A obra de triangulis omnimodis libri quinque de Johann Müller Regiomontanus (1436 1476): uma contribuição para o desenvolvimento da trigonometria

Trigonometry, branch of mathematics related to the study of triangles, developed from practical needs, especially relating to astronomy, Surveying and Navigation. Johann Müller, the Regiomontanus (1436-1476) mathematician and astronomer of the fifteenth century played an important role in the development of this science. His work titled De Triangulis Omnimodis Libri Quinque written around 1464, and published posthumously in 1533, presents the first systematic exposure of European plane and spherical trigonometry, a treatment independent of astronomy. In this study we present a description, translation and analysis of some aspects of this important work in the history of trigonometry. Therefore, the translation was performed using a version of the book Regiomontanus on Triangles of Barnabas Hughes, 1967. In it you will find the original work in Latin and an English translation. For this study, we use for most of our translation in Portuguese, the English version, but some doubt utterance, statement and figures were made by the original Latin. In this work, we can see that trigonometry is considered as a branch of mathematics which is subordinated to geometry, that is, toward the study of triangles. Regiomontanus provides a large number of theorems as the original trigonometric formula for the area of a triangle. Use algebra to solve geometric problems and mainly shows the first practical theorem for the law of cosines in spherical trigonometry. Thus, this study shows some of the development of the trigonometry in the fifteenth century, especially with regard to concepts such as sine and cosine (sine reverse), the work discussed above, is of paramount importance for the research in the history of mathematics more specifically in the area of historical analysis and critique of literary sources or studying the work of a particular mathematician

O processo de trabalho e a composição técnica do trabalho do enfermeiro no cuidado à saúde da criança em unidades de saúde da familia

With the trajectory that the problems related to child health are taking in our society, particularly with regard to infant mortality, beyond the process of decentralization of health and the implementation of the Family Health Strategy in the cities, where it has increased considerably performance of nursing staff in Primary Health Care, they can be considered essential factors for reflections on the care of nurse dispenses the health of these children. In order to check how it is organized the working process of the nurse in caring for these children in USFs as well as the difficulties found in the dynamics of this work, this research aimed to analyze the work processes of nurses in care Child Health in USFs, with emphasis on technologies used in producing care. This is a research exploratory and descriptive with qualitative approach, based on the theoretical reference in about Work Process and Composition Technique of Work. The data were collected through semi-structured interviews of 11 nurses who, at the moment, perform their functions for more than 01 year at USF. The guiding questions were based at theoretical reference. To analyze the results, was used the referential of content analysis, and was refer to thematic analysis. In situations that were involved closed questions of the interview, was used the aid of SPSS 15.0 program for Windows. The results indicated that the process of nurse work in health care of children, focuses on the preventive character, whose focus of the actions are healthy children, following the routines and protocols established by the Ministry of Health with a view to maintaining health them. When analyzing the data through theoretical references of Composition Technique of Work found that the core technologies of daily tasks of the nurse are directed for the use of technology soft-hard and hard, and the reason established between the Dead Working and Alive Working, there is prevalence of the first against the second in the production of this care. These situations contribute to the explanation of the emergence problems related to adhesion of mothers / caregivers to monitoring the CD, due to character prescriptive and normalizer of actions. The results also suggested the presence of "vanishing lines" in the make of nurses, confirming the self-governance of health professionals in daily work. These "vanishing lines" express the own execution of the Work Live in action, guided by the use of soft technologies, however, was not characterized as a process of technology transition. So, to get a better resolution to the problems related to child health, the nurse has reorganize your work process by focusing on the execution of work live in action.

