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Coffee break

• Paula Catarino [ALC], Universidade de Trás-os-Montes e Alto Douro
  Bicomplex k-Pell Quaternions
  We consider the sequence of bicomplex k-Pell quaternions and 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.
• Maria do Rosário Fernandes [ANAP], Universidade do Minho
  Weakly singular Fredholm integral equations of the second kind
  Integral equations appear when modeling problems in science and engineering. In particular, nonlinear integral equations arise in fuid mechanics, solid state physics, biological models, kinetics in chemistry, etc. Moreover, many initial and boundary value problems can be turned into integral equations. One type of particularly interesting equation is the weakly Fredholm integral equation of the second kind.
  In this talk, I will extend the singularity subtraction technique for computing an approximate solution of a linear weakly singular Fredholm integral equation of the second kind to a nonlinear integral equation of the same kind. I will show how the singularity subtraction can be used to get a numerical solution. The convergence of the sequence of approximate solutions to the exact one will be proved. A numerical example will be provided to illustrate some practical aspects of eefective computations.
  This is joint work with M. Ahues (Université de Lyon, France), F. D. d'Almeida (Universidade do Porto, Portugal) and P. B. Vasconcelos (Universidade do Porto, Portugal).

Lunch

• Emilia Athayde [SAPOR], Universidade do Minho
  Inference issues on the fatigue life distribution and its generalizations
  An old family of distributions, (re)introduced in the late sixties as a model for the lifetime distribution of materials exposed to periodic stress loading, has been generalized in several directions in the past twenty years. We discuss the potential of one such generalization and explore some research ideas under progress.
• Altino Santos [GTA], Universidade de Trás-os-Montes e Alto Douro
  Spherical isometric foldings: sets of singularities
  Folding tilings (f-tilings, for short) are intrinsically related to the theory of isometric foldings of Riemannian manifolds (introduced by S. A. Robertson). A spherical f-tiling, as the set of singularities of a spherical isometric folding is an edge-to-edge decomposition of the sphere by geodesic polygons, such that all vertices are of even valency and the sums of alternating angles around each vertex are pi. We present examples of dihedral f-tilings for some pairs of spherical prototiles. In addition, some relations between deformation of isometric foldings and deformation of spherical f-tilings are analyzed.
• José Luís Cardoso [ANAP], Universidade de Trás-os-Montes e Alto Douro
  Developments over basic Fourier expansions
  We will present a brief account on Fourier expansions with special emphasis over the Basic Fourier expansions, both when the $q$-analogues of the classical trigonometric functions or the $q$-analogues of the Bessel function are used. With this respect, we will address the fundamental and related questions such as Orthogonality, Completeness, Convergence, as well as the asymptotic behavior of the corresponding Fourier coefficients (a $q$-analogue of the Riemann-Lebesgue theorem)

• Ahmed Elshafei, UC|UP Joint PhD Program in Mathematics
  Geodesic completeness of pseudo-Riemannian Lie groups
  We study geodesic completeness of pseudo-Riemannian Lie groups by applying techniques from complex dynamics. We recall that, for a semi-simple Lie group, a geodesic corresponds to an integral curve in the Lie algebra of the Euler-Arnold vector field. These vector fields are algebraic and homogeneous of degree 2 thus amenable to be studied by techniques from complex dynamical systems. We present a complete study for SL(2,R) and give some indication on the further application of the techniques to SL(2,C) and SL(3,R).
• Benjamin Anwasia, PhD Program in Applied Mathematics MAP-PDMA
  On the derivation of the reactive Maxwell-Stefan equations
  The Maxwell-Stefan diffusion equations were derived by Maxwell and Stefan to describe diffusion in non-reactive multispecies mixtures. Starting from the simple reacting sphere kinetic equations, we will present an extension of the Maxwell-Stefan diffusion equations to reactive multispecies mixtures. This extension contains additional terms resulting from chemical interactions and will be referred to as the reactive Maxwell-Stefan equations.
• Weronika Wojtak, PhD Program in Applied Mathematics MAP-PDMA
  Numerical continuation of solutions of neural field equations with oscillatory coupling functions
  Neural field models, formalized by integro-differential equations, describe the large-scale spatio-temporal dynamics of neuronal populations. They have been used in the past as a framework for modeling a wide range of brain functions, including multi-item working memory. Neural field equations support spatially localized regions of high activity (or bumps) that are initially triggered by brief sensory inputs and subsequently become self-sustained by recurrent interactions within the neural population. We apply a special class of oscillatory coupling functions and use numerical continuation to find and follow solutions of neural field equations as the parameter controlling the distance between consecutive zeros of the coupling function is varied. We investigate how changes in this parameter affect the shape of bump solutions and therefore the maximum number of bumps that may exist in a given finite interval.
  This is joint work with Flora Ferreira, Estela Bicho and Wolfram Erlhagen.

Coffee-Break + Posters Discussion

• João Matias [SAPOR], Universidade de Trás-os-Montes e Alto Douro
  Observe, Model and Optimize
  We intend to predict the wine industry performance of two of the most relevant Portuguese regions: Douro and Alentejo. The available data from the Portuguese Farm Accountancy Data Network (PTFADN) compiles social, economic and environmental parameters from 2001 until 2012 allowed us to perform function fitting in order to attain information about the variable?s behavior. That information was blended into our selected methodology, an Agent-Based Model (ABM) that emulates the current Douro and Alentejo wine-production reality and simulates their further development.
• Pedro Patrício [ALC], Universidade do Minho
  On the group inverse of a matrix
  In this talk, I will present some properties of group invertible matrices, as the characterization of some types of matrices for which the group inverse exists.