Student mathematical notebook of Thomas Noyes, 1793

This sewn volume contains Noyes’ mathematical exercises in geometry; trigonometry; surveying; measurement of heights and distances; plain, oblique, parallel, middle latitude, and mercator sailing; and dialing. Many of the exercises are illustrated by carefully hand-drawn diagrams, including a mariners’ compass and moon dials.

Student mathematical notebook of William Emerson Faulkner, 1795

Leather hardcover notebook with unruled pages containing the handwritten mathematical exercises of William Emerson Faulkner, begun in 1795 while he was an undergraduate at Harvard College. The volume contains rules, definitions, problems, drawings, and tables on geometry, trigonometry, surveying, calculating distances, sailing, and dialing. Some of the exercises are illustrated by unrefined hand-drawn diagrams, including some of buildings and trees.

Student mathematical notebook of William Tudor, 1795

Notebook containing the handwritten mathematical exercises of William Tudor, kept in 1795 while he was an undergraduate at Harvard College. The volume contains rules, definitions, problems, drawings, and tables on geometry, trigonometry, surveying, calculating distances, sailing, and dialing. Some of the exercises are illustrated with hand-drawn diagrams. The Menusration of Heights and Distances section contains color drawings of buildings and trees, and some have been altered with notes in different hands and with humorous additions. For instance, a drawing of a tower was drawn into a figure titled “Egyptian Mummy.” Some of the images are identified: “A rude sketch of the Middlesex canal,” Genl Warren’s monument on Bunker Hill,” “Noddles Island,” “the fields of Elysium,” and the “Roxbury Canal.” The annotations and additional drawings are unattributed.

Bases de Gröbner e geração de exercícios matemáticos com estrutura não determinada

Definido um enredo concreto, há, frequentemente, uma grande quantidade e variedade de exercícios que sobre ele podemos escrever. Neste artigo, apresenta-se um algoritmo que permite automatizar este processo. Para gerar exercícios matemáticos, parte-se das relações entre as variáveis presentes no enredo, calcula-se os possíveis exercícios, analisa-se a complexidade do seu processo de resolução e a sua viabilidade. O algoritmo recorre a bases de Gröbner para determinar se o exercício é resolúvel e um possível caminho de resolução. Com base na análise dos resultados obtidos, torna-se possível criar uma base de exercícios ligada a esse enredo.

Labirintos da compreensão de regras em matemática: um estudo a partir da regra de três

A presente pesquisa teve como objetivo analisar os procedimentos adotados por alunos do Ensino Fundamental ao interpretarem e aplicarem regras matemáticas na resolução de problemas de regra de três simples e composta, bem como o processo de tratamento que é dado à linguagem, em especial, à linguagem matemática. O processo de reflexão acerca da linguagem desencadeou, a partir do nosso estudo, do movimento conhecido por Virada Linguística, espaço em que se discutiu que seria impossível filosofar a respeito de algo sem anteriormente refletir sobre a linguagem pelo motivo de considerar que qualquer experiência se realiza anteriormente na linguagem. A partir desse momento, surgem as primeiras interpretações daquilo que ficou conhecido como Filosofia da Linguagem. Foi a partir dessa perspectiva filosófica que procuramos ancorar nossas análises, principalmente nas ideias daquele que ficou conhecido como o maior expoente, Ludwig Wittgenstein. As ideias desse filósofo se dividem em duas conflitantes filosofias, a primeira em que busca uma análise lógica da linguagem, e a segunda que discute e analisa a linguagem a partir da noção de contexto, ou seja, onde as expressões linguísticas adquirem sentido. Nesta segunda fase de seu pensamento, discute entre outros temas a necessidade que o sujeito possui de „seguir regras‟, a qual subsidiou uma de nossas seções de análise. O cenário da pesquisa foi uma sala de aula com alunos do 7º ano da Escola de Aplicação da Universidade Federal do Pará. A coleta do material aconteceu a partir de observações in lócus e por meio da aplicação de três baterias de testes envolvendo problemas matemáticos escolares de regra de três. Após o término das atividades, realizamos uma entrevista semiestruturada com alguns desses alunos e com o professor da turma. As análises desse material estão organizadas em três seções, as quais revelaram que grande parte desses alunos fracassou ao aplicar e seguir as regras matemáticas. Destacamos ainda que as ações desses alunos frente ao uso dos algoritmos também acontecem de maneira mecânica, pois aplicaram as regras e as seguiram sem atribuírem sentido, há ainda aqueles que se confundiram com as regras aprendidas em experiências anteriores.

