Repositório RCAAP

Neste artigo abordam-se alguns conceitos fundamentais da Matemática diretamente associados ao Planeta Terra numa perspetiva histórica. Da esfera à linha de rumo, das origens e certas aplicações do Cálculo Infinitesimal aos problemas com fronteira livre, das simetrias nos sólidos platónicos e nos cristais à calçada portuguesa, a Matemática é o elo de ligação entre temas aparentemente díspares associados ao Planeta Terra.

Nesta nota obtém-se o melhor par aproximante de duas variedades lineares enviesadas após determinar a projeção de um ponto sobre uma variedade linear. Concretamente, calculam-se por duas vezes os vetores de norma mínima, adequados em cada caso, pertencentes a duas variedades lineares paralelas. Obtêm-se ainda expressões para as referidas projeções envolvendo a inversa de Moore-Penrose de cada uma das matrizes associadas às variedades lineares consideradas (na sua formulação matricial).

Este artigo está organizado em duas partes distintas, desenvolvidas em paralelo, onde ilustramos a utilidade das conexões de Galois na teoria dos números (primeira parte) e das inversões de Möbius-Rota na combinatória (segunda parte). Estas ferramentas permitem abordar problemas aparentemente difíceis, transformando-os, com um simples processo de inversão, em problemas equivalentes mais simples. O fio condutor comum é a visão conceptual da teoria dos reticulados.

Inclusion-Exclusion identities and inequalities are obtained for valuations. Applications to cardinality, probability, max/min and least common multiples are presented.

Será visto como lidar com problemas de construções com régua e compasso que levem a equações algébricas de grau 4. Mais precisamente, é dado um critério que permite decidir se um tal problema tem ou não solução.

A partir da função modelo f(x) = tan(x/4) − 1, são construídos métodos iterativos de Newton e de Wegstein a fim de produzir novas fórmulas aproximantes do número . Provamos que, para a função modelo, a iteradora de Wegstein possui ordem cúbica de convergência, no intervalo [3, 4]. Apresentam-se resultados numéricos mostrando que a auto composição de iteradoras de Newton/Wegstein pode ser usada recursivamente para obter aproximações de com milhares de dígitos decimais correctos.

A curva descrita pelos pares (a, b) no plano tais que a, b > 0, a ≠ b e a^b = b^a é parametrizável pelos declives 0 < t ≠ 1 do feixe de rectas de equações cartesianas y = tx, o que permite descrever facilmente os pontos do traço desta curva cujas coordenadas são ambas números algébricos, ou inteiros algébricos ou racionais. Em particular, uma tal parametrização fornece um método simples de encontrar coordenadas de pontos desta curva que são números transcendentes.

Professor Irineu Bicudo (1940-2018) In Memoriam

Neste artigo procuramos descrever a situação relativa a género na comunidade científica matemática em Portugal (dados de 2016).

Os leitores são convidados a enviar, para eventual publicação, soluções, comentários, propostas de problemas, etc. Essa correspondência deve ser enviada para a SPM, ao cuidado do editor desta secção. Há livros para sortear entre as soluções recebidas em cada número.

Suplemento do Número 76. Resumos alargados dos 29º, 30º e 31º Seminários Nacionais de História da Matemática.

The relationship between the policies and practices of organizational management and the strategic management of people has been the subject of numerous studies and reflections. However, the constant changes imposed by complex and dynamic environments force organizations to incorporate new operational strategies based on innovation and the development of management practices that stimulate teamwork in a climate of trust and knowledge sharing. This work is the result of a bibliographic study on articles based on dynamic and diversified organizational strategies and intends to reflect an analysis of the current trend in this practice. The advancement of technological innovation has been a facilitating factor in the reorganization of organizations, transferring the most traditional methods to multidisciplinary functions and minimum networks. In a generation where technologies advance unprecedentedly, it is a challenge for management to create conditions for removing excesses and finding people with skills for collaborative work, flexible and available to generate new routines. Thus, this article aims to present the importance of people in organizational development, while contributing with a strategic vision emphasized on sharing knowledge and developing skills in continuous learning.

