Orientador: Nathan J. Berkovits / Banca: Andrei Mikhailov / Banca: Horatiu Nastase / Banca: Diego Trancanelli / Banca: Nelson Braga / Resumo: Nestatese, uma dada amplitude de espalhamento de supercordas envolvendo um operador de vértice da corda fechada e N operadores de vértice da corda aberta em AdS5 ×S5 é detalhadamente estudada, utilizando-se o formalismo de espinores puros. Após rever o material de apoio e realizar alguns cálculos preliminares, mostramos que a amplitude nível-de-árvore contendo um estado de supergravidade e N estados de super-Yang-Mills localizados em uma D3-brana próxima à fronteira de AdS5 pode ser expressa como uma integral no superespaço harmônico N = 4, d = 4 em termos dos supercampos de supergravidade e super-Yang-Mills, demonstrando assim uma conjectura feita recentemente / Abstract: In this thesis, a particular superstring scattering amplitude involving one closed string and N open string vertex operators in AdS5 ×S5 is studied in detail, usingthe pure-spinor formalism. After reviewing some background material and performing a few preliminary calculations, we show that the tree-level amplitude containing one supergravity state and N super-Yang-Mills states located on a D3-brane near the AdS5 boundary can be expressed as an N = 4, d = 4 harmonic superspace integral in terms of the supergravity and super-Yang-Mills superfields, thus proving a conjecture recently made / Doutor

LIMA, Daniel Araújo. A amplitude da imunidade dos templos religiosos: exoneração de impostos diretos e indiretos. 2006. 102 f.: Dissertação (mestrado) - Universidade Federal do Ceará, Programa de Pós-Graduação em Direito, Fortaleza-CE, 2006. / Submitted by Natália Maia Sousa (natalia_maia@ufc.br) on 2015-05-27T13:48:32Z No. of bitstreams: 1 2006_dis_dalima.pdf: 681255 bytes, checksum: 1d91d08aed41280a038f64a6862b880d (MD5) / Approved for entry into archive by Camila Freitas(camila.morais@ufc.br) on 2015-05-27T15:50:35Z (GMT) No. of bitstreams: 1 2006_dis_dalima.pdf: 681255 bytes, checksum: 1d91d08aed41280a038f64a6862b880d (MD5) / Made available in DSpace on 2015-05-27T15:50:35Z (GMT). No. of bitstreams: 1 2006_dis_dalima.pdf: 681255 bytes, checksum: 1d91d08aed41280a038f64a6862b880d (MD5) Previous issue date: 2006 / In this present research we have the objective of analyzing the extent of the religious temples immunity. Our study will aboard the general situation to appoint when the immunity must be considered or not, regarding, in the first view, the religious activity itself. We will see the incidence of direct taxes (on services, property, income tax etc.) and the indirect taxes (on circulation of goods, on services, on energy etc.). Infra constitutional arguments cannot be used to stop the immunity of Constitution. On the other hand, it is not possible recognize the immunity in all opportunities, even against other principles of Constitution. It is a fact that in this research we used the mainspring of constitutional hermeneutics, the best and modern doctrine about the subject and the more recent precedents of jurisprudence. / No presente trabalho temos por objetivo estudar a amplitude da imunidade dos templos religiosos. Conforme determina a Constituição Federal de 1988, as referidas entidades estão exoneradas do recolhimento de quaisquer impostos, de modo que, por conta deste benefício, as igrejas e instituições sacras em geral não devem pagar os impostos previstos em nossa ordem jurídica. Desta feita, nosso estudo está centrado na análise da incidência dos impostos sobre essas entidades imunes, verificando em que circunstâncias a imunidade deve prevalecer quando a atividade, bem, produto ou serviço imunizado diga respeito às finalidades essenciais da instituição. Estudaremos tanto a incidência de impostos diretos, como é o caso do imposto sobre serviços, do imposto sobre a propriedade predial e territorial urbana e do imposto de renda, quanto os impostos indiretos, tais como, v. g., o imposto sobre circulação de mercadorias e serviços incidente sobre energia elétrica e telefonia, o imposto sobre produtos industrializados destacado na compra de materiais utilizados na construção dos templos, dentre outros. Argumentos que repousam na seara infraconstitucional não podem servir de justificativa para refrear os efeitos da imunidade prevista na Carta Magna. Por outro lado, abusos metodológicos não poderão fazer com que a imunidade prevaleça sempre, ainda que em detrimento de outros valores albergados na Lei Fundamental. Em nossa pesquisa, valemo-nos fundamentalmente dos cânones da nova hermenêutica constitucional, da doutrina existente sobre o assunto e de precedentes jurisprudenciais que tratam da matéria.

