Construção de quadrados mágicos pelo método do passo uniforme

Lehmer (1929) analisa matematicamente o método do passo uniforme para construção de quadrados mágicos de ordem impar. Ele divide sua análise em várias etapas. Na primeira delas, envolvendo a discussão de condições necessárias e suficientes para o preenchimento do quadrado pelo método, o autor afirma que se dois números guardarem entre si uma certa relação, eles serão designados a ocupar a mesma célula do quadrado causando seu não preenchimento. A análise do preenchimento pelo método do passo uniforme envolve a resolução de um sistema linear módulo n. Nesse trabalho, discutimos o comportamento das soluções desse sistema quando o método falha no preenchimento. Como consequência, concluímos que números que guardam a relação mencionada nunca ocupam a mesma célula. A análise das condições necessárias e suficientes para obter quadrados mágicos segundo a definição de Lehmer (1929) envolve a resolução de equações de congruências lineares a duas variáveis. Nesse trabalho, detalhamos os resultados de Lehmer (1929). A análise das condições necessárias e suficientes para obtenção de quadrados mágicos, como são reconhecidos usualmente, também envolve a resolução de equações de congruências lineares a duas variáveis. Discutimos o comportamento das soluções dessas equações para obter diagonais principais mágicas. Como consequência, mostramos que diagonais principais mágicas são obtidas se e somente se as coordenadas iniciais guardarem certas relações

Criptografia: Da origem aos dias atuais

Esta pesquisa foi realizada com a intenção de motivar o estudo da criptografia, mostrando que a matemática e a comunicação estão presentes em diversos momentos, tanto no passado quanto no presente. Este trabalho mostra a origem da criptoanálise e toda a sua evolução dando ênfase nos mecanismos de codificação e decodificação através de exemplos práticos. Além disso, alguns métodos criptográficos são destacados como a cifra de substituição monoalfabética, a cifra de Vigenère, a criptografia RSA que é o método mais conhecido de criptografia de chave pública, as cifras de Hill, o método das transformações lineares e o método de Rabin, devido a sua grande importância para a evolução de sistemas computacionais e assinaturas digitais entre outros. Por fim, mostra-se a importância e a necessidade dos recursos criptográficos nos dias de hoje, na tentativa de impedir que hackers e pessoas que fazem mau uso do conhecimento matemático possam causar danos a sociedade, seja por uma simples mensagem ou até mesmo através de situações mais imprudentes como as transações bancárias indevidas

Anfíbios em uma floresta úmida da vertente pacífico ao sudoeste da Colômbia: avaliação da diversidade e sistemática de espécies, e o uso de recursos alimentares

Na Colômbia ocorrem 787 espécies de anfíbios. Por causa da preocupação com o estado de conservação de muitas dessas espécies, tem se sugerido que na Colômbia deveriam-se priorizar as pesquisas em taxonomia e ecologia em regiões sub-amostradas a fim de intensificar o conhecimento e conservação dos anfíbios colombianos. Baseados em uma análise cienciométrica de 319 trabalhos sobre a ecologia dos anfíbios colombianos publicados entre 1840 e 2014 (No Capítulo 1), identificamos as tendências nos esforços realizados em distintos temas de pesquisa, e a distribuição regional e taxonômica desses estudos. A maioria dos estudos (67%) foi realizada na região Andina colombiana em comparação com outras regiões naturais da Colômbia. Apenas 46% das espécies de anfíbios ocorrendo na Colômbia foi tratada nos estudos analizados, e a maioria (58%) delas é da região Andina. Entre as publicações analizadas identificamos 14 temas de pesquisa em ecologia, dos quais ecologia reprodutiva (26%), conservação de espécies (23%) e dieta (14%) foram os mais pesquisados. Nossos dados mostraram que na Colômbia há um considerável avanço na pesquisa sobre a ecologia dos anfíbios do país, mas ainda são necessários esforços para cobrir muitos vazios de informação para muitas regiões e para muitas espécies de anfíbios que possuem dados incipientes. No sudoeste da Cordilheira Ocidental colombiana há pouca informação ecológica sobre os anfíbios ali ocorrendo. A fim de saber alguns aspectos ecológicos dessas espécies, desenvolvimos três estudos sobre a diversidade e ecologia de anfíbios presentes na Reserva Natural Río Ñambí (a seguir RNRÑ). No Capítulo 2 apresentamos uma análise sistemática do gênero Andinophryne (Família Bufonidae), composto por três espécies, A. atelopoides, A. colomai (presente na RNRÑ) e A. olallai. As filogenias mostraram que Andinophryne está incorporado dentro de Rhaebo. Portanto, sinonimizamos Andinophryne sob Rhaebo e discutimos as sinapomorfias morfológicas putativas para Rhaebo. Além, fornecemos informações ecológicas e sobre o estado de conservação das três espécies incluídas na nova combinação taxonômica. No Capítulo 3 apresentamos uma lista de 19 espécies de anfíbios pertencentes a oito famílias, com uma dominância numérica da família Craugastoridae e do gênero Pristimantis. As espécies com a maior abundância relativa (> 25%) foram Pristimantis labiosus e P. verecundus. Sete diferentes modos de reprodução foram reconhecidos, com a maioria das espécies (68%) possuindo desenvolvimento direto de ovos. Cinco (26%) das espécies registradas estão classificadas dentro das categorias de maior ameaça de extinção. Reportamos para sete espécies a extensão da faixa de distribuição geográfica latitudinal na Colômbia. No Capítulo 4 comparamos a dieta de jovens e adultos de P. labiosus para identificar se houve uma mudança ontogenética no tamanho de presa consumido com o aumento na largura da boca. A dieta foi composta por 19 categorias de presas (> artrópodes), com as duas classes de idade consumindo um similar espectro de categorias. Os jovens têm um nicho trófico maior (0,45) do que os adultos (0,25), com uma sobreposição de nicho relativamente baixa (0,39) entre eles. Apesar da diferencia na largura da boca entre jovens e adultos, não houve uma correspondente mudança ontogenética no tamanho de presa consumida. Consideramos P. labiosus como um predador generalista que parece consumer uma ampla gama de tipos e tamanhos de presas

