Representações dos números racionais e a medição de segmentos: possibilidades com tecnologias informáticas

Pós-graduação em Educação Matemática - IGCE

Um estudo sobre a resolução de problemas e suas relações com a afetividade

This research aims at examining the relationship between the performance of elementary school students Cycle I in problem solving and attitudes toward mathematics. For this, a research was conducted at a state school in the city of Bauru which was selected for convenience. Participants were randomly selected consisting of 75 students, of whom 21 were third years and 57 were of three classes of fifth year. The instruments used for data collection were: a informative questionnaire to characterize the students in age, grade, favorite subjects and the least liked, among others, an attitude scale, Likert type, to examine the attitudes toward mathematics; a interviews with 11 selected students according to scores on the attitudes and mathematical problems to be solved through the method of thinking aloud. The results showed that the major difficulties encountered by students in solving problems were: to understand the problems, formalizing the reasoning, recognize in the problem the algorithms needed for its resolution, make calculations with decimal numbers, do combinatorics, using the sum of equal portions instead of multiplying, self-confidence and autonomy in what he was doing, and others; participants with positive attitudes towards mathematics showed greater confidence to solve problems as well as a greater understanding on what was required by them, but were not detected significant relation between the attitudes and performance, since it was unfavorable

Sistemas de numeração e grandezas incomensuráveis

Pós-graduação em Matemática em Rede Nacional - IBILCE

Table of natural logarithms ... /

"One in a series of mathematical tables prepared by the Project for the Computation of Mathematical Tables."--Volume I., Pref.

Late Caledonian magmagenesis in Southern Scotland

The Priestlaw and Cockburn Law intrusions are zoned granitoid plutons intruded into Lower Palaeozoic sediments at the margin of, and prior to closure of, the Iapetus Ocean. They vary from marginal basic rocks to more acid rocks towards their centres. The parental magmas to the plutons were derived from an isotopically depleted mantle modified by melts/fluids during subduction. Zonation in the plutons was caused by combined assimilation and fractional crystallisation (AFC), and rates of assimilation were low relative to rates of fractionation. A series of pyroxene-mica diorites in Priestlaw are however hybrids formed by simple mixing. Porphyrite-acid porphyrite dykes, associated with the plutons, represent chilled portions of the pluton magmas; more evolved quartz porphyry dykes represent crustal melts. Lamprophyre dykes have high LILE and LREE abundances and relative depletions of HFS elements, typical of subduction related ultra-potassic magmas. High Mg numbers, Ni and Cr contents and experimental constraints, imply near primary status for the least evolved lamprophyres. Their enrichments in incompatible elements, high La/Nb, La/Yb, Sr and low Nd indicate derivation from a previously metasomatised mantle source. Granitoid plutons and lavas in the northern Southern Uplands have high Nd and low Sr, whereas the younger plutons of the southern Southern Uplands have higher Sr, La/Yb and lower Nd, consistent with derivation from a more enriched source. No plutons however have remained as closed systems. Three magmatic suites are present in southern Scotland: (1) Midland Valley Suite (2) Northern Southern Uplands Suite and (3) Southern Southern Uplands Suite, consistent with previous models indicating northward underthrusting of English lithosphere below the southern Southern Uplands. Further underthrusting of decoupled lithospheric mantle is indicated by the presence of lamorophyres in the eastern Southern Uplands, and took place between 410 Ma and 400 Ma.

School based youth health nurses and a true health promotion approach : the Ottawa what?

