Book Chapters
17.
Oscillatory behaviour on a nonautonomous hybrid SIRModel
Rocha, Eugénio
Molecular Logic and Computational Synthetic Biology. MLCSB 2018. Lecture Notes in Computer Science
Springer
We study the impact of some abstract agent intervention on the disease spread modelled by a SIRmodel with linear growth infectivity. The intervention is meant to decrease the infectivity, which are activated by a threshold on the number of infected individuals. The coupled model is represented as a nonlinear nonautonomous hybrid system. Stability and reduction results are obtained using the notions of nonautonomous attractors, Bohl exponents, and dichotomy spectrum. Numerical examples are given where the number of infected individuals can oscillate around a equilibrium point or be a succession of bump functions, which are validated with a tool based on the notion of deltacomplete decision procedures for solving satisfiability modulo theories problems over the real numbers and bounded deltareachability. These findings seem to show that hybrid SIRmodels are more flexible than standard models and generate a vast set of solution profiles. It also raises questions regarding the possibility of the agent intervention been somehow responsible for the shape and intensity of future outbreaks.
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16.
Does teacher's education affect student performance?
Murillo, K. and Rocha, E. and Freitas, A. and Pardo, C.
EDULEARN19 Proceedings
IATED
Increasingly questions arise regarding the educational process and which factors are of key importance to increase the quality of education. According to Clare Kosnik, "Quality in education depends directly on the quality of teachers and the quality of the curriculum." However, to what extent is this true? It is known that, many agents intervene in the educational process as the quality of curriculum, students, teachers, teaching methods, governance, financing, evaluation and linkage with other apex institutions. In this sense, it is interesting to analyse how the quality of education should be evaluated, as a direct consequence of teacher training, the results of students, the conditions and strategies in which teaching is developed, or an evaluation in which all do these aspects interfere.
This work aims to address one of the above questions, which causes major debates among educational analysts: to what extent does education level and research outcomes of teachers interfere with the skills and performance of higher education students? Specifically, we examined 165 higher education institutions (HEI), public and private, in Colombia in the year of 2016. The Colombian HEI system is composed of technical institutes focused on vocational education, university institutions focused on technological education, and universities focused on undergraduate degrees (e.g. bachelor or diploma) and postgraduate degrees (e.g. specialisation, master or doctorate). The data include twelve variables: six variables related with teacher education level and research outcomes (i.e. teachers with specialisation, teachers with masters, teachers with doctorate, teachers without postgraduate, number of citations and intellectual production score) and six variables related with student performance (i.e. quantitative reasoning, critical reading, written communication, employability and postgraduate ingresses).
A canonical correlation analysis (CCA) was performed to establish correlations between the formation of the teachers of higher education and the results of their students, aiming to identify the main association degree and the impact of them. The methodology involves CCA with filtering to deal with outliers and the application of BoxCox transformations to transform nonnormal variables in near normal ones. Statistical tests based on Wilks Lambda, HotellingLawley Trace, PillaiBartlett Trace and Roy's Largest Root were applied in order to verify the significance of the results. These approaches identify the degree and the most relevant relationships between variables of teacher training/research and variables of student performance in higher education.
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Articles
15.
Efficiency analysis of optimal inspection management for reinforced concrete structures under carbonationinduced corrosion risk
Benítez, Pablo and Rocha, Eugénio and Talukdar, Sudip and Varum, Humberto and Rodrigues, Fernanda
Construction and Building Materials
Elsevier
Reinforced concrete is one of the most predominant materials used in constructed structures and infrastructures throughout the world. For this reason, the maintenance management of these structures is a frequent subject of study in material science and civil engineering. Thereby, several studies conclude that corrosion of reinforcement in concrete structures may become an expensive degradation mechanism whether a suitable intervention strategy throughout its service life is not applied. In this context, maintenance management is crucial to slow down the degradation process and to extend the lifespan, which can comprise two stages: inspection planning, and an assessment of repair probabilities according to the inspection results. The paper herein presented focuses on a decisionmaking model for the optimal inspection planning for concrete structures subject to carbonationinduced corrosion. A structured approach to optimise inspection times considering the uncertainty inherent in the corrosioninduced degradation and a tradeoff between inspection costs and the structure serviceability is performed.The main objective of this work is to elaborate an efficiency analysis for a set of optimal inspection strategies that is conducted through two approaches: the Stochastic Frontier Analysis (SFA) and the Multidirection Enveloping Analysis (MEA). This analysis provides an appraisal that reduces the number of inspection techniques necessary and the time gap between inspections to provide not only an optimal solution but the most efficient as well. Therefore, the outcome of this paper provides an inspection strategy that establishes the optimal solution for both the inspection times and the most suitable inspection technique to be applied considering the efficiency of the solution.
