Efeitos dos esteroides anabólicos androgênicos sobre funções cognitivas de ratos

The use and the demand for substances that enhance masculinity, strength and sexual power are not novel. Over the years, this search has assisted the research directions in this area, leading to the discovery of the primary male sex hormone testosterone in 1935. Since then, numerous testosterone analogue compounds were synthesized, which are generically called Anabolic Androgenic Steroids (AAS). The AAS were produced for therapeutic purposes, but an increase in the use of these compounds for other purposes occurred over time. Initially they were used mainly to improve performance in athletes. However, recent studies have shown that the use of AAS by non-athletes with aesthetical purposes have been increasing as well. The abuse of AAS with non-clinical purposes can promote a number of physiological alterations, such as heart, liver, respiratory and psychological problems such as changes in mood, levels of anxiety and aggression. Exposure to supraphysiological doses of AAS is associated with behavioral changes, however, little is known about the effects of AAS on cognitive functions. In this work, we aimed to mimic the AAS abuse in humans with intramuscular administration of a supraphysiological dose of testosterone propionate (TP) in rats. We investigated the effects of this treatment on different aspects of cognitive function, specifically learning, memory and anxiety. Adult male Wistar rats were tested in the spontaneous alternation, novel object recognition and plus-maze discriminative avoidance tasks. The control group received intramuscular injections of vegetable oil (vehicle), and the TP group received injections of TP (10 mg/kg, i.m.). The injections were administered for 40 days, with intervals of 48 hours (chronic treatment) or in a single injection (acute treatment). In addition to the behavioral assessments, we performed biochemical analyzes as indicators of the endocrine effects of the treatment. Our results show that chronic treatment with a supraphysiological dose of TP caused memory impairments in the novel object recognition and the discriminative avoidance tasks. The spatial working memory (evaluated by spontaneous alternation task) was not affected. Also, we did not observe changes in anxiety levels. Regarding the biochemical parameters, chronic treatment increased serum levels of glutamicpyruvic transaminase, an indicator of hepatic and pancreatic lesions (as those observed after chronic use of these substances in humans). On the other hand, acute treatment with PT did not promote significant changes in any of these parameters when compared to the control group. In summary, we conclude that chronic treatment with a supraphysiological dose of testosterone propionate produces memory deficits in novel object recognition and retrieval of the discriminative avoidance task in adult male rats

Efeitos da alteração dos níveis de ansiedade no desempenho de ratos em uma tarefa de discriminação apetitiva

The plus-maze discriminative avoidance paradigm has been used to study the relationship between aversive memory and anxiety. The present study aims to verify if the elevated plus-maze can provide information about appetitive memory and anxiety, through a task motivated by food reward. Animals were allowed to explore an elevated plus-maze and received reinforcement in one of the enclosed arms. In a test session performed 24h later, in the absence of reward, rats showed preference for the previously rewarded enclosed arm over the neutral enclosed arm. The administration of diazepam and pentylenetetrazole before training induced, respectively, anxiolytic and anxiogenic effects (as evaluated by open-arm exploration). Both drugs induced amnestic effects, i.e., lack of preference for the rewarded arm in the test session. The results suggest that appetitive memory can be influenced by anxiety levels as well. The plus-maze appetitive discrimination task seems to be a useful model to investigate the relationship between memory and anxiety

Expressão de zif-268 durante a aquisição, evocação e extinção de uma memória aversiva