This study intends to analyse the phenomenon of the anomaly between profitability and risk in the Portuguese capital market. In this context, we collect the information of all the shares that constitute the PSI-Geral index, for the period from January 2002 to December 2013. We constructed portfolios according to the historical volatility and systematic risk for the period under review, as well as for two sub periods, according to economic conditions. The results show a negative correlation between market volatility and return over the period under review, being more pronounced in 2008. The application of performance measures showed the existence of an anomaly between the volatility and the return of portfolios securities, more pronounced for the recession period (2008-2013). However, this type of anomaly did not occur when we consider the systematic risk.

The main purpose of the present study is to analyze the application of IAS 8, by Portuguese companies listed on Euronext Lisbon, regarding to accounting policies changes, estimates changes and errors correction, as well as to evaluate their consequences in financial reporting. The methodology used was the direct collection and content analysis of the consolidated financial statements, and respective audit reports, of Portuguese companies listed on Euronext Lisbon for the period 2008 to 2014. We conclude that restatements frequency is insignificant in the first periods analysed and has increased significantly since 2010 (including). This situation is mainly due to the revision of IAS 19, the changes introduced in IFRS 10 and IFRS 11 and IFRIC 12. Regarding the occurrence of errors and accounting policies changes, there are few situations where we found evidence of significant effects that could affect financial statements quality, although we verify that the effects of errors and policies changes tend to protect present and/or future earnings over of past earnings.

The competition and evolution of the audit market have led to the growing provision, by audit firms, of a diverse range of services other than audit services, so-called non-audit services. The financial scandals that occurred at the beggining of this century launched the discussion about the impact of these services on the auditor's independence. Accordingly, the purpose of this study is to examine the effect of the non-audit services, of entities listed on the Euronext Lisbon, on the auditor's independence. For that, we tested a possible relationship between non-audit fees and audit fees. The results indicate that there is a positive relationship between non-audit fees and audit fees. However, when considering the effect of the simultaneously determination of these fees by common factors, this relationship no longer exists. Hence, one may conclude that both fees for non-audit and audit services are simultaneously determined. In addiction, we found no evidence that the author's independence is affected by the non-audit services.

This study intends to analyze the relation between the short-term financial balance and the profitability, considering a sample of 49 listed firms in the Euronext Lisbon, for the period between 2006 and 2013, considering a panel data approach. The profitability (dependent variable) was measured through the variable return on assets. We consider as independent variables the average duration of inventories, the accounts payable period, the accounts receivable period and the cash conversion cycle. The general debt ratio and the company dimension were considered as control variables. Although all variables present the expected signal, they are not statistically significant, so we cannot consider that the independent variables are explanatory of the profitability, which is consistent with other studies. When we consider the return on equity as a dependent variable, we find a positive and significant relationship between firm size and profitability.

The mystery shopping is a qualitative market research tool that essentially seeks to get real feedback on the quality of service provided. Given the high competitiveness in the current market, measuring customer satisfaction through questionnaires is no longer enough, because to generate competitive advantage it is necessary to achieve excellence in the service experience with customer focus. This dissertation had as its methodology the single case study that was developed in a Portuguese telecommunications company, which for reasons of confidentiality was not made explicit. In the case of the sector with the highest number of complaints in the market, it seems evident that more studies to understand the failures in the service of this sector are relevant. Likewise, the development of tools that will help to develop a higher quality of service delivery and consequently improve customer service satisfaction. In order to carry out the study, the methodology was divided into three stages, literature review, preparation of the semi-structured script that was used as an instrument for data collection, field research carried out through mystery shopping, analysis of scripts and presentation of the results found . The research was applied in two different periods, in order to be able to use the previous data for a possible comparison of results and to help in the perception of the contribution of the mystery shopping application to the organization, being possible to have a comparative analysis of the changes that occurred after the first Mystery shopping visit and the second. After analyzing the data collected, management improvements were suggested and the results were presented, that is, the main failures in the company's attendance. Also regarding the results presented, it was not possible to confirm the effectiveness of the mystery shopping application as an improvement tool for the management of the quality of the services, since there was no employee training by the company in the time interval of the research, evenso, in the study that was done, relevant results were found and it is expected that these results present important contributions to the company, when implementing the suggestions presented, as well as for the other operators of the Portuguese telecommunications sector that can consult this work.