Made available in DSpace on 2015-09-17T15:26:20Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-05-12. Added 1 bitstream(s) on 2015-09-17T15:45:48Z : No. of bitstreams: 1 000848245.pdf: 624236 bytes, checksum: c69b524f4c9580903dec4bfab14e6987 (MD5) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Nestatese, uma dada amplitude de espalhamento de supercordas envolvendo um operador de vértice da corda fechada e N operadores de vértice da corda aberta em AdS5 ×S5 é detalhadamente estudada, utilizando-se o formalismo de espinores puros. Após rever o material de apoio e realizar alguns cálculos preliminares, mostramos que a amplitude nível-de-árvore contendo um estado de supergravidade e N estados de super-Yang-Mills localizados em uma D3-brana próxima à fronteira de AdS5 pode ser expressa como uma integral no superespaço harmônico N = 4, d = 4 em termos dos supercampos de supergravidade e super-Yang-Mills, demonstrando assim uma conjectura feita recentemente / In this thesis, a particular superstring scattering amplitude involving one closed string and N open string vertex operators in AdS5 ×S5 is studied in detail, usingthe pure-spinor formalism. After reviewing some background material and performing a few preliminary calculations, we show that the tree-level amplitude containing one supergravity state and N super-Yang-Mills states located on a D3-brane near the AdS5 boundary can be expressed as an N = 4, d = 4 harmonic superspace integral in terms of the supergravity and super-Yang-Mills superfields, thus proving a conjecture recently made / FAPESP: 2010/19596-2

Submitted by João Arthur Martins (joao.arthur@ufpe.br) on 2015-04-08T19:21:01Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertação final após defesa..pdf: 3311648 bytes, checksum: ffd3e243b189fa696f5bb64b2db6bdff (MD5) / Made available in DSpace on 2015-04-08T19:21:01Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertação final após defesa..pdf: 3311648 bytes, checksum: ffd3e243b189fa696f5bb64b2db6bdff (MD5) Previous issue date: 2012-02-07 / CNPq / Introdução: A laringectomia total é uma forma de tratamento cirúrgico para o câncer de laringe nos estágios mais avançados. Com o procedimento, há a remoção de toda a laringe e dos músculos adjacentes a esta, acarretando alterações, além de anatômicas e estéticas. Interfere em funções básicas do sistema estomatognático, dentre elas, a mastigação, causando desequilíbrios ou desorganização, acrescidas de frequentes sequelas pós- cirúrgicas, como cicatrizes, aderências, encurtamentos musculares, dor, edema e alterações posturais, que podem influenciar na amplitude de movimento e na postura de cabeça e pescoço. Objetivo: Relacionar o lado de preferência mastigatória com os dados goniométricos e posturais da região cervical em indivíduos submetidos à laringectomia total. Métodos: Estudo transversal, descritivo, tipo série de casos, e retrospectivo para o grupo dos laringectomizados totais. A coleta de dados ocorreu no setor de Fonoaudiologia do Hospital de Câncer de Pernambuco (HCP), entre janeiro e junho de 2011. Contou com dois grupos: um composto por 9 pacientes voluntários submetidos à laringectomia total, atendidos no HCP, e um controle com 9 voluntários não laringectomizados. A preferência por um lado mastigatório foi determinada através da análise das gravações do ato mastigatório habitual. A goniometria foi utilizada para avaliação da Amplitude de Movimento (ADM) cervical, que consistiu na mensuração, em graus, da amplitude de movimento, na forma passiva e ativa, da flexão, extensão, inclinação e rotação para a direita e para a esquerda da cabeça. Para avaliar a postura de cabeça e pescoço foi utilizada a fotogrametria, através do Software de Avaliação Postural (SAPO), onde fotos, nas vistas anterior, posterior, perfil direito e perfil esquerdo dos indivíduos foram obtidas com pontos de referências demarcados nas regiões a serem analisadas. Os dados foram organizados em planilha Excel® e analisados com o programa SPSS na versão 17.0. Para análise dos dados foram utilizados o teste não paramétrico