Desenvolvimento de sorvete probiótico a base de leite de cabra: estudo da formulação, características físico químicas, sensoriais e viabilidade das bactérias probióticas

This work targetet the caprine ice cream production added with probiotic bacteria Bifidobacterium animalis subsp. lactis. It is divided into two parts. In the first one, four caprine ice cream formulations were evaluated, in which it was used hydrogenated fat (F1 and F3) or fat substitute (F2 and F4) in two different flavors (F1 and F2, passion fruit, F3 and F4, guava). Statistical differences (p<0.05) were detected for their physical-chemical properties, mainly for total solids and fat, but no differences were observed for melting test results. When it went to sensory acceptance, all four ice cream formulations reached high acceptance indexes, mostly formulation F4, which was selected for further studies. In the second part, F4 formulation was prepared with the addition of probiotic bacteria Bifidobacterium animalis subsp. lactis. The growth kinetics was studied and it was observed that the cellular concentration peak was reached after four fermentation hours (10.14 log UFC/g). This time was selected for pre-fermentation procedure and posterior addition at ice cream syrup. In this part of the study, two experimental groups were evaluated: group G1, in which the probiotic addition occurred before the maturation step and group G2, which included a pre-fermentation step and probiotic addition after ice cream maturation. The physical-chemical properties of these two ice cream groups were similar, except for pH, which was higher for group G2 (p<0.05). G1 samples had superior melting rate (3.566 mL/min) and both groups presented microbiological and sanitary results in accordance to current Brazilian legislation. Also, G1 and G2 were considered sensory accepted due to their acceptance indexes higher than 70%. G1 and G2 sensory profiles were similar (p>0.05), and both ice cream samples exhibited high creaminess (6.76 to 6.91) and mouth melting sensation (6.53 to 6.67) scores, while low sandiness scores (0.85 to 0.86) were observed, positive characteristics for this kind of food product. During the first 24 hours after ice cream production, the population of B. animalis subsp. lactis decreased, reaching 7.15 e 6.92 log CFU/g for G1 and G2, respectively. Probiotic bacteria counts fluctuated in ice cream samples during the first 108 days at frozen storage, especially for G2 group. Decreased probiotic viability was observed for G1 samples during the first 35 days of frozen storage, mild variation between 35 and 63 days and stabilized counts were observed after this time. After 21 days at frozen storage, ice cream samples of G1 and G2 groups reached 1.2 x 109 and 1.3 x 109 CFU/portion, respectively. After 108 days under these storage conditions, the survival rate of B. animalis subsp. lactis was 94.26% and 81.10% for G1 and G2 samples, respectively. After simulation of gastroenteric conditions, G2 group reached 9.72 x 105 CFU/portion. Considering the current requirements of Brazilian legislation, which stipulates that functional foods must have minimum probiotic count between 108 and 109 CFU/portion and detectable probiotic bacteria after being submitted to gastroenteric conditions, it is concluded that the ice cream with the addition of Bifidobacterium animalis subsp. lactis made as shown in this work, can be considered as a dairy functional food

Uma análise dos questionamentos dos alunos nas aulas de números complexos

This work presents a contribution for the studies reffering to the use of the History of Mathematics focusing on the improvement of the Teaching and Learning Process. It considers that the History of Matematics, as a way of giving meaning to the discipline and improve the quality of the Teaching and Learning Process. This research focuses on the questions of the students, classified in three categories of whys: the chronological, the logical and the pedagogical ones. Therefore, it is investigated the teaching of the Complex Numbers, from the questions of the students of the Centro Federal de Educação Tecnológica do Rio Grande do Norte (Educational Institution of Professional and Technology Education from Rio Grande do Norte). The work has the following goals: To classify and to analyse the questions of the students about the Complex Numbers in the classes of second grade of the High School, and to collate with the pointed categories used by Jones; To disccus what are the possible guidings that teachers of Mathematics can give to these questions; To present the resources needed to give support to the teacher in all things involving the History of Mathematics. Finally, to present a bibliographic research, trying to reveal supporting material to the teacher, with contents that articulate the Teaching of Mathematics with the History of Mathematics. It was found that the questionings of the pupils reffers more to the pedagogical whys, and the didatic books little contemplate other aspects of the history and little say about the sprouting and the evolution of methods of calculations used by us as well