Eliminación de nutrientes mediante tratamientos biopelícula : corrientes actuales y necesidades de investigación

Los tratamientos biopelícula fueron unos de los primeros tratamientos biológicos que se aplicaron en las aguas residuales. Los tratamientos biopelícula presentan importantes ventajas frente a los cultivos en suspensión, sin embargo, el control de los tratamientos biopelícula es complicado y su modelización también. Las bases teóricas del comportamiento de las biopelículas empezaron a desarrollarse fundamentalmente a partir de los años 80. Dado que el proceso es complejo con ecuaciones de difícil resolución, estas conceptualizaciones han sido consideradas durante años como ejercicios matemáticos más que como herramientas de diseño y simulación. Los diseños de los reactores estaban basados en experiencias de plantas piloto o en comportamientos empíricos de determinadas plantas. Las ecuaciones de diseño eran regresiones de los datos empíricos. La aplicabilidad de las ecuaciones se reducía a las condiciones particulares de la planta de la que provenían los datos empíricos. De tal forma que existía una gran variedad y diversidad de ecuaciones empíricas para cada tipo de reactor. La investigación médica durante los años 90 centró su atención en la formación y eliminación de las biopelículas. Gracias al desarrollo de nuevas prácticas de laboratorio que permitían estudiar el interior de las biopelículas y gracias también al aumento de la capacidad de los ordenadores, la simulación del comportamiento de las biopelículas tomó un nuevo impulso en esta década. El desarrollo de un tipo de biopelículas, fangos granulares, en condiciones aerobias realizando simultaneamente procesos de eliminación de nutrientes ha sido recientemente patentado. Esta patente ha recibido numerosos premios y reconocimientos internacionales tales como la Eurpean Invention Award (2012). En 1995 se descubrió que determinadas bacterias podían realizar un nuevo proceso de eliminación de nitrógeno denominado Anammox. Este nuevo tipo de proceso de eliminación de nitrógeno tiene el potencial de ofrecer importantes mejoras en el rendimiento de eliminación y en el consumo de energía. En los últimos 10 años, se han desarrollado una serie de tratamientos denominados “innovadores” de eliminación de nutrientes. Dado que no resulta posible el establecimiento de estas bacterias Anammox en fangos activos convencionales, normalmente se recurre al uso de cultivos biopelícula. La investigación se ha centrado en el desarrollo de estos procesos innovadores en cultivos biopelícula, en particular en los fangos granulares y MBBR e IFAs, con el objeto de establecer las condiciones bajo las cuales estos procesos se pueden desarrollar de forma estable. Muchas empresas y organizaciones buscan una segunda patente. Una cuestión principal en el desarrollo de estos procesos se encuentra la correcta selección de las condiciones ambientales y de operación para que unas bacterias desplacen a otras en el interior de las biopelículas. El diseño de plantas basado en cultivos biopelícula con procesos convencionales se ha realizado normalmente mediante el uso de métodos empíricos y semi-empíricos. Sin embargo, los criterios de selección avanzados aplicados en los Tratamientos Innovadores de Eliminación de Nitrógeno unido a la complejidad de los mecanismos de transporte de sustratos y crecimiento de la biomasa en las biopelículas, hace necesario el uso de herramientas de modelización para poder conclusiones no evidentes. Biofilms were one of the first biological treatments used in the wastewater treatment. Biofilms exhibit important advantages over suspended growth activated sludge. However, controlling biofilms growth is complicated and likewise its simulation. The theoretical underpinnings of biofilms performance began to be developed during 80s. As the equations that govern the growth of biofilms are complex and its resolution is challenging, these conceptualisations have been considered for years as mathematical exercises instead of practical design and simulation tools. The design of biofilm reactors has been based on performance information of pilot plants and specific plants. Most of the times, the designing equations were simple regressions of empirical data. The applicability of these equations were confined to the particular conditions of the plant from where the data came from. Consequently, there were a wide range of design equations for each type of reactor During 90s medical research focused its efforts on how biofilm´s growth with the ultimate goal of avoiding it. Thanks to the development of new laboratory techniques that allowed the study the interior of the biofilms and thanks as well to the development of the computers, simulation of biofilms’ performance had a considerable evolution during this decade. In 1995 it was discovered that certain bacteria can carry out a new sort of nutrient removal process named Anammox. This new type of nutrient removal process potentially can enhance considerably the removal performance and the energy consumption. In the last decade, it has been developed a range of treatments based on the Anammox generally named “Innovative Nutrient Removal Treatments”. As it is not possible to cultivate Anammox bacteria in activated sludge, normally scientists and designers resort to the use of biofilms. A critical issue in the development of these innovative processes is the correct selection of environment and operation conditions so as to certain bacterial population displace to others bacteria within the biofilm. The design of biofilm technology plants is normally based on the use of empirical and semi-empirical methods. However, the advanced control strategies used in the Innovative Nutrient Removal Processes together with the complexity of the mass transfer and biomass growth in biofilms, require the use of modeling tools to be able to set non evident conclusions.