Proposta de um otimizador para rastreamento do ponto de máxima potência de um conjunto de painéis solares conectados em um sistema híbrido de energia.

Este trabalho apresenta o projeto e os algoritmos de controle, de um sistema de geração de energia híbrido. Este sistema é formado por conversores de potência conectados em Back-to-Back associados a um arranjo solar fotovoltaico, que por sua vez é conectado no lado CC dos conversores. Em relação ao sistema de geração fotovoltaico, a contribuição consiste no desenvolvimento de cinco algoritmos para determinar o ponto de máxima potência (MPP) do arranjo fotovoltaico. O primeiro algoritmo consiste em uma versão modificada do algoritmo de Perturbar e Observar (PeO); o segundo algoritmo proposto é baseado no método do gradiente (MG); e o terceiro é baseado na otimização do MG (MGO). Porém, são desenvolvidos algoritmos híbridos que combinam rede neural com o método PeO, e rede neural com o algoritmo MGO. O sistema foi desenvolvido e simulado utilizando o Matlab/Simulink, e os resultados de simulação são apresentados com objetivo da avaliar o comportamento do sistema e a resposta dos diferentes algoritmos. Esta resposta foi avaliada para condições transitórias e de regime permanente, considerando diferentes requisitos de consumo na carga, irradiância e temperatura.

The Early Diagenetic Formation of Organic Sulfur in the Sediments of Mangrove Lake, Bermuda

Due to a low mineral content, the sapropelic sediments depositing in Mangrove Lake, Bermuda, provide an excellent opportunity to explore for possible additions of sulfur to organic matter during the early stages of diagenesis. We evaluated early diagenetic organic sulfur transformations by monitoring the concentrations and stable isotopic compositions of a number of inorganic and organic sulfur pools, thereby accounting for all of the sulfur in the sediments. We have identified and quantified the following sulfur pools: porewater sulfate, porewater sulfide, elemental sulfur, pyrite sulfur, hydrolyzable organic sulfur (HYOS), chromium-reducible organic sulfur (CROS), and nonchromium-reducible organic sulfur (Non-CROS). Of the organic sulfur pools, the Non-CROS pool is by far the largest, followed by CROS, and finally HYOS. By 60 cm depth these pools contribute, respectively, to 85, 7.9, and 3.6% of the total solid phase sulfur. The HYOS pool is probably of biological origin and shows no interaction with the sulfur compounds produced during diagenesis. By contrast, CROS is produced, most likely, from the diagenetic addition of polysulfides to functionalized lipids in the upper, H2S-poor, elemental sulfur-rich, region of the sediment. A portion of this sulfur pool is unstable and decomposes on contact with the H2S-rich porewaters. The portion of CROS that remains in the sulfidic waters appears to readily exchange sulfur isotopes with H2S. While some of the Non-CROS pool is of biological origin, some is also formed by the diagenetic addition of sulfur to organic compounds in the upper H2S-poor region of the sediment. By contrast with CROS, Non-CROS is not diagenetically active in the H2S-rich porewaters. Overall, somewhere between 27 and 53 % of the organic sulfur buried in Mangrove Lake sediments is of diagenetic origin, with the remaining organic sulfur derived from biosynthesis. We extrapolate our Mangrove Lake results and calculate that in typical coastal marine sediments between 11 and 29 μmol g−1 of organic sulfur will form during early diagenesis, of which 2–5 μmol g−1 will be chromium reducible.

