Book Chapters
12.
Teachinglearning process under a Multidirectional Efficiency and Canonical Correlation Analysis
Murillo, K. and Rocha, E.
EDULEARN20 Proceedings
IATED
The detailed study of the agents and factors involved in the teachinglearning 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 nonparametric, 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). BoxCox
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.
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Articles
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
Elsevier
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 offdiagonal coefficients [Formula presented], α≠β, have support in some staircase set along the diagonal in the y α ,y β plane
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10.
Variable exponent BesovMorrey spaces
Almeida, Alexandre and Caetano, António
Journal of Fourier Analysis and Applications
Springer Verlag
In this paper we introduce BesovMorrey 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 nonstandard function spaces requires the introduction of variable exponent mixed Morreysequence 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.
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9.
Maximal commutators and commutators of potential operators in new vanishing Morrey spaces
Almeida, Alexandre
Nonlinear Analysis
Elsevier
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.
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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
Springer
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.
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7.
Variable exponent TriebelLizorkinMorrey spaces
Caetano, António and Kempka, Henning
Journal of Mathematical Analysis and Applications
Elsevier
We introduce variable exponent versions of Morreyﬁed TriebelLizorkin spaces. To that end, we prove an important convolution inequality which is a replacement for the HardyLittlewood 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.
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6.
New convolutions and their applicability to integral equations of WienerHopf plus Hankel type
Castro, Luis P. and Guerra, Rita C. and Tuan, Nguyen Minh
Mathematical Methods in the Applied Sciences
Wiley
We propose four new convolutions exhibiting convenient factorization properties associated with two finite interval integral transformations of Fouriertype together with their norm inequalities. Moreover, we study the solvability of a class of integral equations of WienerHopf plus Hankel type (on finite intervals) with the help of the factorization identities of such convolutions. Fouriertype series are used to produce the solution formula of such equations and a Shannontype sampling formula is also obtained.
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5.
Mixed impedance boundary value problems for the Laplace–Beltrami equation
Castro, Luis and Duduchava, Roland and Speck, FrankOlme
Journal of Integral Equations and Applications
Rocky Mountain Mathematics Consortium
This work is devoted to the analysis of the mixed impedanceNeumannDirichlet boundary value problem (MIND~BVP) for the LaplaceBeltrami equation on a compact smooth surface $mathcal{C}$ with smooth boundary. We prove, using the LaxMilgram 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 $s> 1/p$, $1
1/p$ and $1
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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
Elsevier
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 endoflife 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 20062016, 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.
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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 20062013. 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 longterm debts, there is no evidence that this implies the ability of enterprises to grow faster, which affects profitability.
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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
Wiley
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, singulartype 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.
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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
Element
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.
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