Publications 2020

Book Chapters

12.  Teaching-learning process under a Multidirectional Efficiency and Canonical Correlation Analysis

Murillo, K. and Rocha, E.

EDULEARN20 Proceedings


The detailed study of the agents and factors involved in the teaching-learning process is vital to advance in the proposal of strategies that contribute to their improvement in all aspects (methodology, evaluation, resource management, between others). Today, many theoretical studies on the quality of education are known, which makes this a broad topic of discussion. However, education is a universe in constant motion which imposes the necessity of new systematic studies from different and relevant perspectives. This work aims to contribute to the study of the quality of higher education, evaluating the teachinglearning process, under two approaches. First, examining the technical efficiency of the institutions of higher education (approach 1), and also evaluating the performance of the students of these institutions, in accordance with the influence of the training of the teachers assigned to them (approach 2). Specifically, the use case study relates to 335 data units representing Colombian higher education institutions, corresponding to 165 institutions in the year 2016 (47 publics and 118 privates), and 170 institutions in the year 2017 (48 publics and 122 privates). The analysis considers variables of training/research for teacher and variables of graduation/performance for students. For the estimation of the efficiency (approach 1) has used a non-parametric, method based on the Multidirectional Efficiency Analysis (MEA). The study is focused on efficiency score, efficiency ratios and analysis of the output inefficiency index. For the exploration of the relationship, academic qualification/performance (approach 2), is executed a Canonical Correlation Analysis (CCA). Box-Cox transformations and filtering analysis to deal with outliers are applied. The statistical significance of the canonical correlations found, are shown with different statistical tests. The greatest contribution of this work is the appropriate combination of the MEA and CCA methodologies, which allows a broader vision of what happens in the scheme: institution efficiency/student performance/teacher training. Our results allow us to characterize the institutions in terms of efficiency, discriminating them into seven groups according to the training offer (doctoral programs, masters, specialization, etc.) and comparatively establish the most relevant relationships between teacher training / research and performance of the student. | doi | Peer Reviewed


11.  Maximum principles for some quasilinear elliptic systems

Leonardi, Salvatore and Leonetti, Francesco and Pignotti, Cristina and Rocha, Eugénio and Staicu, Vasile

Nonlinear Analysis: Theory, Methods and Applications


We give maximum principles for solutions u:Ω→ℝ N to a class of quasilinear elliptic systems whose prototype is [Formula presented]where α∈{1,…,N} is the equation index and Ω is an open, bounded subset of ℝ n . We assume that coefficients [Formula presented] are measurable with respect to x, continuous with respect to y∈ℝ N , bounded and elliptic. In vectorial problems, when trying to bound the solution by means of the boundary data, we need to bypass De Giorgi's counterexample by means of some additional structure assumptions on the coefficients [Formula presented]. In this paper, we assume that off-diagonal coefficients [Formula presented], α≠β, have support in some staircase set along the diagonal in the y α ,y β plane | doi | Peer Reviewed

10.  Variable exponent Besov-Morrey spaces

Almeida, Alexandre and Caetano, António

Journal of Fourier Analysis and Applications

Springer Verlag

In this paper we introduce Besov-Morrey spaces with all indices variable and study some fundamental properties. This includes a description in terms of Peetre maximal functions and atomic and molecular decompositions. This new scale of non-standard function spaces requires the introduction of variable exponent mixed Morrey-sequence spaces, which in turn are defined within the framework of semimodular spaces. In particular, we obtain a convolution inequality involving special radial kernels, which proves to be a key tool in this work. | doi | Peer Reviewed

9.  Maximal commutators and commutators of potential operators in new vanishing Morrey spaces

Almeida, Alexandre

Nonlinear Analysis


We study mapping properties of commutators in certain vanishing subspaces of Morrey spaces, which were recently used to solve the delicate problem of describing the closure of nice functions in Morrey norm. We show that the vanishing properties defining those subspaces are preserved under the action of maximal commutators and commutators of fractional integral operators. | doi | Peer Reviewed

8.  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

Banach Journal of Mathematical Analysis


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(Rn) in Morrey norm. We show that these subspaces are invariant with respect to some classical operators of harmonic analysis, such as the Hardy–Littlewood 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. | doi | Peer Reviewed

7.  Variable exponent Triebel-Lizorkin-Morrey spaces

Caetano, António and Kempka, Henning

Journal of Mathematical Analysis and Applications


We introduce variable exponent versions of Morreyfied Triebel-Lizorkin spaces. To that end, we prove an important convolution inequality which is a replacement for the Hardy-Littlewood maximal inequality in the fully variable setting. Using it we obtain characterizations by means of Peetre maximal functions and use them to show the independence of the introduced spaces from the admissible system used. | doi | Peer Reviewed

