supervised the research activities of Maria Cristina Campos dos Santos Ferreira, of the Master in Statistics, Mathematics and Computation at Universidade Aberta, concluded. T.A. Oliveira supervised the research activities of Manuel Ana Mário Alberto, of the Master in Statistics, Mathematics and Computation at Universidade Aberta, concluded. T.A. Oliveira supervised the research activities of Ricardo Mendes, of the Master in Statistics, Mathematics and Computation at Universidade Aberta, concluded in november 2012. T.A. Oliveira supervised the research activities of Helga Carina Baptista Martins Correia, of the Master in Statistics, Mathematics and Computation at Universidade Aberta, concluded in july 2012. T.A. Oliveira supervised the research activities of António Francisco da Silva Mondim, of the Master in Statistics, Mathematics and Computation at Universidade Aberta. T.A. Oliveira supervised the research activities of Elisabete Santos, of the Master in Statistics, Mathematics and Computation at Universidade Aberta. 20 T.A. Oliveira supervised the research activities of Hélio Rubens Veçoso, of the Master in Statistics, Mathematics and Computation at Universidade Aberta. T.A. Oliveira is supervisor in collaboration with Angel A. Juan, the research activities of Andreia Monteiro, of the Master in Statistics, Mathematics and Computation at Universidade Aberta. T.A. Oliveira is supervisor in collaboration with A. Oliveira, the research activities of Domingos J. Lopes da Silva, of the Master in Statistics, Mathematics and Computation at Universidade Aberta. T.A. Oliveira is supervisor in collaboration with A. Oliveira, the research activities of Maria da Conceição Leal, of the Master in Statistics, Mathematics and Computation at Universidade Aberta. A. Oliveira is supervisor in collaboration with T.A. Oliveira, the research activities of Elisa Henning, of the Master in Statistics, Mathematics and Computation at Universidade Aberta. T.A. Oliveira is supervisor in collaboration with A. Oliveira, the research activities of Odete Omar, of the Master in Statistics, Mathematics and Computation at Universidade Aberta. A. Oliveira is co-supervisor in collaboration with Angel A. Juan, the research activities of Susana Faria, of the Master in Statistics, Mathematics and Computation at Universidade Aberta. 10.4 Initiation to research P. Serranho is supervising the research activities of Pedro Guimarães and Pedro Rodrigues in the context of the research FCT Project PTDC/SAU-ENB/111139/2009. 11 Varia J. Araújo, F. P. da Costa, M. J. Oliveira, and P. Serranho are reviewers for the Mathematical Reviews of the American Mathematical Society. F. P. da Costa is member of the editorial board of the International Journal of Biomathematics and Biostatistics published by Serials Publications, New Delhi. M. J. Edmundo is member of the editorial commission of the Revista das Ciências de Computação published by Universidade Aberta. A. Araújo Scientific revision of the book ”Godel, Escher, Bach - laços eternos”, Douglas Hofstadter, editora Gradiva. 21 22 Auxiliary Professor Auxiliary Professor Auxiliary Professor Auxiliary Professor Auxiliary Professor Auxiliary Professor Auxiliary Professor Auxiliary Professor Auxiliary Professor Invited Aux. Prof. L. G. Albuquerque A. Araújo M. J. Edmundo A. Oliveira M. J. Oliveira T. A. Oliveira R. Ramos R. Sasportes P. Serranho M. Fonseca Doutor in Mathematics PhD Math. Doutor Math. Doutora Stat. & OR Doutora Stat. & OR Doutora Math. Doutor Stat. & Optim. DPhil Math. Doutor Math. Docteur en Math. Agregado Math. Agregado Math. Degree Statistics Numerical Analysis Differential Equations Statistics Statistics Data Analysis Infinite Dimensional Analysis Statistics Mathematical Logic Model Theory Geometry Non-Standard Analysis Differential Equations Independence Algebras Semigroup Theory Mathematical Analysis Differential Equations Fields Centro de Matemática e Aplicações - FCT/UNL IBILI-Instituto Biomédico de Investigação em Luz e Imagem/UC Centro de Análise Matem., Geom. e Sist. Dinâm./UTL Centro de Matem. e Aplic. Fundamentais/UL Centro de Estatı́stica e Aplicações/UL Centro de Matem. e Aplic. Fundamentais/UL Centro de Estatı́stica e Aplicações/UL Centro de Matem. e Aplic. Fundamentais/UL Centro de Matem. e Aplic. Fundamentais/UL Lab. de Math., Informatique et Appl./Univ. Haute-Alsace Centro de Álgebra/UL Centro de Análise Matem., Geom. e Sist. Dinâm./UTL Research Institutiona Universidade de Lisboa, UNL: Universidade Nova de Lisboa, UTL: Universidade Técnica de Lisboa, UC: Universidade de Coimbra Auxiliary Professor J. Araújo a UL: Associate Professor Position F. P. da Costa Name The following table describes the state of the Secção de Matemática as of December 31, 2012, pointing in particular to the scientific fields of endeavor of its members and to the research institutions they are associated with. In case of members belonging to more than one research institution, only the one at which he/she is a full member is refered. The Secção de Matemática at a glance APPENDIX