Rhythmic Growth-Induced Ring-Banded Spherulites with Radial Periodic Variation of Thicknesses Grown from Poly(epsilon-caprolactone) Solution with Constant Concentration

Birefringent ring-banded spherulites with radial periodic variation of thicknesses were grown from poly(epsilon-caprolactone) (PCL) solutions under conditions for which the Solution concentration was held constant during the whole development of the morphology. The as-grown ring-banded spherulites were investigated by optical (OM) and atomic force (AFM) microscopies, by transmission electron microscopy (TEM) of samples sectioned parallel to the plane of film, and also by electron diffraction (ED) and grazing incidence X-ray diffraction (GIXD) techniques.

Thermodynamics of blends of poly(ethylene oxide) with poly(methyl methacrylate) and poly(vinyl acetate): prediction of miscibility based on Flory solution theory modified by Hamada

Flory solution theory modified by Hamada et al. (Macromolecules, 1980, 13, 729) was used to predict the miscibility of blends of poly(ethylene oxide) with poly(methyl methacrylate) (PEO-aPMMA) and with poly(vinyl acetate) (PEO-PVAc). Interaction parameters of a PEO-aPMMA blend with the weight ratio of PEO/aPMMA = 50/50 at the temperature range of 393-433 K and PEO-PVAc blends with different compositions and temperatures were calculated from the determined equation-of-state parameters based on Flory solution theory modified by Hamada ed al. Results show that interaction parameters of the PEO-aPMMA blend are negative and can be comparable with values obtained from neutron-scattering measurements by Ito et al. (Macromolecules, 1987, 20, 2213). Also, interaction parameters and excess volumes of PEO-PVAc blends are negative and increase with enhancing the content of PEO and the temperature. (C) 1998 Elsevier Science Ltd. All rights reserved.

Study of the miscibility and thermodynamics of cellulose diacetate-poly(vinyl pyrrolidone) blends

The miscibility of blends of cellulose diacetate (CDA) and poly(vinyl pyrrolidone) (PVP) was extensively studied by means of differential thermal analysis and dynamic mechanical thermal analysis, tensile test, measuring viscosity of diluted and concentrated solutions of blends in acetone-ethanol mixture and morphological observations. A single glass transition temperature is observed, which is intermediate between the glass transition temperatures associated with each component and depends on composition. A synergism in mechanical properties of blends was found. The absolute viscosity and the intrinsic viscosity of solutions of blends are much higher than the weight average values of solutions of CDA and PVP. Optically clear and thermodynamically stable films were formed in the composition range of CDA/PVP = 100/0 to 50/50w/w. Fourier transform infrared was used to investigate the nature of CDA-PVP interaction. Hydrogen bonds were formed between hydroxyl groups of CDA and carbonyl groups of PVP. Heats of solutions of CDA/PVP blends and their mechanical mixtures were measured by using a calorimeter. Mixing enthalpy obtained with Hess's law approach was used to quantify interaction parameters of this blending system. It was found that mixing enthalpies and interaction parameters were negative and composition dependent. (C) 1997 Elsevier Science Ltd.

Growth rates of different polymorphs from interspherulitic boundary profiles

Quantitative data on the crystallization kinetics of polymorphic polymers can be derived from the investigation of gross spherulitic morphology formed in isothermal conditions. Depending on distance between centers, and the time lag between their formation and relative growth rates, various types of boundary lines can be generated by the impinging of two spherical bodies whose radii increase linearly with time, In polymorphic polymers, different types of spherulites often develop simultaneously at different rates from sporadic or predetermined nuclei. In same cases, the so-called growth transformation, in which a nucleus of the fast growing specie is formed at the tip of an advancing lamella of the slower crystal form, provides an alternative mode of nucleation, It is shown that if only one event of growth transformation takes place at the front of a slow growing body, the fast growing spherulite swallows the parent one and the resultant shape of interspherulitic boundary is described by two symmetrical logarithmic spirals whose parameters can be extracted from micrographs taken at the end of crystallization. These concepts are applied to determine the radial growth rate of gamma form spherulites of polypivalolactone in a wide range of temperatures through analysis of the alpha/gamma interspherulitic profiles formed in isothermal conditions and direct measurement of the growth rate of the alpha counterparts at the same temperature.