Mathematical Methods 4

Exercises, exams and solutions for a third year maths course.

Mathematical Methods 2

Exercises, exams and solutions for a first year maths course.

Modelling logical expressions exercises

Exercises of application of the systematic procedure to derive linear inequalities for logic expressions (Ejercicios de aplicación del método sistemático de obtención de restricciones lineales para expresiones lógicas).

Student mathematical notebook of Ebenezer Hill, 1785

This mathematical notebook of Ebenezer Hill was kept in 1795 while he was a student at Harvard College. The volume contains rules, definitions, problems, drawings, and tables on arithmetic, geometry, trigonometry, surveying, calculating distances, and dialing. Some of the exercises are illustrated by hand-drawn diagrams, including some of buildings and trees.

Student mathematical notebook of Ephraim Eliot, 1779

Handwritten mathematical notebook of Ephraim Eliot, kept in 1779 while he was a student at Harvard College. The volume contains rules, definitions, problems, drawings, and tables on arithmetic, geometry, trigonometry, surveying, calculating distances, and dialing. Some of the exercises are illustrated by unrefined hand-drawn diagrams, as well as a sketch of a mariner’s compass. The sections on navigation, mensuration of heights, and spherical geometry are titled but not completed. The ink of the later text, beginning with Trigonometry, is faded.

The acute effects of varying strength exercises bouts on 5km running

This study investigated if there were acute interference effects of strength exercises on subsequent continuous and intermittent 5Km aerobic exercises. Eleven physically active males (23.1 +/- 3.1 yrs, 1.75 +/- 0.07 m, 70.5 +/- 8.8 kg, and 58.2 +/- 8.3 VO(2)max) performed the following experimental sessions: A) 5 sets of 5 RM on the leg press followed by a 5km run performed continuously (average velocity of the first and second ventilatory thresholds, nu Delta 50), B) 5 sets of 5 RM on the leg press followed by a 5km run performed intermittently (1 min run at the nu VO(2)max : 1 min of rest); C) 2 sets of 15 RM on the leg press followed by a 5km continuous run; and D) 2 sets of 15 RM on the leg press followed by a 5km intermittent run. Heart rate, blood lactate concentration, rate of perceived exertion, and VO(2) at the first and the fifth km were considered for statistical purposes. There were no significant effects of both strength bouts on any of the variables associated with endurance performance (p > 0.05). It seems that both maximum and strength endurance bouts do not acutely impair aerobic performance.

