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We exhibit a faithful representation of the stylic monoid of every finite rank as a monoid of upper unitriangular matrices over the tropical semiring. Thus, we show that the stylic monoid of finite rank $n$ generates the pseudovariety $\boldsymbol{\mathcal{J}}_n$, which corresponds to the class of all piecewise testable languages of height $n$, in the framework of Eilenberg's correspondence. From this, we obtain the equational theory of the stylic monoids of finite rank, show that they are finitely based if and only if $n \leq 3$, and that their identity checking problem is decidable in linearithmic time. We also establish connections between the stylic monoids and other plactic-like monoids, and solve the finite basis problem for the stylic monoid with involution., Comment: 22 pages. Added results on the finite basis problem for the stylic monoid with involution and updated references

Publisher Copyright: © 2022 Taylor & Francis Group, LLC. In this paper we consider the monoid (Formula presented.) of all partial isometries of a star graph Sn with n vertices. Our main objectives are to determine the rank and to exhibit a presentation of (Formula presented.). We also describe Green’s relations of (Formula presented.) and calculate its cardinal. authorsversion published

Funding Information: This work is funded by national funds through the FCT - Fundação para a Ciência e a Tecnologia , I.P., under the scope of the project DSAIPA/DS/0088/2019 and research and development units UNIDEMI (project UIDB/00667/2020 ) and NOVAMath (projects UIDB/00297/2020 and UIDP/00297/2020 ). Publisher Copyright: © 2023 The Author(s) Fires in urban areas typically carry severe consequences. High population density together with the complexity of urban network potentially imply significant impacts in property loss, physical damage and life losses. However, despite the impact that fires may have in urban areas, research in urban fire prediction remains limited. In this study, we modelled urban fire occurrences while making a comparative analysis of different strategies to account for spatial autocorrelation. Considering space dependence in addition to a range of social-economic explanatory variables has proven to strengthen the validity of the fitted models. The spatial Durbin error model, including population density, degraded buildings density and buying power, was selected as having the best fit. This model allowed to map the estimated probability of fire occurrence across Portugal, revealing a spatial pattern with clusters centred on the two main Portuguese city districts (Lisboa and Porto). Ultimately, the analysis of the relation between the observed urban fire incidence and the actual number of fire stations in each municipality allowed to underline the need for planning the spatial configuration of fire stations, both in number and location, at a regional scale. publishersversion published

Funding Information: The first and third authors were financially supported by the Fundação para a Ciência e a Tecnologia, Portugal (Portuguese Foundation for Science and Technology) through the projects UIDB/MAT/00297/2020 , UIDP/MAT/00297/2020 (Centro de Matemática e Aplicações), and PTDC/CCI-BIO/4180/2020 . The second author was financially supported by the Forest Research Center, a research unit funded by Fundação para a Ciência e a Tecnologia (FCT), Portugal , through the project ( UIDB/00239/2020 ). Publisher Copyright: © 2023 The Author(s) Consider a graph with vertex set V and non-negative weights on the edges. For every subset of vertices S, define ϕ(S) to be the sum of the weights of edges with one vertex in S and the other in V∖S, minus the sum of the weights of the edges with both vertices in S. We consider the problem of finding S⊆V for which ϕ(S) is maximized. We call this combinatorial optimization problem the max-out min-in problem (MOMIP). In this paper we (i) present a linear 0/1 formulation and a quadratic unconstrained binary optimization formulation for MOMIP; (ii) prove that the problem is NP-hard; (iii) report results of computational experiments on simulated data to compare the performances of the two models; (iv) illustrate the applicability of MOMIP for two different topics in the context of data analysis, namely in the selection of variables in exploratory data analysis and in the identification of clusters in the context of cluster analysis; and (v) introduce a generalization of MOMIP that includes, as particular cases, the well-known weighted maximum cut problem and a novel problem related to independent dominant sets in graphs. publishersversion published