Contribuições à análise de robustez de sistemas de controle usando redes neurais

This work develops a robustness analysis with respect to the modeling errors, being applied to the strategies of indirect control using Artificial Neural Networks - ANN s, belong to the multilayer feedforward perceptron class with on-line training based on gradient method (backpropagation). The presented schemes are called Indirect Hybrid Control and Indirect Neural Control. They are presented two Robustness Theorems, being one for each proposed indirect control scheme, which allow the computation of the maximum steady-state control error that will occur due to the modeling error what is caused by the neural identifier, either for the closed loop configuration having a conventional controller - Indirect Hybrid Control, or for the closed loop configuration having a neural controller - Indirect Neural Control. Considering that the robustness analysis is restrict only to the steady-state plant behavior, this work also includes a stability analysis transcription that is suitable for multilayer perceptron class of ANN s trained with backpropagation algorithm, to assure the convergence and stability of the used neural systems. By other side, the boundness of the initial transient behavior is assured by the assumption that the plant is BIBO (Bounded Input, Bounded Output) stable. The Robustness Theorems were tested on the proposed indirect control strategies, while applied to regulation control of simulated examples using nonlinear plants, and its results are presented

Resistência e performance na arte de João Cota

Researching about the art of tell and the tales told by João Cota is somehow revisiting the oral tradition and social practice in the story-telling art. It takes into consideration the resistance this art still exerts, mainly by using the performance of oral transmission and receptiveness to tales. The study of this practice contributes to the vivacious and dynamcis permanence of this authentic and traditional storyteller of his repertory and of his form to tellin our culture. Story-telling is part of the humankind living heritage communicated by means of popular wisdom. Despite the risk of vanishing into thin air, along with their narrators, the tales still manage to resist the contemporary mass culture model. How long further will stories like the ones narrated by João Cota be able to resist to strong and stronger structures dictated by writing and other communication means? João Cota s practice in story-telling will be studied not only as a proposal to identify the presence of this practice and the oral cultural resistance but also, through the performance prospective, to identify the oral transmission and receptiveness to the tales that are part of this storyteller s repertoire. In other words: what he tells, how he tells it, and why he tells it. The advent of new technologies such as internet, through which people can easily communicate with others in different parts of the world, and the greater and greater expansion in the writing skill concept interfere the maintenance of the oral tradition elements present in João Cota s narratives and inserted in the Brazilian culture. This has become more visible in the latest decades although we still notice the living tradition and permanence of the story-telling practice in several parts of the country through their wise storytellers. Our research target will require - in each of its study stages reference to works by several theoreticians namely Paul Zumthor, Mikhail Bakhtin, Câmara Cascudo, theoreticians from the receptiveness aesthetic, from the written culture history, from oral cultures and reading practices, from tradition and the Brazilian Culture of oral story-telling. In order to get to know and draw a profile of this storyteller, we ve chosen to use the comprehensive interview method by French Sociologist Jean Claude Kaufmann. The originality in the method consists of the qualitative data put together in situ , concentrated on the storyteller s narratives/speeches recorded on tape, which will be the focal point of this study. Our analysis method is based on tireless sessions of listening to interviews out of which we gathered information related to the storyteller, his practice in telling the tales, and his repertoire

Fases magnéticas de sistemas nanoestruturados de terras-raras

There is presently a worldwide interest in artificial magnetic systems which guide research activities in universities and companies. Thin films and multilayers have a central role, revealing new magnetic phases which often lead to breakthroughs and new technology standards, never thought otherwise. Surface and confinement effects cause large impact in the magnetic phases of magnetic materials with bulk spatially periodic patterns. New magnetic phases are expected to form in thin film thicknesses comparable to the length of the intrinsic bulk magnetic unit cell. Helimagnetic materials are prototypes in this respect, since the bulk magnetic phases consist in periodic patterns with the length of the helical pitch. In this thesis we study the magnetic phases of thin rare-earth films, with surfaces oriented along the (002) direction. The thesis includes the investigation of the magnetic phases of thin Dy and Ho films, as well as the thermal hysteresis cycles of Dy thin films. The investigation of the thermal hysteresis cycles of thin Dy films has been done in collaboration with the Laboratory of Magnetic Materials of the University of Texas, at Arlington. The theoretical modeling is based on a self-consistent theory developed by the Group of Magnetism of UFRN. Contributions from the first and second neighbors exchange energy, from the anisotropy energy and the Zeeman energy are calculated in a set of nonequivalent magnetic ions, and the equilibrium magnetic phases, from the Curie temperature up to the Nèel temperature, are determined in a self-consistent manner, resulting in a vanishing torque in the magnetic ions at all planes across the thin film. Our results reproduce the known isothermal and iso-field curves of bulk Dy and Ho, and the known spin-slip phases of Ho, and indicate that: (i) the confinement in thin films leads to a new magnetic phase, with alternate helicity, which leads to the measured thermal hysteresis of Dy ultrathin films, with thicknesses ranging from 4 nm to 16 nm; (ii) thin Dy films have anisotropy dominated surface lock-in phases, with alignment of surface spins along the anisotropy easy axis directions, similar to the known spin-slip phases of Ho ( which form in the bulk and are commensurate to the crystal lattice); and (iii) the confinement in thin films change considerably the spin-slip patterns of Ho.

