Submitted by Jaqueline Silva (jtas29@gmail.com) on 2016-09-08T19:58:04Z No. of bitstreams: 2 Dissertação - Gabriel Eliseu Silva - 2014.pdf: 1496066 bytes, checksum: 022a464ffaf53a95f5e7c2aba78aeff4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Jaqueline Silva (jtas29@gmail.com) on 2016-09-08T19:58:15Z (GMT) No. of bitstreams: 2 Dissertação - Gabriel Eliseu Silva - 2014.pdf: 1496066 bytes, checksum: 022a464ffaf53a95f5e7c2aba78aeff4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-09-08T19:58:15Z (GMT). No. of bitstreams: 2 Dissertação - Gabriel Eliseu Silva - 2014.pdf: 1496066 bytes, checksum: 022a464ffaf53a95f5e7c2aba78aeff4 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2014-08-21 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / (Dynamics of the shrub-tree community in three areas of cerrado sensu stricto in the municipality of Jataí, southwest of Goiás). The aim of the study was to assess the changes in shrub-tree community in a range of approximately three years, involving changes in the structure and vegetation composition with soil factors and the fire. The study was conducted in three areas of “cerrado sentido restrito”, using a ten plots of 20 × 50m in each area. All shrub-tree individuals with DAS (diameter at the heigh of the ground) ≥ 5 cm in the first survey (T1) were plaquetados, estimated their heights and identified their species (2009 in BAT and LAJ, and 2010 in FRP). The second survey (T2) was carried out in 2012 in the area of LAJ and in 2013 in the other two areas (BAT and FRP). T2 survivors were re-measured and those who have to enter the inclusion criteria (recruits) were measured and plaquetados. T1 in BAT, it was found 70 species, 853 individuals and basal area of 8.75 m2. T2 is sampled-63 species, 601 individuals and basal area of 9.12 m2. In the interval between the two surveys (4.16 years) nine species disappeared and two joined the community. The diversity index of Shannon and Pielou evenness were 3.26 and 0.77, respectively, for T1. For T2, only the diversity changed, dropping to 3.16. The average annual mortality rate was 11.55% and the recruitment 2.4%. In LAJ met 83 species, 1391 individuals and basal area of 16.82 m2 in T1 and T2 is already sampled-87 species, 1503 individuals and basal area of 18.65 m2. In the period of 3.58 years, eight species entered four disappeared in the community. The diversity index was 3.62 at T1 and T2 3.65. The average annual mortality rate was 2.27% and 4.13% of recruitment. In FARP met 77 species, 1863 individuals and basal area of 10.87 m2 in T1, T2 and already sampled to 75 species, 1395 individuals and basal area of 10.1 m2. In the period of three years, seven species have disappeared and five joined the community. The diversity index was 3,62 at T1 and T2 3,65. For the evenness values were 0,8 for both surveys. The average annual mortality rate was 10,37% and 1,73% of recruitment. The three cerrado narrow sense fragments altered the species richness, the number of individuals and basal area, but no significant changes in the diversity index between the first and the second survey. This may be related to variations in wealth, depending on the species with few individuals. The highest mortality found for BAT and FRP may be related to the presence of fire, while for the LAJ the largest recruitment is associated with absence of disturbance. The change in density and growth of individuals can still be conditioned to the soil characteristics. In LAJ and BAT the clay soil, while allowing the establishment and growth of forest species and individuals susceptible to fire, in BAT, it is believed that the fire has acted as limiting changes in the structure, preventing the density of vegetation; and LAJ, the increased density and increased basal area possibly occurred in the absence of fire. In the FRP, it is suggested that any fire and the sandy soil can contribute to the limitation on structural changes and the wealth of the community. Thus, in the LAJ greater rate of recruitment in relation to the recorded mortality, may possibly be related to the absence of fire and soil characteristics, providing tree compaction stage and a possible succession of the community, indicating the