Coactivation of the shoulder and arm muscles during closed kinetic chain exercises on an unstable surface

Introduction: The purpose of this study was to compare the electromyography index of muscle coactivation of the following muscle pairs: posterior deltoid and pectoralis major (PD/PM); triceps brachii and biceps brachii (TB/BB); and serratus anterior and upper trapezius (SA/UT) during three different closed kinetic chain exercises (wall-press, bench-press and push-up) on an unstable surface at the maximal load. Methods: A total of 20 healthy sedentary men participated in the study. Integral linear values were obtained from three sustained contractions of six seconds each for the three proposed exercises. Mean coactivation index values were compared using the mixed-effects linear model, with a five percent significance level. Results: Electromyography indexes of muscle coactivation showed significant differences for the PD/PM and TB/BB muscle pairs. No differences were found between exercises for the SA/UT muscle pair. Conclusion: Our results seem to differ from those of previous studies, which reported that the similarity in exercises performed is responsible for the comparable muscle activation levels.

Evaluating Patellar Kinematics Through Magnetic Resonance Imaging During Open- and Closed-Kinetic-Chain Exercises

Purpose: To evaluate patellar kinematics of volunteers Without knee pain at rest and during isometric contraction in open- and closed-kinetic-chain exercises. Methods: Twenty individuals took part in this study. All were submitted to magnetic resonance imaging (MRI) during rest and voluntary isometric contraction (VIC) in the open anti closed kinetic chain at 15 degrees, 30 degrees, and 45 degrees of knee flexion. Through MRI and using medical e-film software, the following measurements were evaluated: sulcus angle, patellar-tilt angle, and bisect offset. The mixed-effects linear model was used for comparison between knee positions, between rest and isometric contractions, and between (he exercises. Results: Data analysis revealed that the sulcus angle decreased as knee flexion increased and revealed increases with isometric contractions in both the open and closed kinetic chain for all knee-flexion angles. The patellar-tilt angle decreased with isometric contractions in both the open and closed kinetic chain for every knee position. However, in the closed kinetic chain, patellar tilt increased significantly with the knee flexed at 15 degrees. The bisect offset increased with the knee flexed at 15 degrees during isometric contractions and decreased as knee flexion increased during both exercises. Conclusion: VIC in the last degrees of knee extension may compromise patellar dynamics. On the other hand, it is possible to favor patellar stability by performing muscle contractions with the knee flexed at 30 degrees and 45 degrees in either the open or closed kinetic chain.

Simplified Mathematical Model for an Anaerobic Sequencing Batch Biofilm Reactor Treating Lipid-Rich Wastewater Subject to Rising Organic Loading Rates

This study proposes a simplified mathematical model to describe the processes occurring in an anaerobic sequencing batch biofilm reactor (ASBBR) treating lipid-rich wastewater. The reactor, subjected to rising organic loading rates, contained biomass immobilized cubic polyurethane foam matrices, and was operated at 32 degrees C +/- 2 degrees C, using 24-h batch cycles. In the adaptation period, the reactor was fed with synthetic substrate for 46 days and was operated without agitation. Whereas agitation was raised to 500 rpm, the organic loading rate (OLR) rose from 0.3 g chemical oxygen demand (COD) . L(-1) . day(-1) to 1.2 g COD . L(-1) . day(-1). The ASBBR was fed fat-rich wastewater (dairy wastewater), in an operation period lasting for 116 days, during which four operational conditions (OCs) were tested: 1.1 +/- 0.2 g COD . L(-1) . day(-1) (OC1), 4.5 +/- 0.4 g COD . L(-1) . day(-1) (OC2), 8.0 +/- 0.8 g COD . L(-1) . day(-1) (OC3), and 12.1 +/- 2.4 g COD . L(-1) . day(-1) (OC4). The bicarbonate alkalinity (BA)/COD supplementation ratio was 1:1 at OC1, 1:2 at OC2, and 1:3 at OC3 and OC4. Total COD removal efficiencies were higher than 90%, with a constant production of bicarbonate alkalinity, in all OCs tested. After the process reached stability, temporal profiles of substrate consumption were obtained. Based on these experimental data a simplified first-order model was fit, making possible the inference of kinetic parameters. A simplified mathematical model correlating soluble COD with volatile fatty acids (VFA) was also proposed, and through it the consumption rates of intermediate products as propionic and acetic acid were inferred. Results showed that the microbial consortium worked properly and high efficiencies were obtained, even with high initial substrate concentrations, which led to the accumulation of intermediate metabolites and caused low specific consumption rates.