Análise das provas objetivas de química dos vestibulares da UFRN de 1997 a 2010: uma caracterização a partir das mudanças

Las pruebas de vestibular, en los últimos años en el Brasil, han sido objeto de diversas investigaciones, considerando que ese proceso selectivo es una de las vias para ingresar en las universidades públicas y termina por influenciar la enseñanza en las escuelas. De esa forma, algunos vestibulares han pasado por cambios, de un simple proceso selectivo clasificatorio a un proceso fundamentado en reflexiones sociológica, pedagógica y crítica, lo que ha promovido cuestionamientos respecto del aprendizaje y de su papel en la escuela. Delante de esa realidad, la Universidad Federal de Rio Grande del Norte (UFRN) ha implementado cambios en sus vestibulares procurando una aproximación a las Orientaciones Curriculares Nacionales, como los PCNEM, los PCN+ y las OCEM. Siendo así, el objetivo de este estudio fue caracterizar el avance cualitativo en las pruebas de preguntas objetivas a partir de los cambios ocurridos en el vestibular de la UFRN en el periodo de 1997 a 2010, definiéndose las siguientes cuestiones de estudio: ¿Cuáles son los tipos de preguntas que caracterizan las pruebas objetivas de Química del vestibular? ¿Cuáles cuestiones presentan las mayores dificultades para los candidatos? ¿Cuáles son los contenidos conceptuales privilegiados? ¿En qué tipo de preguntas los candidatos presentan mayores índices de éxitos? ¿Qué diferencias pueden ser establecidas entre las preguntas antes y después del periodo que establece los cambios en el vestibular de la UFRN? Las discusiones teóricas del estudio están fundamentadas en las siguientes referencias: PCNEM (BRASIL, 1999), PCN+ (BRASIL, 2001), OCEM (BRASIL, 2006), Zabala (1999), Jiménez Aleixandre et al. (2003), Pozo (1999), Álvarez de Zayas (1992), Núñez (2009), Relatorios Comperve/UFRN (1997 a 2010), e en relación a las evaluaciones: Pasquali et al. (2003), Silva y Núñez (2008), Marín y Benarrouch (2009). Para el estudio fueran construidas las siguientes categorías que permitieran el análisis de las cuestiones: contextualización de la cuestión, temas conceptuales, problema, representación semiótica, cálculo matemático, pertinencia de la cuestión e índice de acierto. Los resultados muestran un avance cualitativo de las preguntas de Química, en los cuales se observa un modelo de prueba que prioriza el uso de verdaderos problemas, de situaciones contextualizadas, de pocos cálculos, dándose prioridad al razonamiento que implica la comprensión, la aplicación y la interpretación de los conocimientos conceptuales, todo lo que puede estimular una enseñanza más adecuada en relación a las exigencias actuales de la Educación en Química

