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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
161

Percepção de aprendizagens de alunos de cursos de engenharia sobre o Método de Newton-Raphson pelo uso de mapas conceituais

Alves, Paulo Cesar 12 September 2016 (has links)
Submitted by Filipe dos Santos (fsantos@pucsp.br) on 2016-11-29T11:25:36Z No. of bitstreams: 1 Paulo Cesar Alves.pdf: 3064049 bytes, checksum: bbbbb8cfdb6249b85002761ac406c6dd (MD5) / Made available in DSpace on 2016-11-29T11:25:36Z (GMT). No. of bitstreams: 1 Paulo Cesar Alves.pdf: 3064049 bytes, checksum: bbbbb8cfdb6249b85002761ac406c6dd (MD5) Previous issue date: 2016-09-12 / This developed search has the objective of analyse the conceptuals maps as a reflection instrument related to the understandment of a method to calculate the aproaches of real roots for high degree students. The chosen method is known as Newton-Raphson Method (NRM), that is normally part of the Numerical Calculus or Quantitative Methods and Computer subjects, that use the Derivated contant studied for first-year-engeneer students mainly in the subject of Differencial and Integral Cauculus. What was investigated was: how conceptuals maps can be used to understand as engeneer students can understan the NRM and its relation to Differencial and Integral Cauculus? Was used a quantitative aproache to this search that is situated at the educational field of Mathmatics. The theorical part is fundamented to the Learning Significative Theory of David Ausubel, using the Conceptual Maping of Joseph Novak. This search was developed with engeneer high degree students of a private institutuion, it was used the CmapTools software to the elaboration of digital conceptuals maps for the students. The final results were analysed with the objective of: firstly, try to realize students learnings about the NRM, obtained when students studied the subject of Numerical Calculus or Quantitative Methods and Computer. After we tryed to identify possible learnings that had an assimilation obliteradora. For this, the participants developed two conceptual maps using the CmapTools, the first map was elaborated with no influence of the searcher and the second was elaborated after a presentation of the method. The first conceptual digital maps elaborated for the participants revealed they understood how to elaborate a conceptual map using the CmapTools program, although they elaborated simple maps, with little relation to the used concepts. They also could present a NRM description in a logic way, revealing the students still remember some concepts envolved NRM and they also could present some relation that envolve these concepts. In relation to the second digital conceptual map, the students demostrated concepts that were not presented at the first digital conceptual map, some were elaborated with different structures and presented new terms of logic and coherence. In some maps is possible to realize the students remembered concepts studied in NRM and tryed to related to their maps by propositions. However, in some maps it is possible to detect the students only tryed to insert some NRM elements presented by the teacher. We also could realize that some studied concepts related to NRM seem to be interacting in the cognitive structure with previous knowledge, and with the NRM presentation, we concluded that some of these concepts seem to be present in a assimilation obliteradora / A pesquisa desenvolvida teve por objetivo analisar o uso de mapas conceituais como instrumento de reflexão a respeito da compreensão de um método para calcular aproximações de raízes reais por alunos do ensino superior. O método escolhido é conhecido como Método de Newton-Raphson (MNR), normalmente trabalhado na disciplina de Cálculo Numérico ou de Métodos Quantitativos e Computacionais, que utiliza o conteúdo de Derivada estudado por alunos no primeiro ano de cursos de Engenharia, principalmente na disciplina de Cálculo Diferencial e Integral. A questão a investigar foi: Como Mapas Conceituais podem ser utilizados para entender como alunos de cursos de Engenharia compreendem o MNR e sua relação com o Cálculo Diferencial e Integral? Foi utilizada uma abordagem qualitativa para a pesquisa que está situada na área da Educação Matemática. O referente teórico está fundamentado na Teoria da Aprendizagem Significativa de David Ausubel, utilizando a técnica de Mapeamento Conceitual de Joseph Novak. A pesquisa foi desenvolvida junto a alunos de cursos de Engenharia de uma instituição privada de ensino superior, com a utilização do software CmapTools para que os alunos elaborassem mapas conceituais digitais. Os dados foram analisados com o objetivo de, primeiramente, tentar perceber aprendizagens de alunos sobre o MNR, obtidas quando os alunos cursaram a disciplina de Cálculo Numérico ou Métodos Quantitativos e Computacionais. Depois, tentar identificar possíveis aprendizagens que tiveram uma assimilação obliteradora. Para tanto, os participantes desenvolveram dois mapas conceituais utilizando a ferramenta CmapTools, sendo o primeiro mapa elaborado sem nenhuma influência do pesquisador e o segundo após uma apresentação do referido método. As análises dos primeiros mapas conceituais digitais elaborados pelos participantes revelou que os mesmos entenderam como elaborar um mapa conceitual por meio do programa CmapTools, embora tenham elaborado mapas simples, com poucas relações entre os conceitos utilizados. Também conseguiram apresentar de maneira lógica uma descrição do MNR, revelando que os alunos ainda possuíam lembranças de alguns conceitos envolvidos no MNR e conseguiram apresentar algumas relações entre esses conceitos. Em relação ao segundo mapa conceitual digital, os alunos apresentaram conceitos que não estavam presentes no primeiro mapa conceitual digital, alguns foram elaborados com estruturas diferentes e apresentaram novos termos de ligações com lógica e coerência. Em alguns mapas é possível perceber que os alunos relembraram conceitos estudados no MNR e tentaram relacioná-los em seus mapas por meio de proposições. Entretanto, em alguns mapas é possível perceber que os referidos alunos apenas tentaram inseriram alguns elementos do MNR apresentado pelo professor. Notamos, ainda, que alguns conceitos estudados relacionados ao MNR parecem estar interagindo na estrutura cognitiva com conhecimentos prévios e que, com a apresentação do MNR, inferimos que alguns desses conceitos parecem estar presentes em uma assimilação obliteradora
162