formation of a cerradão. Regarding the areas of BAT and FARP the highest mortality rates in relation to recruitment may ester associated with the presence of fire, preventing the thickening in the community and keeping the cerrado vegetation type narrow sense. / (Dinâmica da comunidade arbustivo-arbórea de três áreas de cerrado sentido restrito no município de Jataí, sudoeste de Goiás). O objetivo do trabalho foi verificar as mudanças ocorridas na comunidade lenhosa em um intervalo aproximado de três anos, associando as alterações na estrutura e na composição vegetacionais com os fatores edáficos e o fogo. O estudo foi realizado em três áreas de cerrado sentido restrito, utilizando dez parcelas de 20 × 50m em cada área, onde foram amostrados todos os indivíduos lenhosos com DAS (diâmetro a altura do solo) ≥ 5 cm no primeiro levantamento (T1), plaquetados, estimados suas alturas e identificados suas espécies (2009 no BAT e na LAJ, e 2010 na FRP). O segundo levantamento (T2) foi realizado em 2012 na área da LAJ e em 2013 nas outras duas áreas (BAT e FRP). Em T2 os sobreviventes foram remedidos e aqueles que passaram a entrar no critério de inclusão (recrutas) foram mensurados e plaquetados. Em T1 no BAT, encontrou-se 70 espécies, 853 indivíduos e área basal de 8,75 m2. Em T2 amostrou-se 63 espécies, 601 indivíduos e área basal de 9,12 m2. No intervalo entre os dois levantamentos (4,16 anos) nove espécies desapareceram e duas ingressaram na comunidade. O índice de diversidade de Shannon e a equabilidade de Pielou foram 3,26 e 0,77, respectivamente, para T1. Para T2, apenas a diversidade alterou, caindo para 3,16. A taxa média anual de mortalidade foi 11,55% e a de recrutamento 2,4%. Na LAJ encontrou-se 83 espécies, 1391 indivíduos e área basal de 16,82 m2 em T1, e já em T2 amostrou-se 87 espécies, 1503 indivíduos e área basal de 18,65 m2. No período de 3,58 anos, oito espécies ingressaram e quatro desapareceram na comunidade. O índice de diversidade em T1 foi de 3,62 e em T2 3,65. A taxa média anual de mortalidade foi de 2,27% e a de recrutamento 4,13%. Na FARP encontrou-se 77 espécies, 1863 indivíduos e área basal de 10,87 m2 em T1, e já em T2 amostrou-se 75 espécies, 1395 indivíduos e área basal de 10,1 m2. No período de 3,0 anos, sete espécies desapareceram e cinco ingressaram na comunidade. O índice de diversidade em T1 foi de 3,62 e em T2 3,65. Para a equabilidade os valores foram 0,8 para ambos os levantamentos. A taxa média anual de mortalidade foi de 10,37% e a de recrutamento 1,73%. Os três fragmentos de cerrado sentido restrito alteraram a riqueza de espécies, o número de indivíduos e área basal, porém não houve mudanças consideráveis nos índices de diversidade entre o primeiro e o segundo levantamento. Isso pode estar relacionado à variação da riqueza, em função das espécies que apresentaram poucos indivíduos. As maiores mortalidades encontradas para a BAT e FRP podem estar relacionadas à presença do fogo, enquanto para a LAJ o maior recrutamento esteja associado à ausência da perturbação. A alteração na densidade e o crescimento dos indivíduos podem estar condicionados ainda às características do solo. Na LAJ e no BAT o solo argiloso, apesar de possibilitar o estabelecimento e crescimento dos indivíduos de espécies florestais e sensíveis ao fogo, no BAT, acredita-se que o fogo tem atuado como limitante nas alterações da estrutura, impedindo o adensamento da vegetação; e na LAJ, o aumento da densidade e incremento em área basal, possivelmente ocorreu devido à ausência de queimadas. Já na FRP, sugere-se que o fogo eventual e o solo arenoso possam contribuir com a limitação nas alterações estruturais e na riqueza da comunidade. Assim, na LAJ a maior taxa de recrutamento registrada em relação à de mortalidade, possivelmente pode estar relacionada à ausência do fogo e às características do solo, proporcionando o adensamento arbóreo e um possível estágio sucessional da comunidade, indicando a formação de um cerradão. Em relação às áreas do BAT e da FARP as maiores taxas de mortalidade em relação às de recrutamento podem estar associadas à presença de queimadas, impedindo o adensamento na comunidade e mantendo a fitofisionomia de cerrado sentido restrito.