Os Polímeros como Sistemas Complexos

Neste trabalho, através de simulações computacionais, identificamos os fenômenos físicos associados ao crescimento e a dinâmica de polímeros como sistemas complexos exibindo comportamentos não linearidades, caos, criticalidade auto-organizada, entre outros. No primeiro capítulo, iniciamos com uma breve introdução onde descrevemos alguns conceitos básicos importantes ao entendimento do nosso trabalho. O capítulo 2 consiste na descrição do nosso estudo da distribuição de segmentos num polímero ramificado. Baseado em cálculos semelhantes aos usados em cadeias poliméricas lineares, utilizamos o modelo de crescimento para polímeros ramificados (Branched Polymer Growth Model - BPGM) proposto por Lucena et al., e analisamos a distribuição de probabilidade dos monômeros num polímero ramificado em 2 dimensões, até então desconhecida. No capítulo seguinte estudamos a classe de universalidade dos polímeros ramificados gerados pelo BPGM. Utilizando simulações computacionais em 3 dimensões do modelo proposto por Lucena et al., calculamos algumas dimensões críticas (dimensões fractal, mínima e química) para tentar elucidar a questão da classe de universalidade. Ainda neste Capítulo, descrevemos um novo modelo para a simulação de polímeros ramificados que foi por nós desenvolvido de modo a poupar esforço computacional. Em seguida, no capítulo 4 estudamos o comportamento caótico do crescimento de polímeros gerados pelo BPGM. Partimos de polímeros criticamente organizados e utilizamos uma técnica muito semelhante aquela usada em transições de fase em Modelos de Ising para estudar propagação de danos chamada de Distância de Hamming. Vimos que a distância de Hamming para o caso dos polímeros ramificados se comporta como uma lei de potência, indicando um caráter não-extensivo na dinâmica de crescimento. No Capítulo 5 analisamos o movimento molecular de cadeias poliméricas na presença de obstáculos e de gradientes de potenciais. Usamos um modelo generalizado de reptação para estudar a difusão de polímeros lineares em meios desordenados. Investigamos a evolução temporal destas cadeias em redes quadradas e medimos os tempos característicos de transporte t. Finalizamos esta dissertação com um capítulo contendo a conclusão geral denoss o trabalho (Capítulo 6), mais dois apêndices (Apêndices A e B) contendo a fenomenologia básica para alguns conceitos que utilizaremos ao longo desta tese (Fractais e Percolação respectivamente) e um terceiro e ´ultimo apêndice (Apêndice C) contendo uma descrição de um programa de computador para simular o crescimentos de polímeros ramificados em uma rede quadrada

Propagação de danos em sistemas cooperativos: propriedades termodinâmicas

High-precision calculations of the correlation functions and order parameters were performed in order to investigate the critical properties of several two-dimensional ferro- magnetic systems: (i) the q-state Potts model; (ii) the Ashkin-Teller isotropic model; (iii) the spin-1 Ising model. We deduced exact relations connecting specific damages (the difference between two microscopic configurations of a model) and the above mentioned thermodynamic quanti- ties which permit its numerical calculation, by computer simulation and using any ergodic dynamics. The results obtained (critical temperature and exponents) reproduced all the known values, with an agreement up to several significant figures; of particular relevance were the estimates along the Baxter critical line (Ashkin-Teller model) where the exponents have a continuous variation. We also showed that this approach is less sensitive to the finite-size effects than the standard Monte-Carlo method. This analysis shows that the present approach produces equal or more accurate results, as compared to the usual Monte Carlo simulation, and can be useful to investigate these models in circumstances for which their behavior is not yet fully understood

Propriedades ópticas de nanocristais de SiGe: efeitos de dopagem e desordem

We have used ab initio calculations to investigate the electronic structure of SiGe based nanocrystals (NC s). This work is divided in three parts. In the first one, we focus the excitonic properties of Si(core)/Ge(shell) and Ge(core)/Si(shell) nanocrystals. We also estimate the changes induced by the effect of strain the electronic structure. We show that Ge/Si (Si/Ge) NC s exhibits type II confinement in the conduction (valence) band. The estimated potential barriers for electrons and holes are 0.16 eV (0.34 eV) and 0.64 eV (0.62 eV) for Si/Ge (Ge/Si) NC s. In contradiction to the expected long recombination lifetimes in type II systems, we found that the recombination lifetime of Ge/Si NC s (τR = 13.39μs) is more than one order of magnitude faster than in Si/Ge NC s (τR = 191.84μs). In the second part, we investigate alloyed Si1−xGex NC s in which Ge atoms are randomly positioned. We show that the optical gaps and electron-hole binding energies decrease linearly with x, while the exciton exchange energy increases with x due to the increase of the spatial extent of the electron and hole wave functions. This also increases the electron-hole wave functions overlap, leading to recombination lifetimes that are very sensitive to the Ge content. Finally, we investigate the radiative transitions in Pand B-doped Si nanocrystals. Our NC sizes range between 1.4 and 1.8 nm of diameters. Using a three-levels model, we show that the radiative lifetimes and oscillator strengths of the transitions between the conduction and the impurity bands, as well as the transitions between the impurity and the valence bands are strongly affected by the impurity position. On the other hand, the direct conduction-to-valence band decay is practically unchanged due to the presence of the impurity

