Investigação histórica na formação de professores de matemática: um estudo centrado no conceito de função

In this study we analyzed the development of a teaching experience, involving students with a bachelor s degree in mathematics from UFRN, based on the history of mathematics and mathematical investigations with the aim of contributing to the improvement of the teaching-learning of mathematics. The historical investigation tasks were planned and applied in the classroom, focusing on functional thought. The results obtained during the experience were described and evaluated based on authors who support the assumption of investigation and history as an alternative to the learning of mathematics. We emphasize that the material of analysis consisted of a work diary, audio recordings, questionnaires with testimony of the students involved, and, in addition, the assessment of the teacher of that subject. With regard to the mathematical content, the study was restricted to the concept of function, forms of representation and notation. It was evident that students showed great improvement with regard to the necessary formalization of the mathematical contents which were focused on, and to the active involvement of the students at different stages of the study. We can affirm that the completed study certainly represents significant contributions to an approach in the teaching-learning of functional thought

Se inicia oração com pronome clítico? Atitudes linguísticas, na escola, em relação aos padrões brasileiros de colocação pronominal

Focusing on the empirical assessment issue, proposed by Language change theory (cf. cf. WEINREICH; LABOV; HERZOG, 2006; LABOV, [1972] 2008), this research assists to clarifying Portuguese teacher s attitudes in Natal- RN, regarding (a) to proclisis in three specific contexts: in the beginning of a simple/compound sentence (V1), after the subjects (SV), and proclisis after the secondary verb in complex verbal structures (V1V2); (b) to students who use such patterns in usage. Specific contexts were gathered thanks to their representing of the standard variety, as many studies have proven (Martins, 2012; Schei, 2003; Biazzoli, 2010, 2012). The research aims at: (i) verifying by means of a classroom assessment test, whether Portuguese teachers correct proclisis on referred contexts; (ii) identifying, via attitudinal tests what actions teachers take regarding to the usage of standards above mentioned, as well as students as users of those. Twenty Portuguese teachers, picked at random out of different of public schools in Natal-RN, responded to a classroom assessment test in addition to other two attitudinal ones. Results achieved point to a recurring high proclisis correction index of 50% in simple/compound sentences, even though such variety has been implemented to pronominal usage standards in Brazilian Portuguese. This setting of usage was generally assessed negatively, having no commonality between this assessment and the neutral one used by students. Unlike previous setting, the proclisis after subject did not receive any correction of the twenty teachers, what proves coherence with the positive evaluation both the varieties and the students attained. As for the second verb of complex verbal structures, proclisis correction went negative on presenting single results, despite their proximity, with correction indexes of 20% (infinite structures), 10% (present progressive structures) and 25% (participle structures). The assessment on these contexts of proclisis ranged between positive and neutral, also valid for the one students utilized. It means that proclisis in the beginning of simple/compound sentences are yet seemingly spotted in writing school scenario, much likely due to the negative evaluation, opposite to students . Later to subjects and earlier to secondary verbs in structures, proclisis appears to be acknowledged in writing school scenarios, which reflects on teachers assessment as compared to students who use proclisis in these contexts; being in general either positive or neutral

A heterogeneidade discursiva em revistas de divulgação científica

This research aiming at show an interpretative description about the form and function of Scientific Publication (SP) discursive genre, in two magazines of national circulation. We analyzed subjects published from 2004 to 2006, in the magazines Revista do Professor and Revista Nova Escola. We see at SP subjects reported discourses, into its two main presentation forms of other voices: direct discourse and indirect discourse. We have established some aims, first, we analyzing different forms to mark the discursive heterogeneity, by the reason the writer conceptualize an image of his/her interlocutor. The second one, we intend to look at the differences between marked heterogeneity according to the writer production, journalists and researchers, and finally, we investigate more or less occurrence of cited discourse, in what is concerned with different perspectives at communities that produce this kind of text. As theoretical background to our discussions we followed socio-historical perspective, its language and subject discourse conceptualizations. We did it mainly based on Bakhtin s works (1929; 1995; 2003). We were also based on theoretical discussions about discursive heterogeneity by Authier-Revuz (1990; 1998; 2004) and Maingueneau (1993; 2001). At analyzing the social dimensions of our data, we identified as relevant elements in the construction of the subjects (stories) the image that the writer (reporter) did/construct about his/her interlocutor as well as the use of different strategies, for example: the text produced by the journalists frequently use of direct discourse forms, while texts produced by researchers are almost fulfilled by indirect discourse. Beside this, texts are different in their social voices that are in their discourse. In the case of text produced by journalist are predominant the discursive scene of the school agents: teachers, students, parents, among others. Otherwise, in the texts produced by researchers already-said utterances, that in their majority of times, come from scientific discourse

