Em direção a uma representação para equações algébricas :uma lógica equacional local

The intervalar arithmetic well-known as arithmetic of Moore, doesn't possess the same properties of the real numbers, and for this reason, it is confronted with a problem of operative nature, when we want to solve intervalar equations as extension of real equations by the usual equality and of the intervalar arithmetic, for this not to possess the inverse addictive, as well as, the property of the distributivity of the multiplication for the sum doesn t be valid for any triplet of intervals. The lack of those properties disables the use of equacional logic, so much for the resolution of an intervalar equation using the same, as for a representation of a real equation, and still, for the algebraic verification of properties of a computational system, whose data are real numbers represented by intervals. However, with the notion of order of information and of approach on intervals, introduced by Acióly[6] in 1991, the idea of an intervalar equation appears to represent a real equation satisfactorily, since the terms of the intervalar equation carry the information about the solution of the real equation. In 1999, Santiago proposed the notion of simple equality and, later on, local equality for intervals [8] and [33]. Based on that idea, this dissertation extends Santiago's local groups for local algebras, following the idea of Σ-algebras according to (Hennessy[31], 1988) and (Santiago[7], 1995). One of the contributions of this dissertation, is the theorem 5.1.3.2 that it guarantees that, when deducing a local Σ-equation E t t in the proposed system SDedLoc(E), the interpretations of t and t' will be locally the same in any local Σ-algebra that satisfies the group of fixed equations local E, whenever t and t have meaning in A. This assures to a kind of safety between the local equacional logic and the local algebras

Criação de empresas à luz do modelo de decisão effectuation: um estudo com mulheres empreendedoras no município de Currais Novos/RN

This study analysed the creation of businesses by entrepreneur women in the Currais Novos city, looking for verifying if they used making decision processes aligned to the Effectuation logic throughout the creation of their companies. To this, was accomplished a multiple cases and exploratory study, whit a qualitative approach of analyse, using the thematic life history technique that match accounts and semi-structured interview route, being accomplished like a long interview, where the researcher interact with the informer continuously. The semi-structured interview route was created by the adaptation of the interview route used by Tasic (2007). The present study appealed to a intentional selection of individuals in function of their importance in relation to the boarded theme. This means that the individuals were chosen in function of their social and theoretical representatively inside the considered situation. The participant individuals of this research were five entrepreneur women that act in the Currais Novos city, owners of five different companies. To the data treatment and analyse, was chosen the content analyse technique. This study worked with a priori theoretical categories. The categories of analyse in this study was obtained with base in the Effectuation approach (SARASVATHY, 2001a, 2001b, 2008), that is an alternative model of making decision to the classic model based in the causality principle. These categories are Clarity of Initial Aims , Tolerance to the Lost and Initials Investments , Control of Resources ( who I am , what I know and who I know ) and Promoting Over Contingencies . As result, the entrepreneur women researched, in a general way, hadn t clear initial aims at the companies creation moment, hadn t aversion to the risk to lose the time and the money that they were investing in the company in formation, they highlighted the products and services identity that offered with a strong link with Seridó region, they had experience in the field of activity in which they decided to open their companies, had the commitment of partners in the beginning of the business and they knew to transform the initial difficulties in opportunities. By the end, this study conclude that the entrepreneur women studied used, in a big part, making decision processes aligned to the Effectuation logic throughout the creation of their companies

A história do intemperismo na Província Borborema Oriental, Nordeste do Brasil: implicações paleoclimáticas e tectônicas

