Using the Cayley-Hamilton theorem with N-partitioned matrices

A definition is given for the characteristic equation of anN-partitioned matrix. It is then proved that this matrix satisfies its own characteristic equation. This can then be regarded as a version of the Cayley-Hamilton theorem, of use withN-dimensional systems.

On the Hamilton-Jacobi equation in the framework of generalized functions

In this work we study, in the framework of Colombeau`s generalized functions, the Hamilton-Jacobi equation with a given initial condition. We have obtained theorems on existence of solutions and in some cases uniqueness. Our technique is adapted from the classical method of characteristics with a wide use of generalized functions. We were led also to obtain some general results on invertibility and also on ordinary differential equations of such generalized functions. (C) 2011 Elsevier Inc. All rights reserved.

Avaliação ecotoxicológica de efluentes industriais utilizando Danio rerio Hamilton-Buchanan, 1822 (TELEOSTEI, CYPRINIDAE)

The industrial effluents are one of the main sources of water pollution. For an appropriate characterization and control of their discharges, the most efficient strategy is the integrated use of chemical, physical and ecotoxicological analyses. The aims of this study were to asses the efficiency of the treatment plant of a textile industry performing acute toxicity tests and physical-chemical analyses of the effluents before and after the treatment, besides evaluate the toxicity of the effluents of the Treatment System of Liquids Effluents (Sistema de Tratamento de Efluentes Líquidos - SITEL) of Distrito Industrial de Natal (DIN) and some of their physical-chemical variables. The species used in the ecotoxicological tests was the fish Danio rerio. The results showed that the treatment plant reduced significantly (around 50%) the toxicity of the raw textile effluent in only three of the seven tests but, in general, it promoted the reduction of the physical-chemical parameters analyzed. The toxicity and the physical-chemical factors of the effluents of SITEL of DIN varied among the tests and show the importance of monitoring their discharges in the Potengi river, one of the most important rivers of the Rio Grande do Norte state

Investigação e avaliação da toxicidade aguda dos agrotóxicos mais utilizados no cinturão verde da Grande Natal (RN, Brasil) para o peixe-zebra (Danio rerio Hamilton Buchanan, 1822, Teleostei, Cyprinidae

The objectives of this research were to investigate the agrotoxic most used in the Gramorezinho region in the green belt of Natal, and to evaluate the acute toxicity of these, based on the LC50-48h values estimated in tests for Danio rerio, internationally used as test organism. The acute toxicity tests were performed under laboratory conditions, according to standardized methods (ABNT/NBR/15088/04) for this species. The LC50-48h estimated to Tamaron BR was 352.89 mg.L-1, which characterizes that as practically non-toxic, according to toxicological classes cited by Zucker. For Decis 25EC, the LC50-48h estimated was 0.0004156 mg.L-1 (4.156 X 10-4 mg.L-1), which classifies it as highly toxic to this species

Influence of food restriction on the reproduction and larval performance of matrinxã, Brycon amazonicus (Spix and Agassiz, 1829)

Este estudo avaliou o efeito da restrição alimentar e realimentação na reprodução de fêmeas e no crescimento inicial e sobrevivência de larvas de matrinxã, Brycon amazonicus. Matrizes distribuídas em 8 viveiros (15 peixes/tanque) foram alimentadas diariamente (em 4 tanques - G1) e alimentados em ciclos de 3 dias de alimentação seguidos de 2 dias de restrição (em 4 tanques - G2) por 6 meses antes da desova. Na indução à desova, 57% das fêmeas no G1 e 45% no G2 desovaram. Os pesos médios dos oócitos foram 208,1 g (G1) e 131,6 g (G2), sendo os oócitos G2 menores (1,017 ± 0,003 mm) que os oócitos de G1 (1,048 ± 0,002 mm). As taxas de fertilização (71,9 ± 12,6% e 61,2 ± 13,7%) e de eclosão (61,3 ± 33,9% e 67,5 ± 23,4%) entre os G1 e G2 não diferiram. Larvas foram coletadas na eclosão e às 24, 48 e 72 horas de incubação para medida do crescimento e as restantes transferidas para aquários e amostradas 1, 5, 9 e 15 dias depois. Na transferência, as larvas G1 e G2 tinham pesos similares (1,5 ± 0,15 e 1,46 ± 0,07 mg), mas o comprimento das larvas G2 era maior (6,2 ± 0,13 e 6,7 ± 0,14 mm). Ao 9° dia, quando é recomendada a transferência dos juvenis para tanques externos, os juvenis G2 tinham peso (13,6 ± 0,26 e 18,9 ± 0,07 mg) e comprimento (11,8 ± 0,09 e 14,5 ± 0,04 mm) maiores, mas no 15º dia os juvenis G1 eram maiores em peso (90,2 ± 1,19 e 68,6 ± 0,77 mg) e comprimento (18,8 ± 0,16 e 18,5 ± 0,04 mm). Aos 15 dias, a prole das fêmeas submetidas à restrição alimentar apresentou sobrevivência mais alta que a prole das fêmeas alimentadas diariamente (24,7 ± 2,07% e 19,2 ± 1,91%). A restrição alimentar imposta às fêmeas de matrinxã, apesar de reduzir o número de fêmeas que desovaram e a quantidade de oócitos extrusados, não afetou a fertilização e eclosão das larvas e melhorou a sobrevivência final das larvas.