THERMODYNAMICS OF POLY(ETHYLENE OXIDE)-POLY(VINYL ACETATE) BLENDS

Heat-of-mixing data, obtained on blends of poly(ethylene oxide) (PEO) with whole and fractionated poly(vinyl acetate) (PVAc), were used to feed Patterson's theory of polymer-polymer miscibility. Negative values of mixing enthalpy, contact-energy term, interaction'' parameter and excess volume were obtained only for blends with the lowest molecular weight PVAc fraction. These results show that miscibility of PVAc with PEO strongly depends on its molecular weight. The calculated unfavourable excess volume term of the Patterson equation is small in comparison with the absolute value of the interaction term. Therefore, miscibility of PEO and low-molecular-weight PVAc is dictated by the weak specific interactions between different repeat units and by the entropic gain in the mixing process.

CRYSTALLIZATION OF POLY(ARYL-ETHER-ETHER-KETONE)S BLENDS

The crystallization and melting behaviour of poly(aryl-ether-ether-ketone) (PEEK) in blends with another polymer of the same family containing a bulky pendant phenolphthalein group (PEK-C) have been investigated by thermal methods. The small interaction energy density of the polymer pair (B = -8.99 J/cm3), evaluated from equilibrium melting point depression, is consistent with the T(g) data that indicate partial miscibility in the melt. Two conjugated phases are in equilibrium at 430-degrees-C: one is crystallizable and contains about 35 wt% of PEK-C; the other, containing only 15 wt% of PEEK, does not form crystals upon cooling and it interferes with the development of spherulites in the sample. The analysis of kinetic data according to nucleation theories shows that crystallization of PEEK in the explored temperature range takes place in Regime III and that a transition to Regime II might be a consequence of an increase in the amount of non-crystallizable molecules in the PEEK-rich phase. A composition independent value of the end surface free energy of PEEK lamellae has been derived from kinetic data (sigma-e = 40 +/- 4 erg/cm2) in excellent agreement with previous thermodynamic estimates. A new value for the equilibrium melting temperature of PEEK (T(m)-degrees = 639 K) has been obtained; it is about 30-degrees-C lower than the commonly accepted value and it explains better the "memory effect" in the crystallization from the melt of this high performance polymer.

Exercise for the management of type 2 diabetes: A review of the evidence

The aim is to critically review the more relevant evidence on the interrelationships between exercise and metabolic outcomes. The research questions addressed in the recent specific literature with the most relevant randomized controlled trials, meta-analysis and cohort studies are presented in three domains: aerobic exercise, resistance exercise, combined aerobic and resistance exercise. From this review appear that the effects of aerobic exercise are well established, and interventions with more vigorous aerobic exercise programs resulted in greater reductions in HbA1c, greater increase in VO2max and greater increase in insulin sensitivity. Considering the available evidence, it appears that resistance training could be an effective intervention to help glycemic control, especially considering that the effects of this form of intervention are comparable with what reported with aerobic exercise. Less studies have investigated whether combined resistance and aerobic training offers a synergistic and incremental effect on glycemic control; however, from the available evidences appear that combined exercise training seems to determine additional change in HbA1c that can be seen significant if compared with aerobic training alone and resistance training alone.

Centenarians and their hearts: a prospective registry with comprehensive geriatric assessment, electrocardiogram, echocardiography, and follow-up

Background Data on the cardiac characteristics of centenarians are scarce. Our aim was to describe electrocardiogram (ECG) and echocardiography in a cohort of centenarians and to correlate them with clinical data. Methods We used prospective multicenter registry of 118 centenarians (28 men) with a mean age of 101.5 ± 1.7 years. Electrocardiogram was performed in 103 subjects (87.3%) and echocardiography in 100 (84.7%). All subjects underwent a follow-up for at least 6 months. Results Centenarians with abnormal ECG were less frequently females (72% vs 93%), had higher rates of previous consumption of tobacco (14% vs 0) and alcohol (24% vs 12%), and scored lower in the perception of health status (6.8 ± 2.0 vs 8.3 ± 6.8). Centenarians with significant abnormalities in echocardiography were less frequently able to walk 6 m (33% vs 54%). Atrial fibrillation/flutter was found in 27 subjects (26%). Mean left ventricular (LV) ejection fraction was 60.0 ± 10.5%. Moderate or severe aortic valve stenosis was found in 16%, mitral valve regurgitation in 15%, and aortic valve regurgitation in 13%. Diastolic dysfunction was assessed in 79 subjects and was present in 55 (69.6%). Katz index and LV dilation were independently associated with the ability to walk 6 m. Age, Charlson and Katz indexes, and the presence of significant abnormalities in echocardiography were associated with mortality. Conclusions Centenarians have frequent ECG alterations and abnormalities in echocardiography. More than one fifth has atrial fibrillation, and most have diastolic dysfunction. Left ventricular dilation was associated with the ability to walk 6 m. Significant abnormalities in echocardiography were associated with mortality.