In the behavioral paradigm of discriminative avoidance task, both short and long-term memories have been extensively investigated with behavioral and pharmacological approaches. The aim of the present study was to evaluate, using the abovementioned model, the hippocampal expression of zif-268 - a calcium-dependent immediate early gene involved with synaptic plasticity process - throughout several steps of memory formation, such as acquisition, evocation and extiction. The behavioral apparatus consisted of a modified elevaated plus-maze, with their enclosed arms disposed in "L". A pre-exposure to the maze was made with the animal using all arms enclosed, for 30 minutes, followed by training and test, during 10 minutes each. The between sections interval was 24h. During training, aversive stimuli (bright light and loud noise) were actived whenever the animals entered one of the enclosed armas (aversive arm). Memory acquisiton, retention and extinction were evaluated by the percentage of the total time spent exploring the aversive arm. The parameters evaluated (time spent in the arms and total distance traveled) were estimated with an animal tracking software (Anymaze, Stoelting, USA). Learning during training was estimated by the decrease of the time spent exploring the aversive arm. One hour after the beginning of each section, animals were anaesthetized with sodium-thiopental (i.p.) and perfused with 0.9% heparinized saline solution followed by 4% paraformaldehyde. Brains were cryoprotected with 20% sucrose, separeted in three blocks and frozen. The middle block, containing the hippocampus, was sectioned at 20 micro meters in the coronal plane and the resutant sections were submitted to zif-268 immunohistochemistry. Our results show an increased expression of zif-268 in the dentate gyrus (DG) during the evocation and extinction stages. There is a distinct participation of the DG during the memory evocation, but not during its acquisition. Inaddition, all hippocampal regions (CA1, CA3 and DG) presented an increased zif-268 expression during the process of extinction.

Neurofisiologia hipocampal durante sessões de sono intercaladas por exploração espacial: Reverberação do passado ou predição do futuro?

The ability to predict future rewards or threats is crucial for survival. Recent studies have addressed future event prediction by the hippocampus. Hippocampal neurons exhibit robust selectivity for spatial location. Thus, the activity of hippocampal neurons represents a cognitive map of space during navigation as well as during planning and recall. Spatial selectivity allows the hippocampus to be involved in the formation of spatial and episodic memories, including the sequential ordering of events. On the other hand, the discovery of reverberatory activity in multiple forebrain areas during slow wave and REM sleep underscored the role of sleep on the consolidation of recently acquired memory traces. To this date, there are no studies addressing whether neuronal activity in the hippocampus during sleep can predict regular environmental shifts. The aim of the present study was to investigate the activity of neuronal populations in the hippocampus during sleep sessions intercalated by spatial exploration periods, in which the location of reward changed in a predictable way. To this end, we performed the chronic implantation of 32-channel multielectrode arrays in the CA1 regions of the hippocampus in three male rats of the Wistar strain. In order to activate different neuronal subgroups at each cycle of the task, we exposed the animals to four spatial exploration sessions in a 4-arm elevated maze in which reward was delivered in a single arm per session. Reward location changed regularly at every session in a clockwise manner, traversing all the arms at the end of the daily recordings. Animals were recorded from 2-12 consecutive days. During spatial exploration of the 4-arm elevated maze, 67,5% of the recorded neurons showed firing rate differences across the maze arms. Furthermore, an average of 42% of the neurons showed increased correlation (R>0.3) between neuronal pairs in each arm. This allowed us to sort representative neuronal subgroups for each maze arm, and to analyze the activity of these subgroups across sleep sessions. We found that neuronal subgroups sorted by firing rate differences during spatial exploration sustained these differences across sleep sessions. This was not the case with neuronal subgroups sorted according to synchrony (correlation). In addition, the correlation levels between sleep sessions and waking patterns sampled in each arm were larger for the entire population of neurons than for the rate or synchrony subgroups. Neuronal activity during sleep of the entire neuronal population or subgroups did not show different correlations among the four arm mazes. On the other hand, we verified that neuronal activity during pre-exploration sleep sessions was significantly more similar to the activity patterns of the target arm than neuronal activity during pre-exploration sleep sessions. In other words, neuronal activity during sleep that precedes the task reflects more strongly the location of reward than neuronal activity during sleep that follows the task. Our results suggest that neuronal activity during sleep can predict regular environmental changes

