Não vício assintótico, consistência forte e uniformemente forte de estimadores do tipo núcleo para dados direcionais sobre uma esfera unitária k-dimensional

In this work we studied the asymptotic unbiasedness, the strong and the uniform strong consistencies of a class of kernel estimators fn as an estimator of the density function f taking values on a k-dimensional sphere

Avaliação in vitro da adesão e proliferação de células mesenquimais do ligamento periodontal humano em diferentes superfícies de titânio

In the last years, many scientific researches in implantology have been focused on alternatives that would provide higher speed and quality in the process of osseointegration. Different treatment methods can be used to modify the topographic and chemical properties of titanium surface in order to optimize the tissue-implant reactions by a positive tissue response. This study aimed to evaluate the adhesion and proliferation of mesenchymal cells from human periodontal ligament on two different titanium surfaces, using cell culture techniques. Grade II titanium discs received different surface treatments, forming two distinct groups: polished and cathodic cage plasma nitriding. Human periodontal ligament mesenchymal cells were cultured on titanium discs in 24-well cell culture plates, at a density of 2 x 104 cells per well, including wells with no discs as positive control. Data obtained by counting the cells that adhered to the titanium surfaces (polished group and cathodic cage group) and to the plastic surface (control group), in the 24, 48 and 72-hour periods after plating, were used to analyze cell adhesion and proliferation and to obtain the cell growing curve in the different groups. The data were submitted to nonparametric analysis and the differences between groups were compared by Kruskal-Wallis and Friedman statistical tests. No statistically significant differences were found in the cells counts between the groups (p>0.05). It was concluded that both treatments produced surfaces compatible with the adhesion and proliferation of human periodontal ligament mesenchymal cells

Qualidade de vida, eficiência mastigatória e presença de disfunção temporomandibular em usuários de prótese parcial removível com arco dental curto inferior

Even nowadays there is in Brasil a large number of edentulous and a precarious financial condition of most of the population. In addition, World Health Organization aims for oral health, which consists on the maintenance of a natural dentition, functional and aesthetic composed of at least 20 teeth, without need of prosthetic intervention throughout life. From this and considering the lack of researches about the permanence of edentulous spaces in the oral cavity, and also avoiding overtreatment, this research has been proposed. Thus, the aim was to evaluate the effect of different lengths of the shortened lower dental arch in the presence or absence of a removable partial denture (RPD) on masticatory function, quality of life and occurrence of temporomandibular dysfunction. To achieve this goal, we compared the masticatory efficiency (colorimetric test), the oral comfort through the analysis of the impact of oral health in quality of life (OHIP-14), the presence of temporomandibular dysfunction (RDC/TMD) and the general quality of life (WHOQOL) of patients with shortened dental arches (SDA) (n=60), which is an arch with a reduction of teeth starting posteriorly, and patients with complete dental arch (Complete DA) (n = 34). The group of patients whit SDA was divided among PPR wears (PPD + SDA) (n = 17) and non-wears (n = 43). The population of this study consisted on patients who received or looked for treatment at the clinics of the Department of Dentistry of UFRN, from clinical analysis and records. The sample was chosen by convenience. For statistical analysis, it was a database in SPSS 17.0, followed by descriptive analysis with frequencies, absolute values, tests of central tendency and variability. The statistical tests used were chi-squared and analysis of variance as well as Tukey s post test, when applicable, all with a 95% confidence level. The results shown a prevalence of TMD of 47,1% among patients using PRP and 69,8% among those who didn t, but this result wasn t statistically significant. The mean of the results of masticatory efficiency, WHOQOL and OHIP didn t show association to the presence or absence of PPR and to the lower number of occlusal units of the patients (0, 1, 2 or more occlusal). The association only occurred among the different groups of SDA and the patients with complete dental arch. Taking into account the results, it could be observed that studied patients with low posterior support using lower PRP didn t have better masticatory efficiency, general quality of life, less impacts of their oral conditions in quality of life or not even less temporomandibular dysfunction or better masticatory efficiency when compared to those who didn t use the prosthesis