This study investigates the use of reduplication with predicative signs in Swedish Sign Language (SSL), and also the related phenomena doubling and displacement. Reduplication in SSL typically expresses plurality of events and/or referents, but may also express intensification, ongoing event or generic activity. There is a distinction between external and internal events with reduplication: external reduplication expresses some event happening over and over at different points in time and/or with different referents, and is associated with a frequentative/habitual reading; internal reduplication expresses some event consisting of several e.g. movements/actions and is associated with an ongoing reading. Only external expression seems to be applicable to stative constructions, as one would expect. The study also found a phenomenon not previously described: oral reduplication without manual reduplication. This process is found to have the ongoing functions with telic predicates, such that it focuses on the telic predicate as a single event in progress, and thus replaces the function of manual reduplication, which, with telic predicates, would instead express several events. The reading of reduplicated signs is associated with the semantics of the sign reduplicated, and it is also associated with the phonological citation form of the sign—monosyllabic signs tend to get pluractional reading; bisyllabic signs tend to get an ongoing reading. Also, the reading expressed by reduplication is connected to the presence/absence of oral reduplication. Reduplication generally does not occur in negative constructions. This study shows that inherently negative signs may be reduplicated, but reduplicated predicates are negated according to other strategies than for non-reduplicated predicates, thus reduplication has the largest scope. Doubling and displacement are both associated mainly with plural referents, and it is in this respect that they are related to reduplication, and they both occur frequently with reduplication.

This thesis is chiefly concerned with a classical conjecture of Littlewood's regarding the L¹-norm of the Fourier transform, and the closely related idem-potent theorem. The vast majority of the results regarding these problems are, in some sense, qualitative or at the very least infinitary and it has become increasingly apparent that a quantitative state of affairs is desirable. Broadly speaking, the first part of the thesis develops three new tools for tackling the problems above: We prove a new structural theorem for the spectrum of functions in A(G); we extend the notion of local Fourier analysis, pioneered by Bourgain, to a much more general structure, and localize Chang's classic structure theorem as well as our own spectral structure theorem; and we refine some aspects of Freiman's celebrated theorem regarding the structure of sets with small doubling. These tools lead to improvements in a number of existing additive results which we indicate, but for us the main purpose is in application to the analytic problems mentioned above. The second part of the thesis discusses a natural version of Littlewood's problem for finite abelian groups. Here the situation varies wildly with the underlying group and we pay special attention first to the finite field case (where we use Chang's Theorem) and then to the case of residues modulo a prime where we require our new local structure theorem for A(G). We complete the consideration of Littlewood's problem for finite abelian groups by using the local version of Chang's Theorem we have developed. Finally we deploy the Freiman tools along with the extended Fourier analytic techniques to yield a fully quantitative version of the idempotent theorem.

Four works are selected to demonstrate the stature and demands of this craft and to represent a pinnacle in the art of contemporary woodwind doubling. Concerto for Doubles, by Thomas Filas, Concerto Tri-Chroma. by Michael Kibbe, Rhapsody Nova, by Clare Fischer and Suite for Solo Flute. Clarinet and Alto Saxophone by Claude Smith all represent rare, major solo works written specifically for three individual woodwind doublers. The paper will begin with a history of the practice of woodwind doubling from the fifteenth century to the present. The four works will then be examined by considering form, style and related performance practices.

Polyploidization (whole-genome duplication) is widely considered one of the most important evolutionary forces driving the diversification of flowering plants. Polyploids tend to originate recurrently and many plant species retain individuals of two or more different ploidy levels in certain parts of their distributional range of even within their populations. The main aim of this thesis was to address the understudied aspects of polyploid speciation by employing new, convenient methods and/or studying plant model systems with unique features. Difference in monoploid genome size of Tripleurospermum inodorum (Asteraceae) cytotypes provided a unique opportunity for addressing the rate of spontaneous polyploidization in natural populations by enabling the easy distinction of neopolyploid mutants from long-established polyploids in routine flow-cytometric analyses. Repeated ploidy screening in mixed-ploidy populations of annual T. inodorum have been, to our knowledge, the very first attempt to document temporal changes in cytotype composition in situ. In spite of considerable between- year oscillations in cytotype frequencies, both diploids and tetraploids usually persisted locally for several consecutive years. The common incidence of such ploidy mixtures along with a partial fertility of triploid...