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14.
The orthogonality of the fractional circle polynomials and its application in modeling of ophthalmic surfaces
Rodrigues, Maria Manuela Fernandes and Vieira, Nelson Felipe
Journal of Physics: Conference Series
IOP Publishing
In this paper we establish some new fractional differential properties for a class of fractional circle polynomials. We apply the Zernike polynomials and a new class of fractional circle polynomials in modeling ophthalmic surfaces in visual optics and we compare the obtained results. The total RMS error is presented when addressing capability of these functions in fitting with surfaces, and it is showed that the new fractional circle polynomials can be used as an alternative to the Zernike Polynomials to represent the complete anterior corneal surface.
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13.
Modeling ophthalmic surfaces using Zernike, Bessel and Chebyshev type functions
Rodrigues, Maria Manuela Fernandes and Rosa, Andreia and Vieira, Nelson Felipe Loureiro and Murta, Joaquim
Journal of Physics: Conference Series
IOP Publishing
The visual system of the human eye is a part of the central nervous system by which the human body sees and interprets the information provided by the visible light in order to build a representation of the world around. During the propagations of the light through the eye, the retinal image can be deteriorated by diseases and disorders. For retinal images, the most important sources of images quality degradation are diffraction and optical aberrations. In order to measure and correct aberrations, there is a number of surfaces related to the anatomy and physiology of the eye. It is important to measure and mathematically model these surfaces to study their properties.
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12.
New sampling theorem and multiplicative filtering in the FRFT domain
Anh, P. K. and Castro, Luís P. and Thao, P. T. and Tuan, N. M.
Signal, Image and Video Processing
Springer Verlag
Having in consideration a fractional convolution associated with the fractional Fourier transform (FRFT), we propose a novel reconstruction formula for bandlimited signals in the FRFT domain without using the classical Shannon theorem. This may be considered the main contribution of this work, and numerical experiments are implemented to demonstrate the effectiveness of the proposed sampling theorem. As a second goal, we also look for the designing of multiplicative filters. Indeed, we also convert the multiplicative filtering in FRFT domain to the time domain, which can be realized by Fast Fourier transform. Two concrete examples are included where the use of the present results is illustrated.
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11.
New convolutions weighted by Hermite functions and their applications
Castro, L. P. and Guerra, R. C. and Tuan, N. M.
Mathematical Inequalities and Applications
Element D.O.O.
We introduce eight new convolutions weighted by multidimensional Hermite functions, prove two Youngtype inequalities, and exhibit their applications in different subjects. One application consists in the study of the solvability of a very general class of integral equations whose kernel depends on four different functions. Necessary and sufficient conditions for the unique solvability of such integral equations are here obtained.
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10.
Ground state, bound states and bifurcation properties for a SchrodingerPoisson system with critical exponent
Chen, Jianqing and Huang, Lirong and Rocha, Eugénio
Electronic Journal of Differential Equations
Texas State University, Department of Mathematics
This article concerns the existence of ground state and bound states, and the study of their bifurcation properties for the SchrödingerPoisson system(Forumala Presented). Under suitable assumptions on the coefficient h(x), we prove that the ground state must bifurcate from zero, and that another bound state bifurcates from a solution, when µ = µ 1 is the first eigenvalue of −∆u + u = µh(x)u in H 1 (R 3 )
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9.