Condições de energia de hawking e ellis e a equação de raychaudhuri

In the Einstein s theory of General Relativity the field equations relate the geometry of space-time with the content of matter and energy, sources of the gravitational field. This content is described by a second order tensor, known as energy-momentum tensor. On the other hand, the energy-momentum tensors that have physical meaning are not specified by this theory. In the 700s, Hawking and Ellis set a couple of conditions, considered feasible from a physical point of view, in order to limit the arbitrariness of these tensors. These conditions, which became known as Hawking-Ellis energy conditions, play important roles in the gravitation scenario. They are widely used as powerful tools for analysis; from the demonstration of important theorems concerning to the behavior of gravitational fields and geometries associated, the gravity quantum behavior, to the analysis of cosmological models. In this dissertation we present a rigorous deduction of the several energy conditions currently in vogue in the scientific literature, such as: the Null Energy Condition (NEC), Weak Energy Condition (WEC), the Strong Energy Condition (SEC), the Dominant Energy Condition (DEC) and Null Dominant Energy Condition (NDEC). Bearing in mind the most trivial applications in Cosmology and Gravitation, the deductions were initially made for an energy-momentum tensor of a generalized perfect fluid and then extended to scalar fields with minimal and non-minimal coupling to the gravitational field. We also present a study about the possible violations of some of these energy conditions. Aiming the study of the single nature of some exact solutions of Einstein s General Relativity, in 1955 the Indian physicist Raychaudhuri derived an equation that is today considered fundamental to the study of the gravitational attraction of matter, which became known as the Raychaudhuri equation. This famous equation is fundamental for to understanding of gravitational attraction in Astrophysics and Cosmology and for the comprehension of the singularity theorems, such as, the Hawking and Penrose theorem about the singularity of the gravitational collapse. In this dissertation we derive the Raychaudhuri equation, the Frobenius theorem and the Focusing theorem for congruences time-like and null congruences of a pseudo-riemannian manifold. We discuss the geometric and physical meaning of this equation, its connections with the energy conditions, and some of its several aplications.

Análise e comparação entre algoritmos de percolação

In this work, we study and compare two percolation algorithms, one of then elaborated by Elias, and the other one by Newman and Ziff, using theorical tools of algorithms complexity and another algorithm that makes an experimental comparation. This work is divided in three chapters. The first one approaches some necessary definitions and theorems to a more formal mathematical study of percolation. The second presents technics that were used for the estimative calculation of the algorithms complexity, are they: worse case, better case e average case. We use the technique of the worse case to estimate the complexity of both algorithms and thus we can compare them. The last chapter shows several characteristics of each one of the algorithms and through the theoretical estimate of the complexity and the comparison between the execution time of the most important part of each one, we can compare these important algorithms that simulate the percolation.