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In the study of the weighted p-Laplace equation, it is often important to acquire good estimates of capacities. One useful tool for finding such estimates in metric spaces is exponent sets, which are sets describing the local dimensionality of the measure associated with the space. In this thesis, we limit ourselves to the weighted Rn space, where we investigate the relationship between exponent sets and Muckenhoupt Ap-weights - a certain class of well behaved functions. Additionally, we restrict our scope to radial weights, that is, weights w(x) that only depend on |x|. First, we determine conditions on α such that |x|α ∈ Ap(μ) for doubling measures μ on Rn. From those results, we develop weight exponent sets - a tool for making Ap-classifications of general radial weights, under certain conditions. Finally, we apply our techniques to the weight |x|α(log 1/|x|)β. We find that the weight belongs to Ap(μ) if α ∈ (-q, (p-1)q), where q = sup Q(μ) is a constant associated with the dimensionality of μ. The Ap-conditions in this thesis are found to be sharp.

This thesis consists of four papers and focuses on function spaces related to first-order analysis in abstract metric measure spaces. The classical (i.e., Sobolev) theory in Euclidean spaces makes use of summability of distributional gradients, whose definition depends on the linear structure of Rn. In metric spaces, we can replace the distributional gradients by (weak) upper gradients that control the functions’ behavior along (almost) all rectifiable curves, which gives rise to the so-called Newtonian spaces. The summability condition, considered in the thesis, is expressed using a general Banach function lattice quasi-norm and so an extensive framework is built. Sobolev-type spaces (mainly based on the Lp norm) on metric spaces, and Newtonian spaces in particular, have been under intensive study since the mid-1990s. In Paper I, the elementary theory of Newtonian spaces based on quasi-Banach function lattices is built up. Standard tools such as moduli of curve families and the Sobolev capacity are developed and applied to study the basic properties of Newtonian functions. Summability of a (weak) upper gradient of a function is shown to guarantee the function’s absolute continuity on almost all curves. Moreover, Newtonian spaces are proven complete in this general setting. Paper II investigates the set of all weak upper gradients of a Newtonian function. In particular, existence of minimal weak upper gradients is established. Validity of Lebesgue’s differentiation theorem for the underlying metric measure space ensures that a family of representation formulae for minimal weak upper gradients can be found. Furthermore, the connection between pointwise and norm convergence of a sequence of Newtonian functions is studied. Smooth functions are frequently used as an approximation of Sobolev functions in analysis of partial differential equations. In fact, Lipschitz continuity, which is (unlike <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Cmathcal%7BC%7D%5E1" />-smoothness) well-defined even for functions on metric spaces, often suffices as a regularity condition. Thus, Paper III concentrates on the question when Lipschitz functions provide good approximations of Newtonian functions. As shown in the paper, it suffices that the function lattice quasi-norm is absolutely continuous and a fractional sharp maximal operator satisfies a weak norm estimate, which it does, e.g., in doubling Poincaré spaces if a non-centered maximal operator of Hardy–Littlewood type is locally weakly bounded. Therefore, such a local weak boundedness on rearrangement-invariant spaces is explored as well. Finer qualitative properties of Newtonian functions and the Sobolev capacity get into focus in Paper IV. Under certain hypotheses, Newtonian functions are proven to be quasi-continuous, which yields that the capacity is an outer capacity. Various sufficient conditions for local boundedness and continuity of Newtonian functions are established. Finally, quasi-continuity is applied to discuss density of locally Lipschitz functions in Newtonian spaces on open subsets of doubling Poincaré spaces.