Soluções analíticas e numéricas de equações polinomiais / Analytical and numerical solutions of polynomial equations

Passos, Livia Novaes Teixeira 07 December 2017 (has links)
As equações polinomiais são estudadas desde a antiguidade e atualmente são utilizadas, por exemplo, para modelar problemas do cotidiano nas mais variadas áreas do conhecimento. As técnicas de solução de equações polinomiais nem sempre são triviais, principalmente quando envolvem equações de alta ordem e raízes complexas. O ensino desse tema no Ensino Básico é limitado a equações de segundo ou terceiro grau e coeficientes inteiros, o que restringe a aplicação em problemas mais realistas. Assim, o objetivo deste trabalho é trazer uma contribuição aos estudantes, aos professores do Ensino Básico e aos demais interessados, apresentando um material que aborde técnicas de resolução para equação polinomial de diversas naturezas. Iniciamos por uma revisão dos números complexos e dos polinômios, suas operações e propriedades. Embasamos o trabalho com teoremas e permeamos de exemplos com um crescente grau de dificuldade. Dividimos as técnicas de resolução em analíticas e numéricas. Entre as primeiras, tratamos das relações de Girard, das fórmulas resolventes e de alguns casos particulares de equações. Entre as técnicas numéricas, estudamos o método de Newton, o método das secantes e o método de Newton-Bairstow, este último para encontrar raízes complexas. / Polynomial equations have been studied since antiquity and are currently used, for example, to model everyday problems in the most varied areas of knowledge. The solution techniques of polynomial equations are not always trivial, especially when they involve high order equations and complex roots. The teaching of this subject in Basic Education is limited to second or third degree equations and integer coefficients, which restricts the application to more realistic problems. Thus, the objective of this work is to bring a contribution to students, teachers of Basic Education and other interested parties, presenting a material that treats of resolution techniques for polynomial equation of different natures. We begin with a review of complex numbers and polynomials, their operations and properties. We support the work with theorems and permeate examples with an increasing degree of difficulty. We divide the techniques of resolution into analytical and numerical. Among the first, we deal with Girards relations, the resolvent formulas, and some particular cases of equations. Among numerical techniques, we studied the Newton method, the secant method, and the Newton-Bairstow method, the last one to find complex roots.
163

NÃmeros binomiais: uma abordagem combinatÃria para o ensino mÃdio / Binomial numbers: a combinatorial approach for high school