Aim: The purpose of this research is to examine School Based Youth Health Nurses experience of a true health promotion approach. Background: The School Based Youth Health Nurse Program is a state-wide school nursing initiative in Queensland, Australia. The program employs more than 120 fulltime and fractional school nurses who provide health services in state high schools. The role incorporates two primary components: individual health consultations and health promotion strategies. Design/Methods: This study is a retrospective inquiry generated from a larger qualitative research project about the experience of school based youth health nursing. The original methodology was phenomenography. In-depth interviews were conducted with sixteen school nurses recruited through purposeful and snowball sampling. This study accesses a specific set of raw data about School Based Youth Health Nurses experience of a true health promotion approach. The Ottawa Charter for Health Promotion (1986) is used as a framework for deductive analysis. Results: The findings indicate school nurses have neither an adverse or affirmative conceptual experience of a true health promotion approach and an adverse operational experience of a true health promotion approach based on the action areas of the Ottawa Charter. Conclusions: The findings of this research are important because they challenge the notion that school nurses are the most appropriate health professionals to undertake a true health promotion approach. If school nurses are the most appropriate health professionals to do a true health promotion approach, there are implications for recruitment and training and qualifications. If school nurses are not, who are the most appropriate health professionals to do school health promotion? Implications for Practice: These findings can be applied to other models of school nursing in Australia which emphasises a true health promotion approach because they relate specifically to school nurses’ experience of a true health promotion approach.

Diffusion indices on magnetic resonance imaging and neuropsychological performance in amnestic mild cognitive impairment

Background: Magnetic resonance diffusion tensor imaging (DTI) shows promise in the early detection of microstructural pathophysiological changes in the brain. Objectives: To measure microstructural differences in the brains of participants with amnestic mild cognitive impairment (MCI) compared with an age-matched control group using an optimised DTI technique with fully automated image analysis tools and to investigate the correlation between diffusivity measurements and neuropsychological performance scores across groups. Methods: 34 participants (17 participants with MCI, 17 healthy elderly adults) underwent magnetic resonance imaging (MRI)-based DTI. To control for the effects of anatomical variation, diffusion images of all participants were registered to standard anatomical space. Significant statistical differences in diffusivity measurements between the two groups were determined on a pixel-by-pixel basis using gaussian random field theory. Results: Significantly raised mean diffusivity measurements (p<0.001) were observed in the left and right entorhinal cortices (BA28), posterior occipital-parietal cortex (BA18 and BA19), right parietal supramarginal gyrus (BA40) and right frontal precentral gyri (BA4 and BA6) in participants with MCI. With respect to fractional anisotropy, participants with MCI had significantly reduced measurements (p<0.001) in the limbic parahippocampal subgyral white matter, right thalamus and left posterior cingulate. Pearson's correlation coefficients calculated across all participants showed significant correlations between neuropsychological assessment scores and regional measurements of mean diffusivity and fractional anisotropy. Conclusions: DTI-based diffusivity measures may offer a sensitive method of detecting subtle microstructural brain changes associated with preclinical Alzheimer's disease.

Gaussian Schell-model beams and general shape invariance

We present two six-parameter families of anisotropic Gaussian Schell-model beams that propagate in a shape-invariant manner, with the intensity distribution continuously twisting about the beam axis. The two families differ in the sense or helicity of this beam twist. The propagation characteristics of these shape-invariant beams are studied, and the restrictions on the beam parameters that arise from the optical uncertainty principle are brought out. Shape invariance is traced to a fundamental dynamical symmetry that underlies these beams. This symmetry is the product of spatial rotation and fractional Fourier transformation.

