Thesis (Ph. D.)--University of Washington, 2005. / Vita. Includes bibliographical references (leaves 120-127).

Οι αντιμεταθετικοί δακτύλιοι έχουν την προέλευσή τους από τη θεωρία αριθμών και από την αλγεβρική γεωμετρία στον 19ο αιώνα. Σήμερα είναι ιδιαίτερα σημαντικοί και έχουν ενδιαφέρουσα επίδραση στην αλγεβρική γεωμετρία και στην θεωρία αριθμών, χρησιμοποιώντας μεθόδους αντιμεταθετικής άλγεβρας. Εδώ περιγράφουμε τις βασικές μεθόδους και κάνουμε τα πρώτα βήματα σε αυτό το θέμα. Στο εξής όλοι οι δακτύλιοι θα είναι αντιμεταθετικοί, εκτός αν θεωρήσουμε κάτι άλλο. Το κεντρικό θέμα της αξιωματικής ανάπτυξης της γραμμικής άλγεβρας είναι ένας διανυσματικός χώρος επί ενός σώματος. Η αξιωματοποίηση της γραμμικής άλγεβρας, η οποία επιτεύχθηκε το 1920, μορφοποιήθηκε σε μια μεγάλη έκταση, από την επιθυμία να εισάγουμε γεωμετρικές έννοιες στη μελέτη συγκεκριμένων κλάσεων των συναρτήσεων στην ανάλυση. Κατ’ αρχάς, ασχοληθήκαμε αποκλειστικά με τους διανυσματικούς χώρους των πραγματικών αριθμών ή των μιγαδικών αριθμών. Η έννοια ενός module είναι μια άμεση γενίκευση ενός διανυσματικού χώρου. Η γενίκευση αυτή επιτυγχάνεται απλά αντικαθιστώντας το σώμα των συντελεστών διά ενός δακτυλίου. Ο ευκολότερος τρόπος για να ορίσουμε ένα module μπορούμε να πούμε ότι είναι ένα αλγεβρικό σύστημα το οποίο ικανοποιεί τα ίδια αξιώματα όπως ένας διανυσματικός χώρος εκτός του ότι οι συντελεστές ανήκουν σ’ ένα δακτύλιο R με μονάδα αντί ενός σώματος F. Αυτή η φαινομενικά σεμνή γενίκευση οδηγεί σε μια αλγεβρική δομή η οποία είναι μεγίστης σημασίας. Ιστορικά ο πρώτος δακτύλιος που μελετήθηκε ήταν ο δακτύλιος ℤ των ακεραίων, ο όρος “δακτύλιος” πρωτοχρησιμοποιήθηκε από τον Hilbert (1897) στο “Zahlbericht” του για έναν δακτύλιο αλγεβρικών ακεραίων. Στο ℤ κάθε δακτύλιος είναι κύριος. Στην πραγματικότητα τα ιδεώδη είχαν πρώτα εισαχθεί (από Kummer) ως “ιδεώδεις αριθμοί” στους δακτυλίους αλγεβρικών ακεραίων οι οποίοι εστερούντο μοναδικής παραγοντοντοποίησης (unique factorization). Στο ℤ μπορούμε από δύο αριθμούς a,b να ορίσουμε τον μέγιστο κοινό διαιρέτη (ΜΚΔ) αυτών, (a,b), το γινόμενό τους ab και το ελάχιστο κοινό πολλαπλάσιο (ΕΚΠ) αυτών, [a,b]. Αυτές οι πράξεις αντιστοιχούν σε πράξεις ιδεωδών σε κάθε δακτύλιο. / Commutative ring has its origins in number theory its origins in number theory and algebraic geometry in the 19th century. Today it is of particular importance in algebraic geometry, and there has been an interesting interaction of algebraic geometry and number theory, using the methods of commutative algebra. Here we can do no more than describe the basic techniques and take the first steps in the first steps in the subject. Throughout this chapter all rings will be commutative, unless otherwise stated. The central concept of the axiomatic development of linear algebra is that of a vector space over a field. The axiomatization of linear algebra, which was effected in the 1920’s, was motivated to a large extend by the desire to introduce geometric notions in the study of certain classes of functions in analysis. At first one dealt exclusively with vector spaces over the reals or the complexes. It soon became apparent that this restriction was rather artificial , since a large body of the results depended only on the solution of linear equations and thus were valid for arbitrary fields. This led to the study of vactor spaces over arbitrary fields and this is what presently constitutes linear algebra. The concept of a module is an immediate generalization of that of a vector space. One obtains the generalization by simply replacing the underlying field by any ring.In the first place, one learns from experience that the internal logical structure of mathematics strongly urges the pursuit of such ‘natural’ generalizations. These often result in an improved insight into the theory which led to them in the first place. The easiest way to define a module is to say that it is an algebraic system that satisfies the same axioms as a vector space except that the scalars come from a ring R with a 1 instead of from a field F. This seemingly modest generalization leads to an algebraic structure that is of the greatest importance. We use here the term R-module, it being understood that