MÃrcio RebouÃas da Silva 28 August 2015 (has links)
Este trabalho tem por finalidade apresentar uma abordagem, para o Ensino MÃdio, de nÃmeros binomiais (incluindo as propriedades do triÃngulo de Pascal e binÃmio de Newton), contendo as demonstraÃÃes combinatÃrias, ao utilizar dupla contagem, juntamente com as demonstraÃÃes algÃbricas, como parcialmente jà à feito, alÃm de generalizar, citando os nÃmeros trinomiais (incluindo as propriedades da pirÃmide de Pascal) e os nÃmeros multinomiais (incluindo o polinÃmio de Leibniz). / This project aims at presenting an approach of binomial numbers for high school (including Pascalâs triangle properties and binomial of Newton), containing the combinatorial statements when using double counting, along with algebraic demonstrations, as part is already done in addition to generalize, citing the trinomial numbers (including the properties of the Pascal pyramid) and multinomial numbers (including the Leibnizâs polynomial).
164

A aceitação da óptica newtoniana no século XVIII: subsídios para discutir a Natureza da Ciência do Ensino / The acceptance of Newtonian optics in eighteenth century: discussing Nature of Science in Science Teaching

Moura, Breno Arsioli 06 October 2008 (has links)
A compreensão da Ciência como um empreendimento dinâmico e em constante transformação tem se tornado uma das mais importantes metas da educação científica nos últimos anos. É quase senso comum que discussões sobre a Natureza da Ciência (NdC) sejam incorporadas nos currículos de ciências. De uma forma geral, a NdC pode ser definida como um arcabouço de saberes sobre as bases ou princípios epistemológicos envolvidos na construção do conhecimento científico. Uma das maneiras de se ensinar NdC é a discussão de episódios da História da Ciência. Nesse trabalho, analisamos em detalhes o desenvolvimento, a repercussão e a aceitação da óptica newtoniana; particularmente, estudamos sua popularização na Europa do início do século XVIII, principalmente na Grã-Bretanha. Neste período ocorreram mudanças sociais e culturais significativas, entre elas, a valorização da Filosofia Natural e seus produtos, o estabelecimento da mecânica e óptica newtonianas e da imagem de Isaac Newton como um representante da genuína filosofia natural. Assim, na época, foram selecionados e incorporados aos tratados de física apenas aspectos de sua óptica que evidenciavam o caráter indutivista e que ao mesmo tempo podiam ser conciliados com sua mecânica. A partir deste estudo histórico, aspectos da NdC podem ser explicitamente discutidos, por exemplo, a questão da inexistência de um método científico universal, a influência do contexto e do prestígio do pesquisador em questão na aceitação ou rejeição de suas idéias, o caráter provisório do conhecimento científico, a importância da maneira como as idéias são apresentadas, entre outras coisas. Este tipo de discussão é relevante para diversos âmbitos da formação de professores, favorecendo a construção de uma imagem adequada da Ciência de um modo geral. / Currently, there is a general agreement that Nature of Science (NOS) aspects must be included in science curriculums. The present dissertation analyzes in details the development, the repercussion and the acceptance of Newtonian optics; with particular emphasis on its popularization in early 18th century in Europe, especially in Great Britain. In this period, significant social and cultural changes occurred, among them the valorization of Natural Philosophy and its products, the establishment of Newtonian mechanics, optics and Isaac Newton\'s image as genuine representative of Natural Philosophy. As consequence, only Newtonian optics aspects that evidenced the inductivism and could be conciliated with his mechanics were incorporated in 18th century natural philosophy books. From this historical study, NOS aspects can be explicitly discussed, for instance, the inexistence of an universal scientific method, the influence of social context and how the prestige of a scientist biases the acceptance of her/his ideas, the temporary character of scientific knowledge, the relevance of how ideas are communicated, among other topics. The present work is important for teacher training courses, since it provides adequate view of Science development.
165

Cultural Critique in a Patriarchal World : Revolutionary Suicide in Sylvia Plath's "Lady Lazarus", "Daddy" and The Bell Jar