Antidepressivos modificam a extinção de uma memória aversiva em ratas

Treatment of major depression, posttraumatic stress disorder and other psychopathologies with antidepressants can be associated with improvement of the cognitive deficits related to these disorders. Although the mechanisms of these effects are not completely elucidated, alterations in extinction of aversive memories are believed to be present in these psychopathologies. Moreover, researches with laboratory animals usually focus on male subjects, and we have recently verified that extinction of an aversive task is reduced in female rats when compared to males. In the present study, female rats were long-term treated with clinically used antidepressants (fluoxetine, nortriptyline or mirtazapine) and tested in the plus-maze discriminative avoidance and forced swimming tests in order to evaluate learning, memory, extinction, anxiety and depression-related behaviors. All groups learned the task, but learning was somewhat faster in nortriptyline and mirtazapine-treated animals . Task retrieval was also showed by all experimental groups. Chronic treatment with fluoxetine, but not with the other antidepressants, increased extinction of the discriminative task. In the forced swimming test, animals treated with fluoxetine and mirtazapine showed decreased immobility duration. In conclusion, antidepressants interfere with learning and female rats treated with fluoxetine presented increased extinction of the aversive memory task. On the other hand, both fluoxetine and mirtazapine were effective in the forced swimming test, suggesting dissociation between the antidepressant effects and the extinction of aversive memories

Influência do ciclo estral no efeito do diazepam na ansiedade e memória de ratas

Memory and anxiety are related phenomena. Several evidences suggest that anxiety is fundamental for learnining and may facilitate or impair the memory formation process depending of the context. The majority of animal studies of anxiety and fear use only males as experimental subjects, while studies with females are rare in the literature. However, the prevalence in phobic and anxiety disorders is greater in women than in men. Moreover, it is known that gender maybe influence benzodiazepine effects, the classic drugs used for anxiety disorders treatment. In this respect, to further investigate if fear/anxiety aspects related to learning in female subjects would contribute to the study of phobic and anxiety disorders and their relationship with learning/memory processes, the present work investigates (a) the effects of benzodiazepine diazepam on female rats performance in a aversive memory task that assess concomitantly anxiety/emotionality, as the interaction between both; (b) the influence of estrous cycle phases of female rats on diazepam effects at aversive memory and anxiety/emotionality, and the interaction between both and (c) the role of hormonal fluctuations during estrous cycle phases in absence of diazepam effects in proestrus, because female rats in this phase received or not mifepristone, the antagonist of progesterone receptor, previously to the diazepam treatment. For this purpose, the plus maze discriminative avoidance task, previously validated for studies of anxiety concomitantly to learning/memory, was used. The apparatus employed is an adaptation of a conventional plus maze, with two opens arms and two closed arms, one of which presenting aversive stimulation (noise and light). The parameters used were: time in non-aversive arm compared to time in aversive and percentage of time in aversive arm on several temporal divisions, in order to evaluate memory; percentage of time in open arms, risk assessment, head dipping and end exploring to evaluate anxiety ; and distance traveled for locomotion. In experiment I, we found anxiolytic effect of diazepam only for 4 mg/kg dose, however the amnestic effect appear at a dose of 2 mg/kg. In second experiment, rats were divided in groups according estrous cycle phase (metaestrus/diestrus, proestrus e estrus). In this experiment, when we considered estrous cycle phase or diazepam treatment, the results did not demonstrate any differences in anxiety/emotionality parameters. The amnestic effects of diazepam occur in female rats in metestrus/diestrus and estrus and is absent in proestrous rats. Proestrous female rats that received mifepristone exhibited the amnestic effect of diazepam and also anxiolytic effects, that it was not previously observed in this dose. The results have demonstrated dissociation of anxiolytic and amnestic diazepam effects, not previously observed in males; the absence of amnestic effect of diazepam in proestrous phase; and the possible role of progesterone in aversive memory over diazepam effect, because the mifepristone, associated with diazepam, caused amnestic effect in proestrus

Avaliação dos efeitos do biperideno, diazepam e neuropeptídeos S sobre a memória e a ansiedade na tarefa do labirinto em T elevado em camundongos