the scalars are written on the left. Historically the first ring to studied was the ring Z of integers, the term ‘ring’ was first used by Hilbert (1897) in his ‘Zahlbericht’ for a ring of algebraic integers. In Z every ideal is principal, in fact ideals were first introduced (by Kummer) as ‘ideal numbers’ in rings of algebraic integers which lacked unique factorization. In Z we can from any two numbers a,b form their highest common factor (HCF, also greatest common divisor, GCD) (a,b), their product ab and their least common multiple (LCM) [a,b]. These operations correspond to operations on ideals in any ring. Valuation theory may be described as the study of divisibility (in commutative rings) in its purest form, but that is only one aspect. The general formulation leads to the introduction of topological concepts like completion, which provides a powerful tool. It also emphasizes the parallel with the absolute value on the real and complex numbers. After the initial definitions we shall prove the essential uniqueness of the absolute value on R and C, and go on to describe the p-adic numbers, before looking at simple cases of the extension problem.

MultiDetector-row Computed Tomography (MDCT) or MultiSlice Computed Tomography (MSCT) has undergone remarkable progress since its first introduction at the end of the 1990s. Given that CT examinations are generally recognized as a relatively high-dose procedure, concern has been expressed at the associated increase in doses. The International Committee on Radiation Protection (ICRP) noted in their report No.87 that absorbed doses in tissues from CT are among the highest observed in diagnostic radiology (i.e. 10–100 mGy). Therefore, the purpose of this thesis is to calculate the dosimetric quantities for brain, chest, and abdomen-pelvis examinations that were carried out using Philips Brilliance 16 and Brilliance 64 CT Scanners of the University General Hospital “Attikon”, as well as to perform their intercomparison. For brain examinations, axial technique was utilized. However, for chest and abdomen-pelvis examinations, spiral technique was applied. The effect of overranging (or overscanning) is connected with spiral mode and its contribution to patient dose is really important in case of MSCT scanners. Therefore, the contribution of the overrange effect for body examinations carried out was calculated. In the framework of this thesis, the contribution of overrange to the effective dose received by patients submitted to the forementioned examinations is calculated. Additionally, dose measurements were carried out in order to estimate the radiation burden to the eye lenses and the thyroid during the typical brain examination, both when eye lenses are inside and outside the irradiation field. / Οι Υπολογιστικοί Τομογράφοι (ΥΤ) πολλαπλών τομών έχουν σημειώσει μεγάλη πρόοδο από την κλινική εφαρμογή τους στις αρχές του 1990. Λαμβάνοντας υπ’ όψιν ότι οι εξετάσεις ΥΤ συνεπάγονται υψηλή ακτινική επιβάρυνση του ασθενή, η μελέτη τους έχει συγκεντρώσει το ερευνητικό ενδιαφέρον της επιστημονικής κοινότητας. Η Διεθνής Επιτροπή Ακτινοπροστασίας (ICRP) επισημαίνει στην αναφορά Νο 87 ότι η απορροφούμενη δόση στους ιστούς από εξετάσεις ΥΤ είναι από τις υψηλότερες στη διαγνωστική ακτινολογία (10-100 mGy). Συνεπώς, σκοπός της παρούσας διπλωματικής εργασίας είναι ο υπολογισμός των δοσιμετρικών μεγεθών για τις συνήθεις εξετάσεις εγκεφάλου, θώρακος και άνω-κάτω κοιλίας, οι οποίες πραγματοποιούνται με τους ΥΤ πολλαπλών τομών Brilliance 16 και Βrilliance 64 της Philips στο Π.Γ.Ν “ΑΤΤΙΚΟΝ ”,καθώς επίσης και η σύγκριση των αντίστοιχων δόσεων μεταξύ των συγκεκριμένων ΥΤ. Οι ασθενείς που υποβάλλονται σε εξετάσεις θώρακος και άνω-κάτω κοιλίας που πραγματοποιούνται με ελικοειδή τεχνική λαμβάνουν επιπλέον δόση (overscan) που οφείλεται στην τεχνική αυτή. Η συνεισφορά του “overscan” είναι ιδιαίτερα σημαντική στους ΥΤ πολλαπλών τομών, οπότε επιπλέον στόχος αυτής της διπλωματικής είναι ο υπολογισμός της. Τέλος, πραγματοποιήθηκαν μετρήσεις της δόσης του θυρεοειδή και των φακών των οφθαλμών κατά την υποβολή ασθενών στη συνήθη εξέταση εγκεφάλου, τόσο στην περίπτωση παρουσίας των οφθαλμών εντός όσο και εκτός πεδίου ακτινοβόλησης.