de Mann-Whitney para comparação de amostras não pareadas. Resultados: Nos dois grupos existiu uma preferência por lado mastigatório à esquerda (55,6%). Com a goniometria, observou-se que os laringectomizados, com esta preferência mastigatória, apresentam uma redução significativa da ADM da extensão passiva (p=0,047) e da inclinação para a direita, tanto ativa (p=0,044) quanto passivamente (p=0,027), enquanto que, naqueles preferência mastigatória à direita, somente o movimento de extensão, passiva (p=0,019) e ativa (p=0,020), estava limitado. Na avaliação postural pelo SAPO, a postura não diferiu entre os grupos, porém quando comparada à preferência mastigatória à esquerda, os laringectomizados apresentaram anteriorização de cabeça mais significante (p=0,009). Conclusão: Os laringectomizados totais por câncer apresentaram preferência mastigatória à esquerda, com as amplitudes de movimentos cervicais limitadas, principalmente para extensão passiva e inclinação para a direita passiva e ativamente, com uma postura anteriorizada de cabeça.

Orientador: Lucia Helena Simões da Costa Paiva / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Ciencias Medicas / Made available in DSpace on 2018-08-04T01:12:31Z (GMT). No. of bitstreams: 1 Henriques_SylviaHelenaFerreiradaCunha_D.pdf: 316130 bytes, checksum: b0df6fc722b6e1726b3d1b3723ed888f (MD5) Previous issue date: 2004 / Resumo: Introdução: O crescimento da expectativa de vida tem aumentado a incidência de doenças de idades avançadas, dentre elas a osteoporose. Entretanto as alterações musculoesqueléticas que a acompanham ainda são controversas. Objetivo: avaliar as alterações musculoesqueléticas em mulheres na pós-menopausa, com e sem osteoporose. Sujeitos e Métodos: foi realizado um estudo de corte transversal comparativo com 63 mulheres, acompanhadas no Ambulatório de Menopausa do CAISM/Unicamp, distribuídas em dois grupos, sendo 30 mulheres com osteoporose e 33 sem osteoporose, diagnosticadas através de densitometria óssea. Todas as voluntárias concederam uma entrevista e foram submetidas a uma avaliação física, que constava da medida da força muscular (prova muscular de Daniels) e das amplitudes de movimentos (com flexímetro) da flexão e extensão do tronco, dos ângulos de cifose torácica e lordose lombar (Método de Cobb) e equilíbrios estático e dinâmico (teste de Romberg). Resultados: a idade média das mulheres com osteoporose foi de 57,40, enquanto a das mulheres sem osteoporose foi de 55,76 (p = 0,35) e o tempo médio de menopausa foi de 11 anos nos dois grupos (p=0,97). Os valores médios da força muscular dos flexores e extensores do tronco foram menores nas mulheres com osteoporose (p<0,01). A amplitude de movimento de flexão do tronco foi semelhante nos dois grupos (p=0,91), porém a amplitude do movimento de extensão do tronco nas mulheres com osteoporose foi 20,5° e nas mulheres sem osteoporose 28,4°. Os ângulos de cifose torácica de T1 a T4 (p<0,01) e os ângulos de lordose lombar (p=0,02) foram mais acentuados nas mulheres com osteoporose. Em relação ao equilíbrio, 73,3% das mulheres com osteoporose e 78,8% das mulheres sem osteoporose apresentaram bom equilíbrio estático. As mulheres nos dois grupos apresentavam fraco equilíbrio dinâmico. Não foram observadas diferenças significativas nos equilíbrios estático e dinâmico. As fraturas vertebrais estiveram presentes em 20% das mulheres com osteoporose e ausentes nas mulheres sem osteoporose. Conclusão: Observou-se que mulheres com osteoporose apresentaram menores condições musculoesqueléticas em comparação com as mulheres sem osteoporose, o que pode aumentar o risco de quedas e conseqüentemente de fraturas. Estas observações permitem propor que mulheres com osteoporose participem de programas de exercícios físicos preventivos / Abstract: Introduction: The life expectance increase has to rase the incidence of olders age diseases such as osteoporosis. However the musculosketetal changes doesn't knowed. Objective: this study aimed to investigate the musculoskeletal changes among post menopausal women with and without