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.

Questing mass dimension 1 spinor fields

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Regulation of hepatic TRB3/Akt interaction induced by physical exercise and its effect on the hepatic glucose production in an insulin resistance state

To maintain euglycemia in healthy organisms, hepatic glucose production is increased during fasting and decreased during the postprandial period. This whole process is supported by insulin levels. These responses are associated with the insulin signaling pathway and the reduction in the activity of key gluconeogenic enzymes, resulting in a decrease of hepatic glucose production. On the other hand, defects in the liver insulin signaling pathway might promote inadequate suppression of gluconeogenesis, leading to hyperglycemia during fasting and after meals. The hepatocyte nuclear factor 4, the transcription cofactor PGC1-α, and the transcription factor Foxo1 have fundamental roles in regulating gluconeogenesis. The loss of insulin action is associated with the production of pro-inflammatory biomolecules in obesity conditions. Among the molecular mechanisms involved, we emphasize in this review the participation of TRB3 protein (a mammalian homolog of Drosophila tribbles), which is able to inhibit Akt activity and, thereby, maintain Foxo1 activity in the nucleus of hepatocytes, inducing hyperglycemia. In contrast, physical exercise has been shown as an important tool to reduce insulin resistance in the liver by reducing the inflammatory process, including the inhibition of TRB3 and, therefore, suppressing gluconeogenesis. The understanding of these new mechanisms by which physical exercise regulates glucose homeostasis has critical importance for the understanding and prevention of diabetes.

Downhill running excessive training inhibits hypertrophy in mice skeletal muscles with different fiber type composition

The aim of this study was to verify the effects of running overtraining protocols performed in downhill, uphill, and without inclination on the proteins related to hypertrophy signaling pathway in extensor digitorum longus (EDL) and soleus of C57BL/6 mice. We also performed histological and stereological analyses. Rodents were divided into control (CT; sedentary mice), overtrained by downhill running (OTR/down), overtrained by uphill running (OTR/up), and overtrained by running without inclination (OTR). The incremental load, exhaustive, and grip force tests were used as performance evaluation parameters. 36 h after the grip force test, EDL and soleus were removed and immediately used for immunoblotting analysis or stored at -80°C for histological and stereological analyses. For EDL, OTR/down decreased the protein kinase B (Akt) and tuberous sclerosis protein 2 (TSC2) phosphorylation (p), and increased myostatin, receptor-activated Smads (pSMAD2-3), and insulin receptor substrate-1 (pIRS-1; Ser307/636). OTR/down also presented low and high relative proportions of cytoplasm and connective tissue, respectively. OTR/up increased the mammalian target of rapamycin (pmTOR), 70-kDa ribosomal protein S6 kinase 1 (pS6K1) and pSMAD2-3, and decreased pTSC2. OTR decreased pTSC2 and increased pIRS-1 (Ser636). For soleus, OTR/down increased S6 ribosomal protein (pS6RP) and pSMAD2-3, and decreased pIRS-1 (Ser639). OTR/up decreased pS6K1, pS6RP and pIRS-1 (Ser639), and increased pTSC2 (Ser939), and pSMAD2-3. OTR increased pS6RP, 4E-binding protein-1 (p4E-BP1), pTSC2 (Ser939), and pSMAD2-3, and decreased pIRS-1 (Ser639). In summary, OTR/down inhibited the skeletal muscle hypertrophy with concomitant signs of atrophy in EDL. The effects of OTR/up and OTR depended on the analyzed skeletal muscle type. J. Cell. Physiol. 9999: 1-12, 2015. © 2015 Wiley Periodicals, Inc.

Funções, funcionais e operadores na física matemática, com índices matriciais

With the advance of mathematical methods throughout the centuries, in particular with respect to the differential calculus, the notion of fractional derivative emerged with Leibniz and later developed by several well known scientists. Today that formalism is well used in the study of diffusion phenomena among other areas. We extend the fractional indices to matricial indices and develop a formalism to handle this generalized derivative, as well as other operators, functions and functionals in mathematical physics, originally defined for natural indices. Here we only consider 2x2 hermitian and anti-hermitian matrices. These matrices are associated to the well known Pauli matrices and Hamilton's quaternions. Applications with mathematical physics functions are presented

Brazilian soccer players and no-players adolescents: effect of the maturity status on the physical capacity components performance

The aim of this study was to compare the speed and the agility between Brazilian soccer players and non-players, regarding maturity status in adolescents 11-15 years old. Forty and two soccer players (age – 159.30±17.28 months old; weight – 48.45±9.96 kg; height – 1.53±0.10 m) and 45 non-players (age – 162.62±24.92 months old; weight – 48.30±8.35 kg; height – 1.54±0.12 m) participated of this study. Participants were classified by maturity status. On 2 different days with 1 week of differences between the assessments the participants were evaluated the agility, by Shuttle Run test, and the speed, by 30 m maximum speed test. The results showed that the maturity status was an influential factor in the performance with better results for individuals in a more advanced stage. The soccer practice does not seem to interfere in the performance of the physical capacity components analyzed, only effective when different maturity levels are involved in the analysis. It is also possible that late maturing boys selectively drop-out of soccer as age and sport specialization increase.