Elements of Volatility at High Frequency

Volatility is central in options pricing and risk management. It reflects the uncertainty of investors and the inherent instability of the economy. Time series methods are among the most widely applied scientific methods to analyze and predict volatility. Very frequently sampled data contain much valuable information about the different elements of volatility and may ultimately reveal the reasons for time varying volatility. The use of such ultra-high-frequency data is common to all three essays of the dissertation. The dissertation belongs to the field of financial econometrics. The first essay uses wavelet methods to study the time-varying behavior of scaling laws and long-memory in the five-minute volatility series of Nokia on the Helsinki Stock Exchange around the burst of the IT-bubble. The essay is motivated by earlier findings which suggest that different scaling laws may apply to intraday time-scales and to larger time-scales, implying that the so-called annualized volatility depends on the data sampling frequency. The empirical results confirm the appearance of time varying long-memory and different scaling laws that, for a significant part, can be attributed to investor irrationality and to an intraday volatility periodicity called the New York effect. The findings have potentially important consequences for options pricing and risk management that commonly assume constant memory and scaling. The second essay investigates modelling the duration between trades in stock markets. Durations convoy information about investor intentions and provide an alternative view at volatility. Generalizations of standard autoregressive conditional duration (ACD) models are developed to meet needs observed in previous applications of the standard models. According to the empirical results based on data of actively traded stocks on the New York Stock Exchange and the Helsinki Stock Exchange the proposed generalization clearly outperforms the standard models and also performs well in comparison to another recently proposed alternative to the standard models. The distribution used to derive the generalization may also prove valuable in other areas of risk management. The third essay studies empirically the effect of decimalization on volatility and market microstructure noise. Decimalization refers to the change from fractional pricing to decimal pricing and it was carried out on the New York Stock Exchange in January, 2001. The methods used here are more accurate than in the earlier studies and put more weight on market microstructure. The main result is that decimalization decreased observed volatility by reducing noise variance especially for the highly active stocks. The results help risk management and market mechanism designing.

Geochemistry and petrology of the ferropicrite dikes and associated rocks of Vestfjella, western Dronning Maud Land, Antarctica

This study provides insights into the composition and origin of ferropicrite dikes (FeOtot = 13 17 wt. %; MgO = 13 19 wt. %) and associated meimechite, picrite, picrobasalt, and basalt dikes found at Vestfjella, western Dronning Maud Land, Antarctica. The dikes crosscut Jurassic Karoo continental flood basalts (CFB) that were emplaced during the early stages of the breakup of the Gondwana supercontinent ~180 Ma ago. Selected samples (31 overall from at least eleven dikes) were analyzed for their mineral chemical, major element, trace element, and Sr, Nd, Pb, and Os isotopic compositions. The studied samples can be divided into two geochemically distinct types: (1) The depleted type (24 samples from at least nine dikes) is relatively depleted in the most incompatible elements and exhibits isotopic characteristics (e.g., initial εNd of +4.8 to +8.3 and initial 187Os/188Os of 0.1256 0.1277 at 180 Ma) similar to those of mid-ocean ridge basalts (MORB); (2) The enriched type (7 samples from at least two dikes) exhibits relatively enriched incompatible element and isotopic characteristics (e.g., initial εNd of +1.8 to +3.6 and initial 187Os/188Os of 0.1401 0.1425 at 180 Ma) similar to those of oceanic island basalts. Both magma types have escaped significant contamination by the continental crust. The depleted type is related to the main phase of Karoo magmatism and originated as highly magnesian (MgO up to 25 wt. %) partial melts at high temperatures (mantle potential temperature >1600 °C) and pressures (~5 6 GPa) from a sublithospheric, water-bearing, depleted peridotite mantle source. The enriched type sampled pyroxene-bearing heterogeneities that can be traced down to either recycled oceanic crust or melt-metasomatized portions of the sublithospheric or lithospheric mantle. The source of the depleted type represents a sublithospheric end-member source for many Karoo lavas and has subsequently been sampled by the MORBs of the Indian Ocean. These observations, together with the purported high temperatures, indicate that the Karoo CFBs were formed in an extensive melting episode caused mainly by internal heating of the upper mantle beneath the Gondwana supercontinent. My research supports the view that ferropicritic melts can be generated in several ways: the relative Fe-enrichment of mantle partial melts is most readily achieved by (1) relatively low degree of partial melting, (2) high pressure of partial melting, and (3) melting of enriched source components (e.g., pyroxenite and metasomatized peridotite). Ferropicritic whole-rock compositions could also result from accumulation, secondary alteration, and fractional crystallization, however, and caution is required when addressing the parental magma composition.

Scanning tunneling spectroscopic studies on high-temperature superconductors and Dirac materials

This thesis details the investigations of the unconventional low-energy quasiparticle excitations in electron-type cuprate superconductors and electron-type ferrous superconductors as well as the electronic properties of Dirac fermions in graphene and three-dimensional strong topological insulators through experimental studies using spatially resolved scanning tunneling spectroscopy (STS) experiments.

