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Modelos de Lévy de atividade infinita
(Universidade Federal de São Carlos, 2020-06-12) Almeida, Danila Maria Silva Fernandes de; Pinto Júnior, Dorival Leão; https://lattes.cnpq.br/9633241446303620; https://lattes.cnpq.br/8804513851154838
In this work, we present a class of pure jump Lévy processes A, with internal filtration and Itô-Lévy decomposition and we established an explicit forms for martingale representation, main component of our process. Furthermore, we propose an optimal Itô-Meyer formula for a Lévy functional and Euler-Maruyama approach scheme for a path-dependent SDE driven by A Lévy process. For that, first, we close A by a Poisson process composed of Ae , that we proved to converge strongly in B2 to A, when e ↓ 0. This result is fundamental to show that, given a supermartingale Snell envelope S, we can approach it through an imbedded discrete structure , which is the sequence of value processes, associated with S.
Fluxo de curvatura média e self-shrinkers
(Universidade Federal de São Carlos, 2020-06-12) Vitti, Mannaim Gennaro; Barreto, Alexandre Paiva; https://lattes.cnpq.br/3369766702725474; https://lattes.cnpq.br/6766665423506228
Mean curvature flow is a geometric flow that rises when evolving a hipersurface in the direction of its normal vector field with velocity at each point equal to the mean curvature at the very same point. As it is an evolution flow, a natural question to ask is if it becomes singular (either by losing smoothness or by degenerating). We will see that this is no rare case, so another question that we might ask is regarding the asymptotic behaviour of this evolution or, in other words, what are the hypersurfaces "shapes" when their flow approaches being singular. In his paper of 1990 "Asymptotic behaviour for singularities of the mean curvature flow", Gerard Huisken proved his monotonicity formula and, through that, under certain hypothesis, Huisken concluded that the Self Shrinkers are the hypersurfaces that models the asymptotic behaviour of the flow. This work will discuss all these questions, prove the existence and uniqueness of the mean curvature flow and will also classify the self shrinkers embedded in R3 that have a constant norm of second fundamental form.
Plasticidade morfológica em microalgas verdes do gênero Ankistrodesmus induzida por compostos liberados por Daphnia magna
(Universidade Federal de São Carlos, 2020-06-12) Andolfato, Nathan Eugeni; Freitas, Emanuela Cristina de; https://lattes.cnpq.br/8601993745082402; Bagatini, Inessa Lacativa; https://lattes.cnpq.br/3904631503604006; https://lattes.cnpq.br/3954755217365468
Phenotypic plasticity in phytoplankton can be a defense mechanism against predation, directly affecting primary producers and consumers and the food chain of aquatic ecosystems. However, morphological plasticity as a defensive mechanism is an observed induced defense in only a few groups of microalgae. Some studies have documented that the defense induced in phytoplankton can be triggered merely by the presence of products released by herbivorous microcrustaceans, the kairomones, even in the absence of the predator. However, rare studies address predation-induced morphological plasticity in the cosmopolitan green microalgae of the family Selenastraceae. In this study, we evaluated the morphological variation (length and width) in 4 different species of 8 strains of microalgae of the genus Ankistrodesmus under the effect of kairomones by a cladoceran, Daphnia magna. The results showed that the presence of kairomones released by the predator induced an increase in the length and width of the cells of most strains of Ankistrodesmus. The width increased more sharply than the length, which may be related to the orientation of cell intake by the predator. As reported in another study for an A. falcatus strain, we found no colony maintenance or cell aggregation as an important morphological plasticity. However, the results suggest that a single strain of A. fusiformis (CCMA-UFSCar 605) produced colonies in the presence of kairomones excreted by the cladoceran. Despite the differences in time, intensity of response and type of induced change, all 8 strains (4 species) of the genus Ankistrodesmus studied showed some type of phenotypic plasticity in the presence of the predator's kairomones. This is the first report of changes in Ankistrodemus cell size under the influence of zooplankton predation (kairomones). The results are important to understand the ecology of these microalgae and highlight the importance of ecological studies for a better description of the taxonomic characteristics of the coccoid green microalgae.
Estudo da fisiologia do crescimento, produção de biomoléculas e fotossíntese em 30 espécies de microalgas verdes de água doce
(Universidade Federal de São Carlos, 2020-06-12) Camargo, Eduardo Caffagni de; Lombardi, Ana Teresa; https://lattes.cnpq.br/6737850858443813; https://lattes.cnpq.br/1351715221998491
Studies on the physiology and photosynthesis of microalgae are an essential contribution to projects aimed at carbon fixation and biomass production for commercial purposes. Green microalgae (Chlorophyta stricto sensu) comprise a vast diversity of species, yet few of them have been massively cultured. The present research aimed at screening 30 species of Chlorophyta for their growth, photochemical performance, primary production and ability to accumulate biomolecules (chlorophyll, carotenoids, proteins and carbohydrates). All cultures were kept under controlled laboratory conditions. The results showed that Chlorella sorokiniana stood out in virtually every analyzed aspect. Muriella decolor presented a significant growth rate and cell density. The accumulation of total carotenoids was substantial in Monoraphidium griffithii, Chlorolobion braunii and Curvastrum pantanale. New information was found regarding protein productivity in Hariotina reticulata and Chlorolobion lunulatum. C. lunulatum, C. pantanale, H. reticulata, Scenedesmus quadricauda and Desmodesmus spinosus are potential carbohydrate producers. The evaluation of different photochemical parameters and the estimation of the microalgae’s gross primary production (PB) were carried out through Pulse-Amplitude-Modulation (PAM) fluorometry, the main assessment tool applied in this research. C. sorokiniana, D. spinosus and D. communis stood out in terms of PB. As a consequence, they are potential organisms for carbon mitigation. Inferring PB based only on the algae’s specific growth rate, as we initially hypothesized, was found not to be possible, since both variables are moderately correlated. Nonetheless, a strong correlation between PB (under in vivo conditions) and total carbohydrate productivity was observed. Using in vivo samples was considered a more appropriate way of quantifying PB rather than adding a chlorophyll-a extraction step to the same method, since it affects the samples integrity, thus compromising the interpretation of physiological data. This study thereby provides a solid basis for researchers interested in carbon mitigation and potential biotechnological applications involving the 30 strains investigated.