MA160exam01pdf

Exam questions and solutions in PDF

MA160exam00pdf

Exam questions and solutions in PDF

MA167exam01

Exam questions and solutions in LaTex. Diagrams for the questions are all together in the support.zip file, as .eps files

Exercises A pdf

Exercises and solutions in PDF

O processo de construção de objetos de aprendizagem em cálculo diferencial e integral durante uma atividade de design

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

O problema isoperimétrico e aplicações para o ensino médio

Pós-graduação em Matemática em Rede Nacional - IBILCE

Problemas de máximos e mínimos no Ensino Médio

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Máximos e mínimos na geometria euclidiana: uma abordagem histórica

The goal of this work is to perform a historical approach of important results about maxima and minima, on Euclidean geometry, involving perimeters, areas and volumes. As a highlight, we can mention the Dido’s isoperimetric problem and the Papus’s problem about the wit of the bees. In this context, with a concern didactic, we tried to use, whenever possible, the geometry classical formulas to the calculus of areas. On the other hand, in the case of isoperimetric inequality the techniques of differential and integral calculus became more suitable for our purposes.

Movement control of manipulative tasks in patients with Gilles de la Tourette syndrome

When a hand-held object is moved, grip and load force are accurately coordinated for establishing grasp stability. In the present work, the question was raised whether patients with Gilles de la Tourette syndrome (TS), who show tic-like movements, are impaired in grip-load force control when executing a manipulative task. To this end, we assessed force regulation during action patterns that required rhythmical unimanual or bimanual (iso-directional/anti-directional) movements. Results showed that the profile of grip-load force ratio was characterized by maxima and minima that were realized at upward and downward hand positions, respectively. TS patients showed increased force ratios during unimanual and bimanual movements, compared with control subjects, indicative of an inaccurate specification of the precision grip. Functional imaging data complemented the behavioural results and revealed that secondary motor areas showed no (or greatly reduced) activation in TS patients when executing the movement tasks as compared with baseline conditions. This indicates that the metabolic level in the secondary motor areas was equal during rest and task performance. At the neuronal level, this observation suggests that these cortical areas were continuously involved in movement preparation. Based on these data, we conclude that the ongoing activation of secondary motor areas may be explained by the TS patients' involuntary urges to move. Accordingly, interference will prevent an accurate planning of voluntary behaviour. Together, these findings reveal modulations in movement organization in patients with TS and exemplify degrading consequences for manual function.

Age determination of sediment core SO75-26KL, Portuguese margin

A benthic isotope record has been measured for core SO75-26KL from the upper Portuguese margin (1099 m water depth) to monitor the response of thermohaline overturn in the North Atlantic during Heinrich events. Evaluating benthic delta18O in TS diagrams in conjunction with equilibrium deltac fractionation implies that advection of Mediterranean outflow water (MOW) to the upper Portuguese margin was significantly reduced during the last glacial (< 15% compared to 30% today). The benthic isotope record along core SO75-26KL therefore primarily monitors variability of glacial North Atlantic conveyor circulation. The 14C-accelerator mass spectrometry ages of 13.54±.07 and 20.46±.12 ka for two ice-rafted detritus (IRD) layers in the upper core section and an interpolated age of 36.1 ka for a third IRD layer deeper in the core are in the range of published 14C ages for Heinrich events H1, H2, and H4. Marked depletion of benthic delta13C by 0.7-1.1 per mil during the Heinrich events suggests reduced thermohaline overturn in the North Atlantic during these events. Close similarity between meltwater patterns (inferred from planktonic delta18O) at Site 609 and ventilation patterns (inferred from benthic delta13C) in core SO75-26KL implies coupling between thermohaline overturn and surface forcing, as is also suggested by ocean circulation models. Benthic delta13C starts to decrease 1.5-2.5 kyr before Heinrich events Hl and H4, fully increased values are reached 1.5-3 kyr after the events, indicating a successive slowdown of thermohaline circulation well before the events and resumption of the conveyor's full strength well after the events. Benthic delta13C changes in the course of the Heinrich events show subtle maxima and minima suggesting oscillatory behavior of thermohaline circulation, a distinct feature of thermohaline instability in numerical models. Inferrred gradual spin-up of thermohaline circulation after Hl and H4 is in contrast to abrupt wanning in the North Atlantic region that is indicated by sudden increases in Greenland ice core delta18O and in marine faunal records from the northern North Atlantic. From this we infer that thermohaline circulation can explain only in part the rapid climatic oscillations seen in glacial sections of the Greenland ice core record.