Anxiety is an emotional phenomenon, and normally it is interpreted as an adaptative behavior front to adversities. In its pathological form, anxiety can severely affect aspects related to the personal and professional life. Studies have shown a close relationship between anxiety disorders and aversive memory processing. Considering that the pharmacotherapy of anxiety disorders is still limited, innovative anxiolytic agents are needed. In this regard, neuropeptides systems are interesting therapeutic targets to the treatment of psychopathologies. Neuropeptide S (NPS), a 20-aminoacid peptide, is the endogenous ligand of a G-protein coupled receptor (NPSR), which has been reported to evoke hyperlocomotion, awakefull states, besides anxiolysis and memory improvements in rodents. This study aimed to investigate the effects of biperiden (BPR; an amnesic drug), diazepam (DZP; an anxiolytic drug) and NPS at three distinct times: pre-training, post-training, and pre-test, in order to assess anxiety and memory process in the same animal model. The elevated Tmaze (ETM) is an apparatus derived from the elevated plus-maze test, which consists of one enclosed and two open arms. The procedure is based on the avoidance of open spaces learned during training session, in which mice were exposed to the enclosed arm as many times as needed to stay 300 s. In the test session, memory is assessed by re-exposing the mouse to the enclosed arm and the latency to enter an open arm was recorded. When injected pre-training, BPR (1 mg/kg) impaired learning and memory processing; DZP (1 and 2 mg/kg) evoked anxiolysis, but only at the dose of 2 mg/kg impaired memory; and NPS 0.1 nmol induced anxiolysis without affecting memory. Post-training injection of DZP (2 mg/kg) or BPR (1 and 3 mg/kg) did not affect memory consolidation, while the post-trainning administration of NPS 1 nmol, but not 0.1 nmol, improved memory in mice. Indeed, pre-trainning administration of NPS 1 nmol did not prevent memory impairment elicited by BPR (2 mg/kg, injected before training). In the open field test, BPR 1 mg/kg and NPS 1 nmol induced hyperlocomotion in mice. In conclusion, the proposed ETM task is practical for the detection of the anxiolytic and amnesic effects of drugs. The anxiolytic and memory enhancement effects of NPS were detected in the ETM task, and reinforce the role of NPS system as an interesting therapeutic target to the treatment of anxiety disorders

Alterações na evocação de uma memória aversiva ao liongo do ciclo estral de ratas: influências da transmissão gabaérgica na amígdala

GABAergic neurotransmission has been implicated in many aspects of learning and memory, as well as mood and anxiety disorders. The amygdala has been one of the major focuses in this area, given its essential role in modulating emotionally relevant memories. However, studies with male subjects are still predominant in the field. Here we investigated the consequences for an aversive memory of enhancing or decreasing GABAergic transmission in the basolateral nucleus of the amygdala (BLA). Wistar female rats were trained in the plus-maze discriminative avoidance task, in which they had to learn to avoid one of the enclosed arms where an aversive stimulus consisting of a bright light and a loud noise was given (day 1). Fifteen minutes before the test session (day 2) animals received 0,2 μL infusions of either saline solution, the GABAergic agonist muscimol (0,05 mg/ml), or the GABAergic antagonist bicuculine (0,025 mg/ml) bilaterally intra-BLA. On the test day, females in proestrous or estrous presented adequate retrieval and did not extinguish the task, while females in metestrous or diestrous presented impaired retrieval. In the first group, muscimol infusion impaired retrieval and bicuculline had no effect, suggesting naturally low levels of GABAergic transmission in the BLA of proestrous and estrous females. In the second group, muscimol infusion had no effect and bicuculline reversed retrieval impairment, suggesting naturally high levels of GABAergic transmission in the BLA of metestrous and diestous females. Additionally, proestrous and estrous females presented higher anxiety levels compared to metestrous and diestrous females, which could explain better performance of this group. On the other hand, BLA GABAergic system did not interfere with the innate fear response because drug infusions had no effect in anxiety. Thus, retrieval alterations caused by the GABAergic drugs were probably related specifically to memory processes

