888 resultados para trigonometric functions


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MSC 2010: 33B10, 33E20

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Dedicated to 75th birthday of Prof. A.M. Mathai, Mathematical Subject Classification 2010:26A33, 33C10, 33C20, 33C50, 33C60, 26A09

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We analyze crash data collected by the Iowa Department of Transportation using Bayesian methods. The data set includes monthly crash numbers, estimated monthly traffic volumes, site length and other information collected at 30 paired sites in Iowa over more than 20 years during which an intervention experiment was set up. The intervention consisted in transforming 15 undivided road segments from four-lane to three lanes, while an additional 15 segments, thought to be comparable in terms of traffic safety-related characteristics were not converted. The main objective of this work is to find out whether the intervention reduces the number of crashes and the crash rates at the treated sites. We fitted a hierarchical Poisson regression model with a change-point to the number of monthly crashes per mile at each of the sites. Explanatory variables in the model included estimated monthly traffic volume, time, an indicator for intervention reflecting whether the site was a “treatment” or a “control” site, and various interactions. We accounted for seasonal effects in the number of crashes at a site by including smooth trigonometric functions with three different periods to reflect the four seasons of the year. A change-point at the month and year in which the intervention was completed for treated sites was also included. The number of crashes at a site can be thought to follow a Poisson distribution. To estimate the association between crashes and the explanatory variables, we used a log link function and added a random effect to account for overdispersion and for autocorrelation among observations obtained at the same site. We used proper but non-informative priors for all parameters in the model, and carried out all calculations using Markov chain Monte Carlo methods implemented in WinBUGS. We evaluated the effect of the four to three-lane conversion by comparing the expected number of crashes per year per mile during the years preceding the conversion and following the conversion for treatment and control sites. We estimated this difference using the observed traffic volumes at each site and also on a per 100,000,000 vehicles. We also conducted a prospective analysis to forecast the expected number of crashes per mile at each site in the study one year, three years and five years following the four to three-lane conversion. Posterior predictive distributions of the number of crashes, the crash rate and the percent reduction in crashes per mile were obtained for each site for the months of January and June one, three and five years after completion of the intervention. The model appears to fit the data well. We found that in most sites, the intervention was effective and reduced the number of crashes. Overall, and for the observed traffic volumes, the reduction in the expected number of crashes per year and mile at converted sites was 32.3% (31.4% to 33.5% with 95% probability) while at the control sites, the reduction was estimated to be 7.1% (5.7% to 8.2% with 95% probability). When the reduction in the expected number of crashes per year, mile and 100,000,000 AADT was computed, the estimates were 44.3% (43.9% to 44.6%) and 25.5% (24.6% to 26.0%) for converted and control sites, respectively. In both cases, the difference in the percent reduction in the expected number of crashes during the years following the conversion was significantly larger at converted sites than at control sites, even though the number of crashes appears to decline over time at all sites. Results indicate that the reduction in the expected number of sites per mile has a steeper negative slope at converted than at control sites. Consistent with this, the forecasted reduction in the number of crashes per year and mile during the years after completion of the conversion at converted sites is more pronounced than at control sites. Seasonal effects on the number of crashes have been well-documented. In this dataset, we found that, as expected, the expected number of monthly crashes per mile tends to be higher during winter months than during the rest of the year. Perhaps more interestingly, we found that there is an interaction between the four to three-lane conversion and season; the reduction in the number of crashes appears to be more pronounced during months, when the weather is nice than during other times of the year, even though a reduction was estimated for the entire year. Thus, it appears that the four to three-lane conversion, while effective year-round, is particularly effective in reducing the expected number of crashes in nice weather.