Orientador: Sebastião Gobbi / Banca: Alex Antonio Florindo / Banca: Eduardo Kokubun / Resumo: A prática regular de atividade física (AF) está associada a melhor saúde e maior longevidade, porém mais de 60% da população adulta brasileira não incorpora tal prática no seu estilo de vida. Diversos fatores podem estar associados para facilitar, dificultar ou impedir a prática de AF e, quando impedem ou dificultam, são chamados de barreiras. O presente estudo teve por objetivo analisar o nível de AF e as principais barreiras percebidas por indivíduos adultos moradores na zona urbana do município de Rio Claro - SP. Para a seleção da amostra utilizou-se a técnica de amostragem aleatória e estratificada por conglomerado, sendo a amostra final composta por 1596 indivíduos, com 20 anos ou mais de idade, selecionados dentre os 100 setores censitários sorteados para o estudo. Os indivíduos responderam a quatro questionários, a saber: domiciliar; Internacional de atividade física (IPAQ - versão longa); Barreiras à Prática de Atividade Física (QBPAFI) e; Classificação Sócio-Econômica (ANEP). Os dados foram analisados por meio de análise descritiva (média, desvio-padrão, porcentagem) e posteriormente análises de comparação (Qui-quadrado; Mann-Whitney; Kruskall Wallis) e associação (regressão logística). Os resultados mostraram alta prevalência de inatividade física em todos os domínios abrangidos pelo IPAQ, com exceção do domínio atividades domésticas, no qual a prevalência foi abaixo de 45%. Observou-se também que nos domínios trabalho, lazer e locomoção as mulheres, bem como os idosos e os de menor poder aquisitivo são mais inativos. Na análise associativa, as variáveis sociodemográficas que se relacionaram positivamente à inatividade física no tempo livre foram: sexo feminino, escolaridade abaixo de 11 anos e pertencer às classes de menor poder aquisitivo. Em relação às barreiras, as mais relatadas pela foram: já sou... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Engagement in physical activity (PA) on a regular basis is associated with a better health and longevity. However, more than 60% of Brazilian adults do not incorporate such habit on their lifestyle. Several factors can be crucial to facilitate or to prevent engagement in PA. When these factors prevent or difficulty, they are called barriers. Thus, the aim of the study is to analyze PA level and main-perceived barriers of adults living at urban zone of Rio Claro-SP city. The sample was composed by 1596 subjects (20 year-old and over) selected by means of randomized and stratified by conglomerates technique within a 100 census sections. The subjects were asked to answer four questionnaires (Identification and Social Demographic; International Physical Activity (IPAQ - Long version); Barriers to Physical Activity Practice and; d) Social Economic Classification). The data were analyzed by means of descriptive statistics (means, standard deviations, percentage) in addition to comparative analyses (Chi-square; Mann-Whitney; Kruskall Wallis) and logistic regression. The results showed high prevalence of physical inactivity in all domains comprised by IPAQ, with exception to household domain, for which the prevalence was less than 45%. Regarding the work, leisure and locomotion domains, the women, elderly people or those included in low-income groups were more inactive. The sociodemographics variables that presented positive association with leisure-time physical inactivity were: female gender; schooling less than 11 years and lowincome. Regarding the barriers, the most reported ones were: already enough active, lack of company, lack of money, no suitable place near my home, need to relax, no time and too lazy. However, lack of energy, no time, need to relax, too lazy, do not enjoy exercise and quit soon were the barriers which presented positive association with physical inactivity during... (Complete abstract click electronic access abaixo) / Mestre

