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Item Acesso Restrito Variations around a general quantum operator2020-02-17 - Cardoso, José Luís dos SantosLet I ⊆ R be an interval and β : I → I a strictly increasing and continuous function with a unique fixed point s0 ∈ I that satisfies (s0 − t)(β(t) − t) ≥ 0 for all t ∈ I, where the equality holds only when t = s0. For appropriate choices of the function β, the quantum operator defined by Hamza et al., Dβ[ f ](t) := f β(t) − f (t) β(t) − t if t = s0 and Dβ[ f ](s0) := f (s0) if t = s0, generalizes both the Jackson q-operator Dq and the Hahn (quantum derivative) operator, Dq,ω. With respect to the inverse of this general quantum difference operator, the β-integral, we study properties of the corresponding Lebesgue spaces L p β ([a, b]).Item Acesso Aberto Bicomplex k-Pell Quaternions2019-03 - Catarino, Paula Maria Machado CruzThe aim of this work is to consider the bicomplex k-Pell quaternions and to present some properties involving this sequence, including the Binet-style formulae and the generating functions. Furthermore, Cassini’s identity, Catalan’s identity, and d’Ocagne’s identity for this type of bicomplex quaternions are given, and a different way to find the nth term of this sequence is stated using the determinant of a tridiagonal matrix whose entries are bicomplex k-Pell quaternions.Item Acesso Aberto Generalized fibonacci and k-Pell matrix sequences2019 - Wani, Arfat Ahmad; Badshah, V. H.; Rathore, G. P. S.; Catarino, Paula Maria Machado CruzIn the present article first and foremost we define generalized Fibonacci sequence and k-Pell sequence. After that by using these sequences we delineate generalized Fibonacci matrix sequence and k-Pell matrix sequence. At the hindmost we obtain results by some matrix technique for both general sequences as well as for matrix sequences.Item Acesso Aberto k-Pell, k-Pell–Lucas and modified k-Pell sedenions2019 - Catarino, PaulaThe aim of this work is to present the k-Pell, the k-Pell–Lucas and the Modified k-Pell sedenions and we give some properties involving these sequences, including the Binet-style formulae and the ordinary generating functions.Item Acesso Aberto On k-Pell hybrid numbers2019-02-13 - Catarino, PaulaThe aim of this work is to introduce a new sequence of numbers called k-Pell hybrid numbers and the presentation of some algebraic properties involving this sequence. In addition, we present the Binet formula, the generating functions and some identities related with different terms of the sequence.Item Acesso Aberto On the bicomplex generalized tribonacci quaternions2019-01-14 - Kızılateş, C.; Catarino, Paula Maria Machado Cruz; Tuğlu, N.In this paper, we introduce the bicomplex generalized tribonacci quaternions. Furthermore, Binet’s formula, generating functions, and the summation formula for this type of quaternion are given. Lastly, as an application, we present the determinant of a special matrix, and we show that the determinant is equal to the nth term of the bicomplex generalized tribonacci quaternions.Item Acesso Aberto Topological Mirror Symmetry for Parabolic Higgs bundles2018-08-30 - Peter Gothen; André OliveiraWe prove the topological mirror symmetry conjecture of Hausel–Thaddeus [19, 20] for the moduli space of strongly parabolic Higgs bundles of rank two and three, with full flags, for any generic weights. Although the main theorem is proved only for rank at most three, most of the results are proved for any prime rank.Item Acesso Restrito On Basic Fourier-Bessel Expansions2018 - Cardoso, José Luís Dos SantosItem Acesso Aberto On the mersenne sequence2016 - Catarino, Paula Maria Machado Cruz; Campos, H.; Vasco, PauloItem Acesso Aberto A influência da escola nova no ensino da língua materna na educação primária em Portugal: análise de um manuscrito inédito de uma professora (década de 30, Século XX) inf2018-04 - Escola, Joaquim José Jacinto; Catarino, Paula Maria Machado Cruz; Aires, Ana Paula FlorêncioItem Acesso Aberto Breaking the habit: engineering students' understanding of mathematical creativity2017 - Paula Catarino; Maria M. Nascimento; Eva Morais; Helena Campos; Paulo VascoItem Acesso Restrito Web information for food operators: is it enough to comply with the food safety and public heath policy?2017 - Díez, J. G.; Moura, D.; Nascimento, M. M.; Saraiva, C.In the recent years, the European Commission (EC) identified food safety as one of its top priorities and established a program of legislative action based on the concept from farm to table’. In 2004, the EC published several regulations called the‘food package’ with the aim to harmonize the food safety in the European Union by enforcing the implementation of food safety programs based on the Hazard Analysis and Critical Control Point (HACCP) principles in all food companies. This report showed that food safety manuals available from internet could help FOs to accomplish a food safety program. However, the information provided by the manuals about HACCP and re-requisites was not enough to ensure compliance with food law.Item Acesso Aberto Estudio de las Actitudes hacia la Estadística en Estudiantes de Psicología2017-05-19 - Comas, C.; Martins, J. A.; Estrada, A.; Nasicmento, Maria M.Statistics has been incorporated in most university courses and among them in the degree of Psychology where the teaching of statistical concepts presents specific learning problems because students enrolled have a very heterogeneous mathematical basis. In this work we focus on the study of those students’ attitudes for their influence on the learning process and we analyze it through the Scale of Attitudes toward Statistics of Estrada, Spanish acronym EAEE (Estrada, 2002). The results indicate moderate or positive attitudes in general with an overall average score slightly higher than the theoretical position of indifference. The course and the previous studies in this area affect their attitude. We emphasize that the overall attitude towards statistics is worsened with the increase of the number years of studies although total lowest scores are presented in students who never studied statistics, results that invite us to reflect on how statistics is been taught through the different educational levels.Item Acesso Aberto Maximal Higgs bundles for adjoint forms via Cayley correspondence2017-02-16 - Garcia-Prada, Oscar; Oliveira, AndréItem Acesso Restrito On the C-determinantal range for special classes of matrices2016 - Guterman, Alexander; Lemos, Rute; Soares, GraçaItem Acesso Restrito The Modified Pell and the Modified k-Pell Quaternions and Octonions2016 - Catarino, PaulaIn this paper we consider the Modified Pell and the Modified k-Pell quaternions and octonions and we present some properties involving these sequences, including the Binet-style formulas and the ordinary generating functions.Item Acesso Restrito Generalized Growth Orders for Polymonogenic Functions and Related Inequalities2016-02 - De Almeida, Regina; Kraußhar, R.S.In this paper we introduce generalized growth orders and growth types in the sense of Shah and Seremeta in the context of polymonogenic functions. They provide a refinement of previously introduced growth orders in the study of the asymptotic growth behavior of functions satisfying higher dimensional Cauchy–Riemann type equations. We prove a number of insight giving inequalities and manage to extend some basic results that were recently proved for the context of the usual first order Cauchy–Riemann system in Clifford analysis.Item Acesso Restrito A few properties of the Third Jackson q-Bessel Function2016-12 - Cardoso, J. L.The Hahn–Exton (third Jackson) q-Bessel function attracts the attention of many researchers in mathematics. We add a few more properties of this important function, such as some identities and upper bounds involving this function, in relation with the coefficients of the corresponding basic Fourier–Bessel expansions.Item Acesso Aberto On the Mersenne sequence2016-12-21 - Catarino, Paula; Campos, Helena; Vasco, PauloFrom Binet’s formula of Mersenne sequence we get some properties for this sequence. Mersenne, Jacobsthal and Jacobsthal-Lucas sequences are considered in order to achieve some relations between them, sums and certain products involving terms of these sequences. We also present some results with matrices involving Mersenne numbers such as the generating matrix, tridiagonal matrices and circulant type matrices.Item Acesso Aberto Quadric bundles applied to non-maximal Higgs bundles2016 - Oliveira, André
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