Percepção dos idosos sobre saúde bucal

The assessment of oral health status in elderly patients is essential for the development of specific health policies. The prevalence of oral diseases is high in this population. The self-perception of oral health conditions influences the demand for oral care and quality of life for seniors. The aim of this study was to assess self-perception of oral health status in 100 elderly of both sexes, aged 60 years or older and functionally independent the Basic Health Unit of Felipe Camarão II, Natal, Brazil. For comparison of self-perception data was collected in Bom Pastor, Natal / RN. In this research data were collected a questionnaire grouped into two parts. The first part with the socio-demographic data, subjective and objective condition of oral health and access to the service, the second part GOHAI Index. This index consists of 12 items that make it possible to obtain information involving aspects of chewing, speech, phonation, and self-assessed oral health. The results were subjected to statistical tests of Mann-Whitney and Kruskal-Wallis test (α = 0.05), to identify possible predictors of self-evaluation. As a result, 69% were female, ages ranged from 60 to 86 years, with a median of 65 years. In relation to marital status 48% were married. For the years of study, the sample had an average of 3 years. For the last visit to the dentist, only 27% of seniors had visited the Dentist for less than a year. Regarding the questions about the presence of gingival and dental problems were answered by 46% and 21% respectively. The data on the perception of your teeth and gums, 44%. The index showed GOHAI value for self-perception of 30 points to Felipe Camarão and 28 points for the Bom Pastor, both considered a low perception. We identified predictors of self-rated number of people in the room, participate in any associational activity, there is problems with your teeth and your gums. Concluded a negative self-perception of oral health condition by Gone in both areas, influenced by socioeconomic and cultural issues, although they realize the importance given to oral health, but by the misfortunes of other prominent favored little valuing of oral health

Análise comparativa da imunoexpressão das proteínas hmlh1 e hmsh2 em carcinomas epidermóides de lábio inferior e queilites actínicas com graus variados de displasia

Lip squamous cell carcinoma (SCC) may develop from a premalignant condition, actinic cheilitis (AC) in 95% of the cases. Both premalignant and neoplastic lip diseases are caused mainly by chronic exposure to the ultraviolet component of solar radiation, especially UVB. This exposure causes disruption of the cell cycle and damage to DNA repair systems, like mismatch repair, altering proteins repair as hMLH1 and hMSH2. This research aimed to investigate the immunohistochemical expression of hMLH1 and hMSH2 proteins in lower lip SCCs and ACs, providing additional information about carcinogenesis of the lower lip. The sample consisted 40 cases of ACs and 40 cases of lower lip SCCs. Histological sections of 3 μm were submitted to immunoperoxidase method, for immunohistochemical analysis of lesions were counted in 1000 cells (positive and negative), data were evaluated both in absolute numbers and percentage of immunostained cells, the latter by assigning scores. Associations of the variables and comparative analysis of biomarker expression were performed by Fisher s exact and Pearson s chi-square, "t" student, one-way ANOVA, Mann- Whitney e Kruskal-Wallis tests. The level of significance was 5%. It was found that, in lower lip SCC, the mean of the proteins was higher in female patients (hMLH1= 369,80 + 223,98; hMHS2 = 534,80 + 343,62), less than 50 years old (hMLH1 = 285,50 + 190,65; hMHS2 = 540,00 + 274,79) and classified as low-grade malignancy (hMLH1 = 264,59 + 179,21; hMHS2 = 519,32 + 302,58), in these data only to sex, for hMLH1 protein, was statistically significant (p=0.034). Comparing the different lesions, we observed that for both hMLH1 and hMSH2 protein, the average of positive epithelial cells decreased as the lesion was graded at later stages. The ACs classified without dysplasia or mild dysplasia had the highest average of immunostained cells (hMLH1 = 721.23 + 88.116; hMHS2 = 781.50 + 156.93). The ACs classified as moderate or severe dysplasia had intermediate values (hMLH1 = 532,86 + 197,72; hMHS2 = 611,14 + 172,48) and SSCs of the lower lip had the lowest averages (hMLH1 = 255,03 + 199,47; hMHS2 = 518,38 + 265,68). There was a statistically significant difference between groups (p<0.001). In conclusion, our data support the hypothesis that changes in immunoexpression of these proteins is related to the process of carcinogenesis of the lower lip

Variações horárias na entrada e saída dos golfinhos-rotadores e sua relação com fatores ambientais, na Baía dos Golfinhos em Fernando de Noronha PE