Endurance exercise training increases APPL1 expression and improves insulin signaling in the hepatic tissue of diet-induced obese mice, independently of weight loss

Hepatic insulin resistance is the major contributor to fasting hyperglycemia in type 2 diabetes. The protein kinase Akt plays a central role in the suppression of gluconeogenesis involving forkhead box O1 (Foxo1) and peroxisome proliferator-activated receptor gamma co-activator 1 alpha (PGC-1a), and in the control of glycogen synthesis involving the glycogen synthase kinase beta (GSK3 beta) in the liver. It has been demonstrated that endosomal adaptor protein APPL1 interacts with Akt and blocks the association of Akt with its endogenous inhibitor, tribbles-related protein 3 (TRB3), improving the action of insulin in the liver. Here, we demonstrated that chronic exercise increased the basal levels and insulin-induced Akt serine phosphorylation in the liver of diet-induced obese mice. Endurance training was able to increase APPL1 expression and the interaction between APPL1 and Akt. Conversely, training reduced both TRB3 expression and TRB3 and Akt association. The positive effects of exercise on insulin action are reinforced by our findings that showed that trained mice presented an increase in Foxo1 phosphorylation and Foxo1/PGC-1a association, which was accompanied by a reduction in gluconeogenic gene expressions (PEPCK and G6Pase). Finally, exercised animals demonstrated increased at basal and insulin-induced GSK3 beta phosphorylation levels and glycogen content at 24?h after the last session of exercise. Our findings demonstrate that exercise increases insulin action, at least in part, through the enhancement of APPL1 and the reduction of TRB3 expression in the liver of obese mice, independently of weight loss. J. Cell. Physiol. 227: 29172926, 2012. (C) 2011 Wiley Periodicals, Inc.

A new overtraining protocol for mice based on downhill running sessions

The purpose of the present study was to verify whether a downhill running protocol was able to induce non-functional overreaching in > 75% of mice. Mice were divided into control (C), trained (TR) and overtrained (OTR) groups. Bodyweight and food intake were recorded weekly. The incremental load test (ILT) and the exhaustive test (ET) were used to measure performance before and after aerobic training and overtraining protocols. Although the bodyweight of the OTR group was lower than that of the C group at the end of Week 7, the food intake of the OTR group was higher than that of the C and TR groups at the end of Week 8. Evaluation of results from the ILT and ET revealed significant intra- and inter-group differences: whereas the parameters measured by both tests increased significantly in the TR group, they were significantly decreased in the OTR group. In conclusion, this new overtraining protocol based on downhill running sessions induced non-functional overreaching in 100% of mice.

Fostering Children and Adolescents in Situations of Abandonment, Violence and Separation

Childhood protection is undergoing several changes. Our study aimed to outline the complex network of meanings which includes adoption as well as institutional and family foster care, by combining theory, research and practice. We investigated various contexts and protagonists: judicial system, foster institutions, birth parents, foster and adoptive parents, and families and their children. Diverse data collection procedures were used: socio-demographic investigations, case-studies, follow-ups, interviews, analysis of foster institutions and legal court documents. Results pointed to "invisibility" of birth family, frequent child (re)abuse, failures in the network of protection, meanings of "healthy family" and role of attachment concepts. Implications for social policies and social practices are discussed.

Preparation of percentile tables through anthropometric, performance, biochemical, hematological, hormonal and psychological parameters in professional soccer players

Introduction: The lack of reference values of anthropometric, performance, biochemical, hematological, hormonal and psychological parameters is an important limitation in the investigations with soccer players. Objective: To elaborate percentile tables to be used as comparison reference for further studies. Methods: 82 professional soccer players were evaluated approximately 30 days after the beginning of the main competition played by their teams. On the first day of evaluation, fast blood samples were collected for measurement of hematological parameters (i.e. erythrocytes, hemoglobin, hematocrit, mean corpuscular volume - MCV, mean corpuscular hemoglobin - MCH, mean corpuscular hemoglobin concentration - MCHC, leukocytes, eosinophils, lymphocytes, monocytes and platelets) and of concentrations of adrenaline, cortisol, creatine kinase, creatinine, norepinephrine, testosterone and urea. Subsequently, the soccer players had their anthropometric characteristics and psychological parameters assessed. In addition, the evaluation of the lactic anaerobic system efficiency was performed on a 400-m track. On the second day, both the alactic anaerobic and aerobic system efficiency was measured. Results: The percentile distribution (P-0, P-15, P-30, P-50, P-70, P-85 e P-100) was used to present the results. Conclusion: The elaboration of the percentile tables can be used as comparison reference for further studies.