Ondas de spin em super-redes ferromagnéticas com campo de anisotropia

Conselho Nacional de Desenvolvimento Científico e Tecnológico

Ondas de spin em nanofilmes nagnéticos acoplados quasiperiodicamente

We studied the spin waves modes that can propagate in magnetic multilayers composed of ferromagnetic metallic films in the nanometer scale. The ferromagnetic films (iron) are separated and coupled through the nonmagnetic spacer films (chromium). The films that make up the multilayer are stacked in a quasiperiodic pattern, following the Fibonacci and double period sequences. We used a phenomenological theory taking into account: the Zeeman energy (between the ferromagnetic films and the external magnetic field), the energy of the magneto-crystalline anisotropy (present in the ferromagnetic films), the energy of the bilinear and biquadratic couplings (between the ferromagnetic films) and the energy of the dipole-dipole interaction (between the ferromagnetic films), to describe the system. The total magnetic energy of the system is numerically minimized and the equilibrium angles of the magnetization of each ferromagnetic film are determined. We solved the equation of motion of the multilayer to find the dispersion relation for the system and, as a consequence, the spin waves modes frequencies. Our theoretical results show that, in the case of trilayers (Fe/Cr/Fe), our model reproduces with excellent agreement experimental results of Brillouin light scattering, known from the literature, by adjusting the physical parameters of the nanofilms. Furthermore, we generalize the model to N ferromagnetic layers which allowed us to determine how complex these systems become when we increase the number of components. It is worth noting that our theoretical calculations generalize all the results known from the literature

O enigmático problema das gigantes ricas em Lítio e as perspectivas com o satélite Kepler

Lithium (Li) is a chemical element with atomic number 3 and it is among the lightest known elements in the universe. In general, the Lithium is found in the nature under the form of two stable isotopes, the 6Li and 7Li. This last one is the most dominant and responds for about 93% of the Li found in the Universe. Due to its fragileness this element is largely used in the astrophysics, especially in what refers to the understanding of the physical process that has occurred since the Big Bang going through the evolution of the galaxies and stars. In the primordial nucleosynthesis in the Big Bang moment (BBN), the theoretical calculation forecasts a Li production along with all the light elements such as Deuterium and Beryllium. To the Li the BNB theory reviews a primordial abundance of Log log ǫ(Li) =2.72 dex in a logarithmic scale related to the H. The abundance of Li found on the poor metal stars, or pop II stars type, is called as being the abundance of Li primordial and is the measure as being log ǫ(Li) =2.27 dex. In the ISM (Interstellar medium), that reflects the current value, the abundance of Lithium is log ǫ(Li) = 3.2 dex. This value has great importance for our comprehension on the chemical evolution of the galaxy. The process responsible for the increasing of the primordial value present in the Li is not clearly understood until nowadays. In fact there is a real contribution of Li from the giant stars of little mass and this contribution needs to be well streamed if we want to understand our galaxy. The main objection in this logical sequence is the appearing of some giant stars with little mass of G and K spectral types which atmosphere is highly enriched with Li. Such elevated values are exactly the opposite of what could happen with the typical abundance of giant low mass stars, where convective envelops pass through a mass deepening in which all the Li should be diluted and present abundances around log ǫ(Li) ∼1.4 dex following the model of stellar evolution. In the Literature three suggestions are found that try to reconcile the values of the abundance of Li theoretical and observed in these rich in Li giants, but any of them bring conclusive answers. In the present work, we propose a qualitative study of the evolutionary state of the rich in Li stars in the literature along with the recent discovery of the first star rich in Li observed by the Kepler Satellite. The main objective of this work is to promote a solid discussion about the evolutionary state based on the characteristic obtained from the seismic analysis of the object observed by Kepler. We used evolutionary traces and simulation done with the population synthesis code TRILEGAL intending to evaluate as precisely as possible the evolutionary state of the internal structure of these groups of stars. The results indicate a very short characteristic time when compared to the evolutionary scale related to the enrichment of these stars