The dolphins are found in all world s marine environments, except for poles. On Brazil, the major concentration of this animals is on Fernando de Noronha Islands, wich have a tropical climate with two well-defined rainfall seasons: dry and rainy season. The Baía dos Golfinhos, wich is the most crowded piece of dolphins on the archipelago. These research looks for to characterize the circadian rhythms of the spinner dolphin behavior, Stenella longirostris, on the Baía dos Golfinhos occupation, at the Fernando de Noronha islands, Brazil s northeast, according to the fluctuations of environment that they all are inserted. The research was realized daily between 1991 January and 2009 December, with observations from a fixed point up to Mirante dos Golfinhos, located on Baía dos Golfinhos. The data was examined with the PASW Statistics 18 program, up to nonparametric tests, being analyzed on the incoming and out coming time of the spinner dolphins and the relationship with moon phases, the wind incidence, and the rainfall season, the dolphins were inserted. The spinner dolphins diurnal rhythms are influenced by moon phases, the spinner dolphins arrival at Baía dos Golfinhos earlier when it s full moon because of the high luminosity at night cause a bigger food efficiency for these animals. The outgoing time of spinner dolphins didn t show statistic difference between moon phases, despite follows the same pattern for the incoming time. When the spinner dolphins are submitted to bigger wind incidence conditions around the archipelago, the dolphins come early to the Baía dos Golfinhos, since that one is protected from wind that reaches Fernando de Noronha, the spinner dolphins tends to arrive later and leave earlier of the bay because the rain may cause adverse conditions for your rest.

Adaptação e validação da escala de motivação à prática de atividades físicas

The study of the motivation to practice physical activities is relevant once through this it is possible to develop intervention strategies for sedentary population. In this way, the present dissertation aimed to adapt and validate for the Brazilian context the Motives for Physical Activity Measure Revised (MPAM-R). It was investigated yet the relation of some socio-demographic variables (age, gender, Body Mass Index - BMI, types of physical activity; way to practice and time of practice) and the participants means in the motives studied. The physical activity (PA) is defined as any bodily movement produced by skeletal muscles resulting in energy expenditure above the basal level. However, in the present study it was considered motivation for two types of PA: the physical exercises and sports. The Self-Determination Theory (SDT) underlay this research, once it has been used in the sportive context, beyond the facto of it was used as theoretical base to the development of MPAM-R. To attain the proposed goals, it was accomplished translations to Portuguese of the original English scale. Next, was carried out the semantic analysis and the judge analysis. For the empirical analysis of items, participated 309 practitioner of PA, classified in physical exercises practitioners and sports practitioners, with ages between 16 and 74 years, distributed equally by sex. They answered the final version in Portuguese of the MPAM-R and socio-demographic questions. The data was collected in Natal/RN, where the researcher approached people in some places where the PA is practiced, following she communicated that their involvement will be spontaneous and their responses will be confidential. The obtained results pointed the confirmation of the existence of five factors in the final version of the instrument, that was composed by 26 items that presented the following statistics indexes: x² (289) = 757.75, p < 0.000, x²/DF = 2.62, with GFI of 0.83, AGFI of 0.80 and RMSEA of 0.07. The reliability (Cronbach Alpha) of the complete instrument was 0.90, and the indexes of each factor were considered satisfactory too: Enjoyment (α = 0.88), Health (α = 0.84), Appearance (α = 0.79), Competence (α = 0.85) and Social (α = 0.75). It was observed that, in general, the main motive presented by the participants to practice PA was Health. It was verified yet, that women and aged had a higher mean in the Health factor; among the exercise practitioners was found a higher mean in the Appearance factor; and a higher mean in the Social factor was found among those that practice PA with accompaniment. It was concluded that the MPAM-R presented satisfactory psychometric parameters, became it useful in futures researches. Moreover, proposed the accomplishment of new studies that considered others variables to the intent of the better understanding of motivation to practice physical activity

Mudanças climáticas globais e o compromisso pró-ecológico de adolescentes natalenses