Until some years ago, weathering geochronology was primarily based on the K-Ar and 40Ar/39Ar dating of supergene minerals. Recent advances in the analysis of supergene goethite by the (U-Th)/He method expanded the number of suitable minerals for such purpose, as well as the time of application for weathering geochronology. This study represents the first systematic approach in Brazil, combining both the 40Ar/39Ar e (U-Th)/He methodologies to improve the knowledge on the weathering and the age of nonfossiliferous sediments. Supported by geologic and geomorphologic correlations, we identified different types of weathering profiles occurring in the interior and coastal areas of northeastern Brazil. These profiles were correlated to main regional geomorphological domains: the Borborema Plateau , the Sertaneja Depression , and the Coastal Cuestas and Plains, and respective planation surfaces, which study is fundamental to understand the landscape evolution of the northern portion of the eastern Borborema Province. The depth and stratigraphic organization of the weathering profiles in each of the geomorphological domains permitted to establish that: (i) the profiles on the highlands that cap the Borborema Surface are deeper (up to 100 m) and can be considered as typical lateritic profiles; (ii) on the lowlands that form the Sertaneja Surface , the weathering profiles are shallow and poorly developed (2-5 m deep); (iii) the profiles along the coastal area are moderately developed (up to 25 m deep), and are characterized by thick saprolites and mottle zones. Aiming to establish the timing of the evolution of northeastern Brazil, we studied 29 weathering profiles representing distinct topographic levels of the Borborema Province, from the highlands to the coast, through the analysis of 248 grains of supergene manganese oxides using laser step-heating 40Ar/39Ar geochronology. Additionally, we applied the (U-Th)/He method in 20 weathering profiles, by dating 171 grains of supergene iron oxides and hydroxides. Geochronological results for 248 grains of manganese oxides analyzed by the 40Ar/39Ar method indicate that the weathering profiles in the study area record the history of weathering from the Oligocene to the Pleistocene, with ages in the order of 31.4 ± 1.0 Ma to 0.8 ± 0.4 Ma. Dating of 171 grains of goethite by the (U-Th)/He method yielded ages ranging from 43.2 ± 4.3 Ma to 0.8 ± 0.1 Ma, suggesting the weathering processes last from the Eocene to the Pleistocene. The precipitation of supergene goethite in this interval confirms the age of the weathering processes identified from the manganese oxides record. 105 goethite grains from 8 different occurrences of the Barreiras Formation were dated by the (U-Th)/He method. Five grains collected from the cement in the Barreiras Formation sandstones, in the Lagoa Salgada and Rio do Fogo coastal cuestas, yielded ages of 17.6 ± 1.8 Ma, 17.3 ± 1.7 Ma, 16.3 ± 1.6 Ma, 16.2 ± 1.6 Ma and 13.6 ± 1.4 Ma. Results of 69 goethite grains from authigenic pisoliths collected in 7 different localities also yielded concordant ages, varying from 17.8 ± 1.8 to 7.5 ± 0.8 Ma. Results obtained from 31 detrital grains are concordant in 3 distinct localities (Lagoa Salgada, Praia da Garças e Ponta Grossa); they vary in the range of 43.2 ± 4.3 to 21.6 ± 2.2 Ma, and indicate that the maximum age for the Barreiras Formation deposition is around 22 Ma. 40Ar/39Ar results for 15 manganese oxides grains associated with the Barreiras Formation weathering profiles, in 3 different localities, vary from 13.1 ± 0.9 to 7.7 ± 0.4 Ma, in the same range of ages obtained by the (U-Th)/He method. The systematic application of the 40Ar/39Ar and (U-Th)/He methods, respectively for manganese oxides and goethites, show that the Barreiras Formation sediments were already deposited since ca. 17 Ma, and that the weathering processes were active until ca. 7 Ma ago. The ages obtained from manganese oxides collected in the Cenozoic basalts (Macau Formation) also reveal a weathering history between 19 and 7 Ma, pointing to hot and humid conditions during most of the Miocene. 40Ar/39Ar ages yielded by manganese oxides associated with the Serra do Martins Formation vary from 14.1 ± 0.4 to 10.5 ± 0.3 Ma. On the other hand, (U-Th)/He ages from iron oxides/hydroxides collected in the Serra do Martins Formation mesas vary from 20.0 ± 2.0 to 5.5 ± 0.6 Ma, indicating that those sediments are older than 20 Ma. 40Ar/39Ar and (U-Th)/He results produced in this study are in agreement with paleoclimatic interpretations based on stable isotopes and clay index values measured in the Atlantic Ocean sediments, validating the use of weathering geochronology to investigate paleoclimatic variations. The direct dating of the Barreiras Formation permitted, for the first time, confident inferences on the age of the brittle deformation recorded by this sedimentary unit in the Rio Grande do Norte and Ceará states. The first event, syn-deposition, occurred during the early Miocene; an younger event, related to the post-depositional deformation of the Barreiras Formation, is associated with tectonic activity from the very early Miocene to the Holocene. In agreement with data from other areas, results obtained in this study reveal that the depth and complexity of the weathering profiles reflect the time of exposition of such areas to the weathering agents close to the surface. However, there is no clear relationship between ages vs. altitude. The depth and the stratigraphic organization of weathering profiles in northeastern Brazil, contrary to the southeastern Brazil pattern, do not vary toward the coast. In our study area, field observations reveal the presence of ancient, thick and complex lateritic profiles preserved in the sedimentary mesas on the Borborema Plateau, as younger, narrow and incipient ones occur in the dissected areas. Geochronological results obtained for these profiles yielded older ages on the high altitudes, and younger ages in the lowlands, suggesting the scarp retreatment is the most reliable model to explain the regional landscape evolution. However, in the coastal lowlands, the relatively older ages obtained indicate that more complexes processes were involved in the modeling of the local relief