Three nontrivial solutions for nonlocal anisotropic inclusions under nonresonance
Frassu, Silvia and Rocha, Eugénio and Staicu, Vasile
Electronic Journal of Differential Equations
Texas State University, Department of Mathematics
In this article, we study a pseudodifferential inclusion driven by a nonlocal anisotropic operator and a Clarke generalized subdifferential of a nonsmooth potential, which satisfies nonresonance conditions both at the origin and at infinity. We prove the existence of three nontrivial solutions: one positive, one negative and one of unknown sign, using variational methods based on nosmooth critical point theory, more precisely applying the second deformation theorem and spectral theory. Here, a nosmooth anisotropic version of the Holder versus Sobolev minimizers relation play an important role.
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8.
On Wiener’s Tauberian theorems and convolution for oscillatory integral operators
Castro, Luís Pinheiro de and Guerra, Rita Correia and Tuan, Nguyen Minh
Turkish Journal of Mathematics
TÜBİTAK  The Scientific and Technological Research Council of Turkey
The main aim of this work is to obtain Paley–Wiener and Wiener’s Tauberian results associated with an oscillatory integral operator, which depends on cosine and sine kernels, as well as to introduce a consequent new convolution. Additionally, a new Youngtype inequality for the obtained convolution is proven, and a new Wienertype algebra is also associated with this convolution.
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7.
Construction sectors efficiency analysis on seven European countries
Murillo, Kelly Patricia and Rocha, Eugénio and Rodrigues, Maria Fernanda
Engineering, Construction and Architectural Management
Emerald
Purpose – The purpose of this paper is to measure and compare the technical efficiency of construction companies in seven European countries: Austria, Germany, Hungary, Italy, Poland, Portugal and Spain, during the 2008–2015 period. The analysis involves nine sectors grouped into three divisions: construction of buildings (F41), civil engineering (F42) and specialized construction activities (F43), by NACE classification.
Design/methodology/approach – Multidirectional efficiency analysis was adopted to investigate the levels of efficiencies, the differences in those levels and the possible causes of such differences by further defining two new indices.
Findings – It showed that F43 is the most efficient division during the study period, followed by F42 and F41. The sectors/countries with less efficiency are: construction of roads and railways/Poland, construction of other civil engineering projects/Hungary, demolition and site preparation/Poland, other specialized construction activities/Portugal. Globally, the development of building projects sector uses resources in the most inefficient way and there was a drop in the efficiency in 2011 and 2013, showing a delay in the crisis impact. After 2010, civil engineering projects required a substantial effort to access resources. Other features regarding (in)efficiency were further identified.
Originality/value – The analysis was conducted with one of the most effective techniques in frontier analysis. The first introduced index allows for comparing efficient/inefficient subgroups, and the other index measures the resource acquisition effort, allowing a better comparison along years. The study provides a good understanding of the performance of the construction industry and indirectly exposes the strategies to overcome the crisis, through the identification of the inputs/outputs which are well/badly used.
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6.
Convolution theorems related with the solvability of WienerHopf plus Hankel integral equations and Shannon’s sampling formula
Castro, Luís Pinheiro and Guerra, Rita Correia and Tuan, Nguyen Minh
Mathematica Slovaca
De Gruyter
This paper considers two nite integral transforms of Fouriertype, in view to propose a set of eight new convolutions, and to analyze the solvability of a class of the integral equations of WienerHopf plus Hankel type, de ned on nite intervals, which is involved in engineering problems. The solvability and solution of the considered equations are investigated by means of Fouriertype series, and a Shannontype sampling formula is obtained. Some concluding remarks with respect to theoretical issues and engineering applications are emphasized in the last section, along with the analysis of some illustrative cases, which exemplify that the present method solves cases which are not under
the conditions of previously known techniques.
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5.