A organização da interação professor-aluno em sala de aula: turnos e o par pergunta-resposta

Este trabalho tem como foco principal a interação em sala de aula, especificando aspectos da organização linguístico-discursiva, na produção conjunta da fala da professora e dos alunos, materializada em turnos, ressaltando o par pergunta-resposta na aula de Língua Portuguesa. Para alcançarmos esse objetivo, inspiramo-nos em alguns trabalhos acerca da organização da interação que adotaram a perspectiva dos estudos interacionais e a abordagem etnográfica, a fim de explicitar o conhecimento nos espaços de ensino e aprendizagem. Entre eles, citamos as pesquisas de Galvão (1996, 2004) e de Matêncio (2001). Nessa direção, descrevemos o processo de interação em sala de aula em uma escola pública, analisando e interpretando as ações de linguagem realizadas pela professora e pelos alunos. Teoricamente, embasamo-nos, principalmente, na Análise da Conversação, ancorando-nos no estudo pioneiro de Sacks, Schegloff e Jefferson ([1974] 2003); nos postulados de Marcuschi ([1986] 2007a); nas pesquisas de Kerbrat-Orecchioni (2006), dentre outros. Explicitamos uma tipologia de perguntas e respostas em sala de aula, quanto à sua forma e função, conforme os postulados teóricos de Stubbs (1987), Araújo (2003), Fávero, Andrade e Aquino (2006), Silva (2006) e Koshik (2010). Analisamos a organização da tomada de turno, seguida de uma investigação sobre perguntas e respostas no discurso desenvolvido face a face. Na tentativa de compreendermos o cotidiano dos envolvidos no cenário de sala de aula, adotamos a abordagem etnográfica e o método indutivo, nas perspectivas de André (2010) e Chizzotti (2006). Os dados foram gerados através de pesquisa de campo, por meio de gravações (em áudio) de aulas de Língua Portuguesa, posteriormente transcritas e transformadas no corpus de pesquisa. As análises demonstraram que a interação entre professora e alunos organizou-se em trocas de turnos, na maioria das vezes, controladas pela professora, evidenciando-se uma relação de assimetria entre os participantes. Esses turnos concretizados, geralmente, no par adjacente pergunta-resposta revelaram como a construção do conhecimento se realiza em sala de aula. Por fim, observamos que a interação em sala de aula de Língua Portuguesa é organizada por aspectos sociais e pedagógicos intrinsecamente imbricados

As sentenças com é ruim que no português brasileiro

Based on studies on the structure of copulates sentences in Brazilian Portuguese (PB), according to grammar theory, it s analyzed on this dissertation, the complex copulate sentences what, in the PB, initiated by the formation é ruim que in the PB, bringing the hypothesis that they can have one predicacional reading (PRED) and other especificacional reading (ESP). It s revealed what, though they are similar slightly, that makes the different that are triggered is structural configuration of sentence and the form as come emerged the its constituents: that of PRED interpretation, that we defined as Common Copulate Sentence (or SCC), it s checked that the constituent ruim, and only it, is predicate of a Small Clause, and appears in the structure on even position wherein is pronounced, not passing by the method of movement, from where introduce wide predication on all subject, that is the CP built-in; those sentences é ruim que understanding ESP, that denominate of Negative Copulate Sentence (or SCN), whereas the fixed expression contradict or right what is asserted in built-in, it s perceived what the ruim is a part of this fixed expression, and surely crystallized, which appears in structure per movement, germinated as adjunct of Inflexional Phrase (IP) and being elevation to specifier to FocP (or SpecFocP), where acquires discursive interpretation of focus. Besides the mode as the ruim or the fixed expression emerge in that sentences, the relation between the copula and main verb likewise contribute to distinguish the sentences: 1) regarding flexion of mode, when is a SCC, the copula must be in the mode indicative, and the main verb, in the subjunctive; when is a SCN, copula and main verb must be always on indicative; 2) regarding flexion of temp, both the copula as main verb of the SCC can be flexed, whereas at the SCN, the main verb can vary in present, past and future, but the copula should appear, necessarily, in third persona of present of indicative, what confirms our hypothesis that there is an fixed expression at the copulate sentences with é ruim que ESP. Other two evidences are pointed as characteristics that distinguish the sentence with é ruim que PRED of sentence with é ruim que ESP: 1) in semantics, the constituent ruim equals not good, that has appreciation, when the reading will PRED; already the pair é ruim equals not, at the ESP; 2) in prosody, there discrete sound elevation the ruim on the other constituents of SCC, PRED, while there is accentuated acoustic elevation on the ruim of SCN, ESP. Our search it is grounded in authors as Zanfeliz (2000), Modesto (2001), Mioto (2003), Kato & Ribeiro (2006), Lobo (2006), Quarezemin (2006, 2009, 2011, 2012) e Resenes (2009), researchers that devoted their attention on studies the formation and organization of the constituents of cleaved sentences and focalization of constituent, basing itself in approach generative of linguistic