Let X X be a rearrangement-invariant Banach function space on the unit circle T \mathbb {T} and let H [ X ] H[X] be the abstract Hardy space built upon X X . We prove that if the Cauchy singular integral operator ( H f ) ( t ) = 1 π i ∫ T f ( τ ) τ − t d τ (Hf)(t)=\frac {1}{\pi i}\int _{\mathbb {T}}\frac {f(\tau )}{\tau -t}\,d\tau is bounded on the space X X , then the norm, the essential norm, and the Hausdorff measure of non-compactness of the operator a I + b H aI+bH with a , b ∈ C a,b\in \mathbb {C} , acting on the space X X , coincide. We also show that similar equalities hold for the backward shift operator ( S f ) ( t ) = ( f ( t ) − f ^ ( 0 ) ) / t (Sf)(t)=(f(t)-\widehat {f}(0))/t on the abstract Hardy space H [ X ] H[X] . Our results extend those by Krupnik and Polonskiĭ [Funkcional. Anal. i Priloz̆en. 9 (1975), pp. 73-74] for the operator a I + b H aI+bH and by the second author [J. Funct. Anal. 280 (2021), p. 11] for the operator S S .

Funding Information: The presented research was funded by national funds through the FCT—Fundação para a Ciência e a Tecnologia, I.P., under the scope of the research units UIDB/04035/2020 (GeoBioTec Research Centre), UIDB/00297/2020 and UIDP/00297/2020 (Centre for Mathematics and Applications). Publisher Copyright: © 2023 by the authors. In recent years, cocoa and dark chocolate have attracted the interest of consumers not only for their sensory characteristics but also for their nutritional properties and positive impact on health. The baobab is a fruit of African origin with a sour and slightly sweet flavour, widely consumed by local communities due to its unique nutritional features. The aim of this work was to evaluate the impact of the concentration of baobab flour in the development of functional dark chocolate, including physical, chemical, nutritional and sensory evaluations. The results presented a positive correlation between the incorporation of baobab flour and the antioxidant activity (up to 2297 mmol TE/100 g), vitamin C content (up to 49.7 mg/100 g), calcium (up to 1052 mg/kg), potassium (up to 10,175 mg/kg), phosphorus (up to 795.9 mg/kg), chlorine (up to 235.4 mg/kg) and sulphur (up to 1158 mg/kg). The sensory evaluation of dark chocolate with 3% baobab presented the highest evaluation on the parameters “texture” and “overall flavour”, while the parameter “overall flavour” presented the lowest evaluation on chocolate with 9% baobab. No influence was observed on fatty acid profile, protein, fat and hardness. publishersversion published

Publisher Copyright: © 2023 Wiley-VCH GmbH. For (Formula presented.) and variable exponents (Formula presented.) and (Formula presented.) with values in [1, ∞], let the variable exponents (Formula presented.) be defined by (Formula presented.) The Riesz–Thorin–type interpolation theorem for variable Lebesgue spaces says that if a linear operator T acts boundedly from the variable Lebesgue space (Formula presented.) to the variable Lebesgue space (Formula presented.) for (Formula presented.), then (Formula presented.) where C is an interpolation constant independent of T. We consider two different modulars (Formula presented.) and (Formula presented.) generating variable Lebesgue spaces and give upper estimates for the corresponding interpolation constants Cmax and Csum, which imply that (Formula presented.) and (Formula presented.), as well as, lead to sufficient conditions for (Formula presented.) and (Formula presented.). We also construct an example showing that, in many cases, our upper estimates are sharp and the interpolation constant is greater than one, even if one requires that (Formula presented.), (Formula presented.) are Lipschitz continuous and bounded away from one and infinity (in this case, (Formula presented.)). authorsversion published