In recent years, much has been discussed about global climate changes (GCCs), popularly known as global warming. The scientific evidences point out to the influence of human actions for its drastic intensification. Therefore, studies of the psychological aspects involved become relevant. This study aimed at the investigation of the views of adolescents concerning GCCs, and the possible relations between those views and their pro-ecological commitment. Such commitment is measured by willingness for engagement in pro-environmental behaviors; environmentalism attitudes, like ecocentric and anthropocentric; consideration of future consequences; and ecological worldviews. Participants were 348 adolescents who answered a questionnaire containing questions about socio-demographic data, open questions about the practice of environmental care, and about GCCs, and the scales of Ecocentric and Anthropocentric Environmentalism, the Consideration of Future Consequences and the Ecological Worldviews assessment scale. From the inter-relationships between variables, procedures carried out by means of descriptive and correlacional statistics, it was observed that 55% of teenagers said that they did not engage in actions of environmental care, which was associated with apathyanthropocentric, immediatism, and individualism. The consideration of future consequences joined the practice of environmental care, corroborating evidence from the literature. It was evident that views concerning GCCs were superficial; adolescents perceive it as a generic environmental problem, and are confused with other problems such as pollution. This study found no association between views about GCCs and the indicators of pro-ecological commitment, perhaps due to the conceptual confusion about the subject. However, the lack of environmental care actions and other indicators of non-commitment (apathy-anthropocentric, individualism and immediatism) were associated with conceptually poor or incomplete responses (with no indication of cause, consequence or responsibility for the problem), demonstrating diminished knowledge and the failure to consider these issues

Dados normativos do teste de atenção por cancelamento em estudantes de Natal/RN

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior

Espectroscopia no infravermelho próximo e métodos de calibração multivariada aplicados à determinação simultânea de parâmetros bioquímicos em plasma sanguíneo

In this work, the quantitative analysis of glucose, triglycerides and cholesterol (total and HDL) in both rat and human blood plasma was performed without any kind of pretreatment of samples, by using near infrared spectroscopy (NIR) combined with multivariate methods. For this purpose, different techniques and algorithms used to pre-process data, to select variables and to build multivariate regression models were compared between each other, such as partial least squares regression (PLS), non linear regression by artificial neural networks, interval partial least squares regression (iPLS), genetic algorithm (GA), successive projections algorithm (SPA), amongst others. Related to the determinations of rat blood plasma samples, the variables selection algorithms showed satisfactory results both for the correlation coefficients (R²) and for the values of root mean square error of prediction (RMSEP) for the three analytes, especially for triglycerides and cholesterol-HDL. The RMSEP values for glucose, triglycerides and cholesterol-HDL obtained through the best PLS model were 6.08, 16.07 e 2.03 mg dL-1, respectively. In the other case, for the determinations in human blood plasma, the predictions obtained by the PLS models provided unsatisfactory results with non linear tendency and presence of bias. Then, the ANN regression was applied as an alternative to PLS, considering its ability of modeling data from non linear systems. The root mean square error of monitoring (RMSEM) for glucose, triglycerides and total cholesterol, for the best ANN models, were 13.20, 10.31 e 12.35 mg dL-1, respectively. Statistical tests (F and t) suggest that NIR spectroscopy combined with multivariate regression methods (PLS and ANN) are capable to quantify the analytes (glucose, triglycerides and cholesterol) even when they are present in highly complex biological fluids, such as blood plasma

Influência das condições de saúde bucal no desempenho das atividades diárias de adolescentes escolares

Instruments are used in odontology to measure the Quality of Life Related to Oral Health (OHRQoL) to scale how the oral condition interferes with functional areas, of the people s psychological and social life. This cross-sectional study, held in Natal/RN, with 215 students from the Federal Institute of Education, Science and Technology of Rio Grande do Norte (IFRN) has investigated the association between the performance of daily activities and oral health status of school adolescents from 15 to 19 years of age, through the normative index DMFT (permanent teeth decayed, missing and filled), CPI (Community Periodontal Index) and DAI (dental Aesthetic Index) and subjective questionnaire assessment of quality of life related oral health OIDP index (oral impacts on daily performance). It was also carried out the socioeconomic characteristics of students through IFRN own data. Concerning the analysis of data was performed a descriptive analysis of the variables by their absolute and relative frequencies and measures of central tendency. The chi-square test was used to assess the association between the dependent variable and the independent categorical variables and the Student t test for quantitative. It was also conducted a further multiple analysis out using Poisson regression with robust variance between the outcome "presence of impact" and the independent variables that showed p <0.20. It was used for all the statistical tests a significance level of 5%. Among the adolescents surveyed, 51.16% reported that at least one activity assessed by OIDP had hampered its implementation due to some dental problem. The difficulties were more pronounced in the activities of eating (31.6%), oral hygiene (25.6%) and smile (25.1%).The tooth position, followed by toothache, were the causes of the impacts reported by most teenagers. There was a significant association between the presence and impact of the presence of one or more decayed teeth (p = 0.012), the presence of gum bleeding (p = 0.012) and for orthodontic treatment (p = 0.003), independently of other variables. There was no significant association between oral health status and socioeconomic and demographic characteristics of the adolescents. The survey results showed that there is an association between oral health status of the population studied and reports of difficulties in carrying out daily activities evaluated. The worse the oral health status, the greater the impact of this condition on the adolescents quality of life

