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

The Teleparallel Lagrangian and Hamilton-Jacobi formalism

We analyze the Teleparallel Equivalent of General Relativity (TEGR) from the point of view of Hamilton-Jacobi approach for singular systems.

The Hamilton-Jacobi approach to Teleparallelism

We intend to analyse the constraint structure of Teleparallelism employing the Hamilton-Jacobi formalism for singular systems. This study is conducted without using an ADM 3+1 decomposition and without fixing time gauge condition. It can be verified that the field equations constitute an integrable system.

Generalization of the Hamilton-Jacobi approach for higher-order singular systems

We generalize the Hamilton-Jacobi formulation for higher-order singular systems and obtain the equations of motion as total differential equations. To do this we first study the constraints structure present in such systems.

Hamilton-Jacobi approach to Berezinian singular systems

In this work we present a formal generalization of the Hamilton-Jacobi formalism, recently developed For singular systems, to include the case of Lagrangians containing variables which are elements of Berezin algebra. We derive the Hamilton-Jacobi equation for such systems, analyzing the singular case in order to obtain the equations of motion as total differential equations and study the integrability conditions for such equations. An example is solved using both Hamilton-Jacobi and Dirac's Hamiltonian formalisms and the results are compared. (C) 1998 Academic Press.

Hamilton-Jacobi formalism for linearized gravity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Non-involutive constrained systems and Hamilton-Jacobi formalism

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Hamilton-Jacobi approach for first order actions and theories with higher derivatives

In this work, we analyze systems described by Lagrangians with higher order derivatives in the context of the Hamilton-Jacobi formalism for first order actions. Two different approaches are studied here: the first one is analogous to the description of theories with higher derivatives in the hamiltonian formalism according to [D.M. Gitman, S.L. Lyakhovich, I.V. Tyutin, Soviet Phys. J. 26 (1983) 730; D.M. Gitman, I.V. Tyutin, Quantization of Fields with Constraints, Springer-Verlag, New York, Berlin, 1990] the second treats the case where degenerate coordinate are present, in an analogy to reference [D.M. Gitman, I.V. Tyutin, Nucl. Phys. B 630 (2002) 509]. Several examples are analyzed where a comparison between both approaches is made. (C) 2007 Elsevier B.V. All rights reserved.