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.

Square of the Error Octonionic Theorem and Hypercomplex Fourier Series

The focus of this paper is to address some classical results for a class of hypercomplex numbers. More specifically we present an extension of the Square of the Error Theorem and a Bessel inequality for octonions.

A decoding procedure which improves code rate and error corrections

Corresponding to $C_{0}[n,n-r]$, a binary cyclic code generated by a primitive irreducible polynomial $p(X)\in \mathbb{F}_{2}[X]$ of degree $r=2b$, where $b\in \mathbb{Z}^{+}$, we can constitute a binary cyclic code $C[(n+1)^{3^{k}}-1,(n+1)^{3^{k}}-1-3^{k}r]$, which is generated by primitive irreducible generalized polynomial $p(X^{\frac{1}{3^{k}}})\in \mathbb{F}_{2}[X;\frac{1}{3^{k}}\mathbb{Z}_{0}]$ with degree $3^{k}r$, where $k\in \mathbb{Z}^{+}$. This new code $C$ improves the code rate and has error corrections capability higher than $C_{0}$. The purpose of this study is to establish a decoding procedure for $C_{0}$ by using $C$ in such a way that one can obtain an improved code rate and error-correcting capabilities for $C_{0}$.

Ferramentas da qualidade na colheita mecanizada de cana-de-açúcar

Pós-graduação em Agronomia (Produção Vegetal) - FCAV

Reference evapotranspiration models using different time scales in the Jaboticabal region of Sao Paulo, Brazil

The aim of this paper is to compare 18 reference evapotranspiration models to the standard Penman-Monteith model in the Jaboticabal, Sao Paulo, region for the following time scales: daily, 5-day, 15-day and seasonal. A total of 5 years of daily meteorological data was used for the following analyses: accuracy (mean absolute percentage error, Mape), precision (R-2) and tendency (bias) (systematic error, SE). The results were also compared at the 95% probability level with Tukey's test. The Priestley-Taylor (1972) method was the most accurate for all time scales, the Tanner-Pelton (1960) method was the most accurate in the winter, and the Thornthwaite (1948) method was the most accurate of the methods that only used temperature data in the equations.

Estimation of a preference map of new consumers for spatial load forecasting simulation methods using a spatial analysis of points

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Use of the probability of stone formation (PSF) score to assess stone forming risk and treatment response in a cohort of Brazilian stone formers

Introduction: The aim was to confirm that PSF (probability of stone formation) changed appropriately following medical therapy on recurrent stone formers.Materials and Methods: Data were collected on 26 Brazilian stone-formers. A baseline 24-hour urine collection was performed prior to treatment. Details of the medical treatment initiated for stone-disease were recorded. A PSF calculation was performed on the 24 hour urine sample using the 7 urinary parameters required: voided volume, oxalate, calcium, urate, pH, citrate and magnesium. A repeat 24-hour urine sample was performed for PSF calculation after treatment. Comparison was made between the PSF scores before and during treatment.Results: At baseline, 20 of the 26 patients (77%) had a high PSF score (> 0.5). Of the 26 patients, 17 (65%) showed an overall reduction in their PSF profiles with a medical treatment regimen. Eleven patients (42%) changed from a high risk (PSF > 0.5) to a low risk (PSF < 0.5) and 6 patients reduced their risk score but did not change risk category. Six (23%) patients remained in a high risk category (> 0.5) during both assessments.Conclusions: The PSF score reduced following medical treatment in the majority of patients in this cohort.

Simulações de onda de cheia na sub-bacia do Ribeirão Claro - SP

Watersheds are considered important study units when it comes to environmental planning, with regard to the optimal use of water resources. Water scarcity is predicted and feared by many societies, and proves to be an increasingly tangible problem nowadays. Still from the perspective of extreme events, this dissertation considers the study of flood waves in the sub-basin of the stream Claro, which belongs to the Corumbataí watershed. - SP, since thay can also have devastating effects for the population, A Decision Support System for Flood Routing Analysis in Complex Basins, ABC 6 software was applied in order to obtain hydrographs and peak flows in the sub-basin of the stream Claro, for return periods of 10 and 100 years, aiming to comprise events of different magnitudes. The model Soil Conservation Service (SCS) and the triangular SCS hydrograph were adopted for the simulations. Simultaneously, the Kokei Uehara method was applied for the obtainment of peak flow values under the same conditions, seeking to compare results. Data collection was performed using geoprocessing tools. For data entry in ABC 6, the fragmentation of sub-basin of the stream Claro was necessary, which generated 7 small watersheds, in order to fulfill a software demand, as the maximum drainage area it accepts is 50km² for each watershed analyzed. For RT = 10 and 100 years, respectively, the results of peak flow with use of ABC 6 were 46.10 and 95.45 m³/s, while for Kokei Uehara method, the results were 47.17 and 65.26 m³/s. The adoption of a single value of discretization time for all watersheds was indicated as limitation of ABC 6, which interfered in the final results. Kokei method Uehara considered the sub-basin of the stream Claro as a whole, which reduced the error accumulation probability

Alternative distributions to estimate usual intake of nutrients for groups

When assessing food intake patterns in groups of individuals, a major problem is finding usual intake distribution. This study aimed at searching for a probability distribution to estimate the usual intake of nutrients using data from a cross-sectional investigation on nutrition students from a public university in São Paulo state, Brazil. Data on 119 women aged 19 to 30 years old were used. All women answered a questionnaire about their lifestyle, diet and demographics. Food intake was evaluated from a non-consecutive three-day 24-hour food record. Different probability distributions were tested for vitamins C and E, panthotenic acid, folate, zinc, copper and calcium where data normalization was not possible. Empirical comparisons were performed, and inadequacy prevalence was calculated by comparing with the NRC method. It was concluded that if a more realistic distribution for usual intake is found, results can be more accurate as compared to those achieved by other methods.

Avaliação dos riscos assistenciais relacionados ao uso de equipamentos hospitalares na unidade de terapia intensiva de adultos de um hospital público da cidade de São Paulo, Brasil

Pós-graduação em Bases Gerais da Cirurgia - FMB