Influência da laserterapia na proliferação de células-tronco do ligamento periodontal humano

Low level laser irradiation (LLLI) has been used in Dentistry to promote wound healing and tissue regeneration. The literature shows a positive effect of LLLI on cell proliferation, but little is known about their effectiveness in promoting stem cells proliferation. The aim of this study was to evaluate the effect of LLLI on the proliferative rate of human periodontal ligament stem cells. Extracts of periodontal ligament were isolated from two third molars removed by surgical and/or orthodontic indication. After enzymatic digestion, the cells were grown in α-MEM culture medium supplemented with antibiotics and 15% fetal bovine serum. On the third subculture, the cells were irradiated with a InGaAlP-diode laser, using two different energy densities (0,5J/cm 2 - 16 seconds and 1,0J/cm² - 33 seconds), with wavelength of 660nm and output power of 30mW. A new irradiation, using the same parameters, was performed 48h after the first. A control group (non irradiated) was kept under the same experimental culture conditions. The Trypan blue exclusion test and the mitochondrial activity of the cells measured by MTT [3-(4,5-Dimethylthiazol-2-yl)-2,5-Diphenyltetrazolium Bromide] essay were performed to assess the cell proliferation in the intervals of 0, 24, 48 e 72 h after irradiation. The data of cell counts were submitted to nonparametrical statistical tests (Kruskal-Wallis and Mann-Whitney), considering a confidence interval of 95%. DAPI (4 -6-Diamidino-2-phenylindole) staining of the cells was performed at 72h interval to evaluate possible nuclear morphological changes induced by LLLI. The results of this study show that the energy density of 1,0 J/cm² promoted greater cell proliferation compared to the other groups (control and 0,5 J/cm²) at intervals of 48 and 72h. The mitochondrial activity measured by MTT essay showed similar results to the Trypan blue cell counting test. The group irradiated with 1,0J/cm² exhibited a significantly higher MTT activity in the intervals of 48 and 72h, when compared to the group irradiated with 0,5J/cm². No nuclear morphological change was observed in the cells from the three groups studied. It is concluded that LLLI has stimulatory effects on the proliferation of human periodontal ligament stem cells. Therefore, the use of laser irradiation in this cell type may be important to promote future advances in periodontal regeneration

Produção e validação de um indicador de saúde bucal para idosos a partir de dados secundários do SB Brasil 2010

Dentre os vários aspectos da saúde do idoso, a saúde bucal merece atenção especial pelo fato de que, historicamente, nos serviços odontológicos, não se considera esse grupo populacional como prioridade de atenção. Por isso, se faz necessária a produção de um indicador multidimensional capaz de mensurar todas as alterações bucais encontradas em um idoso, facilitando a categorização da saúde bucal como um todo. Tal indicador representará um importante instrumento capaz de elencar prioridades de atenção voltadas à população idosa. Portanto, o estudo em questão propõe a produção e validação de um indicador de saúde bucal a partir dos dados secundários coletados pelo projeto SB Brasil 2010 referente ao grupo etário de 65 a 74 anos. A amostra foi representada pelos 7619 indivíduos do grupo etário de 65 a 74 anos que participaram da pesquisa nas 5 (cinco) regiões do Brasil. Tais indivíduos foram submetidos à avaliação epidemiológica das condições de saúde bucal, a partir dos índices CPO-d, CPI e PIP. Além disso, verificou-se o uso e necessidade de prótese, bem como características sociais, econômicas e demográficas. Uma análise fatorial identificou um número relativamente pequeno de fatores comuns, através da análise de componentes principais. Após a nomenclatura dos fatores, foi realizada a soma dos escores fatoriais por indivíduo. Por último, a dicotomização dessa soma nos forneceu o indicador de saúde bucal proposto. Para esse estudo foram incluídas na análise fatorial 12 variáveis de saúde bucal oriundas do banco de dados do SB Brasil 2010 e, também 3 variáveis socioeconômicas e demográficas. Com base no critério de Kaiser, observa-se que foram retidos cinco fatores que explicaram 70,28% da variância total das variáveis incluídas no modelo. O fator 1 (um) explica sozinho 32,02% dessa variância, o fator 2 (dois) 14,78%, enquanto que os fatores 3 (três), 4 (quatro) e 5 (cinco) explicam 8,90%, 7,89% e 6,68%, respectivamente. Por meio das cargas fatoriais, o fator um foi denominado dente hígido e pouco uso de prótese , o dois doença periodontal presente , o três necessidade de reabilitação , já o quarto e quinto fator foram denominados de cárie e condição social favorável , respectivamente. Para garantir a representatividade do indicador proposto, realizou-se uma segunda análise fatorial em uma subamostra da população de idosos investigados. Por outro lado, a aplicabilidade do indicador produzido foi testada por meio da associação do mesmo com outras variáveis do estudo. Por fim, Cabe ressaltar que, o indicador aqui produzido foi capaz de agregar diver sas informações a respeito da saúde bucal e das condições sociais desses indivíduos, traduzindo assim, diversos dados em uma informação simples, que facilita o olhar dos gestores de saúde sobre as reais necessidades de intervenções em relação à saúde bucal de determinada população