osteoporosis. Subjects and methods: it is a comparative cross-sectional study. The sample was constituted of 63 women in the CAISM/UNICAMP post menopausal ambulatory, which 30 with densitometric diagnosis of osteoporosis in the spine (mean age: 55.76) and 33 without osteoporosis (mean age: 57.40). All subjects were submitted to a questionaire and a physical evaluation, which consist of the strength of back flexors and extensors (Daniels muscles test), upper body range of motion (fleximeter), thoracic kyphosis and lumbar lordosis degree (Cobb), and static and dynamic equilíbrium (Romberg test). Results: the mean age of the post menopausal women with osteoporosis was 57.40, while the women without osteoporosis was 55.76 (p=0.35) and the mean of the menopause time was 11 years to two groups (p=0.97). The mean of strength of back extensors and flexors muscles of upper body were less in women with osteoporosis (p<0.01). At upper body flexion was not verified any significant changes in rang of motion, as the upper body extention women with osteoporosis showed range of motion of the 20.5° and the women without osteoporosis showed 28.4° (p<0,01). The greatest thoracic kyphosis of T1 to T4 (p<0.01) and lumbar lordosis (p=0.02) degree was noticed in women with steoporosis. About equilibrium, 73.3% of the women with osteoporosis and 78,8% without osteoporosis showed a good static equilibrium and dinamic were poor in both groups. It was not verified any significant changes in both equilibrium. 20% of the women with osteoporosis had fractures and the women without osteoporosis hadn't fractures. Conclutions: these results suggest a distinctive least of the musculoskeletal conditions in women with post menopausal osteoporosis. The musculosketetal changes can increase the risk of a fall and consequently of fracture. These observations can recomend exercise intervention for osteoporotic women / Doutorado / Ciencias Biomedicas / Doutor em Tocoginecologia

Dans la première partie de cette thèse, nous établissons la Conjectured'amplitude de Debarre : Le fibré cotangent T_X* d'une intersection X =H_1 cap ... cap H_c de c >= N/2 hypersurfaces génériques H_i dansP^N de degrés élevés d_1, ..., d_c >> 1 est ample.Tout d'abord, nous élaborons une interprétation géométrique desdifférentielles symétriques sur les espaces projectifs. De cettemanière, nous reconstruisons les différentielles symétriques deBrotbek sur X, lorsque les équations définissantes des hypersurfacesH_1, ..., H_c sont de type Fermat généralisé. De plus, nous dévoilonsdes familles nouvelles de différentielles symétriques de degréinférieur sur toutes les intersections possibles de X avec deshyperplans de coordonnées.Ensuite, nous introduisons ce que nous appelons la Méthode desCoefficients Mobiles ainsi que le Coup du Produit afin d'accomplir unedémonstration de la conjecture d'amplitude de Debarre. De plus, nousobtenons une borne effective inférieure sur les degrés : d_1,...,d_c >=N^N^2. Enfin, grace à des résultats connus au sujet de la conjecturede Fujita, nous établissons que Sym^k T_X* est très ample pour tout k>= 64 (d_1 + ... + d_c)^2.Dans la seconde partie de cette thèse, nous étudions la Conjectured'amplitude généralisée de Debarre stipulant que sur un corpsalgébriquement clos K de caractéristique quelconque, sur une variétéK-projective lisse P de dimension N munie de c >= N/2 fibrés endroites très amples L_1, ..., L_c, pour tous degrés élevés d_1,...,d_c >= d_* >> 1, pour c hypersurfaces génériques H_i dans lessystèmes linéaires L_i^d_i, l'intersection complète X := H_1 cap ... capH_c possède un fibré cotangent T_X* qui est ample.Sur de telles intersections X, nous construisons ce que nous appelonsdes `formes différentielles symétriques de Brotbek généralisées', etnous établissons que si L_1, ..., L_c sont presque proportionnelsmutuellement, alors la conjecture d'amplitude généralisée de Debarreest valide. Notre méthode est effective, et dans le cas où L_1 = ... =L_c, nous obtenons la meme borne inférieure d_* = N^N^2 que dans lapremière partie.Ces deux travaux sont parus sur