Sequential variation of carbonate cycles in South Atlantic DSDP locations

We report well-dated Late Cretaceous and Early Tertiary precessional climatic cycles, recorded by rhythmic carbonate maxima and minima in South Atlantic deep sea sites. Spectral analyses of digitized sediment color, a suitable carbonate proxy, show prominent regularities in the spacing marl-carbonate beds. Magnetostratigraphic dating over a number of magnetic chrons constrains the duration of the cycles, which can be detected over at least 20 Myr of sedimentation at 7 coring locations. Their mean absolute period of 23.5 +/- 4.4kyr agrees closely with the predicted late Cretaceous precessional period of 20.8 kyr. Because they can be matched to a physical forcing mechanism with a known repeat time, the cycles offer a new high-resolution tool to measure rates of climate change before and after the Cretaceous-Tertiary (K/T) boundary. From counts of carbonate cycles, we derive the position of the K/T boundary within C29R at 350 kyr after the base of the reversal. The constancy of cycle thickness (linearly related to sedimentation rate) and amplitude up to the "boundary clay" does not give evidence for climate instability preceding the boundary. Orbital chronometry records a step-function decrease in sediment accumulation rate at the Cretaceous-Tertiary boundary that is consistent with a geologically instantaneous event.

An approximation method for solving the sofa problem,

"C00-2118-0026."

On computing the rank function for a set of vectors /

Includes bibliographical references.

Blue-detuned optical ring trap for Bose-Einstein condensates based on conical refraction

We present a novel approach for the optical manipulation of neutral atoms in annular light structures produced by the phenomenon of conical refraction occurring in biaxial optical crystals. For a beam focused to a plane behind the crystal, the focal plane exhibits two concentric bright rings enclosing a ring of null intensity called the Poggendorff ring. We demonstrate both theoretically and experimentally that the Poggendorff dark ring of conical refraction is confined in three dimensions by regions of higher intensity. We derive the positions of the confining intensity maxima and minima and discuss the application of the Poggendorff ring for trapping ultra-cold atoms using the repulsive dipole force of blue-detuned light. We give analytical expressions for the trapping frequencies and potential depths along both the radial and the axial directions. Finally, we present realistic numerical simulations of the dynamics of a 87Rb Bose-Einstein condensate trapped inside the Poggendorff ring which are in good agreement with corresponding experimental results.

Achilles tendon loading patterns during barefoot walking and slow running on a treadmill: An ultrasonic propagation study

Measurement of tendon loading patterns during gait is important for understanding the pathogenesis of tendon "overuse" injury. Given that the speed of propagation of ultrasound in tendon is proportional to the applied load, this study used a noninvasive ultrasonic transmission technique to measure axial ultrasonic velocity in the right Achilles tendon of 27 healthy adults (11 females and 16 males; age, 26 ± 9 years; height, 1.73 ± 0.07 m; weight, 70.6 ± 21.2 kg), walking at self-selected speed (1.1 ± 0.1 m/s), and running at fixed slow speed (2 m/s) on a treadmill. Synchronous measures of ankle kinematics, spatiotemporal gait parameters, and vertical ground reaction forces were simultaneously measured. Slow running was associated with significantly higher cadence, shorter step length, but greater range of ankle movement, higher magnitude and rate of vertical ground reaction force, and higher ultrasonic velocity in the tendon than walking (P < 0.05). Ultrasonic velocity in the Achilles tendon was highly reproducible during walking and slow running (mean within-subject coefficient of variation < 2%). Ultrasonic maxima (P1, P2) and minima (M1, M2) were significantly higher and occurred earlier in the gait cycle (P1, M1, and M2) during running than walking (P < 0.05). Slow running was associated with higher and earlier peaks in loading of the Achilles tendon than walking.