Meneses, Sandra January 2009 (has links)
<p>This work studies three texts by Sylvia Plath: “Lady Lazarus”, “Daddy” and <em>The Bell Jar </em>from a feminist, gender and cultural perspective. I investigate how the texts take a stand regarding the motive and meaning of the representations of suicide in these works through the theoretical framework of African-American activist Huey Newton. The Black Panther party cofounder Newton redefines the concept of suicide. First and foremost he views suicide as a reaction to social conditions, coining the terms Reactionary Suicide and Revolutionary Suicide. Revolutionary Suicide is fueled by hope, when refusing to take part in any game of slave and master in society; instead of the normative view that suicide may be fueled by powerlessness and despair, as in the case of Reactionary Suicide. A feminist and gendered perspective on representations of suicide deconstructs traditional preconceptions of femininity and masculinity in the case of suicide and a normative reading: an embodiment by women and men of madness and rationality; viewing them as objects and subjects respectively. This study proposes that the representations of suicide in the texts from a cultural reading show the refusal of women to partake in a life defined by patriarchy, limiting and oppressing women’s everyday life. Suicide is seen through this unusual approach as an emptying out, a repositioning of the self through these performative suicides. Furthermore, through Revolutionary Suicide agency is claimed, with a hope for a better reality for the oppressed, in the intersection of the dichotomies of reality and utopia, literature and history, oppression and freedom. From a feminist perspective suicide is the catalyst to express social, political and cultural critique.</p>
166

Bridging the gap between post-Newtonian theory and numerical relativity in gravitational-wave data analysis

Ohme, Frank January 2012 (has links)
One of the most exciting predictions of Einstein's theory of gravitation that have not yet been proven experimentally by a direct detection are gravitational waves. These are tiny distortions of the spacetime itself, and a world-wide effort to directly measure them for the first time with a network of large-scale laser interferometers is currently ongoing and expected to provide positive results within this decade. One potential source of measurable gravitational waves is the inspiral and merger of two compact objects, such as binary black holes. Successfully finding their signature in the noise-dominated data of the detectors crucially relies on accurate predictions of what we are looking for. In this thesis, we present a detailed study of how the most complete waveform templates can be constructed by combining the results from (A) analytical expansions within the post-Newtonian framework and (B) numerical simulations of the full relativistic dynamics. We analyze various strategies to construct complete hybrid waveforms that consist of a post-Newtonian inspiral part matched to numerical-relativity data. We elaborate on exsisting approaches for nonspinning systems by extending the accessible parameter space and introducing an alternative scheme based in the Fourier domain. Our methods can now be readily applied to multiple spherical-harmonic modes and precessing systems. In addition to that, we analyze in detail the accuracy of hybrid waveforms with the goal to quantify how numerous sources of error in the approximation techniques affect the application of such templates in real gravitational-wave searches. This is of major importance for the future construction of improved models, but also for the correct interpretation of gravitational-wave observations that are made utilizing any complete waveform family. In particular, we comprehensively discuss how long the numerical-relativity contribution to the signal has to be in order to make the resulting hybrids accurate enough, and for currently feasible simulation lengths we assess the physics one can potentially do with template-based searches. / Eine der aufregendsten Vorhersagen aus Einsteins Gravitationstheorie, die bisher noch nicht direkt durch ein Experiment nachgewiesen werden konnten, sind Gravitationswellen. Dies sind winzige Verzerrungen der Raumzeit selbst, und es wird erwartet, dass das aktuelle Netzwerk von groß angelegten Laserinterferometern im kommenden Jahrzehnt die erste direkte Gravitationswellenmessung realisieren kann. Eine potentielle Quelle von messbaren Gravitationswellen ist das Einspiralen und Verschmelzen zweier kompakter Objekte, wie z.B. ein Binärsystem von Schwarzen Löchern. Die erfolgreiche Identifizierung ihrer charakteristischen Signatur im Rausch-dominierten Datenstrom der Detektoren hängt allerdings entscheidend von genauen Vorhersagen ab, was wir eigentlich suchen. In dieser Arbeit wird detailliert untersucht, wie die komplettesten Wellenformenmodelle konstruiert werden können, indem die Ergebnisse von (A) analytischen Entwicklungen im post-Newtonschen Verfahren und (B) numerische Simulationen der voll-relativistischen Bewegungen verknüpft werden. Es werden verschiedene Verfahren zur Erstellung solcher "hybriden Wellenformen", bei denen der post-Newtonsche Teil mit numerischen Daten vervollständigt wird, analysiert. Existierende Strategien für nicht-rotierende Systeme werden vertieft und der beschriebene Parameterraum erweitert. Des Weiteren wird eine Alternative im Fourierraum eingeführt. Die entwickelten Methoden können nun auf multiple sphärisch-harmonische Moden und präzedierende Systeme angewandt werden. Zusätzlich wird die Genauigkeit der hybriden Wellenformen mit dem Ziel analysiert, den Einfluss verschiedener Fehlerquellen in den Näherungstechniken zu quantifizieren und die resultierenden Einschränkungen bei realen Anwendungen abzuschätzen. Dies ist von größter Bedeutung für die zukünftige Entwicklung von verbesserten Modellen, aber auch für die korrekte Interpretation von Gravitationswellenbeobachtungen, die auf Grundlage solcher Familien von Wellenformen gemacht worden sind. Insbesondere wird diskutiert, wie lang der numerische Anteil des Signals sein muss, um die Hybride genau genug konstruieren zu können. Für die aktuell umsetzbaren Simulationslängen wird die Physik eingeschätzt, die mit Hilfe von Modell-basierten Suchen potentiell untersucht werden kann.
167

