Fourier series for quaternions and the square of the error theorem

In this paper we introduce a type of Hypercomplex Fourier Series based on Quaternions, and discuss on a Hypercomplex version of the Square of the Error Theorem. Since their discovery by Hamilton (Sinegre [1]), quaternions have provided beautifully insights either on the structure of different areas of Mathematics or in the connections of Mathematics with other fields. For instance: I) Pauli spin matrices used in Physics can be easily explained through quaternions analysis (Lan [2]); II) Fundamental theorem of Algebra (Eilenberg [3]), which asserts that the polynomial analysis in quaternions maps into itself the four dimensional sphere of all real quaternions, with the point infinity added, and the degree of this map is n. Motivated on earlier works by two of us on Power Series (Pendeza et al. [4]), and in a recent paper on Liouville’s Theorem (Borges and Mar˜o [5]), we obtain an Hypercomplex version of the Fourier Series, which hopefully can be used for the treatment of hypergeometric partial differential equations such as the dumped harmonic oscillation.

A note on pairs of regular foliations on the solid torus

We discuss the geometry of the pair of foliations on a solid torus given by the Reeb foliation together with discs transverse to the boundary of the torus.

Avaliação dos componentes de óleos essenciais 1,8-cineol, β-cariofileno e α-humuleno como possíveis repelentes para Aedes (Stegomyia) aegypti (Diptera: Culicidae)

Aedes aegypti, mosquito da família Culicidae responsável pela transmissão dos vírus da dengue, da febre amarela urbana e da febre chikungunya, apresenta grande proliferação em áreas urbanas das regiões tropicais e subtropicais, além de representar um fator de incômodo por causar alergias devido à inoculação dos componentes salivares durante o processo do repasto sanguíneo. Como forma de evitar os problemas causados por eles, o repelente mais usado e registrado comercialmente desde 1957 é o DEET (N,N-dietil-3-metilbenzamida ou N,N-dietil-meta-toluamida), que apesar de apresentar eficácia comprovada possui determinada toxicidade quando utilizado por crianças e por mulheres grávidas ou lactantes. Atualmente, grande parte dos estudos sobre novas substâncias repelentes envolvem óleos essenciais de plantas, principalmente por serem atóxicos, biodegradáveis, possuírem um preço mais acessível e uma ampla atividade contra diferentes espécies de mosquitos. Os terpenos 1,8-cineol, β-cariofileno e α-humuleno podem ser encontrados em óleos essenciais de uma grande variedade de plantas e apesar de dados da literatura mostrarem uma eficácia dessas substâncias como repelentes para outras espécies de insetos, até o presente momento não existem estudos que relacionam porcentagem de repelência ao longo do tempo para avaliar o potencial de repelência das mesmas para culicídeos.O presente estudo avaliou tais substâncias como possíveis repelentes para A. aegypti, utilizando o DEET como controle positivo. Para avaliar a eficácia do β-cariofileno foi utilizada a BG-cage, uma gaiola desenvolvida especificamente para testes de repelência onde o voluntário expõe um braço sob uma abertura coberta por uma tela onde os mosquitos pousam, mas não picam. Os testes foram repetidos a cada 30 minutos após a aplicação do produto por um tempo máximo de duas horas (seguindo a recomendação de reaplicação do produto comercial ...

Potential quimioprotetor do DIM (3, 3' - Di-indolil-metano) e da Genisteína em linhagens de células tumorais prostáticas humanas LNCaP e PC-3 expostas ao Bisfenol A

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Immunolocalization of markers for bone formation during guided bone regeneration in osteopenic rats

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Biomass burning fuel consumption rates: a field measurement database

Landscape fires show large variability in the amount of biomass or fuel consumed per unit area burned. Fuel consumption (FC) depends on the biomass available to burn and the fraction of the biomass that is actually combusted, and can be combined with estimates of area burned to assess emissions. While burned area can be detected from space and estimates are becoming more reliable due to improved algorithms and sensors, FC is usually modeled or taken selectively from the literature. We compiled the peerreviewed literature on FC for various biomes and fuel categories to understand FC and its variability better, and to provide a database that can be used to constrain biogeochemical models with fire modules. We compiled in total 77 studies covering 11 biomes including savanna (15 studies, average FC of 4.6 t DM (dry matter) ha 1 with a standard deviation of 2.2), tropical forest (n = 19, FC = 126 +/- 77), temperate forest (n = 12, FC = 58 +/- 72), boreal forest (n = 16, FC = 35 +/- 24), pasture (n = 4, FC = 28 +/- 9.3), shifting cultivation (n = 2, FC = 23, with a range of 4.0-43), crop residue (n = 4, FC = 6.5 +/- 9.0), chaparral (n = 3, FC = 27 +/- 19), tropical peatland (n = 4, FC = 314 +/- 196), boreal peatland (n = 2, FC = 42 [42-43]), and tundra (n = 1, FC = 40). Within biomes the regional variability in the number of measurements was sometimes large, with e. g. only three measurement locations in boreal Russia and 35 sites in North America. Substantial regional differences in FC were found within the defined biomes: for example, FC of temperate pine forests in the USA was 37% lower than Australian forests dominated by eucalypt trees. Besides showing the differences between biomes, FC estimates were also grouped into different fuel classes. Our results highlight the large variability in FC, not only between biomes but also within biomes and fuel classes. This implies that substantial uncertainties are associated with using biome-averaged values to represent FC for whole biomes. Comparing the compiled FC values with co-located Global Fire Emissions Database version 3 (GFED3) FC indicates that modeling studies that aim to represent variability in FC also within biomes, still require improvements as they have difficulty in representing the dynamics governing FC.

Genotipagem dos isolados de Giardia duodenalis em famílias de pescadores da colônia de Porto Said, Botucatu, São Paulo

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Theorem for series in three-parameter mittag-leffler function

The new result presented here is a theorem involving series in the three-parameter Mittag-Le er function. As a by-product, we recover some known results and discuss corollaries. As an application, we obtain the solution of a fractional di erential equation associated with a RLC electrical circuit in a closed form, in terms of the two-parameter Mittag-Le er function.

Switching-off in a minimal time a fitzhugh-nagumo system

This paper deals with a system that describes an electrical circuitcomposed by a linear system coupled to a nonlinear one involving a tunneldiode in a flush-and-fill circuit. One of the most comprehensive models for thiskind of circuits was introduced by R. Fitzhugh in 1961, when taking on carebiological tasks. The equation has in its phase plane only two periodic solutions,namely, the unstable singular point S0 and the stable cycle Γ. If the system isat rest on S0, the natural flow of orbits seeks to switch-on the process by going- as time goes by - toward its steady-state, Γ. By using suitable controls it ispossible to reverse such natural tendency going in a minimal time from Γ toS0, switching-off in this way the system. To achieve this goal it is mandatorya minimal enough strength on controls. These facts will be shown by means ofconsiderations on the null control sets in the process.

Effects of mineral stress on the vegetative development of greenhouse-grown bell pepper plants

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)