arxiv.org. / In the first part of this thesis, we establish the Debarre AmplenessConjecture: The cotangent bundle T_X^* of the intersection X = H_1cap ... cap H_c of c >= N/2 generic hypersurfaces H_i in P^N of highdegrees d_1, ..., d_c >> 1 is ample.First of all, we provide a geometric interpretation of symmetricdifferential forms in projective spaces. Thereby, we reconstructBrotbek's symmetric differential forms on X, where the defininghypersurfaces H_1, ..., H_c are generalized Fermat-type. Moreover, weexhibit unveiled families of lower degree symmetric differential formson all possible intersections of X with coordinate hyperplanes.Thereafter, we introduce what we call the `moving coefficients method'and the `product coup' to settle the Debarre Ampleness Conjecture. Inaddition, we obtain an effective lower degree bound: d_1, ...,d_c >=N^{N^2}. Lastly, thanks to known results about the Fujita Conjecture,we establish the very-ampleness of Sym^k T_X^* for all k >= 64 (d_1 +... + d_c)^2.In the second part, we study the General Debarre Ampleness Conjecture,which stipulates that, over an algebraically closed field K with anycharacteristic, on an N-dimensional smooth projective K-variety Pequipped with c >= N/2 very ample line bundles L_1, ..., L_c, for alllarge degrees d_1, ..., d_c >= d_* >> 1, for generic c hypersurfacesH_i in the complete linear system L_i^d_i, the complete intersection X:= H_1 cap ... cap H_c has ample cotangent bundle T_X^*.On such an intersection variety X, we construct what we call`generalized Brotbek's symmetric differential forms', and we establishthat, if L_1,...,L_c are almost proportional mutually, then theGeneral Debarre Ampleness Conjecture holds true. Our method iseffective, and in the case where L_1 = ... = L_c, we obtain the samelower degree bound d_* = N^{N^2} as in the first part.These two works have been posted on arxiv.org.

NiTi (also known as Nitinol) is an almost equiatomic alloy of nickel and titanium and has many applications in various industries, such as biomedical, automotive, and aerospace. NiTi shape memory alloys undergo martensitic phase transformations under both thermal and mechanical loading and exhibit unique properties, such as superelasticity (SE) and shape memory effects (SME). Modeling the fatigue behavior of this alloy is very challenging due to the unique mechanical response of the material. Moreover, there are very limited studies on the fatigue behavior of this alloy under more realistic loading conditions, such as variable amplitude loading and multiaxial loading. In this study, strain-controlled cyclic experiments have been conducted in different conditions to study the variable amplitude fatigue behavior of superelastic NiTi. Nonzero mean strain/stress behavior of superelastic NiTi is investigated, and it is demonstrated that the classical fatigue models for mean strain/stress correction do not appropriately model the nonzero mean strain/stress fatigue behavior of superelastic NiTi. It is shown that, despite common metals (e.g., steel, aluminum, and titanium alloys), mean strain also affects the fatigue behavior of superelastic NiTi, as the resulting mean stress does not fully relax under cyclic load. Two energy-based fatigue models have been proposed based on the results in this study and provide acceptable correlation with experimental observations. The models proposed in this research, account for the effects of mean strain/stress and variations in cyclic deformation. The variations in the cyclic deformation can be due to several factors, such as slight changes in chemical composition, heat treatment processes, texture, etc. The predicted fatigue lives using the proposed fatigue model fall within scatter bands of 1.5 times the experimental life for constant amplitude loading. Analyses also show that the proposed total fatigue toughness parameter, ΣWt, together with the Rainflow cycle counting technique can accurately predict the fatigue life under more realistic loading condition, such as two-step (i.e. high-low and low-high) and variable amplitude load-paths.