Essa marca de suor numa canção: o processo de redução estrutural na poesia de Zila Mamede

Die Beziehung zwischen Literatur und Gesellschaft wurden, im Laufe der Jahrhunderte, aus unterschiedlichen Perspektiven analysiert. Die Wissenschaftler analysieren manchmal die Aspekten der sozialen Realität, sie betonen manchmal die Natur der literarischen Werk. Wir glauben, dass Antonio Candido einen Gleichgewichtszustand erreicht, als er das Konzept der strukturellen Reduktion oder Formalisierung entwickelt. Nämlich, der Prozess, bei dem die menschliche und soziale Leben zu einem Bestandteil der literarischen Struktur wird. Der Autor tritt eine Einbahnstraße und er kann Daten aus der sozialen Ordnung aufholen, ohne dabei die Materialität des Textes den Augen verlieren. Und das sind die theoretische Annahmen, die die Entwicklung dieser Arbeit leiten. Wir wollen zu zeigen, dass die Struktur der mamediana Lyrik aufdeckt, signifikante Daten der Gesellschaft, in der der Autore eingefügt wurde enthüllt. Folglich, wir analysieren soziale Thema, das sein Werk durchzieht. Zuerst, wir untersuchen, wie Zila Mamede den Alltag der Gesellschaft vertreten. Von der strukturellen Organisation der Gedichte, wir erkennen, das die Episode aus kleiner Städte ein Akt des Widerstands gegen die fragmentierte Profil der kapitalistischen Gesellschaf sind. Das ist, warum sie doch eng mit der Idee der Tradition erscheinen. Die dichotome Beziehung zwischen den regionalen Daten und der Element der Modernisierung etabliert, sie wird durch die Organisation des Raumes verstärkt. Während die Stadt bei konkrete gesellschaftliche Ordnung Spitzenbeträge verweist, hat die Landschaft eine harmonische und warme Form. Allgemeinen, die moderne Stadt von Zila Mamede geformt, ist eine Abbild der Industriegesellschaft. Die Bilder die Landschaft sind ein Gegenmittel gegen die Feindseligkeiten Merkmale der neuen urbanen Zustand. So, die Landschaft hat die Funktion von Umstrukturierung der Persönlichkeit des Einzelnen durch die Erfahrung der großen Städte betroffen verdinglichenden. Der Konflikt, der durch das lyrische mamediana läuft, sind Reflexionen des Prozesses der Modernisierung der Stadt Natal, ihres eigenen Landes die politische Instabilität, sie durch verschiedene staatliche Programme ging, während Der Autor seine literarische Tätigkeit verfolgt

Ambiente de textualização no ensino a distância: o caso do fórum educacional

This research deals with textualization issues present in educational forums in distance learning environment. The research aims to analyze textualization regarding communication practices between tutors and distance learning students. Specifically the research aims to verify if the educational forum is considered pertinent for knowledge construction as well as identify subject´s behavior in e-Proinfo environment. The research also aims to understand the dynamics of the teaching and learning techniques related to the forum´s printed material. This is done in order to acknowledge discourse on behalf of subjects through the presented educational assignments. In order to address the issue, the work dealt with the relations present in distance learning forums, the forms in which the assignments are made, the way social actors interact and how this debate happens in the virtual environment. The research emphasized an educational forum used in a higher education institution at Rio Grande do Norte/Brazil. Thus the research corpus is composed by messages that were posted in the forum in the module called computer material . This module is one of the last in a set of six modules that are part of The Basic Cycle for Media Training promoted by the Center for Distance Learning in a public university at Rio Grande do Norte/Brazil. The research deals with a qualitative type approach in the perspectives of Merriam (1988), Cresswell (1994) and Minayo (1996). In order to achieve this analysis, the research dealt with theoretical landmarks related to distance learning present in (Silva, 2008; Brait, 1993; Sperbe and Wilson, 1986; Marquesi and Elias 2008 as well as Xavier, 2005, amongst others. As for aspects related to media and technological perspectives present in the forum, the research dealt with (Baranov, 1989; Neuner, 1981; Kearsley and Moore, 1996). Textualization was dealt according to (Marcuschi, 2008; Costa Val, 2004) and the conceptions and functions regarding tutors was seen according to (Salgado, 2002). In the conclusion and recommendations it was seen that these discussions present relevant contributions to distance learning and go beyond the practical universe present in electronical interaction. In the final considerations it is pointed out that this research is relevant for areas such as applied linguistics and presents guidelines for those involved in continuous education and aim meaningful knowledge that is coherent with distance learning education