Funding Information: For the second and third authors, this work was partially supported through the project of the Centro de Matemática e Aplicações, UID/MAT/00297/2020, financed by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology). The APC was by supported by Fidelidade-Companhia de Seguras, S.A. Funding Information: This work was published with financial support from Fidelidade-Companhia de Seguras, S.A. to which the authors express their warmest acknowledgment. The authors express gratitude to the three referees for their comments, corrections and questions that led to a revised and better version of this work. Publisher Copyright: © 2023 by the authors. We present an analysis on variability Bitcoin characteristics that help to quantitatively differentiate Bitcoin from the state-owned traditional currencies and the asset Gold. We provide a detailed study on returns of exchange rates—against the Swiss Franc—of several traditional currencies together with Bitcoin and Gold; for that purpose, we define a distance between currencies by means of the spectral densities of the ARMA models of the returns of the exchange rates, and we present the computed matrix of the distances between the chosen currencies. A statistical analysis of these matrix distances is further proposed, which shows that the distance between Bitcoin and any other currency or Gold is not comparable to any of the distances between currencies or between currencies and Gold and not involving Bitcoin. This result shows that Bitcoin is essentially different from the traditional currencies and from Gold, at least in what concerns the structure of its variance and auto-covariances. publishersversion published

Let X be a Banach function space on the unit circle $${\mathbb {T}}$$ T , let $$X'$$ X ′ be its associate space, and let H[X] and $$H[X']$$ H [ X ′ ] be the abstract Hardy spaces built upon X and $$X'$$ X ′ , respectively. Suppose that the Riesz projection P is bounded on X and $$a\in L^\infty {\setminus }\{0\}$$ a ∈ L ∞ \ { 0 } . We show that P is bounded on $$X'$$ X ′ . So, we can consider the Toeplitz operators $$T(a)f=P(af)$$ T ( a ) f = P ( a f ) and $$T({\overline{a}})g=P({\overline{a}}g)$$ T ( a ¯ ) g = P ( a ¯ g ) on H[X] and $$H[X']$$ H [ X ′ ] , respectively. In our previous paper, we have shown that if X is not separable, then one cannot rephrase Coburn’s lemma as in the case of classical Hardy spaces $$H^p$$ H p , $$1 1 < p < ∞ , and guarantee that T(a) has a trivial kernel or a dense range on H[X]. The first main result of the present paper is the following extension of Coburn’s lemma: the kernel of T(a) or the kernel of $$T({\overline{a}})$$ T ( a ¯ ) is trivial. The second main result is a generalisation of the Hartman–Wintner–Simonenko theorem saying that if T(a) is normally solvable on the space H[X], then $$1/a\in L^\infty $$ 1 / a ∈ L ∞ .

This work is funded by national funds through the FCT-Fundacao para a Ciencia e a Tecnologia, I.P., under the scope of the projects UIDB/00297/2020 and UIDP/00297/2020 (Center for Mathematics and Applications). The log-logistic distribution is widely used in different fields of study such as survival analysis, hydrology, insurance, and economics. Recently, Ahsanullah and Alzaatreh studied the best linear unbiased estimators for the location and the scale parameters of the three-parameter log-logistic model. The same authors also propose a shift-invariant Hill estimator for the unknown shape parameter. In this work, we propose a new estimation method for the shape parameter. We derive its nondegenerate asymptotic behaviour and analyse its finite sample performance through a Monte Carlo simulation study. To have precise estimates, we present a method for selecting the threshold. To illustrate the improvement achieved, efficiency comparisons are also provided. publishersversion published