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We introduce transreal analysis as a generalisation of real analysis. We find that the generalisation of the real exponential and logarithmic functions is well defined for all transreal numbers. Hence, we derive well defined values of all transreal powers of all non-negative transreal numbers. In particular, we find a well defined value for zero to the power of zero. We also note that the computation of products via the transreal logarithm is identical to the transreal product, as expected. We then generalise all of the common, real, trigonometric functions to transreal functions and show that transreal (sin x)/x is well defined everywhere. This raises the possibility that transreal analysis is total, in other words, that every function and every limit is everywhere well defined. If so, transreal analysis should be an adequate mathematical basis for analysing the perspex machine - a theoretical, super-Turing machine that operates on a total geometry. We go on to dispel all of the standard counter "proofs" that purport to show that division by zero is impossible. This is done simply by carrying the proof through in transreal arithmetic or transreal analysis. We find that either the supposed counter proof has no content or else that it supports the contention that division by zero is possible. The supposed counter proofs rely on extending the standard systems in arbitrary and inconsistent ways and then showing, tautologously, that the chosen extensions are not consistent. This shows only that the chosen extensions are inconsistent and does not bear on the question of whether division by zero is logically possible. By contrast, transreal arithmetic is total and consistent so it defeats any possible "straw man" argument. Finally, we show how to arrange that a function has finite or else unmeasurable (nullity) values, but no infinite values. This arithmetical arrangement might prove useful in mathematical physics because it outlaws naked singularities in all equations.

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Foi estudada a transferência de calor transiente na agitação linear e intermitente (ALI) de embalagens metálicas contendo simulantes de alimentos, objetivando-se sua aplicação em processos de pasteurização ou esterilização e conseqüentes tratamentos térmicos mais eficientes, homogêneos e com produto de melhor qualidade. Foram utilizados quatro meios fluidos simulantes de alimentos de diferentes viscosidades e massas específicas: três óleos e água. Foram combinados efeitos de cinco tratamentos, sendo: meio simulante (4 níveis), espaço livre (3 níveis), freqüência de agitação (4 níveis), amplitude de agitação (2 níveis) e posição das latas (4 níveis). Os ensaios de aquecimento e resfriamento foram feitos em tanque com água à temperatura de 98 °C e 17-20 °C, respectivamente. Com os dados de penetração de calor em cada experimento, foram calculados os parâmetros de penetração de calor fh, jh, fc e jc. Os resultados foram modelados utilizando-se grupos de números adimensionais e expressos em termos de Nusselt, Prandtl, Reynolds e funções trigonométricas (com medidas de amplitude e freqüência de agitação, espaço livre e dimensões da embalagem). Foram estabelecidas as duas Equações gerais para as fases de aquecimento e resfriamento: Nu = ReA 0,199.Pr 0,288.sen(xa/AM)0,406.cos(xf/FA) 1,039.cos((xf/FA).(EL/H).p) 4,556 Aquecimento Nu = 0,1295.ReA 0,047.Pr 0,193.sen(xa/AM)0,114.cos(xf/FA) 0,641.cos((xf/FA).(EL/H).p) 2,476 Resfriamento O processo de ALI pode ser aplicado em pasteurizadores ou autoclaves estáticas horizontais e verticais, com modificações simples. Concluiu-se que a ALI aumenta significativamente a taxa de transferência de calor, tanto no aquecimento como no resfriamento.

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In this study, we sought to address the weaknesses faced by most students when they were studying trigonometric functions sine and cosine. For this, we proposed the use of software Geogebra in performing a sequence of activities about the content covered. The research was a qualitative approach based on observations of the activities performed by the students of 2nd year of high school IFRN - Campus Caicfio. The activities enabled check some diculties encountered by students, well as the interaction between them during the tasks. The results were satisfactory, since they indicate that the use of software contributed to a better understanding of these mathematical concepts studied

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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Pós-graduação em Agronomia (Energia na Agricultura) - FCA

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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Paper submitted to the XVIII Conference on Design of Circuits and Integrated Systems (DCIS), Ciudad Real, España, 2003.

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Paper submitted to International Workshop on Spectral Methods and Multirate Signal Processing (SMMSP), Barcelona, España, 2003.

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Paper submitted to the IFIP International Conference on Very Large Scale Integration (VLSI-SOC), Darmstadt, Germany, 2003.

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Includes index.

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"Answers": p. 273-277.