Interação no rádio: a participação do ouvinte no programa debates do povo

The radio is just not seen as conveying information, but a media able to establish ways that generate certain direction. We see an inclusion of the listener in the construction of programs, is exposing their life stories, commenting on facts, answering questions, choosing subjects and participating in some form of radio programming. This insertion of the listener in radio programs is generally thought of as a constituent element of the message. This study aims to analyze the participation of the listener and the forms of interaction in the " Debates of the People" that thirty- past two years is the schedule for CBN Fortaleza. The investigation was conducted through observation in studio, interview, transcription, content analysis and association analysis. This is a qualitative and quantitative research while. We found that the listeners of the program had no acceptance of interactive tools such as the Internet and social networks to make their holdings. In clipping analyzed, we noted that the participation of the listener was selected according to their relationship and proximity to the topic discussed. Also detected that the opinion is superior to the listener questions on the topic. The presenter has the function to put the questions in the listener program. Among the public comments are questions and opinions on the subject and speaks of the debaters. Among the authors, use Barbosa (2009 ), Ferraretto (2007 ), Lopez (2010 ), Ortriwano (2001 ), Peruzzo (2004 ), Prata (2009 ), Primo (2006 ), Thompson (2009 ), among others

Modelos analíticos para rádio fontes extragalácticas

The great majority of analytical models for extragalactic radio sources suppose self-similarity and can be classified into three types: I, II and III. We have developed a model that represents a generalization of most models found in the literature and showed that these three types are particular cases. The model assumes that the area of the head of the jet varies with the jet size according to a power law and the jet luminosity is a function of time. As it is usually done, the basic hypothesis is that there is an equilibrium between the pressure exerted both by the head of the jet and the cocoon walls and the ram pressure of the ambient medium. The equilibrium equations and energy conservation equation allow us to express the size and width of the source and the pressure in the cocoon as a power law and find the respective exponents. All these assumptions can be used to calculate the evolution of the source size, width and radio luminosity. This can then be compared with the observed width-size relation for radio lobes and the power-size (P-D) diagram of both compact (GPS and CSS) and extended sources from the 3CR catalogue. In this work we introduce two important improvement as compared with a previous work: (1)We have put together a larger sample of both compact and extended radio sources

Fractais e Percolação na Recuperação de Petróleo

The complex behavior of a wide variety of phenomena that are of interest to physicists, chemists, and engineers has been quantitatively characterized by using the ideas of fractal and multifractal distributions, which correspond in a unique way to the geometrical shape and dynamical properties of the systems under study. In this thesis we present the Space of Fractals and the methods of Hausdorff-Besicovitch, box-counting and Scaling to calculate the fractal dimension of a set. In this Thesis we investigate also percolation phenomena in multifractal objects that are built in a simple way. The central object of our analysis is a multifractal object that we call Qmf . In these objects the multifractality comes directly from the geometric tiling. We identify some differences between percolation in the proposed multifractals and in a regular lattice. There are basically two sources of these differences. The first is related to the coordination number, c, which changes along the multifractal. The second comes from the way the weight of each cell in the multifractal affects the percolation cluster. We use many samples of finite size lattices and draw the histogram of percolating lattices against site occupation probability p. Depending on a parameter, ρ, characterizing the multifractal and the lattice size, L, the histogram can have two peaks. We observe that the probability of occupation at the percolation threshold, pc, for the multifractal is lower than that for the square lattice. We compute the fractal dimension of the percolating cluster and the critical exponent β. Despite the topological differences, we find that the percolation in a multifractal support is in the same universality class as standard percolation. The area and the number of neighbors of the blocks of Qmf show a non-trivial behavior. A general view of the object Qmf shows an anisotropy. The value of pc is a function of ρ which is related to its anisotropy. We investigate the relation between pc and the average number of neighbors of the blocks as well as the anisotropy of Qmf. In this Thesis we study likewise the distribution of shortest paths in percolation systems at the percolation threshold in two dimensions (2D). We study paths from one given point to multiple other points