As a result of the increasing demand on the credibility of the financial information disclosure, internal auditing has been playing an increasingly important role in organizations. Currently, there is a need to ensure the compliance of organizational transactions in real time in order to increase the reliability of the information and to reduce risks. In this context, the concept of Continuous Assurance has emerged, allowing to reduce potential errors and risks and obtain useful information in real time, supporting more effectively the decision making. As a central objective of this dissertation, we sought to understand the importance and the use of Continuous Assurance services from the perspective of the internal auditor. The methodology used is exploratory-descriptive, of a qualitative nature and used a questionnaire survey. The main results demonstrate, among other findings, that the Continuous Assurance services are considered by the internal auditors as very important. Despite this, its implementation in the organizations does not follow the importance assigned to it, and is still far from being fully deployed. The dimension of the audit department is an influential factor im the use of some Continuous Assurance services.

The most popular frauds known in the early 21st century eroded investors' and society's confidence in the financial markets contributing to economic and social destruction. In response to cases such as Enron and WorldCom, the United States of America enacted the Sarbanes-Oxley Act (SOX) and at the European Union side, responding not only to Enron as well as to the frauds in Europe, several regulatory instruments were enacted. Despite these actions, more recently, the two sides of the Atlantic have again been the target of large- scale fraud cases. The purpose of this dissertation is to understand the most relevant causes to the eruption of the fraudulent phenomenon in these two geographies and two periods of time (before and after the implementation of SOX). Subsequently, it is also analyzed whether between periods there were changes in the relevance of the causes. Through the analysis of several cases of fraud and the definition of a group of common causes to trigger fraud, it is made the classification of the relevance of each cause to the eruption of the fraud in each case of fraud. The conclusions allow observing the tendencies of the more and less relevant causes in the pre and post-SOX periods. The lack of ethical tone at the top proves to be the most relevant and cross-cutting cause of the various frauds, while the passivity of investors is the less relevant cross-cutting cause. When passing from pre to post-SOX, there is a tendency for inflated financial statements to cease to be one of the most relevant causes for giving way to weak internal controls, even though SOX is particularly strong in this latest area. Poor regulation is replaced by overexpansion of the business as one of the least relevant causes after SOX implementation.

This dissertation presents a marketing approach to operational risk management in portuguese newborn SMEs’ internationalisation process. Based on the comprehensive explanation of internationalisation stategies, with an emphasys on exportation, this paper intends to offer a more pragmatic perspective on newbordn SME’s managers’ decision making process regarding b2b international marketing strategies formulation in order to propose a benchmark in the above mentioned matter. In order to do so, the research work hereby presented was carried out using a mixed methodology based on a secondary research for theoretical support and then, on a qualitative analysis operationalized through interviews. Results comply with theoretical predictions sustained by previous investigations and show an overall tendency towards a progressive aknowledgment of the marketing role in internationalisation strategies. In summary it is concluded that: (1) the export volume of Portuguese newborn SMEs is mainly destined to EU members; (2) in international b2b marketing, communication is the marketing mix component most adapted by Portuguese newborn SMEs to the international markets; (3) in international b2b marketing, distribution is the marketing mix component most standardized by Portuguese newborn SMEs to the international markets; (4) regarding Portuguese newborn SMEs’ marketing mix, standardization is the most adopted international management strategy; and (5) regarding Portuguese newborn SMEs’ marketing mix, adaptation is the management strategy with greater capacity to mitigate operational risk. Therefore, it is expected that the present dissertation may have profound implications for future studies in the field.