Diagnóstico ambiental das águas do estuário Jundiaí-Potengi pela determinação dos índices de qualidade da água e toxidez

This study is an environmental diagnosis of the Jundiaí-Potengi/RN estuarine system waters, using calculations of pollution indicator indices such as the Water Quality Index (WQI) and the Toxicity Index (TI). The samples were collected at twelve points on the estuary, at high and low tide, between August and November 2007, over four campaigns. The study area, located in a high impact region, has various activities on its banks such as: discharge of untreated or undertreated domestic and industrial sewage, shrimp farming, immunizer stabilization lakes, riverside communities, etc. All the parameters analyzed were compared to the limits of CONAMA Resolution No. 357 of 2005 for healthy and saline Class 1 waters. The results found prove the impact caused by various activities, mainly the parameters related to the presence of organic material, such as DQO, DBO, COT and thermotolerant colliforms. The IQA for most of the collection points was of medium quality. For the metals, although values above the Resolution limits were found, most of them were lower than the detection limits of ICP-OES used, indicating that they tend to be transported by the dynamic of the tides or rainfall and are deposited in bottom sediments, resulting in a TI of 1.0 in this water, when they are absent, which occurs in most cases, or 0.0, when heavy metals are found in these waters

Síntese, caracterização e estudo cinético da degradação de quitosana impregnada em SBA-15

O recente interesse em se obter materiais nanoporosos funcionalizados para aplicações como calisadores heterogêneos e adsorção de CO2, tem aumentado no meio industrial e cientifico. Nesta última aplicação, a introdução de grupos aminas, como os presentes em quitosana, em materiais nanoporosos do tipo SBA-15 para gerar interações específicas com o CO2 tem ganhado importância. Assim, neste trabalho foram realizadas a síntese do SBA-15 e posterior impregnação da CS no suporte mesoporoso através do método de impregnação por via úmida. Os materiais obtidos foram caracterizados por meio DRX, TG, DSC, MEV, FTIR e adsorção/dessorção de N2. Os resultados de DRX indicaram que a estrutura ordenada do suporte SBA-15 foi preservada após a impregnação e os cálculos mostraram que o diâmetro médio do poro e/ou a espessura média da parede (wt) foram alterados devido a introdução da quitosana nas amostras funcionalizadas. As curvas de TG e de DSC,corroboraram com os dados de DRX, indicando a presença da quitosana na estrutura mesoporosa do SBA-15, assim como as micrografias das amostras funcionalizadas, que possibilitou visualizar o estado de agregação do material obtido. As bandas características de absorção da CS na região IV foram identificadas e interpretadas nas amostras funcionalizadas confirmando as outras caracterizações. Foi visto também que a área superficial diminuiu nas amostras funcionalizadas, indicando a sucessiva incorporação do polímero no suporte mesoporoso. A energia de ativação do processo de degradação térmica da quitosana impregnada no suporte foi determinada por meio do método de cinética livre de Viazovkin e pelo método de Ozawa-Flay-Wall com os resultados indicando que o aumento da quitosana diminui em aproximadamente 10% a energia de ativação para sua degradação.

Síntese, caracterização e estudo cinético da degradação de quitosana impregnada em SBA-15

The recent interest in obtaining functionalized nanoporous materials for applications such as heterogeneous catalysts and adsorption of CO2 has increased today. In the latter application, the introduction of amino groups such as present in the chitosan (CS), in the nanoporous materials like SBA-15 to generate specific interactions with CO2 has gained importance. In this work were performed to hydrothermal synthesis of SBA-15 and subsequent impregnation of the CS in the support mesoporous by the method of the wet impregnation. The materials were characterized by TG/DTG, DSC, XRD, SEM, FTIR and adsorption / desorption of N2. The XRD showed that the ordered structure of the support SBA-15 was preserved after the impregnation and calculations have shown that the average pore diameter (Dp) and / or the average wall thickness (wt) have been changed due to introduction of the CS in the samples functionalized. The curves of TG and DSC data corroborates the XRD, indicating the presence of CS in the nanoporous structure of SBA-15, as well as micrographs of samples, which allowed the display state of aggregation of the material obtained. The characteristics of bands absorption in the region of the CS in the FTIR were identified and interpreted in the samples functionalized, confirming the further characterization. Measurements showed that the BET surface area decreases in the functionalized samples, indicating the successive incorporation of the polymer in the nanoporous support. The activation energy apparent (Ea) for the process of thermal degradation of CS in the impregnated support was determined by the methods of kinetic freedom Vyazovkin and Ozawa-Flynn-Wall with the results indicating that the sample functionalized CS/SBA-15 2,5 % was decrease of the Ea in their degradation of about 10% compared to 1,0 % CS/SBA-15 sample