Álcool e comportamento: efeitos na aprendizagem e memória

Excessive alcohol consumption is responsible for many harmful effects on individuals and society. Despite years of research, the mechanisms by which alcohol affects neurological functions and the exact causes of cognitive impairment related to long-term use are unknown. In this sense, this master study proposed to observe how different doses of alcohol affect the addiction response and the learning ability of two fish species: Betta splendens and Danio rerio, the latter a commonly model due to organizational and functional characteristics shared with mammals. For this, different concentrations of ethanol (0%, 0.1%, 0.25%, 1% and 1.5%) were used in acute, chronic and withdrawal treatments. We tested the fish in three experimental protocols: 1) alcohol addiction potential using conditioned place preference, 2) associative conditioning using light as unconditioned stimulus and food as conditioned stimulus and 3) spatial learning using a maze without cues. For the alcohol addiction potential, preference between two different places in a shuttle box was tested before and after alcohol exposure (chronic and acute). In this test, the animals intoxicated by 0.1% did not change behavior, while animals receiving 1% and 1.5% alcohol changed the initial preference to the side where they received alcohol For the associative conditioning, the results show that the groups undergoing low dose (0.1%), both in chronic and withdrawal treatment, learned the task faster than control; groups under 0.25 and 1% alcohol withdrawal learned the task after control; groups chronically intoxicated with these doses did not learn the task. For the spatial learning test, fish submitted to acute and chronic treatments decreased the time to exit the maze; there were significant differences in the animal s performance in a dose-dependent pattern. This difference was not observed for the withdrawal treatment. Given these results, we conclude that the effects of alcohol on learning are dependent on the dosage. Furthermore, low doses of alcohol seem to maximize animal performance on learning tasks and do not alter their seeking behavior, while higher doses induced addition and hinder learning

Influência da idade, do sexo e da hora do dia no desempenho em teste de labirinto

The increase of elderly population in the world and in Brazil has indicated the necessity of health systems capable to evaluate, to diagnose and to intervene in the conditions of health and disease of that segment. During that stage of human development, physical and cognitive changes happen and they are capable to influence the functional acting. It s important to distinguish the limit between the normal and the pathological. Besides the common changes during the aging, biological rhithmicity changes happen, as alterations in the cycle vigil-sleep that can influence in certain tasks performance. This study aimed to verify the influence of the age, of the sex and of the hour in a maze test performance. Eighty individuals were evaluated, 40 youths (20 men and 20 women) and 40 senior (20 men and 20 women). They were separated in 2 different groups that were tested at 9:00 o clock and at 15:00 o clock. Initially they were submitted to health evaluation, cognitive evaluation and of sleep quality and chronotype. They were instructed to accomplish the maze test whose time of execution was timed and registered. Significant differences were observed according to age for the masculine group between elderly in the morning and in the afternoon and in the feminine group between youth and elderly in the test accomplished in the morning and in the afternoon. Significant differences were not observed according to sex and hour of the day and also between attempts. In compare between the 30th and the31st, accomplished in a 15minutes of interval, significant difference was observed just for the elderly group in the morning and in the afternoon. We observed significant correlations in the maze test performance with the cronotype, with the age, with the education and with the cognitive acting. The maze test was capable to detect differences between age in the acting profile and in the evaluation of the information maintenance after 15 minutes, however it was not possible to verify difference between sex and hour of the day. Finally the correlations of the maze test with another varied may indicate your importance as coadjutant instrument in those functions evaluation

O Tratamento com a fluoxetina (mas não com outros farmacos antidepressivo e ansioíiticos) reverte o déficit de memória aversiva causado por estresse agudo de contenção em camundongos

The physiologist H. Selye defined stress as the nonspecific response of the body to any factors that endanger homeostasis (balance of internal environment) of the individual. These factors, agents stressors, are able to activate the Hypothalamic-Pituitary-Adrenal (HPA) axis, thus resulting in the physiological responses to stress by the release of glucocorticoids that leads to psychophysiological changes, including effects on cognitive functions such as learning and memory. When this axis is acutely stimulated occurs a repertoire of behavioral and physiological changes can be adaptive to the individual. Notwithstanding, when the HPA axis is chronically stimulated, changes may favor the development of, such as anxiety disorders. Some drugs used in the clinic for the treatment of anxiety disorders these can exert effects on cognitive function, on the HPA axis and on the anxiety. In this context, the aim of our study was to investigate the effects of administration i.p. acute of diazepam (DZP, 2 mg/kg), buspirone (BUS, 3 mg/kg), mirtazapine (MIR, 10 mg/kg) and fluoxetine (FLU, 10 mg/kg) in male mice submitted to acute restraint stress, and evaluated using plus-maze discriminative avoidance task (PMDAT), which simultaneously evaluates parameters such as learning, memory and anxiety. Our results demonstrated that (1) the administration of DZP and BUS, but not FLU, promoted anxiolytic effects in animals; (2) administration mirtazapine caused sedative effect to animals; (3) in the training session, the animals treated with BUS, MIR and FLU learned the task, on the other hand DZP group showed impairment in learning; (4) in the test session, animals treated with DZP, BUS, and MIR showed deficits in relation to discrimination between the enclosed arms, aversive versus non-aversive arm, demonstrating an impairment in memory, however, animals treated with FLU showed no interference in the retrieval of this memory; (5) acute stress did not interfere in locomotor activity, anxiety, or learning on the learning task, but induced impairment in retrieval memory, and the group treated with FLU did not demonstrated this deficit of memory . These results suggest that acute administration of drugs with anxiolytic and antidepressant activity does not interfere with the learning process this aversive task, but impair its retrieval, as well as the acute restraint stress. However, the antidepressant fluoxetine was able to reverse memory deficits promoted by acute stress, which may suggest that modulation, even acutely serotonergic neurotransmission, by selectively inhibiting the reuptake of this neurotransmitter, interferes on the process of retrieval of an aversive memory