O campo e o jogo: uma História do Estádio Castelão (1963-1991)

The study aims to examine the planning, the construction and uses of the stadium Presidente Castelo Branco (Castelão), opened in Natal, capital of Rio Grande do Norte, in 1972. Used as main sources of documents printed newspapers A República, Tribuna do Norte e Diário de Natal; photographs of the 1960s, 1970s and 1980s and, finally, an interview with Moacyr Gomes da Costa, architect responsible for building the stadium Castelão. Seeks to understand the changes and continuities stemming from the construction of this stadium for football history and the city. Articulated in the text the inauguration of the stadium with the process of commodification and massification of football norte-rio-grandense, that occurred from the 1970s. Indicates the places where they practiced football in Natal before the construction of a stadium and analyzes the historical needs that led to the construction of a sports square. Discusses the transformation of football matches in shows profit, which now involve large economic interests. Investigates how political potiguares made use of football stadiums as a mechanism of legitimation and realize this debate with the performances of Djalma Maranhão and the Cortez Pereira, that at different times using this mechanism. Search elements that favored the popularization experienced by football potiguar from the 1970s, the role of the sports press this process and the emergence organized supporters

Usando a história da resolução de alguns problemas para introduzir conceitos: sistemas lineares, determinantes e matrizes.

In this work we studied the method to solving linear equations system, presented in the book titled "The nine chapters on the mathematical art", which was written in the first century of this era. This work has the intent of showing how the mathematics history can be used to motivate the introduction of some topics in high school. Through observations of patterns which repeats itself in the presented method, we were able to introduce, in a very natural way, the concept of linear equations, linear equations system, solution of linear equations, determinants and matrices, besides the Laplacian development for determinants calculations of square matrices of order bigger than 3, then considering some of their general applications

Sistema de numeração posicional e a lógica da divisão de inteiros

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

A integração do tutorial interativo TryLogic via IMS Learning Tools Interoperability: construindo uma infraestrutura para o ensino de Lógica através de estratégias de demonstração e refutação

Logic courses represent a pedagogical challenge and the recorded number of cases of failures and of discontinuity in them is often high. Amont other difficulties, students face a cognitive overload to understand logical concepts in a relevant way. On that track, computational tools for learning are resources that help both in alleviating the cognitive overload scenarios and in allowing for the practical experimenting with theoretical concepts. The present study proposes an interactive tutorial, namely the TryLogic, aimed at teaching to solve logical conjectures either by proofs or refutations. The tool was developed from the architecture of the tool TryOcaml, through support of the communication of the web interface ProofWeb in accessing the proof assistant Coq. The goals of TryLogic are: (1) presenting a set of lessons for applying heuristic strategies in solving problems set in Propositional Logic; (2) stepwise organizing the exposition of concepts related to Natural Deduction and to Propositional Semantics in sequential steps; (3) providing interactive tasks to the students. The present study also aims at: presenting our implementation of a formal system for refutation; describing the integration of our infrastructure with the Virtual Learning Environment Moodle through the IMS Learning Tools Interoperability specification; presenting the Conjecture Generator that works for the tasks involving proving and refuting; and, finally to evaluate the learning experience of Logic students through the application of the conjecture solving task associated to the use of the TryLogic