Dans cette thèse, nous étudions les fonctions propres de l'opérateur de Laplace-Beltrami - ou simplement laplacien - sur une surface fermée, c'est-à-dire une variété riemannienne lisse, compacte et sans bord de dimension 2. Ces fonctions propres satisfont l'équation $\Delta_g \phi_\lambda + \lambda \phi_\lambda = 0$ et les valeurs propres forment une suite infinie. L'ensemble nodal d'une fonction propre du laplacien est celui de ses zéros et est d'intérêt depuis les expériences de plaques vibrantes de Chladni qui remontent au début du 19ème siècle et, plus récemment, dans le contexte de la mécanique quantique. La taille de cet ensemble nodal a été largement étudiée ces dernières années, notamment par Donnelly et Fefferman, Colding et Minicozzi, Hezari et Sogge, Mangoubi ainsi que Sogge et Zelditch. L'étude de la croissance de fonctions propres n'est pas en reste, avec entre autres les récents travaux de Donnelly et Fefferman, Sogge, Toth et Zelditch, pour ne nommer que ceux-là. Notre thèse s'inscrit dans la foulée du travail de Nazarov, Polterovich et Sodin et relie les propriétés de croissance des fonctions propres avec la taille de leur ensemble nodal dans l'asymptotique $\lambda \nearrow \infty$. Pour ce faire, nous considérons d'abord les exposants de croissance, qui mesurent la croissance locale de fonctions propres et qui sont obtenus à partir de la norme uniforme de celles-ci. Nous construisons ensuite la croissance locale moyenne d'une fonction propre en calculant la moyenne sur toute la surface de ces exposants de croissance, définis sur de petits disques de rayon comparable à la longueur d'onde. Nous montrons alors que la taille de l'ensemble nodal est contrôlée par le produit de cette croissance locale moyenne et de la fréquence $\sqrt{\lambda}$. Ce résultat permet une reformulation centrée sur les fonctions propres de la célèbre conjecture de Yau, qui prévoit que la mesure de l'ensemble nodal croît au rythme de la fréquence. Notre travail renforce également l'intuition répandue selon laquelle une fonction propre se comporte comme un polynôme de degré $\sqrt{\lambda}$. Nous généralisons ensuite nos résultats pour des exposants de croissance construits à partir de normes $L^q$. Nous sommes également amenés à étudier les fonctions appartenant au noyau d'opérateurs de Schrödinger avec petit potentiel dans le plan. Pour de telles fonctions, nous obtenons deux résultats qui relient croissance et taille de l'ensemble nodal. / In this thesis, we study eigenfunctions of the Laplace-Beltrami operator - or simply the Laplacian - on a closed surface, i.e. a two dimensional smooth, compact Riemannian manifold without boundary. These functions satisfy $\Delta_g \phi_\lambda + \lambda \phi_\lambda = 0$ and the eigenvalues form an infinite sequence. The nodal set of a Laplace eigenfunction is its zero set and is of interest since the vibrating plates experiments of Chladni at the beginning of the 19th century as well as, more recently, in the context of quantum mechanics. The size of the nodal sets has been largely studied recently, notably by Donnelly and Fefferman, Colding and Minicozzi, Hezari and Sogge, Mangoubi as well as Sogge and Zelditch.The study of eigenfunction growth is also an active topic, with the recent works of Donnelly and Fefferman, Sogge, Toth and Zelditch to name only a few. Our thesis follows the work of Nazarov, Polterovich and Sodin and links growth and nodal sets of eigenfunctions in the asymptotic $\lambda \nearrow \infty$. To do so, we first consider growth exponents, which measure the local growth of eigenfunctions via their uniform norm. The average local growth of an eigenfunction is built by averaging growth exponents defined on small disks of wavelength like radius over the whole surface. We show that the size of the nodal set is controlled by the product of this average local growth with the frequency $\sqrt{\lambda}$. This result allows a function theoretical reformulation of the famous conjecture of Yau, which predicts that the size of the nodal set grows like the frequency. Our work also strengthens the common intuition that an eigenfunction behaves in many ways like a polynomial of degree $\sqrt{\lambda}$. We then generalize our results to growth exponents built upon $L^q$ norms. We are also led to study functions belonging to the kernel of Schrödinger operators with small potential in the plane. For such functions, we obtain two results linking growth and size of nodal sets.