Cultural Critique in a Patriarchal World : Revolutionary Suicide in Sylvia Plath's "Lady Lazarus", "Daddy" and The Bell Jar

Meneses, Sandra January 2009 (has links)
This work studies three texts by Sylvia Plath: “Lady Lazarus”, “Daddy” and The Bell Jar from a feminist, gender and cultural perspective. I investigate how the texts take a stand regarding the motive and meaning of the representations of suicide in these works through the theoretical framework of African-American activist Huey Newton. The Black Panther party cofounder Newton redefines the concept of suicide. First and foremost he views suicide as a reaction to social conditions, coining the terms Reactionary Suicide and Revolutionary Suicide. Revolutionary Suicide is fueled by hope, when refusing to take part in any game of slave and master in society; instead of the normative view that suicide may be fueled by powerlessness and despair, as in the case of Reactionary Suicide. A feminist and gendered perspective on representations of suicide deconstructs traditional preconceptions of femininity and masculinity in the case of suicide and a normative reading: an embodiment by women and men of madness and rationality; viewing them as objects and subjects respectively. This study proposes that the representations of suicide in the texts from a cultural reading show the refusal of women to partake in a life defined by patriarchy, limiting and oppressing women’s everyday life. Suicide is seen through this unusual approach as an emptying out, a repositioning of the self through these performative suicides. Furthermore, through Revolutionary Suicide agency is claimed, with a hope for a better reality for the oppressed, in the intersection of the dichotomies of reality and utopia, literature and history, oppression and freedom. From a feminist perspective suicide is the catalyst to express social, political and cultural critique.
168

Indispensible Hume : from Isaac Newton's natural philosophy to Adam Smith's "Science of man" /

Schliesser, Eric. January 2002 (has links)
Thesis (Ph. D.)--University of Chicago, Dept. of Philosophy, Dec. 2002. / Includes bibliographical references (p. 260-280) Also available on the Internet.
169

Fluxo de potência continuado baseado em equações de injeção de corrente expressas em coordenadas polares / Power flow continued based on current injection equations expressed in polar coordinates