Magnetic-field- and temperature-dependent evolution of the spatially resolved quasiparticle spectra in the electron-type cuprate La_0.1Sr_0.9CuO₂ (La-112) T_C = 43 K, are investigated experimentally. For temperature (T) less than the superconducting transition temperature (TC), and in zero field, the quasiparticle spectra of La-112 exhibits gapped behavior with two coherence peaks and no satellite features. For magnetic field measurements at T < TC, first ever observation of vortices in La-112 are reported. Moreover, pseudogap-like spectra are revealed inside the core of vortices, where superconductivity is suppressed. The intra-vortex pseudogap-like spectra are characterized by an energy gap of V_PG = 8.5 ± 0.6 meV, while the inter-vortex quasiparticle spectra shows larger peak-to-peak gap values characterized by Δ_pk-pk(H) >V_PG, and Δ_pk-pk (0)=12.2 ± 0.8 meV > Δ_pk-pk (H > 0). The quasiparticle spectra are found to be gapped at all locations up to the highest magnetic field examined (H = 6T) and reveal an apparent low-energy cutoff at the V_PG energy scale.

Magnetic-field- and temperature-dependent evolution of the spatially resolved quasiparticle spectra in the electron-type "122" iron-based Ba(Fe_1-xCo_x)₂A_s2 are investigated for multiple doping levels (x = 0.06, 0.08, 0.12 with T_C= 14 K, 24 K, and 20 K). For all doping levels and the T < T_C, two-gap superconductivity is observed. Both superconducting gaps decrease monotonically in size with increasing temperature and disappear for temperatures above the superconducting transition temperature, T_C. Magnetic resonant modes that follow the temperature dependence of the superconducting gaps have been identified in the tunneling quasiparticle spectra. Together with quasiparticle interference (QPI) analysis and magnetic field studies, this provides strong evidence for two-gap sign-changing s-wave superconductivity.

Additionally spatial scanning tunneling spectroscopic studies are performed on mechanically exfoliated graphene and chemical vapor deposition grown graphene. In all cases lattice strain exerts a strong influence on the electronic properties of the sample. In particular topological defects give rise to pseudomagnetic fields (B ~ 50 Tesla) and charging effects resulting in quantized conductance peaks associated with the integer and fractional Quantum Hall States.

Finally, spectroscopic studies on the 3D-STI, Bi₂Se₃ found evidence of impurity resonance in the surface state. The impurities are in the unitary limit and the spectral resonances are localized spatially to within ~ 0.2 nm of the impurity. The spectral weight of the impurity resonance diverges as the Fermi energy approaches the Dirac point and the rapid recovery of the surface state suggests robust topological protection against perturbations that preserve time reversal symmetry.

Mineral chemistry and its genetic significance of olivine in Cenozoic basalts from the South China Sea

We dredged lots of Cenozoic basalts from areas covered from the northern sub-slope to the southern sub- slope of the South China Sea. Based on the study on mineral chemistry of clinopyroxenes in these Cenozoic hasalts, this paper indicates that pyroxenes are mostly enstatite and a few of augite, sahlite and Ca-rich pyroxene. Pyroxene microlite has higher content in, Ca, Ti and Fe than pyroxene phenocryst, it may reflect that the evolution trend of host magma of pyroxene is coincidence with that of alkali rock series. The depth of magma chambers which calculated from equilibrium temperatures and pressures between clinopyroxene and melt are as follows, that of magma of tephrite is about 49km, that of magma of trachybasalt is about 25km, and that of magma of basalt is about 15km. Correspondingly, Equilibrium temperatures( K) of three types rocks mentioned above gradually decrease from 1535 1498 to 1429 to 1369. By using discriminant plot which developed from pyroxene and alkali discriminant diagram of host rock, Cenozoic basalt from the South China Sea belongs to intraplate alkali basalt. The results suggest that alkali basalt series in the study area may be the products of continuous evolution of mantle plume, which result from some physical and chemistry process including partial melting and fractional crystallization of mantle plume during the course of its ascent to the surface.

