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    Variations around a general quantum operator
    2020-02-17 - Cardoso, José Luís dos Santos
    Let 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]).
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    Bicomplex k-Pell Quaternions
    2019-03 - Catarino, Paula Maria Machado Cruz
    The 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.
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    Generalized fibonacci and k-Pell matrix sequences
    2019 - Wani, Arfat Ahmad; Badshah, V. H.; Rathore, G. P. S.; Catarino, Paula Maria Machado Cruz
    In 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.
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    k-Pell, k-Pell–Lucas and modified k-Pell sedenions
    2019 - Catarino, Paula
    The 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.
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    On k-Pell hybrid numbers
    2019-02-13 - Catarino, Paula
    The 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.
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    On the bicomplex generalized tribonacci quaternions
    2019-01-14 - 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.
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    Topological Mirror Symmetry for Parabolic Higgs bundles
    2018-08-30 - Peter Gothen; André Oliveira
    We 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.
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    On Basic Fourier-Bessel Expansions
    2018 - Cardoso, José Luís Dos Santos
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    On the mersenne sequence
    2016 - Catarino, Paula Maria Machado Cruz; Campos, H.; Vasco, Paulo
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    Breaking the habit: engineering students' understanding of mathematical creativity
    2017 - Paula Catarino; Maria M. Nascimento; Eva Morais; Helena Campos; Paulo Vasco
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    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.
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    Estudio de las Actitudes hacia la Estadística en Estudiantes de Psicología
    2017-05-19 - 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.
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    Maximal Higgs bundles for adjoint forms via Cayley correspondence
    2017-02-16 - Garcia-Prada, Oscar; Oliveira, André
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    On the C-determinantal range for special classes of matrices
    2016 - Guterman, Alexander; Lemos, Rute; Soares, Graça
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    The Modified Pell and the Modified k-Pell Quaternions and Octonions
    2016 - Catarino, Paula
    In 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.
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    Generalized Growth Orders for Polymonogenic Functions and Related Inequalities
    2016-02 - 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.
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    A few properties of the Third Jackson q-Bessel Function
    2016-12 - 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.
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    On the Mersenne sequence
    2016-12-21 - Catarino, Paula; Campos, Helena; Vasco, Paulo
    From 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.
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    Quadric bundles applied to non-maximal Higgs bundles
    2016 - Oliveira, André