Fractais e percolação na recuperação de Petróleo

The complex behavior of a wide variety of phenomena that are of interest to physicists, chemists, and engineers has been quantitatively characterized by using the ideas of fractal and multifractal distributions, which correspond in a unique way to the geometrical shape and dynamical properties of the systems under study. In this thesis we present the Space of Fractals and the methods of Hausdorff-Besicovitch, box-counting and Scaling to calculate the fractal dimension of a set. In this Thesis we investigate also percolation phenomena in multifractal objects that are built in a simple way. The central object of our analysis is a multifractal object that we call Qmf . In these objects the multifractality comes directly from the geometric tiling. We identify some differences between percolation in the proposed multifractals and in a regular lattice. There are basically two sources of these differences. The first is related to the coordination number, c, which changes along the multifractal. The second comes from the way the weight of each cell in the multifractal affects the percolation cluster. We use many samples of finite size lattices and draw the histogram of percolating lattices against site occupation probability p. Depending on a parameter, ρ, characterizing the multifractal and the lattice size, L, the histogram can have two peaks. We observe that the probability of occupation at the percolation threshold, pc, for the multifractal is lower than that for the square lattice. We compute the fractal dimension of the percolating cluster and the critical exponent β. Despite the topological differences, we find that the percolation in a multifractal support is in the same universality class as standard percolation. The area and the number of neighbors of the blocks of Qmf show a non-trivial behavior. A general view of the object Qmf shows an anisotropy. The value of pc is a function of ρ which is related to its anisotropy. We investigate the relation between pc and the average number of neighbors of the blocks as well as the anisotropy of Qmf. In this Thesis we study likewise the distribution of shortest paths in percolation systems at the percolation threshold in two dimensions (2D). We study paths from one given point to multiple other points. In oil recovery terminology, the given single point can be mapped to an injection well (injector) and the multiple other points to production wells (producers). In the previously standard case of one injection well and one production well separated by Euclidean distance r, the distribution of shortest paths l, P(l|r), shows a power-law behavior with exponent gl = 2.14 in 2D. Here we analyze the situation of one injector and an array A of producers. Symmetric arrays of producers lead to one peak in the distribution P(l|A), the probability that the shortest path between the injector and any of the producers is l, while the asymmetric configurations lead to several peaks in the distribution. We analyze configurations in which the injector is outside and inside the set of producers. The peak in P(l|A) for the symmetric arrays decays faster than for the standard case. For very long paths all the studied arrays exhibit a power-law behavior with exponent g ∼= gl.

Parâmetros físico-químicos de estrelas nos campos de exoplanetas do satélite corot