Score for neonatal acute physiology-II and neonatal pain predict corticospinal tract development in premature newborns

Premature infants are at risk for adverse motor outcomes, including cerebral palsy and developmental coordination disorder. The purpose of this study was to examine the relationship of antenatal, perinatal, and postnatal risk factors for abnormal development of the corticospinal tract, the major voluntary motor pathway, during the neonatal period. In a prospective cohort study, 126 premature neonates (24-32 weeks' gestational age) underwent serial brain imaging near birth and at term-equivalent age. With diffusion tensor tractography, mean diffusivity and fractional anisotropy of the corticospinal tract were measured to reflect microstructural development. Generalized estimating equation models examined associations of risk factors on corticospinal tract development. The perinatal risk factor of greater early illness severity (as measured by the Score for Neonatal Acute Physiology-II [SNAP-II]) was associated with a slower rise in fractional anisotropy of the corticospinal tract (P = 0.02), even after correcting for gestational age at birth and postnatal risk factors (P = 0.009). Consistent with previous findings, neonatal pain adjusted for morphine and postnatal infection were also associated with a slower rise in fractional anisotropy of the corticospinal tract (P = 0.03 and 0.02, respectively). Lessening illness severity in the first hours of life might offer potential to improve motor pathway development in premature newborns.

Implementation of phantom-less IMRT delivery verification using Varian DynaLog files and R/V output

This study aims to evaluate the use of Varian radiotherapy dynamic treatment log (DynaLog) files to verify IMRT plan delivery as part of a routine quality assurance procedure. Delivery accuracy in terms of machine performance was quantified by multileaf collimator (MLC) position errors and fluence delivery accuracy for patients receiving intensity modulated radiation therapy (IMRT) treatment. The relationship between machine performance and plan complexity, quantified by the modulation complexity score (MCS) was also investigated. Actual MLC positions and delivered fraction of monitor units (MU), recorded every 50 ms during IMRT delivery, were extracted from the DynaLog files. The planned MLC positions and fractional MU were taken from the record and verify system MLC control file. Planned and delivered beam data were compared to determine leaf position errors with and without the overshoot effect. Analysis was also performed on planned and actual fluence maps reconstructed from the MLC control file and delivered treatment log files respectively. This analysis was performed for all treatment fractions for 5 prostate, 5 prostate and pelvic node (PPN) and 5 head and neck (H&N) IMRT plans, totalling 82 IMRT fields in ∼5500 DynaLog files. The root mean square (RMS) leaf position errors without the overshoot effect were 0.09, 0.26, 0.19 mm for the prostate, PPN and H&N plans respectively, which increased to 0.30, 0.39 and 0.30 mm when the overshoot effect was considered. Average errors were not affected by the overshoot effect and were 0.05, 0.13 and 0.17 mm for prostate, PPN and H&N plans respectively. The percentage of pixels passing fluence map gamma analysis at 3%/3 mm was 99.94 ± 0.25%, which reduced to 91.62 ± 11.39% at 1%/1 mm criterion. Leaf position errors, but not gamma passing rate, were directly related to plan complexity as determined by the MCS. Site specific confidence intervals for average leaf position errors were set at -0.03-0.12 mm for prostate and -0.02-0.28 mm for more complex PPN and H&N plans. For all treatment sites confidence intervals for RMS errors with the overshoot was set at 0-0.50 mm and for the percentage of pixels passing a gamma analysis at 1%/1 mm a confidence interval of 68.83% was set also for all treatment sites. This work demonstrates the successful implementation of treatment log files to validate IMRT deliveries and how dynamic log files can diagnose delivery errors not possible with phantom based QC. Machine performance was found to be directly related to plan complexity but this is not the dominant determinant of delivery accuracy.

Fractional dynamics in DNA

This paper addresses the DNA code analysis in the perspective of dynamics and fractional calculus. Several mathematical tools are selected to establish a quantitative method without distorting the alphabet represented by the sequence of DNA bases. The association of Gray code, Fourier transform and fractional calculus leads to a categorical representation of species and chromosomes.