Amplitude envelope is an important aspect of auditory perception. As one article included (Chapter 3) goes into great detail regarding this, it will not be discussed here. Included are two articles that explore the importance and influence of amplitude envelope in auditory perception research. The first article (Chapter 2) explores the role of amplitude envelope in an associative memory task, with the aim of improving the associability of auditory alarms in medical devices. Although we found no difference in performance based on amplitude envelope, the paper discusses the patterns of incorrect alarm identification and identifies potential sources of confusion. While this was not our initial goal, we feel this article is a valuable contribution that connects two distinct fields: music cognition and alarm design. The second article (Chapter 3) encompasses a meta-analysis, surveying the temporal structure of sounds used in auditory perception research, namely in the journal Attention, Perception & Psychophysics. This articles discusses several studies in which amplitude envelope has categorically influenced experimental outcomes and suggests that the standard ‘flat’ temporal structure (i.e. abrupt onset, period of sustain and abrupt offset) may not be the best way to evaluate the auditory system. The goal of this article is to determine what proportion of studies are using the standard ‘flat’ tones vs. other types of temporal structures we may encounter during everyday listening. These two articles collectively illustrate the original research I have completed on amplitude envelope during my Master’s Degree. / Thesis / Master of Science (MSc)

Auditory alarm annoyance plagues clinicians, which results in alarms desensitization and ultimately affects patient care. Contributing to this problem are the International Electrotechnical Commission (IEC) 60601-1-8 alarms, a standardized set of melodic alarms used to convey information to clinicians in intensive care units. By design, IEC alarms employ flat amplitude (i.e., amplitude invariant) envelopes and are not reflective of naturally occurring sounds with percussive amplitude (i.e., decaying) envelopes. We present a series of three experiments evaluating the effect of amplitude envelope manipulation (i.e., incorporating percussive envelope) on memory and annoyance in IEC alarms synthesized using pure tones (experiment 1), complex tones (experiment 2) and assessing annoyance pre and post memory assessment (experiment 3). For the memory assessment, participants were assigned to learn either the flat alarms or percussive alarms. During the memory assessment, participants were informed of the alarm–referent pairings (study phase), practised identifying alarms (training phase), had a short break, and tested on their ability to identify alarms (evaluation phase). The annoyance assessment was a two alternative forced choice task where participants identified which alarm they perceived to be more annoying from a pair of alarms differing in either envelope-type or alarm-type. Across all experiments there was no difference in alarm learnability between those learning either flat or percussive alarms during the memory assessment. Annoyance assessments revealed that all participants chose the flat alarms to be more annoying than the percussive alarms, independent of the memory assessment condition. These results showcase the potential of using percussive alarms to reduce alarm annoyance without harming learnability, a cost-efficient manipulation. / Thesis / Master of Science (MSc) / Alarms in intensive care units are perceived as annoying, ultimately negatively affecting both clinicians and patients. These alarms are mandated by the International Electrotechnical Commission to have sustained or flat amplitude envelopes (i.e., referring to the change in loudness over time), which does not reflect naturally occurring stimuli that typically have decaying or percussive amplitude envelopes. The current experiments assessed the effect of percussive envelopes on alarm learnability and annoyance. We showed in a series of experiments that there is no difference in learning alarms with flat or percussive envelopes. However, we showed that alarms with percussive envelopes are perceived to be less annoying than alarms with flat envelopes. These results offer one potential solution to reduce alarm annoyance in intensive care units without harming the learnability of these alarms.