Conçues à partir d’une approche rationnelle, nous avons créé de nouvelles sondes membranaires permettant l’imagerie de l’organisation de la membrane plasmique cellulaire. Dans ce travail, nous avons d’abord développé un groupe d’outils, à partir du fluorophore solvatochrome Nile Red et de Black Hole Quencher-2, capable de marquer spécifiquement les domaines ordonnés et désordonnés (radeaux) en les identifiant par leur couleur d’émission. Les études cellulaires, à l’aide de ces sondes, suggèrent que la membrane plasmique est composée de deux phases distinctes. Puis dans le but de créer de nouvelles sondes basées sur Nile Red compatibles avec le sérum et fixables par formaldéhyde/glutaraldéhyde, nous avons modifié la sonde, préalablement développée, NR12S avec un groupement PEG ou amino, respectivement. Etonnamment, la sonde PEGylée est rapidement internalisée dans la cellule et le dérivé animo agrège avec l’agent fixant. D’un autre côté,basée sur Nile Red, nous avons conçu une sonde capable de détecter un récepteur donné et de visualiser son environnement lipidique. Initialement, nous avons obtenu des sondes capables d’allumer leur fluorescence en se liant sur le RCPG à l’ocytocine. Puis, nous avons conjugué NR12Spar l’intermédiaire d’un espaceur PEG(12) au ligand de l’intégrine, RGD. Les résultats préliminaires montrent que la molécule peut se lier à la membrane et détecter l’ordre lipidique, cependant les études cellulaires nécessitent un achèvement. Nous avons aussi travaillé sur des sondes membranaires fluorogéniques (turn-on) pour de l’imagerie multi-couleurs. Basées sur le fluorophore3-méthoxychromone, nous avons obtenu des sondes plus brillantes et plus photostables que la sonde développée originellement à partir de 3-hydroxychromone (F2N12S). Grâce à l’important déplacement de Stokes, elles permettent une imagerie de la membrane cellulaire avec une autofluorescence minimale dans la région spectrale bleue, compatible avec les marqueurs communs verts et rouges. Pour finir, basées sur le fluorophore squaraine, nous avons développé trois nouvelles sondes opérant dans la région rouge lointain, qui est particulièrement intéressante pour l’imagerie in vitro et in vivo. Ces sondes montrent une orientation parallèle avec la membrane lipidique, alors que les expériences cellulaires indiquent que seule la sonde avec deux ancres lipidiques est capable de marquer de façon stable la membrane plasmique. Ces sondes développées ici sont prévues pour être utilisées dans la recherche des radeaux lipidiques aussi bien que pour l’imagerie super-résolution et multi-couleurs de cellules vivantes. / Based on rational molecular design, we design new membrane probes that enable fluorescence imaging of cell plasma membrane organization. In this work, we first synthesized a toolkit, based on solvatochromic Nile Red dye and Black Hole Quencher-2, that can stain specifically ordered and disordered lipid domains (rafts) and identify them by the emission color. Cellular studies with these probes suggested that the plasma membrane is composed of two distinct phases. Then,with the idea to make Nile Red-based probes compatible with serum medium and fixable by formaldehyde/glutaraldehyde, we modified previously developed probe NR12S with PEG and aminogroups, respectively. Surprisingly, the PEGylated probe is quickly internalized inside the cell and the amino-derivative aggregates with the fixing agent. On the other hand, based on Nile Red we designed probes capable to detect a given receptor and visualize its lipid environment. Initially, we obtained probes that can turn-on fluorescence on binding to the oxytocin GPCR receptor. Then, we conjugated NR12S through a PEG(12) spacer to the ligand of intergrin, RGD. The first data show that the molecule can bind to the membrane and detect the lipid order, though cellular studies have to be completed. We also worked on fluorogenic (turn-on) membrane probes for multi-color imaging. Based on blue 3-methoxychromone dyes, we obtained probes that are brighter and more photostable than the originally developed probe based on 3-hydroxychromone (F2N12S). Due to large Stocks shift, they enabled cell membrane imaging with minimal auto-fluorescence in the blue spectral region, compatible with common green and red probes. At the end, based on squaraine fluorophore, we developed three new probes operating in the far red region, which is also very interesting for in vitro and in vivo imaging. These dyes show a parallel orientation with the lipid membrane, while the cellular experiments point out that only the probe with two anchor groups is able to stain stably the plasma membrane. The probes developed here are expected to be used for lipid rafts research as well as for super-resolution and multi-color imaging of living cells.