A rotação estelar é um dos mais importantes observáveis da evolução estelar. Neste sentido, o satélite CoRoT representa uma oportunidade única de medir os períodos rotacionais para uma amostra de estrelas estatisticamente robusta, oferecendo dados absolutamente necessários para o estudo da rotação e seu papel na evolução estelar. Para conseguir isto, um passo fundamental é a caracterização física e química das estrelas observadas pelo CoRoT, especificamente devido ao fato de que o cálculo de períodos rotacionais confiáveis é um trabalho difícil sem a ajuda dos parâmetros estelares. Desta forma, foi elaborado um importante seguimento observacional das estrelas nos campos do CoRoT do anticentro LRa01 e do centro LRc01, permitindo a correta identificação dos períodos que reflitam a modulação rotacional. Nesta tese de doutorado são apresentados os resultados de tal seguimento. Parâmetros físicos e químicos, tais como temperatura efetiva Teff , gravidade superficial log(g), velocidade de microturbulência Vmic, abundância de ferro [Fe/H], velocidade de rotação projetada Vsin(i), e abundância de lítio A(Li) são apresentados para uma amostra de 116 estrelas dos campos CoRoT. Elas se encontram em diferentes estágios evolutivos, desde a sequência principal (SP) até o ramo das gigantes vermelhas (GV). As observações foram feitas utilizando os espectrógrafos UVES (VLT) e HYDRA (CTIO). Para a derivação de tais parâmetros foram utilizados o programa TurboSpectrum e os modelos de atmosfera de MARCS. Paralelamente, velocidades rotacionais Vsin(i) foram obtidas a partir do ajuste dos perfis observados e sintéticos das linhas de ferro e por meio de uma calibração de função de correlação cruzada (CCF). Períodos rotacionais Prot para 77 estrelas da amostra foram obtidos a partir das curvas de luz do satélite CoRoT. Extensas tabelas destes parâmetros e seus respectivos erros são apresentadas. Foram encontradas diferenças nas distribuições de Teff , [Fe/H] e estágios evolutivos entre os diferentes campos do CoRoT, indicando possíveis efeitos de seleção na amostra, assim como a existência de diferentes populações estelares do disco Galáctico. Por outro lado, o comportamento rotacional e as abundâncias de lítio não apresentam diferenças entre estrelas de parâmetros físicos similares, mas que pertencem a diferentes campos do CoRoT. A partir da análise de temperaturas, foi encontrada uma maior extinção por avermelhamento para estrelas do CoRoT localizadas no campo LRc01, assim como um gradiente deste valor em função da distância. Os resultados mostram que as abundâncias de lítio, as velocidades de rotação e os períodos rotacionais apresentam o mesmo comportamento descrito na literatura. Por outro lado, é apresentada pela primeira vez a relação que existe entre o lítio e o período de rotação em diferentes estágios evolutivos, mostrando, tal como era esperado, que ambas as grandezas possuem uma anticorrelação. Também é apresentada a evolução simultânea da rotação e do lítio, e foram calculadas relações que permitem obter valores médios de A(Li) como função da temperatura efetiva e do período rotacional. Os dados apresentados nesta tese de doutorado representam um importante ponto de partida para serem utilizados como uma amostra de calibração para diferentes programas no contexto da missão do satélite CoRoT, uma vez que a lista de estrelas aqui analisadas são parte das mais brilhantes que compõem o campo Exo do CoRoT

Sobre a relação entre rotação, atividade crosmosférica e abundância de lítio em estrelas subgigantes

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Competição entre caminhantes aleatórios

Conselho Nacional de Desenvolvimento Científico e Tecnológico

Um estudo da abundância de lítio, rotação, atividade cromosférica e magnetismo das estrelas análogas e gêmeas solares

The study physical process that control the stellar evolution is strength influenced by several stellar parameters, like as rotational velocity, convective envelope mass deepening, and magnetic field intensity. In this study we analyzed the interconnection of some stellar parameters, as Lithium abundance A(Li), chromospheric activity and magnetic field intensity as well as the variation of these parameters as a function of age, rotational velocity, and the convective envelope mass deepening for a selected sample of solar analogs and twins stars. In particular, we analyzed the convective envelope mass deepening and the dispersion of lithium abundance for these stars. We also studied the evolution of rotation in subgiants stars, because its belong to the following evolutionary stage of solar analogs, and twins stars. For this analyze, we compute evolutionary models with the TGEC code to derive the evolutionary stage, as well as the convective envelope mass deepening, and derive more precisely the stellar mass, and age for this 118 stars. Our Investigation shows a considerable dispersion of lithium abundance for the solar analogs stars. We also realize that this dispersion is not by the convective zone deep, in this way we observed which the scattering of A(Li) can not be explained by classical theories of mixing in the convective zone. In conclusion we have that are necessary extra-mixing process to explain this decrease of Lithium abundance in solar analogs and twins stars. We analyzed the subgiant stars because this are the subsequent evolutionary stage after the solar analogs and twins stars. For this analysis, we compute the rotational period for 30 subgiants stars observed by Co- RoT satellite. For this task we apply two different methods: Lomb-Scargle algorithm, and the Plavchan Periodogram. We apply the TGEC code we compute models with internal distribution of angular momentum to confront the predict results with the models, and the observational results. With this analyze, we showed which solid body rotation models are incompatible with the physical interpretation of observational results. As a result of our study we still concluded that the magnetic field, convective envelope mass deepening, and internal redistribution of angular momentum are essential to explain the evolution of low-mass stars, and its observational characteristics. Based on population synthesis simulation, we concluded that the solar neighborhood presents a considerable quantity of solar twins when compared with the discovered set nowadays. Altogether we foresee the existence around 400 solar analogs in the solar neighborhood (distance of 100 pc). We also study the angular momentum of solar analogs and twins, in this study we concluded that added angular momentum from a Jupiter type planet, putted in the Jupiter position, is not enough to explain the angular momentum predicted by Kraft law (Kraft 1970)