Efeitos do tratamento com lítio na memória aversiva, comportamentos relacionados à ansiedade e depressão e na expressão de BDNF em ratos

Lithium (Li) is the first choice to treat bipolar disorder, a psychiatric illness characterized by mood oscillations between mania and depression. However, studies have demonstrated that this drug might influence mnemonic process due to its neuroprotector, antiapoptotic and neurogenic effects. The use of Li in the treatment of cognitive deficits caused by brain injury or neurodegenerative disorders have been widely studied, and this drug shows to be effective in preventing or even alleviating the memory impairment. The effects of Li on anxiety and depression are controversial and the relationship of the effects of lithium on memory, anxiety and depression remain unknown. In this context, this study aims to: evaluate the effects of acute and chronic administration of lithium carbonate in aversive memory and anxiety, simultaneously, using the plus maze discriminative avoidance task (PMDAT); test the antidepressant effect of the drug through the forced swimming test (FS) and analyze brainderived neurotrophic factor (BDNF) expression in structures related to memory and emotion. To evaluation of the acute effects, male Wistar rats were submitted to i.p. administration of lithium carbonate (50, 100 or 200 mg/kg) one hour before the training session (PMDAT) or lithium carbonate (50 or 100 mg/kg) one hour before the test session (FS). To evaluation of the chronic effects, the doses administered were 50 or 100 mg/kg or vehicle once a day for 21 days before the beginning of behavioral tasks (PMDAT and FS). Afterwards, the animals were euthanized and their brains removed and submitted to immunohistochemistry procedure to quantify BDNF. The animals that received acute treatment with 100 and 200 mg/kg of Li did not discriminated between the enclosed arms (aversive and non-aversive) in the training session of PMDAT, showing that these animal did not learned the task. This lack of discrimination was also observed in the test session, showing that the animals did not recall the aversive task. We also observed an increased exploration of the open arms of these same groups, indicating an anxiolytic effect. The same groups showed a reduction of locomotor activity, however, this effect does not seem to be related with the anxiolytic effect of the drug. Chronic treatment with Li did not promote alterations on learning or memory processes. Nevertheless, we observed a reduction of open arms exploration by animals treated with 50 mg/kg when compared to the other groups, showing an anxiogenic effect caused by this dose. This effect it is not related to locomotor alterations since there were no alterations in these parameters. Both acute and chronic treatment were ineffective in the FS. Chronic treatment with lithium was not able to modify BDNF expression in hippocampus, amygdala and pre-frontal cortex. These results suggest that acute administration of lithium promote impairments on learning in an aversive task, blocking the occurrence of memory consolidation and retrieval. The reduction of anxiety following acute treatment may have prevented the learning of the aversive task, as it has been found that optimum levels of anxiety are necessary for the occurrence of learning with emotional context. With continued, treatment the animals recover the ability to learn and recall the task. Indeed, they do not show differences in relation to control group, and the lack of alterations on BDNF expression corroborates this result. Possibly, the regimen of treatment used was not able to promote cognitive improvement. Li showed acute anxiolytic effect, however chronic administration 4 promoted the opposite effect. More studies are necessary to clarify the potential beneficial effect of Li on aversive memory

