# Talks

Ana P. Lemos-Paião, CIDMA, Department of Mathematics, University of Aveiro

A parametric optimal control problem applied to agricultural irrigation

In this work a parametric optimal control problem applied to agricultural irrigation is proposed. It consists in minimizing the square of the amount of water used to irrigate, while ensuring the health grow of the crop. A crucial parameter of this problem is the percentage of water loss due to deep percolation, $\beta$, a parameter hard to estimate and subject to perturbations. So, the problem under study is a parametric state constrained optimal control one with a $L^2$ cost. The main goal of this work is to study how perturbations of $\beta$ affect the optimal solution and the optimal cost of the considered problem, with the help of the parameter sensitivity analysis. Some numerical simulations are carried out to illustrate the analysis of the proposed problem.

Artur M. C. Brito da Cruz, Escola Superior de Tecnologia de Setúbal, Instituto Politécnico de Setúbal; CIDMA, Universidade de Aveiro

Compartment models in epidemiology and optimal control

Compartment models is a technique where the population is divided in labels such as S-susceptible, I-infected and R-recovered. Studying the rate of change of these compartments, one can model the dynamics of human and/or animal populations. Furthermore, if one adds one or several controls, for example using insect repellent to prevent mosquito bites, we can predict or give an optimal scenario where an objective function is optimized, for example, the number of infected persons.

Carlos Vela Cabello, CIDMA, Department of Mathematics, University of Aveiro

Decoding Convolutional Codes with generator matrix

In communications earasures are the most usual kind of errors that channel produces. Convolutional codes has been proved to be a competitive alternative to block codes in the last decades. Usually, when decoding erasures by using convolutional codes the parity check matrix is used, but not all convolutional codes have a parity check matrix. We propose a decoding algorithm by using generator matrix, as an alternative. Furthermore, we give a construction for optimal codes and compare the performance of decoding with the parity-check matrix (when this comparison is possible).

Delfim F. M. Torres, CIDMA, Department of Mathematics, University of Aveiro

Exact Solution for a Discrete-Time SIR model

We derive a nonstandard finite difference scheme for Bailey's Susceptible-Infected-Removed continuous model. We prove that our discretized system is dynamically consistent with its continuous counterpart and we derive its exact solution. We end with the analysis of the long-term behavior of susceptible, infected and removed individuals, illustrating our results with numerical simulations. This is a joint work with Márcia Lemos-Silva and Sandra Vaz.

Hanaa Zitane, CIDMA, Department of Mathematics, University of Aveiro

Finite time stability of generalized proportional fractional equations with time delays

We investigate the notion of finite time stability for generalized proportional fractional systems (GPFSs) with time delays and variable coefficients. Then, we examine some sufficient conditions that allow concluding the GPFSs stability in a finite time interval, which include the nonhomogeneous and the homogeneous delayed cases. We present two different approaches. The first one is based on Holder's and Jensen's inequalities, while the second one concerns the Bellman--Gronwall method using the recently introduced proportional generalized Gronwall inequality. Finally, we provide two numerical examples to show the practicability of the developed procedures.

Helena Sofia Rodrigues, IPVC and CIDMA

Optimization in the sustainable cities context

Sustainable Development Goal 11, from Agenda 2030 promoted by United Nations, is about making cities and human settlements inclusive, safe, resilient and sustainable. Nowadays optimization significantly contributes to the success of companies. In this talk, the aim to present optimization problems, to contribute to non-profit organizations and societal challenges. Two examples are given how it is possible use simple optimization features to help in the achievement of a better community. The first example is the study of a new location of an electric vehicle charging point in a city. The methodology used was the centre of gravity method, using as data the number of charging stations available in the city. The aim was to find a central location that minimises the distance between the new charging station and the existing ones. The second one, it was a linear programming approach, developed in order to determine the best shifts of the working week, minimizing the number of firefighters necessary to satisfy the already registered and emergency tasks in a fire station.

Hugo Alonso, Universidade Lusófona, CIDMA, Department of Mathematics, University of Aveiro

Predicting how much a consumer is willing to pay for a bottle of wine

The wine industry has becoming increasingly important worldwide and is one of the most significant industries in Portugal. In this talk, I will present some results regarding the problem of predicting how much a Portuguese consumer is willing to pay for a bottle of wine to drink at home, in a regular occasion.

Natália Martins, CIDMA, Department of Mathematics, University of Aveiro

Tempered fractional differential equations involving arbitrary smooth kernels

In this talk, we extend the notion of the tempered fractional derivatives in the Riemann-Liouville and Caputo senses to a new class of fractional operators. In this context, we investigate the existence and uniqueness of solutions for a class of fractional differential equations under certain initial conditions. This is a joint work with Ricardo Almeida and J. Vanterler da C. Sousa.

Raquel Pinto, CIDMA, Department of Mathematics, University of Aveiro

Realizations of Periodic Convolutional Codes

In this talk we consider periodic convolutional codes of period 2 and study their representation by means of linear systems. Namely, we present two different but equivalent types of state-space realizations for these codes.

Ricardo Almeida, CIDMA, Department of Mathematics, University of Aveiro

Some optimization conditions for the fractional calculus of variations

In this work we combine two ideas: fractional derivatives of variable order and fractional derivatives depending on another function. With such operators, we develop a variational problem theory by presenting necessary conditions of optimization. The fundamental problem will be addressed, proving an Euler-Lagrange equation, and then other versions will be considered such as the isoperimetric problem or the Herglotz problem. An integration by parts formula is also proven. To end, we provide a numerical tool to solve fractional problems dealing with such fractional derivatives. The main idea is to approach the fractional derivative by an expansion formula in terms of integer order derivatives and then rewrite the fractional problema as a classical one.

Ricardo Pereira, CIDMA, Department of Mathematics, University of Aveiro

Feasible-reachability of 1D and 2D state-space systems

In this talk we define the property of feasible reachability both for 1D state-space systems evolving over Z and for 2D state-space systems evolving over Z^2 described by Fornasini-Marchesini models. Feasible reachability consists in the reachability of the feasible subspaces associated with those systems.

Rita Simões, CIDMA, Department of Mathematics, University of Aveiro

ISO representations of noncatastrophic and delay-free 2D convolutional codes

In this work we consider two-dimensional (2D) convolutional codes. In particular, we study the input-state-output (ISO) representations of noncatastrophic and delay-free 2D convolutional code, by considering the Fornasini-Marchesini state-space model. Moreover, we present an algorithm that constructs an ISO representation of a noncatastrophic and delay-free 2D convolutional code.

Sandra Pinelas, Academia Militar, Portugal

Existence and stabilization results for impulsive differential equations of second order including multiple delays

This work addresses the existence of solutions and exponentially stabilization with regard to impulsive multiple delay differential equations (ImMDDEs) of second order including multiple delays. In the article, two new qualitative results including sufficient conditions regarding these concepts are provided.

Zita Abreu, CIDMA, Department of Mathematics, University of Aveiro

A new construction of binary convolutional codes with optimal column distances

In the past little progress has been made in finding good binary convolutional codes and so far optimal binary convolutional codes have only been presented for some special values of the code rate. In this talk, a construction of binary convolutional codes with optimal column distances for more general code rates will be presented and for that we focus on maximizing especially the small column distances that are most important for low delay decoding. In order to achieve such optimal constructions, we use a class of punctured simplex (block) codes, which we call partial simplex codes.