Funding Information: This work was supported in part by Centro de Matematica e Aplicaçoes, UID (MAT/00297/2020), Portuguese Foundation of Science and Technology. Acknowledgments Publisher Copyright: Copyright © 2023 Torrente, Sousa, Guerreiro, Franco, Hernández, Parejo, Sousa, Campo-Cañaveral, Pimentão and Provencio. Background: Current prognosis in oncology is reduced to the tumour stage and performance status, leaving out many other factors that may impact the patient´s management. Prognostic stratification of early stage non-small-cell lung cancer (NSCLC) patients with poor prognosis after surgery is of considerable clinical relevance. The objective of this study was to identify clinical factors associated with long-term overall survival in a real-life cohort of patients with stage I-II NSCLC and develop a prognostic model that identifies features associated with poor prognosis and stratifies patients by risk. Methods: This is a cohort study including 505 patients, diagnosed with stage I-II NSCLC, who underwent curative surgical procedures at a tertiary hospital in Madrid, Spain. Results: Median OS (in months) was 63.7 (95% CI, 58.7-68.7) for the whole cohort, 62.4 in patients submitted to surgery and 65 in patients submitted to surgery and adjuvant treatment. The univariate analysis estimated that a female diagnosed with NSCLC has a 0.967 (95% CI 0.936 - 0.999) probability of survival one year after diagnosis and a 0.784 (95% CI 0.712 - 0.863) five years after diagnosis. For males, these probabilities drop to 0.904 (95% CI 0.875 - 0.934) and 0.613 (95% CI 0.566 - 0.665), respectively. Multivariable analysis shows that sex, age at diagnosis, type of treatment, ECOG-PS, and stage are statistically significant variables (p1) while adjuvant chemotherapy is a good prognostic variable (HR

Publisher Copyright: © 2023 International Academic Press In a system of regression models, finding a feasible shrinkage is demanding since the covariance structure is unknown and cannot be ignored. On the other hand, specifying sub-space restrictions for adequate shrinkage is vital. This study proposes feasible shrinkage estimation strategies where the sub-space restriction is obtained from LASSO. Therefore, some feasible LASSO-based Stein-type estimators are introduced, and their asymptotic performance is studied. publishersversion published

Funding Information: This study was supported by national funds through FCT–Foundation for Science and Technology, I.P., within the scope of the project 2022.03892.PTDC. Declaration of interest: The author declares no competing interest. Data availability: Data generated or analyzed during this study are available from the author on request. Publisher Copyright: © 2023 by authors; license EJSME by Bastas. Teachers’ knowledge plays a central role in technology integration. In this study we analyze situations, where there is some divergence between the mathematical results and the information offered by the graphing calculator (lack of mathematical fidelity), putting the focus in the teachers and in their approaches. The goal of this study is to analyze, in the light of knowledge for teaching mathematics with technology (KTMT) model, the teachers’ professional knowledge, assuming the situations of lack of mathematical fidelity as having the potential to reveal some characteristics of their knowledge. Specifically, considering the teaching of functions at 10th grade (age 16), we intend to analyze: (1) What knowledge do the teachers have of technology and of its mathematical fidelity? (2) What can the teachers’ options related to situations of lack of mathematical fidelity tell us about their knowledge in other KTMT domains? The study adopts a qualitative and interpretative approach based on the case studies of two teachers. Data were collected by interviews and class observation, being the analysis guided by the KTMT model. The main result points to the relevance of the mathematics and technology knowledge. However, there is evidence of some difficulties to integrate the information provided by the technology with the mathematics, and also of some interference of the teaching and learning and technology knowledge, and specifically of the knowledge related to the students. This suggests that the analysis of the teachers’ actions in relation to situations of lack of mathematical fidelity, can be useful to characterize their KTMT. publishersversion published

Funding Information: Funding information : This work is a contribution to the Project UIDB/04035/2020, funded by FCT - Fundação para a Ciência e a Tecnologia, Portugal. Publisher Copyright: © 2023 João Lita da Silva, published by De Gruyter. In this article, we express the eigenvalues of real antitridiagonal Hankel matrices as the zeros of given rational functions. We still derive eigenvectors for these structured matrices at the expense of prescribed eigenvalues. publishersversion published

UIDB/04647/2020 UIDP/04647/2020 PTDC/CED-EDG/32422/2017 A Coleção História e Memória do Ensino da Matemática, apoiada pelo Grupo de Trabalho sobre História e Memória do Ensino da Matemática da Associação de Professores de Matemática, pretende divulgar trabalhos científicos sobre história do ensino da Matemática, difundindo perspetivas, metodologias e temas entre investigadores da área e divulgando junto de professores e do público em geral produções nesta área. Esse livro em específico contém a transcrição de artigos sobre matemática publicados em Portugal entre 1857 e 1872. Nele consta a proposta de cada um dos quatro volumes da série e um índice. Os artigos transcritos estão separados por seus anos, entre 1857 – 1872. publishersversion published