Especificação do tipo intervalar parametrizado em CASL

The interval datatype applications in several areas is important to construct a interval type reusable, i.e., a interval constructor can be applied to any datatype and get intervals this datatype. Since the interval is, of certain form, a set of elements limited for two bounds, left and right, with a order notions, then it s reasonable that interval constructor enclose datatypes with partial order. On the order hand, what we want is work with interval of any datatype like this we work with this datatype then. it s important to guarantee the properties of the datatype when maps to interval of this datatype. Thus, the interval constructor get a theory to parametrized interval type, i.e., a interval with generics parameters (for example rational, real, complex). Sometimes, the interval application in some algebras doesn t guarantee the mainutenance of their properties, for example, when we use interval of real, that satisfies the field properties, it doesn t guarantee the distributivity propertie. A form to surpass this problem Santiago introduced the local equality theory that weakened the notion of strong equality, and thus, allowing some properties are local keeped, what can be discard before. The interval arithmetic generalization aim to apply the interval constructor on ordered algebras weakened for local equality with the purpose of the keep their properties. How the intervals are important in applications with continuous data, it s interesting specify that theory using a specification language that supply a system development using intervals of form disciplined, trustworth and safe. Currently, the algebraic specification language, based in math models, have been use to that intention often. We choose CASL (Common Algebraic Specification Language) among others languages because CASL has several characteristics excellent to parametrized interval type, such as, provide parcialiy and parametrization

Os jogos com regras na educação matemática inclusiva

This present study aimed to examine the use of games with rules in working with math education in regular classes included in Elementary School, in the municipal education schools of Natal/RN, observing the learning process and development of all students, especially those with disabilities. The theoretical references used are based on Vygotsky's works and other authors from the historical-cultural perspective, as well as researchers in the field of Inclusive Education and Mathematics Education. The investigation was based on the qualitative research guidelines, with the application of semi-structured interviews with educational coordinators and teachers from the schools involved as well as classroom observations, looking for, in the speeches of those involved and in their teaching practices, elements to reflect on the Mathematics Inclusive Education, the use of games with rules -starting from its goals, the participation of disabled students, the pedagogical mediations, up to its accessibility - and from the learning of disabled students. The analysis results showed that the concepts underlying the development of inclusive teaching practices still refer to the clinical-medical paradigm, understanding the student with disabilities from their deficiencies; which teachers use, in their majority, the mathematical games with rules in their classes, but which the teaching mediation, during these activities, still needs to be qualified so that they can, effectively, contribute to the learning and development of all students; students with disabilities do not always participate in games with others colleagues; games with rules are rarely accessible; and that the Universal Design principles are not adopted in the selected classrooms for this study. Thus, it is clear that much remains to be done so that Mathematics Education can contribute to the learning and development of all students, and among those actions the teacher continuing education is recommended

Termodinâmica de um gás de fótons no contexto de eletrodinâmicas não-lineares

The objective of this dissertation is the development of a general formalism to analyze the thermodynamical properties of a photon gas under the context of nonlinear electrodynamics (NLED). To this end it is obtained, through the systematic analysis of Maxwell s electromagnetism (EM) properties, the general dependence of the Lagrangian that describes this kind of theories. From this Lagrangian and in the background of classical field theory, we derive the general dispersion relation that photons must obey in terms of a background field and the NLED properties. It is important to note that, in order to achieve this result, an aproximation has been made in order to allow the separation of the total electromagnetic field into a strong background electromagnetic field and a perturbation. Once the dispersion relation is in hand, the usual Bose-Einstein statistical procedure is followed through which the thermodynamical properties, energy density and pressure relations are obtained. An important result of this work is the fact that equation of state remains identical to the one obtained under EM. Then, two examples are made where the thermodynamic properties are explicitly derived in the context of two NLED, Born-Infelds and a quadratic approximation. The choice of the first one is due to the vast appearance in literature and, the second one, because it is a first order approximation of a large class of NLED. Ultimately, both are chosen because of their simplicity. Finally, the results are compared to EM and interpreted, suggesting possible tests to verify the internal consistency of NLED and motivating further developement into the formalism s quantum case