Calculando distância em geometria espacial usando material manipulável como recurso didático

This work presents a proposal for introducing the teaching of Geometry Space study attempts to demonstrate that the use of manipulatives as a teaching resource can be an alternative learning facilitator for fixing the primitive concepts of geometry, the postulates and theorems, position relationships between points, lines and planes and calculating distances. The development makes use of a sequence of activities aimed at ensuring that students can build a more systematic learning and these are divided into four steps

Uma justificava da validade do teorema fundamental da álgebra para o ensino médio

Among several theorems which are taught in basic education some of them can be proved in the classroom and others do not, because the degree of difficulty of its formal proof. A classic example is the Fundamental Theorem of Algebra which is not proved, it is necessary higher-level knowledge in mathematics. In this paper, we justify the validity of this theorem intuitively using the software Geogebra. And, based on [2] we will present a clear formal proof of this theorem that is addressed to school teachers and undergraduate students in mathematics

Petrologia do plúton Serra da Macambira, neoproterozóico da faixa seridó, província Borborema (NE do Brasil)

The final stage of Brasiliano/Pan-African orogeny in the Borborema Province is marked by widespread plutonic magmatism. The Serra da Macambira Pluton is an example of such plutonism in Seridó Belt, northeastern Borborema Province, and it is here subject of geological, petrographic, textural, geochemical and petrogenetic studies. The pluton is located in the State of Rio Grande do Norte, intrusive into Paleoproterozoic orthogneisses of the Caicó Complex and Neoproterozoic metassupracrustal rocks of the Seridó Group. Based upon intrusion/inclusion field relationships, mineralogy and texture, the rocks are classified as follows: intermediate enclaves (quartz-bearing monzonite and biotite-bearing tonalite), porphyritic monzogranite, equigranular syenogranite to monzogranite, and late granite and pegmatite dykes. Porphyritic granites and quartz-bearing monzonites represent mingling formed by the injection of an intermediate magma into a granitic one, which had already started crystallization. Both rocks are slightly older than the equigranular granites. Quartz-bearing monzonite has K-feldspar, plagioclase, biotite, hornblende and few quartz, meanwhile biotite-bearing tonalite are rich in quartz, poor in K-feldspar and hornblende is absent. Porphyritic and equigranular granites display mainly biotite and rare hornblende, myrmekite and pertitic textures, and zoned plagioclase pointing out to the relevance of fractional crystallization during magma evolution. Such granites have Rare Earth Elements (REE) pattern with negative Eu anomaly and light REE enrichment when compared to heavy REE. They are slight metaluminous to slight peraluminous, following a high-K calc-alkaline path. Petrogenesis started with 27,5% partial melting of Paleoproterozoic continental crust, generating an acid hydrous liquid, leaving a granulitic residue with orthopyroxene, plagioclase (An40-50), K-feldspar, quartz, epidote, magnetite, ilmenite, apatite and zircon. The liquid evolved mainly by fractional crystallization (10-25%) of plagioclase (An20), biotite and hornblende during the first stages of magmatic evolution. Granitic dykes are hololeucocratic with granophyric texture, indicating hypabissal crystallization and REE patterns similar to A-Type granites. Preserved igneous textures, absence or weak imprint of ductile tectonics, association with mafic to intermediate enclaves and alignment of samples according to monzonitic (high-K calcalkaline) series all indicate post-collisional to post-orogenic complexes as described in the literature. Such interpretation is supported by trace element discrimination diagrams that place the Serra da Macambira pluton as late-orogenic, probably reflecting the vanishing stages of the exhumation and collapse of the Brasiliano/Pan-African orogen.

