Monomiality Principle and Eigenfunctions of Differential Operators

We apply the so-calledmonomiality principlein order to construct eigenfunctions for a wide set of ordinary differential operators, relevant to special functions and polynomials, including Bessel functions and generalized Gould-Hopper polynomials

Vietoris' number sequence and its generalizations through hypercomplex function theory

The so-called Vietoris' number sequence is a sequence of rational numbers that appeared for the first time in a celebrated theorem by Vietoris (1958) about the positivity of certain trigonometric sums with important applications in harmonic analysis (Askey/Steinig, 1974) and in the theory of stable holomorphic functions (Ruscheweyh/ Salinas, 2004). In the context of hypercomplex function theory those numbers appear as coefficients of special homogeneous polynomials in R^3 whose generalization to an arbitrary dimension n lead to a n-parameter generalized Vietoris' number sequence that characterizes hypercomplex Appell polynomials in R^n.The work of the second author was supported by Portuguese funds through the CMAT - Centre of Mathematics and FCT within the Project UID/MAT/00013/2013. The work of the other authors was supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (“FCT-Fundação para a Ciência e Tecnologia”), within project PEst-OE/MAT/UI4106/2013

Combinatorial Identities Associated with a Multidimensional Polynomial Sequence

In this paper we combine the knowledge of different structures of a special Appell multidimensional polynomial sequence with the problem of establishing combinatorial identities. The elements of this special polynomial sequence have values in a Clifford algebra, are homogeneous hypercomplex differentiable functions of different degrees and their coefficients properties can be used to stress interesting matrix and combinatorial relations

Melhoria do serviço, experiência de cliente e satisfação : caso de uma empresa de energia elétrica

Mestrado em Gestão e Estratégia IndustrialA liberalização do mercado de comercialização da energia elétrica trouxe concorrentes e a necessidade das empresas se diferenciarem pelo serviço. O desafio atual consiste na otimização da relação entre a empresa e o cliente, para que o segundo obtenha o máximo nível de experiência e satisfação. O principal objetivo do presente estudo foi compreender como é que a experiência e satisfação de cliente são afetadas com uma melhoria de serviço. Neste caso, a melhoria do serviço consistiu na introdução de um alerta adicional a cliente, de forma a prevenir que o mesmo não tivesse o seu serviço interrompido. Este estudo teve por base dois momentos de contacto distintos. O primeiro foi um alerta a cliente que consistiu num contacto proactivo da empresa a prevenir o cliente que estava em situação iminente de corte. O segundo contacto consistiu num questionário a cliente para aferir a satisfação do mesmo, relativamente ao alerta anteriormente recebido. Relativamente à experiência de cliente, concluiu-se que esta foi positivamente afetada com a introdução deste novo contacto. A nível da satisfação, as principais conclusões obtidas foram que os clientes, não só acharam o alerta muito útil, como também se mostraram muito interessados em revê-lo no futuro. Como estudo futuro, sugere-se uma avaliação da experiência de cliente mais abrangente, com recurso a uma escala adequada.The liberalization of the electricity market brought competition and the need for companies to differentiate the service. Therefore, it is crucial to optimize relationships with clients in order to maximize their experience and their satisfaction. Henceforth, the main aim of the present study was to gain new insights about the impact that the service improvement has on the client's experience and satisfaction. In this case, the service improvement consisted on the institution of an additional alert which goal is to prevent the client of having the service outage. The study in question is composed by two distinct moments of contact with the client. Firstly, the client was proactively alerted that he was in the imminent situation of having the power cut by the company. After such situation was surpassed, a questionnaire was sent in order to assess the client's satisfaction with the previous alert. Regarding the customer experience, we concluded that it was positively affected by the introduction of this new contact. Concerning the satisfaction level, several clients not only affirmed the alert was very useful but were also very interested in experiencing it again hereafter. As future study, it is suggested to evaluate the client's experience with greater depth and using a more adequate measurement scale.N/

Enriching traditional higher STEM education with online teaching and learning practices: students’ perspective

