A difícil aceitação dos números negativos: um estudo da teoria dos números de Peter Barlow (1776-1862)

The present study seeks to present a historico-epistemological analysis of the development of the mathematical concept of negative number. In order to do so, we analyzed the different forms and conditions of the construction of mathematical knowledge in different mathematical communities and, thus, identified the characteristics in the establishment of this concept. By understanding the historically constructed barriers, especially, the ones having ontologicas significant, that made the concept of negative number incompatible with that of natural number, thereby hindering the development of the concept of negative, we were able to sketch the reasons for the rejection of negative numbers by the English author Peter Barlow (1776 -1862) in his An Elementary Investigation of the Theory of Numbers, published in 1811. We also show the continuity of his difficulties with the treatment of negative numbers in the middle of the nineteenth century

Fundamentos da filosofia moral de Peter Singer

This research aims to reconstruct and explain the argument proposed by Peter Singer to justify the principle of equal consideration of interests (PECI). The PECI is the basic normative principle according to people should consider the interests of all sentient beings affected when somebody taking a moral decision. It is the join that Singer proposes between universalizability and the principle of equal consideration of interests that constitutes a compelling reason to justify it. The universalizability requires to disregard the numerical differences, putting yourself in other people s shoes, and to consider preferences, interests, desires and ideals of those affected. Singer joins universalizability to normative principle and molds the form and content of his theory. The first chapter introduces the discussion will be developed in this essay. The second chapter deals the historical and philosophical viewpoint from which Singer starts his studies. The third chapter is about the Singer s critiques of naturalism, intuitionism, relativism, simple subjectivism and emotivism. The fourth chapter exposes the design of universal prescriptivism proposed by R. M. Hare. The universal prescriptivism indicates, in the Singer s viewpoint, a consistent way to create the join between the universalizability and PECI. It highlights also the criticism designed by J. L. Mackie and Singer himself to universal prescriptivism. The second part of this chapter shows briefly some of the main points of the classical conception of utilitarianism and its possible relationship with the theory of Singer. The fifth chapter introduces the Singer s thesis about the origin of ethics and the universalizability as a feature necessary to the point of view of ethic, and the way which this argument is developed to form the PECI. The sixth chapter exposes the main distinctions that characterize the PECI. Finally the seventh chapter provides a discussion about the reasons highlighted by Singer for one who wants orient his life according to the standpoint of ethics. This structure allows explaining the main ideas of the author concerning the theoretical foundations of his moral philosophy

Comportamento do camarão de água doce macrobrachium rosenbergii (De Man, 1879) em cultivos misto e monossexo

Understanding the behavioral activities of freshwater shrimp in captivity is of paramount importance for the appropriate management of the species. In Brazil, the shrimp Macrobrachium rosenbergii is currently the most widely used species in the freshwater shrimp culture due to its high potential for cultivation and good market acceptance. Thus, the present study aimed to describe and characterize the behavioral activities of M. rosenbergii in monosex and in mixed (male and female) (manuscript 1, 2 and 3) populations and the growth performance of this species in restrictive feeding conditions and in different feeding management (manuscript 4 and 5, respectively) . Juvenile and adult shrimps were collected from ponds of the Aquaculture Station - Unidade Especializada em Ciências Agrárias - Universidade Federal do Rio Grande do Norte (UFRN), Macaíba/RN and then transferred to the Laboratório de Estudos do Comportamento do Camarão LECC (Laboratory for Shrimp Behavioral Studies) of the Universidade Federal do Rio Grande do Norte (UFRN). For each treatment , eight aquaria of 250 L (50 cm x 50 cm x 100 cm) were used in a closed recirculating water system with artificial lighting, constant aeration , continuous filtration through a biochemical and biological filter (canister filter), and fine sand as substrate . The water quality was monitored daily. The lab consisted of two rooms with artificial lighting system , controlled by a timer with dark / light cycle of 12:12 h . In manuscript 1, the behavioral categories of the species were presented through an ethogram, which described 31 behaviors, subdivided into general and agonistic behaviors. Manuscript 2 compared the behavioral profile of shrimps in male and in female monosex and mixed populations over 24 hours in laboratory. In three types (mixed, male monosex and female monosex) of populations during the light and dark phases of the 24 hour cycle, the shrimps showed higher occurrence of cleaning behavior. Manuscript 3 examined the influence of the color of the shelter on the frequency of its use and behavioral activities of shrimp in mixed, in male monosex and in female monosex populations over 24 hours. We observed that the shrimp M. rosenbergii burrow more frequently during the light phase in male monosex and mixed populations; they also tend to choose the black shelters. Female monosex populations tend to use red and orange shelters. In manuscript 4, we evaluated in laboratory the behavioral activities and growth performance of juvenile shrimps under food restriction. We observed that a mild food restriction may be used since there is no loss concerning the growth of the animals; feeding management on alternate days , compared to daily management can be financially productive both reducing labor costs and reducing the amount of feed used . Manuscript 5 evaluated the behavior of shrimps in monosex and in mixed populations, as well as the latency of reach the food according to feed offer (tray or food dispersal) . Our results indicate that animals adjust to both types of feed offer food dispersal as much as tray, but they spend more time to reach the feed when it is offered in trays (feeders). Comparing culture types (mixed, male monosex and female monosex), the latency to reach the food was lower for female monosex population. The data obtained in this study demonstrate the importance of identifying different pressures and environmental stimuli on the behavioral responses of this species. This knowledge would support management improvement to optimize the levels of animals‟ welfare, resulting in a better zootecnical performance