O circuito espacial da indústria de cerâmica vermelha no seridó potiguar

This research has as an empirical universe, the productive territory of red ware in the Seridó region of Rio Grande do Norte. In the last years this territory has gone through a process of appropriation that has been substantially changing the environmental and social dynamism of the place. However, the industry of red ware has been focusing in some areas, mainly, in the county of Parelhas and Carnaúba dos Dantas. From this point of view, the aim of this work consists in analyze the use of these areas by the red ware industry and the transformations occurred with the expansion of the number of industries and the productivity raise, that requires bigger amounts of earthenware and wood, resources that are low in referred territory. As the result of this process, the suitable alternative has been to acquire inputs in other Rio Grande do Norte counties, as well as in Paraíba counties. To reach the proposed objective, the methodology of this work was consisted of bibliographic and empirical research, regarding the occupation that this activity covers in the Seridó region. From the information obtained during the research, it can be stated that the inputs to the production execution in the red ware industry are acquired in the geographic nearby lands. The analysis of the stages of the production(acquisition of raw material, production and commercialization) showed that the activity acts in a continuous area, having as principal consumer market other northeastern states and the state of Pará. The present study revealed that the pottery activity is set as untenable, because of non-stopping use of the argil and wood, resources that are vanishing from the area, which consume causes a many problems such as deforestation and erosion. Besides, the sale of productive lands for the red ware industries makes harder its good use by the familiar agriculturists in the development of agriculture and cattle raising activity, which for many times is the main economic activity of the place. The precariousness reveals in the constant accidents at work, that most of them are neglected by the local authorities, without any penalty to the industries. Therefore, the industry of red ware in Seridó uses the territory as a resource, leaving its environmental problems that my compromise the quality of life of the actual and future generations

Lacan, Gödel, a ciência e a verdade

Jaques Lacan, the thinker who proposes a return to the fundamentals of psychoanalysis in Freud states that the math would face as a privileged way of transmission of knowledge by the science. Although he was a follower of the mathematization of nature as the foundation of modern science, for him this principle does not imply eliminating the subject that produces it. That would be equivalent to saying that there can not be a language, whatever, even the math, that may "erases" the subject assumption in science. In the text The science and the truth we will try to introduce the idea, not so simple, by the way, the truth as the cause. Citing the framework of the causes in Aristotle, Lacan will speak of a homology between the truth as formal cause, in the case of science, and the truth as material cause, on the side of psychoanalysis. Among its aims with this text, he wants to establish that the unconscious of the subject would be none other than the subject of science. The famous incompleteness theorems of logical-mathematical Kurt Gödel enter here as a chapter of this issue. Recognized as true watershed, these theorems have to be remembered as revealing even outside the mathematical environment, and Lacan himself is not indifferent to this. He makes mention of Gödel's name and draws some observations apparently modest support for his own theory. Since some technical sophisticated knowledges awaits the reader who intends understand this supposed corroboration that Gödel provides to psychoanalysis, introduce the student of Lacan in the use he makes of the incompleteness theorems is the objective of this work. In The science and the truth, which fits us to locate the name of Gödel, one must question how seize such an idea without incurring the extrapolation and abuse of mathematical knowledge, almost trivial in this case. Thus, this paper aims to introduce the reader to the reasoning behind the theorems of Gödel, acquaint him about the Lacan’s mathematical claims, and indicate how to proceed using this implicit math in the text The science and the truth.

O paradoxo da superdifusão de uma caminhada aleatória com memória exponencial

The random walk models with temporal correlation (i.e. memory) are of interest in the study of anomalous diffusion phenomena. The random walk and its generalizations are of prominent place in the characterization of various physical, chemical and biological phenomena. The temporal correlation is an essential feature in anomalous diffusion models. These temporal long-range correlation models can be called non-Markovian models, otherwise, the short-range time correlation counterparts are Markovian ones. Within this context, we reviewed the existing models with temporal correlation, i.e. entire memory, the elephant walk model, or partial memory, alzheimer walk model and walk model with a gaussian memory with profile. It is noticed that these models shows superdiffusion with a Hurst exponent H > 1/2. We study in this work a superdiffusive random walk model with exponentially decaying memory. This seems to be a self-contradictory statement, since it is well known that random walks with exponentially decaying temporal correlations can be approximated arbitrarily well by Markov processes and that central limit theorems prohibit superdiffusion for Markovian walks with finite variance of step sizes. The solution to the apparent paradox is that the model is genuinely non-Markovian, due to a time-dependent decay constant associated with the exponential behavior. In the end, we discuss ideas for future investigations.