On the invariance of certain vanishing subspaces of Morrey spaces with respect to some classical operators
Alabalik, Aysegul Ç. and Almeida, Alexandre and Samko, Stefan
ArXiv
ArXiv
We consider subspaces of Morrey spaces defined in terms of various vanishing properties of functions. Such subspaces were recently used to describe the closure of $C_0^infty(mathbb{R}^n)$ in Morrey norm. We show that these subspaces are invariant with respect to some classical operators of harmonic analysis, such as the HardyLittlewood maximal operator, singular type operators and Hardy operators. We also show that the vanishing properties defining those subspaces are preserved under the action of Riesz potential operators and fractional maximal operators.
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4.
On the competitive harvesting of marine resources
Bressan, Alberto and Staicu, Vasile
SIAM Journal on Control and Optimization
Society for Industrial and Applied Mathematics
The paper is concerned with the optimal harvesting of a marine resource, described by an elliptic equation with Neumann boundary conditions and a nonlinear source term. We first consider a single agent, whose harvesting effort at various locations is described by a positive Radon measure. Necessary conditions for optimality are derived, complementing the existence result proved in [A. Bressan, G. Coclite, and W. Shen, SIAM J. Control Optim., 51 (2013), pp. 11861202]. The second part of the paper deals with a competitive scenario, where several groups of fishermen, from different coastal towns and hence with different cost functions, harvest the same marine resource. We prove the existence of a Nash equilibrium, which is characterized in terms of a suitable variational inequality.
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3.
On timeperiodic solutions of some nonlinear parabolic equations with nonmonotone multivalued terms
Otani, Mitsuharu and Staicu, Vasile
Topological Methods in Nonlinear Analysis
Nicolaus Copernicus University in Torun
In this paper we study the existence of time periodic solutions
to a class of nonlinear parabolic equations with multivalued nonlinear terms
subject to the homogeneous Dirichlet boundary condition. We give two
types of existence results: one for large periodic solutions with any large
data, and the other for small periodic solutions with small data. Both
concern the case where the nonlinear terms contain either a upper semi
continuous multivalued term or a lower semicontinuous multivalued term.
Some applications of our results are also given.
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2.
Nonlinear periodic systems with unilateral constraints
Aizicovici, Sergiu and Papageorgiou, Nikolaos S. and Staicu, Vasile
Topological Methods in Nonlinear Analysis
Nicolaus Copernicus University in Torun
We consider a general periodic system driven by a nonlinear,
nonhomogeneous differential operator, with a maximal monotone term
which is not defined everywhere. Using a topological approach based on
LeraySchauder alternative principle, we show the existence of a periodic
solution.
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Proceedings
1.
About the financial efficiency of the Iberian Peninsula education
Murillo, K. and Rocha, E.
INTED2019 Proceedings
IATED
This work examines the financial efficiency of private institutions of secondary and higher education in the Iberian Peninsula, during the period 20132016. In particular, we study the evolution of 117 Portuguese institutions and 1885 Spanish institutions. To this end, we analyze the evolution of financial statements of each institution regarding its efficiency at three distinct stages: efficiency levels; efficiency patterns; and efficiency determinants.
We use a nonparametric method that allows us to investigate changes in the institutions' efficiency standards, namely a model based on the Multidirectional Efficiency Analysis (MEA) in combination with other mathematical techniques, such that principal component analysis, clustering analysis and accumulated effort.
The study allows a parallel between Spain and Portugal, characterizing the behavior of the educational levels after the financial crisis that Europe suffered in mid2008. Our results indicate which are the levels of education that are more efficient and those that are less efficient, and which improvements could be applied to propose more effective measures according to other European experiences. The results show that Spanish higher education is more efficient than Portuguese one and the same conclusion can be inferred, with a lower degree, for the secondary education, except in 2016. Looking to higher versus secondary education, secondary education presents the biggest resource management inefficiency. Cluster analysis was applied to avoid the disparity of data in Spain. In 2015, Spain cluster 1 presents the greatest difference between the accumulated efforts of the two education levels. In contrast, Spain cluster 2 attains the smallest difference.
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