In this paper, we aim to identify online teaching and learning practices that would be beneficial for blended and traditional on-campus education within STEM (Science, Technology, Engineering, and Mathematics) courses. Our university, as well as the majority of higher education institutions worldwide, has had few to no experience in delivering full online courses before 2020. The teaching process was, however, severely affected and modified by the COVID-19 pandemic, forcing an abrupt and unprepared shift towards online education. In this work, we look at the pandemic as causing a very favorable side effect that forced the university to study, test, apply, and evaluate the benefits and drawbacks of online education and assessment methods. The study is a result of joint efforts from different departments at the University of Aveiro, Portugal, connected to STEM undergraduate and graduate programs and is based on a questionnaire targeted towards students. In total, 167 valid STEM students’ answers have been collected and analyzed, both quantitatively and qualitatively. As the result, the best teaching and learning practices are identified and the main difficulties and obstacles experienced by students are detected. Some of the problems are common to many higher education institutions, such as the lack of teacher preparation in delivering quality online synchronous and asynchronous classes, technical limitations (network bandwidth/weak equipment), ineffective communication during synchronous classes, gaps in student skills, and low activity of some students and even teachers. We believe that the presented results would allow for improving future on-campus, distance, and blended learning courses, particularly through avoiding less effective teaching and assessment methods and favoring those techniques that students consider more efficient. This ultimately would lead to a more rewarding teaching/learning experience.publishe

Intrinsic properties of a non-symmetric number triangle

Several authors are currently working on generalized Appell polynomials and their applications in the framework of hypercomplex function theory in Rn+1. A few years ago, two of the authors of this paper introduced a prototype of these generalized Appell polynomials, which heavily draws on a one-parameter family of non-symmetric number triangles T (n), n ≥ 2. In this paper, we prove several new and interesting properties of finite and infinite sums constructed from entries of T (n), similar to the ordinary Pascal triangle, which is not a part of that family. In particular, we obtain a recurrence relation for a family of finite sums, analogous to the ordinary Fibonacci sequence, and derive its corresponding generating function.UA - Universidade de Aveiro(UIDB/00013/2020)This work was supported by Portuguese funds through the CMAT - Research Centre of Mathematics of University of Minho - and through the CIDMA - Center of Research and De velopment in Mathematics and Applications (University of Aveiro) and the Portuguese Foun dation for Science and Technology (“FCT - Funda¸c˜ao para a Ciˆencia e Tecnologia”), within projects UIDB/00013/2020, UIDP/00013/2020, UIDB/04106/2020 and UIDP/04106/2020

Non-symmetric number triangles arising from hypercomplex function theory in R^(n+1)

The paper is focused on intrinsic properties of a one-parameter family of non-symmetric number triangles T(n),n≥2, which arises in the construction of hyperholomorphic Appell polynomials.UA -Universidade de Aveiro(UIDB/00013/2020

Remarks on the Vietoris sequence and corresponding convolution formulas

In this paper we consider the so-called Vietoris sequence, a sequence of rational numbers of the form ck=12k(k⌊k2⌋), k= 0, 1, ⋯. This sequence plays an important role in many applications and has received a lot of attention over the years. In this work we present the main properties of the Vietoris sequence, having in mind its role in the context of hypercomplex function theory. Properties and patterns of the convolution triangles associated with (ck)k are also presented.Research at CMAT was partially financed by Portuguese funds through FCT - Funda¸c˜ao para a Ciˆencia e a Tecnologia, within the Projects UIDB/00013/2020 and UIDP/00013/2020. Research at CIDMA has been financed by FCT, within the Projects UIDB/04106/2020 and UIDP/04106/2020

Non-symmetric Number Triangles Arising from Hypercomplex Function Theory in IR^{n+1}

The paper is focused on intrinsic properties of a one parameter family of non-symmetric number triangles T(n), n ≥ 2, which arises in the construction of hyperholomorphic Appell polynomials

Hypercomplex polynomials, vietoris’ rational numbers and a related integer numbers sequence

This paper aims to give new insights into homogeneous hypercomplex Appell polynomials through the study of some interesting arithmetical properties of their coefficients. Here Appell polynomials are introduced as constituting a hypercomplex generalized geometric series whose fundamental role sometimes seems to have been neglected. Surprisingly, in the simplest non-commutative case their rational coefficient sequence reduces to a coefficient sequence S used in a celebrated theorem on positive trigonometric sums by Vietoris (Sitzungsber Österr Akad Wiss 167:125–135, 1958). For S a generating function is obtained which allows to derive an interesting relation to a result deduced by Askey and Steinig (Trans AMS 187(1):295–307, 1974) about some trigonometric series. The further study of S is concerned with a sequence of integers leading to its irreducible representation and its relation to central binomial coefficients.The work of the first and third authors was supported by Portuguese funds through the CIDMA - Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (“FCT-Fundação para a Ciência e Tecnologia”), within project PEstOE/MAT/UI4106/2013. The work of the second author was supported by Portuguese funds through the CMAT - Centre of Mathematics and FCT within the Project UID/MAT/00013/2013.info:eu-repo/semantics/publishedVersio