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1A2C1A01100526). Publisher Copyright: © 2022 by the authors. The Behrens–Fisher problem occurs when testing the equality of means of two normal distributions without the assumption that the two variances are equal. This paper presents approaches based on the exact and near-exact distributions for the test statistic of the Behrens–Fisher problem, depending on different combinations of even or odd sample sizes. We present the exact distribution when both sample sizes are odd and the near-exact distribution when one or both sample sizes are even. The near-exact distributions are based on a finite mixture of generalized integer gamma (GIG) distributions, used as an approximation to the exact distribution, which consists of an infinite series. The proposed tests, based on the exact and the near-exact distributions, are compared with Welch’s t-test through Monte Carlo simulations, in particular for small and unbalanced sample sizes. The results show that the proposed approaches are competent solutions to the Behrens–Fisher problem, exhibiting precise sizes and better powers than Welch’s approach for those cases. Numerical studies show that the Welch’s t-test tends to be a bit more conservative than the test statistics based on the exact or near-exact distribution, in particular when sample sizes are small and unbalanced, situations in which the proposed exact or near-exact distributions obtain higher powers than Welch’s t-test. publishersversion published

Funding Information: This work was partially supported by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through the projects UIDB/00297/2020 (Centro de Matemática e Aplicações) and UIDB/00006/2020 (Centro de Estatística e Aplicações/UL). Publisher Copyright: © 2022 American Institute of Physics Inc.. All rights reserved. When extending the analysis of the limiting behaviour of the extreme values from independent and identically distributed sequences to stationary sequences a key parameter appears, the extremal index θ, whose accurate estimation is not easy and is not completely solved. Here we focus on the estimation of θ using blocks estimators, that can be constructed by using disjoint or sliding blocks. Both blocks construction require the choice of a threshold and a block length. The main objective of this work is to revisit another block estimation procedure that only depends on the block length, although some conditions on the underlying process need to be verified. An application will be presented for illustrating the proposed procedure. publishersversion published

Funding Information: For the first author this work was partially supported through the project of the Centro de Matemática e Aplicações, UID/MAT/00297/2020 financed by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology). The APC was by supported by Fidelidade-Companhia de Seguros, S.A. to which the authors express their warmest acknowledgment. Funding Information: This work was published with financial support from by the New University of Lisbon. The authors express gratitude to the comments, corrections, and questions of the referees that led to a revised and better version of this work. Publisher Copyright: © 2023 by the authors. The structure of the random matrices introduced in this work is given by deterministic matrices—the skeletons of the random matrices—built with an algorithm of matrix substitutions with entries in a finite field of integers modulo some prime number, akin to the algorithm of one dimensional automatic sequences. A random matrix has the structure of a given skeleton if to the same number of an entry of the skeleton, in the finite field, it corresponds a random variable having, at least, as its expected value the correspondent value of the number in the finite field. Affine matrix substitutions are introduced and fixed point theorems are proven that allow the consideration of steady states of the structure which are essential for an efficient observation. For some more restricted classes of structured random matrices the parameter estimation of the entries is addressed, as well as the convergence in law and also some aspects of the spectral analysis of the random operators associated with the random matrix. Finally, aiming at possible applications, it is shown that there is a procedure to associate a canonical random surface to every random structured matrix of a certain class. publishersversion published

Publisher Copyright: © 2021 Elsevier Inc. In this paper we construct a new set of basis functions for the numerical solution of nonhomogeneous heat conduction problems with Dirichlet boundary conditions and null initial data. These functions can be seen as Newtonian potentials of plane waves for the heat equation and satisfy a null initial condition. Density results for adapted waves will be established and several numerical simulations will be presented in order to discuss the accuracy and feasibility of the proposed method. An application of the method for heat problems with non null initial temperature will also be discussed. authorsversion published