Oliveira, Cristina Coutinho de [UNESP] 24 February 2016 (has links)
Submitted by Cristina Coutinho de Oliveira null (35131907861) on 2016-04-18T18:23:10Z No. of bitstreams: 1 Defesa_final.pdf: 1997390 bytes, checksum: 8300a03e6985d3d69b82de41b61bb274 (MD5) / Approved for entry into archive by Felipe Augusto Arakaki (arakaki@reitoria.unesp.br) on 2016-04-19T15:01:21Z (GMT) No. of bitstreams: 1 oliveira_cc_me_ilha.pdf: 1997390 bytes, checksum: 8300a03e6985d3d69b82de41b61bb274 (MD5) / Made available in DSpace on 2016-04-19T15:01:21Z (GMT). No. of bitstreams: 1 oliveira_cc_me_ilha.pdf: 1997390 bytes, checksum: 8300a03e6985d3d69b82de41b61bb274 (MD5) Previous issue date: 2016-02-24 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Nesta proposta apresenta-se um estudo comparativo entre algumas das diversas metodologias existentes na literatura específica para a resolução do Fluxo de Potência (FP) e Fluxo de Potência Continuado (FPC), utilizando métodos baseados em equações de injeção de potência e em equações de injeção de corrente. A formulação de injeção de potência é baseada nas equações de balanço de potência ativa e reativa de cada barra, enquanto que a de injeção de corrente utiliza expressões referentes ao balanço de corrente. É realizada a comparação da influência de três formas de tratamento das barras de geração (PV) nas características de convergência do método de Newton-Raphson simplificado utilizado na solução das equações de fluxo de potência escritas em coordenadas polares, considerando a formulação de injeção de corrente. Também são apresentados os resultados de análises de desempenho entre o método simplificado e o convencional, o qual utiliza as equações de injeção de potência expressa em termos de coordenadas polares. As análises de desempenho são realizadas para os sistemas testes do IEEE de 14, 30, 57, 118 e 300 barras e duas versões reais de grande porte do sistema elétrico SUL/SULDESTE brasileiro 638 e 787 barras considerando: diferentes relações R/X para os ramos e diferentes condições de carregamentos. Os resultados obtidos com duas das formas de tratamento das barras PV mostram que é possível se obter uma melhora nas características de convergência do método simplificado. / This work presents a comparative study on the various existing methods in the literature to solve the power flow (PF) and continuation power flow (CPF), using the methods which are based on power injection equations and current injection equations. The power injection formulation works based on active and reactive power balance equations at each bus, while the current injection using expressions relating to the current balance. In order to make the comparison, the influence of three forms of handling the generation buses (PV) in the convergence characteristics of simplified Newton-Raphson method, used in the solution of the power flow equations in polar coordinates, and by considering the current injection formulation is considered. Moreover, the results of performance tests between the simplified and the conventional methods, which use the power injection equations expressed in terms of polar coordinates, are presented. In order to performance analysis five IEEE test systems such as 14, 30, 57, 118, and 300 bus and two large-scale real electrical power systems such as south Brazilian 638 and 787 bus systems are conducted. The aforementioned systems are tested under different R/X ratios for the branches and different loading conditions. The results show that an improvement in convergence characteristics can be obtained for the simplified method.
170

Autour du problème des arcs de Nash pour les singularités isolées d'hypersurfaces / Around the Nash problem on arcs for the isolated singularities of hypersurfaces

Leyton-Alvarez, Maximiliano 16 September 2011 (has links)
Soient k un corps algébriquement clos et V une variété algébrique sur k. Dans le but d'étudier la géométrie du lieu singulier de V, John Nash a introduit l'espace d'arcs et les espaces de m-jets, m>0, dans une prépublication de 1968 qui a été publiée en 1995. Il a aussi défini une application, actuellement connue sous le nom d'application de Nash, qui associe à chaque famille d'arcs passant par le lieu singulier de V (composante de Nash) un diviseur essentiel sur V. Nash a démontré que cette application est injective. Le problème de Nash consiste à étudier la surjectivité de l'application de Nash. Dans plusieurs cas de variétés V, la bijectivité de cette application a été prouvée. Or, un exemple d'une singularité isolée d'hypersurface de l'espace affine de dimension 5 avec deux diviseurs essentiels et une composante de Nash a été donné dans un article de 2003. À l'heure actuelle, déterminer l'image de l'application de Nash reste un problème difficile, mêmes dans le cas de singularités bien connues. Dans cette thèse, on démontre la bijectivité de l'application de Nash pour certaines familles de singularités isolées d'hypersurfaces des espaces affines de dimension 3 et 4. / Be it that K is a closed algebraic field and V an algebraic variety on K. In the goal of studying the geometry of a singular space on V, John Nash introduced the space of arcs and the spaces of m-jets, m>0, in a 1968 preprint, published in 1995. He also defined an application, currently known as Nash's application, which associates an essential divisor on V to each arc family passing by V's singular space. Nash proved that this application is injective. The Nash problem consists of studying the surjectivity of the Nash application. In several cases of V varieties the bijectivity of this application has been proven. However an example of an isolated hypersurface singularity of affine space of dimension 5 with two essential divisors and one Nash component has been given in a 2003 article. Currently determining the image of the Nash application remains a difficult problem, even in the case of well known singularities. This thesis proves the bijectivity of the Nash application for certain families of isolated hypersurface singularities of the affine spaces of dimension 3 and 4.

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