Assessing joint effusion and bone changes of the head of the mandible in MR images of symptomatic patients

The aim of the present study was to investigate the relationship between degenerative bone changes of the head of the mandible and the presence of joint effusion (JE). This study was based on sagittal magnetic resonance imaging (MRI) reports of 148 temporomandibular joints (TMJs) of 74 patients complaining of pain and/or dysfunction in the TMJ area. The mandible heads were surveyed for osteoarthritis characteristics, which were classified as osteophytosis, sclerosis or erosion. The presence of JE was checked whenever high signal intensity was observed in the articular space. The results evidenced the presence of bone changes in 30% of the sample. Osteophytes and erosions were the changes most commonly observed. JE was reported in 10% of TMJs. The results from the statistical tests revealed that bone changes in the head of the mandible are associated with the presence of JE.

Mudança estrutural e mercado de trabalho no Brasil

Structural changes and labor market in Brazil. In the present article, we attempt to identify the sources of the changes in the labor schooling level in the three main sectors of the Brazilian economy: manufacturing, services and agriculture. It was verified that, despite the changes in the product and employment among sectors, mainly in the 1990s, the relative demands for qualified workers has not experimented significant changes. Moreover, in the periods in which schooling has increased more, the workers' wage has decreased more. This fact suggests that the increase in labor qualification was mainly due to the increase of this factor supply. The structural changes had contributed, in general, in a marginal and negative way to labor force level of qualification demand in all the three sectors.

Acolhimento de crianças e adolescentes em situações de abandono, violência e rupturas

A proteção integral à infância encontra-se em reordenamento. Baseadas nas experiências do GIAAA-CINDEDI (Grupo de Investigação sobre Abrigamento, Acolhimento Familiar e Adoção - Centro de Investigações sobre Desenvolvimento Humano e Educação Infantil), buscamos compreender a rede de significações que permeia as práticas de acolhimento familiar, institucional e adoção. Investigamos vários contextos e protagonistas: sistema judiciário, abrigos, mães e famílias de origem, de acolhimento e adotivas. Diversos procedimentos foram utilizados: investigações sócio-demográficas, estudos de caso, entrevistas, pesquisa documental nos abrigos e no Fórum, grupos de discussão. Ressaltamos achados comuns: "invisibilidade" da família de origem; freqüente (re)violação da criança; falhas na Rede de Proteção; significações sobre "família saudável" e papel das concepções sobre apego que permeiam o campo. Implicações para políticas públicas e práticas sociais na área são discutidas.

Elaboração de tabelas de percentis através de parâmetros antropométricos, de desempenho, bioquímicos, hematológicos, hormonais e psicológicos em futebolistas profissionais

INTRODUÇÃO: A carência de valores de referência de parâmetros antropométricos, de desempenho, bioquímicos, hematológicos, hormonais e psicológicos é uma limitação importante nas investigações envolvendo futebolistas profissionais. OBJETIVO: Elaborar tabelas de percentis para servirem como referencial de comparação para estudos posteriores. MÉTODOS: Foram utilizados 82 jogadores profissionais de futebol que foram avaliados aproximadamente 30 dias após o início da principal competição disputada pelas equipes. No primeiro dia de avaliação foram coletadas amostras de sangue (25mL) em jejum para determinação dos parâmetros hematológicos (eritrócitos, hemoglobina, hematócrito, volume corpuscular médio - VCM, hemoglobina corpuscular média - HCM, concentração de hemoglobina corpuscular média - CHCM, leucócitos, neutrófilos, eosinófilos, linfócitos, monócitos e plaquetas) e das concentrações de adrenalina, cortisol, creatina quinase, creatinina, noradrenalina, testosterona e ureia. Posteriormente, os atletas foram submetidos à avaliação antropométrica e psicológica. Em seguida, a avaliação da eficiência do sistema anaeróbio lático foi realizada em pista oficial de atletismo. No segundo dia foram realizadas as avaliações para determinação da eficiência do sistema anaeróbio alático e aeróbio. RESULTADOS: A distribuição de percentis (P0, P15, P30, P50, P70, P85 e P100) foi utilizada para apresentação dos resultados. CONCLUSÃO: A elaboração de tabelas de percentis pode ser utilizada como referencial de comparação para investigações posteriores.