The purpose of this study was to develop an instrument to assess probation officers knowledge levels of offenders with intellectual disabilities by utilizing a synthesis of subject matter analysis technique and a comprehensive review of literature. This study was conducted in two phases. The first phase was devoted to establishing the knowledge domain and development of the needs assessment instrument. For this phase the available population consisted of four subject matter experts in southern Illinois and one subject matter expert (SME) from London, England. In order to develop an instrument to assess knowledge that probation officers have about offenders with ID, an establishment of knowledge domains through face-to-face interviews with subject matter experts were completed in this phase. In addition to the content analysis from SME interviews, a comprehensive review of literature on intellectual disabilities was conducted. Outcomes from both methods were compared and similar findings were combined and used to construct items for the first draft of the instrument. A pilot test for the newly developed needs assessment instrument was conducted in the second phase. In order to obtain this validation a pilot field test and re-test, a sample of 25 Jackson County, Illinois, First Circuit Probation, Western Region, juvenile and adult probation officers was used to administer assessment (developed in phase I). Approximately two weeks after first administration, the assessment was re-administered on the same sample population of probation officers. The data source was Probation Officer Knowledge of Intellectual Disabilities Assessment instrument test-retest scores. Responses were scored by giving correct answers one point, and incorrect answers zero. This yielded a total score for knowledge of intellectual disabilities. Scores from the first test administration was compared to scores from the second administration by reviewing overall score correlations. Once each item was computed separately, then all item-total correlations were computed. Cronbach's alpha estimate of reliability was also computed for both the first and second administrations (Trochim & Donnelly, 2007). Additional analysis performed in this study included (a) cut offs for high or low scores based on means, (b) item difficulty, (c) inter-item correlations and, (d) descriptive frequencies on items that assessed probation officers' opinions on organizational structure and attitudes about supervising offenders intellectual disabilities. The ultimate goal of this study was to establish knowledge domains and develop an instrument to assess probation officers' knowledge of offenders with intellectual disabilities. The results of the study can be used to add information to the body of literature to eventually build up enough support to determine a need for criminal justice agency administrators to incorporate effective training material on offenders with intellectual disabilities within curriculum development for new staff orientation, in-service or academy training of probation officers.

No contexto do gerenciamento de redes de computadores, domínios são recursos utilizados para agrupar objetos gerenciáveis. Os mapas de rede utilizados pelos sistemas de gerenciamento são exemplos bastante comuns do uso de domínios. Domínios são importantes porque as ações de gerenciamento podem ser aplicadas a todos os objetos gerenciáveis membros de um domínio ao mesmo tempo, não sendo necessário, então, repetir a mesma ação em cada objeto gerenciável, um a um. Domínios que necessitam ser rapidamente criados, utilizados e descartados são referenciados nesta dissertação de mestrado como domínios dinâmicos. Atualmente, na maioria dos sistemas de gerenciamento de redes não existem facilidades disponíveis para suportar o conceito desse tipo de domínios. Em relação aos aspectos de visualização, a apresentação visual de domínios deve ser realizada de forma adequada, visto que, atualmente, as GUIs estão presentes na maioria dos sistemas de gerenciamento. Entretanto, os processos de visualização de domínios utilizados pelos sistemas de gerenciamento atuais apresentam limitações em relação à configuração de características visuais dos domínios apresentados. Essas características são estáticas, não permitindo ao usuário, dessa forma, escolher como deseja visualizar um determinado domínio. Nesta dissertação de mestrado são apresentados a definição e o desenvolvimento de duas novas linguagens que têm por objetivo aperfeiçoar a criação e a visualização de domínios dinâmicos. A primeira linguagem é baseada em um modelo de informação do ambiente gerenciado e é utilizada para criar, de forma automatizada, novos domínios dinâmicos. Tal modelo de informação é formado por classes, atributos e relacionamentos entre as classes. A segunda linguagem, por sua vez, é usada para configurar características visuais dos domínios dinâmicos criados por meio da primeira linguagem. Esta dissertação apresenta, também, um protótipo desenvolvido para suportar as linguagens de criação e visualização de domínios dinâmicos criadas. A partir desse protótipo, é possível criar domínios dinâmicos relacionados a informações da rede de computadores utilizada, bem como personalizar a visualização dos domínios dinâmicos criados. Além disso, o protótipo possibilita, também, a obtenção de algumas informações dos membros dos domínios dinâmicos criados. O protótipo é baseado na Web e foi desenvolvido utilizando-se