6.  New convolutions and their applicability to integral equations of Wiener-Hopf plus Hankel type

Castro, Luis P. and Guerra, Rita C. and Tuan, Nguyen Minh

Mathematical Methods in the Applied Sciences


We propose four new convolutions exhibiting convenient factorization properties associated with two finite interval integral transformations of Fourier-type together with their norm inequalities. Moreover, we study the solvability of a class of integral equations of Wiener-Hopf plus Hankel type (on finite intervals) with the help of the factorization identities of such convolutions. Fourier-type series are used to produce the solution formula of such equations and a Shannon-type sampling formula is also obtained. | doi | Peer Reviewed

5.  Mixed impedance boundary value problems for the Laplace–Beltrami equation

Castro, Luis and Duduchava, Roland and Speck, Frank-Olme

Journal of Integral Equations and Applications

Rocky Mountain Mathematics Consortium

This work is devoted to the analysis of the mixed impedance-Neumann-Dirichlet boundary value problem (MIND~BVP) for the Laplace-Beltrami equation on a compact smooth surface $mathcal{C}$ with smooth boundary. We prove, using the Lax-Milgram Lemma, that this MIND BVP has a unique solution in the classical weak setting $mathbb{H}^1(mathcal{C})$ when considering positive constants in the impedance condition. The main purpose is to consider the MIND~BVP in a nonclassical setting of the Bessel potential space $mathbb{H}^s_p(mathcal{C})$, for $s> 1/p$, $11/p$ and $1 | doi | Peer Reviewed

4.  Circular economy in plastic waste: efficiency analysis of European countries

Robaina, Margarita and Murillo, Kelly and Rocha, Eugénio and Villar, José

Science of the Total Environment


The way plastics are currently produced, used and disposed does not capture the economic benefits of a more 'circular' approach and is dramatically harming the environment. It is relevant to determine which European countries can be considered more or less efficient in the end-of-life of plastic products processes, what the sources of the inefficiencies are, and how those less efficient countries could improve their performance towards a more circular economy. Although some countries have developed a variety of quantitative indicators, there is scarcity of adequate metrics for performance measurements. This paper estimates the efficiency of 26 European countries in the context of Circular Economy, for the period 2006-2016, considering the generation of waste, recovery and recycling of plastic, with a methodology based on the Multidirectional Efficiency Analysis. Apart from identifying the most efficient countries in the studied period, results show that efficiency increases for most countries with time, and that many countries reach the full efficiency by the end of the study period, and especially by 2016. Input analysis shows that increasing capital seems to be a main driver towards efficiency, since the other inputs are used with a similar efficiency by most countries. Output analysis suggest that the difference among countries efficiency is not in their reduction of total waste or emissions, but rather in the improvement of their economic growth in a circular way, that is, improving GDP but also the recovering and recycling activities. These results could be useful to design policies towards a more efficient and circular use of plastics. | doi | Peer Reviewed

3.  Factors influencing the economic behavior of the food, beverages and tobacco industry: a case study for Portuguese enterprises

Murillo, Kelly P. and Rocha, Eugénio M.

World Journal of Applied Economics

World Economic Research Institute (WERI)

In today's world, it is increasingly important to conduct economic and financial analyzes of enterprises in all sectors to determine strengths, identify weaknesses and adopt strategies that allow them to be at the highest competitive level. In particular, the food sector plays an essential role in the economy of any country, representing a significant contribution to gross domestic product, total employment, and disposable income of households. In this work, we adopt a methodology for measuring efficiency based on the multidirectional efficiency analysis and other mathematical techniques (the calculation of the normal distribution intersection coefficient (NC value), analysis of clusters and principal components, and model fitting) in order to examine the factors that influence the performance of Portuguese enterprises in the food, beverages and tobacco industry for the period of 2006-2013. The results show a characterization of the financial structure of the sector and diagnosis through indexes that identify the strategic positioning of the enterprises in terms of efficiency scores. In addition, we also show that an analysis of the variables that must be approached differently to obtain better results regarding economic performance. Although there is an increase in credit with the acquisition of long-term debts, there is no evidence that this implies the ability of enterprises to grow faster, which affects profitability. | doi | Peer Reviewed

2.  Preservation of certain vanishing properties of generalized Morrey spaces by some classical operators

Alabalik, Aysegul Ç. and Almeida, Alexandre and Samko, Stefan

Mathematical Methods in the Applied Sciences


We show that certain vanishing properties defining closed subspaces of generalized Morrey spaces are preserved under the action of various classical operators of harmonic analysis, such as maximal operators, singular-type operators, Hardy operators, and fractional integral operators. Those vanishing subspaces were recently used to deal with the delicate problem on the description of the closure of nice functions in Morrey norm. | doi | Peer Reviewed

1.  New convolutions associated with the Mellin transform and their applications in integral equations

Castro, L. P. and Silva, A. S. and Tuan, N. M.

Journal of Classical Analysis


In this paper, we introduce two new convolutions associated with the Mellin transform which exhibit factorization properties upon the use of certain weight functions. This is applied to the solvability analysis of classes of integral equations. In particular, we present sufficient conditions for the solvability of an integral equation and a system of integral equations of convolution type. | doi | Peer Reviewed
(latest changes on 2021-09-13 18:39)

© 2019 CIDMA, all rights reserved