With the extreme miniaturization of NEMS, the role of nonlinear dynamics has become increasingly important -- even when the dynamics are driven by the Brownian force. This nonlinearity has imposed a mechanical noise floor on the linear frequency measurements made in sensing applications. Given that NEMS also become more sensitive as they become smaller, this floor has resulted in a complex interplay between the nonlinear regime and the linear sensitivity required to make continued advancements in exercising ultra-sensitive measurements. Recently, this has led to efforts to more accurately characterize the edge of the linear regime. Inside of the nonlinear regime, there are also ongoing fundamental studies in theory and experiment to partially characterize the nonlinear behavior of NEMS. Theoretically, these systems are frequently studied by decomposing the nonlinear continuous system into one or more nonlinear oscillators. However, in many of these works, the nonlinear spring constants are estimated at the lowest order. As such, there is a clear need to more accurately characterize and scale the nonlinear coefficients for NEMS. This work considers a long and slender NEMS resonator in the form of a doubly-clamped beam in tension. Using nonlinear Euler-Bernoulli beam theory, the geometric nonlinearity due to the stretching of the neutral axis is considered. We extensively explore simplifications in using a Galerkin discretization of the continuous system, where a single mode's dynamics are described as a damped, Duffing oscillator. We examine limitations of current approaches and find that using a tensioned and doubly-clamped mode shape for the trial function more accurately predicts experiment. Additionally, we find that doubly-clamped beams of finite tension may have their boundary conditions modified to that of a hinged-hinged beam in tension with little to no loss of generality. This modification allows for closed-form scaling of the critical amplitude and dynamic range at arbitrary mode number and tension. We extend this approach to scale the relative influence of bending, tension, and nonlinearity with increasing mode number n, finding that bending and nonlinear influences quickly outgrow the contributions of the intrinsic tension. Where applicable, these results are compared with experiment, and we obtain good agreement. To validate the approximate Galerkin formulations, we develop a finite element method to calculate the nonlinear coefficients of symmetric NEMS resonators. Unlike previous works, the present formulation may include all nonlinearity due to geometry, and the nonlinear amplitude-frequency backbone described by the Duffing oscillator is found as an excellent approximation for large amplitude beams. For beams of zero intrinsic tension, the finite element method obtains excellent agreement with the literature. For beams of finite tension and varying mode number, we find the error from the Galerkin discretization is small (≈5%). In addition, we theoretically explore the stochastic dynamics of a Duffing oscillator driven nonlinearly by the Brownian force. To access this regime experimentally with current nanomechanical systems, we motivate an experimental "synthetic noise" to approximate the Brownian force in the proximity of a single mode. As a measure of drive magnitude, we vary an effective temperature to explore the linear and nonlinear stochastic dynamics of a doubly-clamped nanoresonator. Using similitude and the Fluctuation-Dissipation theorem, we show that varying the effective temperature of the synthetic noise offers a window into the fundamental limits of thermally-driven nonlinearities. We compare theory, numerics, and experiment where applicable, obtaining good agreement for both limits of frequency shifts in the weakly nonlinear case. This research was supported by the National Science Foundation, grant number CMMI-2001559, and portions of the computations were conducted using the resources of Virginia Tech's Advanced Research Computing (ARC) center. / Master of Science / Nanoelectromechanical systems (NEMS) are nanoscale mechanical structures that convert physical stimuli (force, mass, acceleration, charge, etc.) to measurable electrical signals. Due to the extremely small size of NEMS, they offer an unprecedented level of sensitivity in a variety of measurement applications. However, as NEMS become smaller, the response of these mechanical structures begin to exhibit nonlinear behaviors. Said otherwise, proportional inputs (such as drive strength) do not result in proportional outputs. These nonlinear behaviors include a variety of undesired effects, such as multi-valued unstable/stable solutions and a noisy resonant frequency. In this work, we study a NEMS resonator in the form of a doubly-clamped beam, and we consider the stretching of the mid-plane as the nonlinearity. Here, the stretching of the mid-plane (an axial strain) is nonlinearly dependent on the amplitude of vibration, inducing a nonlinear tension force. With this model, it is typical to represent a singular nonlinear vibrational mode as a simple harmonic oscillator with an additional cubic term. In order to better characterize the edge of the nonlinear regime, the relative strength of the cubic term must be known. We thoroughly explore existing and new simplifications to obtain the nonlinear coefficient for the cubic term, demonstrating two possible approaches for better accuracy in beams of varying tension and mode number. These simplifications are validated by comparing with the present finite element method to determine the nonlinearity in symmetric NEMS resonators. Using these new insights, theory and numerics are used to explore the behavior of a doubly-clamped beam in a stochastic (random) force field. This force field is tailored to represent the collisions of surrounding molecules at the nanoscale, allowing exploration of nonlinear behavior at its fundamental limits. Where applicable, theory and numerics are compared to experiment, and we obtain good agreement. This research was supported by the National Science Foundation, grant number CMMI-2001559, and portions of the computations were conducted using the resources of Virginia Tech's Advanced Research Computing (ARC) center.