as tecnologias PRECCX, PHP, MySQL e SNMP. Como será visto ao final, as linguagens definidas e o protótipo desenvolvido mostram que o suporte a domínios dinâmicos objetivado pode ser efetivo e melhorar, sensivelmente, os processos de gerenciamento de redes. A integração da implementação desenvolvida junto ao ambiente QAME, por exemplo, permite atualmente que os administradores possam selecionar, através das linguagens, os equipamentos de uma rede com QoS que precisam ser configurados através do processo de aplicação de políticas original do QAME. / In the computer networks management context, domains are facilities used to group managed objects. The network maps presented in the management systems are the most common examples of the use of domains. Domains are important because the management actions can be applied to all managed objects that are members of a domain at the same time, not being necessary, then, to repeat the same action in each managed object one by one. Domains that need to be quickly created, used and discarded are referenced in this work as dynamic domains. Currently, in the majority of the available network management systems there are no proper facilities to support this type of domains. Concerning the visualization aspects, the domains visual presentation must be carried through of adjusted form, since, currently, the GUIs are present in the majority of the management systems. However, the domains visualization processes used by the current management systems present limitations related to the visual features configuration of the presented domains. These features are static, not allowing the user, this way, to choose how he or she desires to visualize one determined domain. This work presents the definition and the development of two new languages whose goals is to enhance the creation and the visualization of dynamic domains. The first language is based on a managed environment information model and is used to create, forming an automated fashion, new dynamic domains. Such information model is formed by classes, attributes and relationships between the classes. The second language, on its turn, is used to configure visual features of the dynamic domains created by the first language. This work also presents a prototype developed to support the defined dynamic domains creation and visualization languages. With this prototype it is possible to create dynamic domains based on the information of the computer network used, as well as customizing the visualization of the dynamic domains created. Moreover, the prototype makes possible the attainment of some members information of the dynamic domains created. The prototype is based on the Web and was developed using technologies as PRECCX, PHP, MySQL and SNMP. As will be seen in the end, the defined languages and the developed prototype shows that the desired dynamic domains support can be effective and improve, significantly, the network management processes. The integration of the implementation developed together to the QAME environment, for example, allows currently that the administrators can select, through the languages, the QoS network devices that need to be configured through the original policies application process of the QAME.

Este trabalho trata de estimativas inferiores para o primeiro autovalor de Dirichlet para dom nios multiplamente conexos contidos em variedades riemannianas. Essas estimativas consideram o supremo da curvatura seccional da variedade e a curvatura do bordo do domínio. Para obter os resultados, usa-se uma estimativa C0 para solucões da equação de Poisson. / Lower bounds for the rst Dirichlet eigenvalue are presented. We consider multiply connected domains in riemannian manifolds. The estimates are obtained using hypothesis on the supremum of the manifold's sectional curvature and on the domain's boundary curvature. C0 estimates for solutions of Poissons equation are used to prove the results.

Neste trabalho, apresenta-se o resultado da existência de soluções fracas em domínios não-limitados para as equações de Navier-Stokes, desde que a fronteira satisfaça uma certa condição de regularidade que é necessária para a obtenção de estimativas em domínios não-limitados semelhantes à desigualdade de Poincaré em domínios limitados. Apresenta-se o desenvolvimento detalhado do método de Galerkin para as equações de Navier-Stokes em domínios não-limitados com cálculo explícito de várias constantes e com forças externas não nulas. Apresenta-se dois teoremas fundamentais: um fornecendo condições para existência de soluções do problema estacionário e o outro fornecendo condições para existência de soluções do problema não-estacionário. / In the work it is presented results of existence of weak solutions in unbounded doroains for the Navier-Stokes equations. The roain condition to obtain similar results as those for bounded doroains; for e."'Carople the Poincaré inequality; is a certain condition of regularity at the boundary of the doroain. It is presented the detailed developroent of the Galerkin roethod for the t.he Navier-Stokes equations in unbounded doroains ~vith the explicit calculat ions of many constants and ''rith non null externai forces. It is presented two basic theorern: one presenting condition for the existence of solutions for the stationary problem and the other presenting conditions for existence of solution for the non stationary problem.

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