Uma Análise Comparativa entre Sistemas de Combinação de Classificadores com Distribuição Vertical dos Dados

In systems that combine the outputs of classification methods (combination systems), such as ensembles and multi-agent systems, one of the main constraints is that the base components (classifiers or agents) should be diverse among themselves. In other words, there is clearly no accuracy gain in a system that is composed of a set of identical base components. One way of increasing diversity is through the use of feature selection or data distribution methods in combination systems. In this work, an investigation of the impact of using data distribution methods among the components of combination systems will be performed. In this investigation, different methods of data distribution will be used and an analysis of the combination systems, using several different configurations, will be performed. As a result of this analysis, it is aimed to detect which combination systems are more suitable to use feature distribution among the components

A Linguagem de Especificação algébrica CASL e o Tipo de Dados Intervalos

Na computação científica é necessário que os dados sejam o mais precisos e exatos possível, porém a imprecisão dos dados de entrada desse tipo de computação pode estar associada às medidas obtidas por equipamentos que fornecem dados truncados ou arredondados, fazendo com que os cálculos com esses dados produzam resultados imprecisos. Os erros mais comuns durante a computação científica são: erros de truncamentos, que surgem em dados infinitos e que muitas vezes são truncados", ou interrompidos; erros de arredondamento que são responsáveis pela imprecisão de cálculos em seqüências finitas de operações aritméticas. Diante desse tipo de problema Moore, na década de 60, introduziu a matemática intervalar, onde foi definido um tipo de dado que permitiu trabalhar dados contínuos,possibilitando, inclusive prever o tamanho máximo do erro. A matemática intervalar é uma saída para essa questão, já que permite um controle e análise de erros de maneira automática. Porém, as propriedades algébricas dos intervalos não são as mesmas dos números reais, apesar dos números reais serem vistos como intervalos degenerados, e as propriedades algébricas dos intervalos degenerados serem exatamente as dos números reais. Partindo disso, e pensando nas técnicas de especificação algébrica, precisa-se de uma linguagem capaz de implementar uma noção auxiliar de equivalência introduzida por Santiago [6] que ``simule" as propriedades algébricas dos números reais nos intervalos. A linguagem de especificação CASL, Common Algebraic Specification Language, [1] é uma linguagem de especificação algébrica para a descrição de requisitos funcionais e projetos modulares de software, que vem sendo desenvolvida pelo CoFI, The Common Framework Initiative [2] a partir do ano de 1996. O desenvolvimento de CASL se encontra em andamento e representa um esforço conjunto de grandes expoentes da área de especificações algébricas no sentido de criar um padrão para a área. A dissertação proposta apresenta uma especificação em CASL do tipo intervalo, munido da aritmética de Moore, afim de que ele venha a estender os sistemas que manipulem dados contínuos, sendo possível não só o controle e a análise dos erros de aproximação, como também a verificação algébrica de propriedades do tipo de sistema aqui mencionado. A especificação de intervalos apresentada aqui foi feita apartir das especificações dos números racionais proposta por Mossakowaski em 2001 [3] e introduz a noção de igualdade local proposta por Santiago [6, 5, 4]