Estudo teórico aplicado ao petróleo: estabilidade dos alcenos e recuperação terciária

The present work aims to study the theoretical level of some processes employed in the refining of petroleum fractions and tertiary recovery of this fluid. In the third chapter, we investigate a method of hydrogenation of oil fractions by QTAIM (Quantum Theory of Atoms in Molecules) and thermodynamic parameters. The study of hydrogenation reactions, and the stability of the products formed, is directly related to product improvement in the petrochemical refining. In the fourth chapter, we study the theoretical level of intermolecular interactions that occur in the process of tertiary oil recovery, or competitive interactions involving molecules of non-ionic surfactants, oil and quartz rock where oil is accumulated. Calculations were developed using the semiempirical PM3 method (Parametric Model 3). We studied a set of ten non-ionic surfactants, natural and synthetic origin. The study of rock-surfactant interactions was performed on the surface of the quartz (001) completely hydroxylated. Results were obtained energetic and geometric orientations of various surfactants on quartz. QTAIM was obtained through the analysis of the electron density of interactions, and thus, providing details about the formation of hydrogen bonds and hydrogen-hydrogen systems studied. The results show that the adsorption of ethoxylated surfactants in the rock surface occurs through the hydrogen bonding of the type CH---O, and surfactants derivatives of polyols occurs by OH---O bonds. For structures adsorption studied, the large distance of the surfactant to the surface together with the low values of charge density, indicate that there is a very low interaction, characterizing physical adsorption in all surfactants studied. We demonstrated that surfactants with polar group comprising oxyethylene units, showed the lowest adsorption onto the surface of quartz, unlike the derivatives of polyols

Índice de aromaticidade baseado na deslocalização, degenerescência e densidade (D3BIA) para acenos e moléculas homoaromáticas

The aromaticity index is an important tool for the investigation of aromatic molecules. This work consists on new applications of the aromaticity index developed by teacher Caio Lima Firme, so-called D3BIA (density, delocalization, degeneracy-based index of aromaticity). It was investigated its correlation with other well-known aromaticity indexes, such as HOMA (harmonic oscillator model of aromaticity), NICS (nucleus independent chemical shielding), PDI (para-delocalization index), magnetic susceptibility (), and energetic factor in the study of aromaticity of acenes and homoaromatic species based on bisnoradamantanyl cage. The density functional theory (DFT) was used for optimization calculations and for obtaining energetic factors associated with aromaticity and indexes HOMA and NICS. From quantum theory of atoms in molecules (QTAIM) it was obtained the indexes D3BIA, PDI and . For acenes, when the over-mentioned indexes were applied it was observed no correlation except for D3BIA and HOMA (R2=0.752). For bisnoradamantenyl dication and its derivatives, it was obtained a good correlation between D3BIA and NICS. Moreover, it was evaluated solely one of the factors used on D3BIA calculation, the delocalization index uniformity (DIU), so as to investigate its possible influence on stability of chemical species. Then, the DIU was compared with the formation Gibbs free energy of some pairs of carbocations, isomers or not, which each pair had small difference in point group symmetry and no difference among other well-known stability factors. The obtained results indicate that DIU is a new stability factor related to carbocations, that is, the more uniform the electron density delocalization, the more stable the is carbocation. The results of this work validate D3BIA and show its importance on the concept of aromaticity, indicating that it can be understood from degeneracy of atoms belonging the aromatic site, the electronic density in the aromatic site and the degree of uniformity of electron delocalization

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]