Constructing the CKVs of Bianchi III and V spacetimes

We determine the conformal algebra of Bianchi III and Bianchi V spacetimes or, equivalently, we determine all Bianchi III and Bianchi V spacetimes which admit a proper conformal Killing vector (CKV). The algorithm that we use has been developed in [M. Tsamparlis et al.Class. Quantum. Grav. 15, 2909 (1998)] and concerns the computation of the CKVs of decomposable spacetimes. The main point of this method is that a decomposable space admits a CKV if the reduced space admits a gradient homothetic vector, the latter being possible only if the reduced space is flat or a space of constant curvature. We apply this method in a stepwise manner starting from the two-dimensional spacetime which admits an infinite number of CKVs and we construct step by step the Bianchi III and V spacetimes by assuming that CKVs survive as we increase the dimension of the space. We find that there is only one Bianchi III and one Bianchi V spacetime which admit at maximum one proper CKV. In each case, we determine the CKV and the corresponding conformal factor. As a first application in these two spacetimes, we study the kinematics of the comoving observers and the dynamics of the corresponding cosmological fluid. As a second application, we determine in these spacetimes generators of the Lie symmetries of the wave equation.

Non-minimal matter-geometry coupling in the Bianchi-V spacetime within the formalism of f(R, T) = f1(R) + f2(R)f3(T) cosmology

The models of [Formula: see text] gravity are efficient in describing a non-minimal coupling between geometry and matter. In this paper, the extended theory of gravity describes the non-minimal coupling between matter and geometry using special cosmological model of [Formula: see text] in Bianchi-V spacetime; whose functional relations are [Formula: see text] and [Formula: see text], where [Formula: see text] is a constant. The Einstein’s field equation has been solved by taking special choice of scale factor as [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] are constants. The energy and other stability conditions obtained in this paper explain the physical behavior of phase transition of universe and it also confirms the stability of the derived model.

GESTÃO DOS RECURSOS HÍDRICOS NA SUB-BACIA HIDROGRÁFICA DO BOI BRANCO – SP

GESTÃO DOS RECURSOS HÍDRICOS NA SUB-BACIA HIDROGRÁFICA DO BOI BRANCO – SP GIVALDO DANTAS SAMPAIO NETO1; VINÍCIUS RAFAEL BIANCHI2; LEONARDO DE BARROS PINTO3 E RODRIGO MÁXIMO SÁNCHEZ ROMÁN4 1Departamento de Ensino, Campus de Diamantino IFMT, Rodovia Roberto Campos s/n, Novo Diamantino, CEP:78402-000, Diamantino – MT, Brasil. email: [email protected]. 2 Departamento de Engenharia Rural, Faculdade de Ciências Agronômicas, Universidade Estadual Paulista (UNESP) Campus de Botucatu. Fazenda Experimental Lageado, Avenida Universitária, nº 3780, Altos do Paraíso, CEP: 18610-034, Botucatu – SP. Brasil. email: [email protected]. 3 Departamento de Economia, Sociologia e Tecnologia, Faculdade de Ciências Agronômicas, Universidade Estadual Paulista (UNESP) Campus de Botucatu. Fazenda Experimental Lageado, Avenida Universitária, nº 3780, Altos do Paraíso, CEP: 18610-034, Botucatu – SP. Brasil. email: [email protected] 4 Departamento de Engenharia Rural, Faculdade de Ciências Agronômicas, Universidade Estadual Paulista (UNESP) Campus de Botucatu. Fazenda Experimental Lageado, Avenida Universitária, nº 3780, Altos do Paraíso, CEP: 18610-034, Botucatu – SP. Brasil. email: [email protected]. 1 RESUMO A escassez dos recursos hídricos devido a fatores climáticos ou pelo aumento de consumo devido a intensidade de algumas atividades, tem gerado conflitos em diversas regiões do Brasil. A agricultura é responsável por 70% da demanda hídrica no Brasil, isso devido fundamentalmente à prática de irrigação. Por outro lado a agricultura irrigada produz 2,7 vezes a mais que a lavoura de sequeiro e emprega em média 1,5 empregos diretos e indiretos por cada hectare irrigado. Classificada em situação crítica a sub-bacia do Boi Branco, localizada na região do Alto Paranapanema, entre os município de Itaí e Paranapanema é um forte polo de agricultura irrigada. O objetivo deste trabalho foi levantar as questões relacionadas aos aspectos de gestão dos recursos hídricos, agricultura irrigada e a participação dos diversos setores de usuários de água da sub-bacia do Boi Branco. Onde se pode observar que os dados quantitativos e qualitativos relacionados aos recursos hídricos nas bacias, apresentam inconsistência tanto na demanda real de água como na disponibilidade efetiva. É preciso uma maior divulgação das informações da sub-bacia do Boi Branco juntamente com investimento em pesquisa e capacitação de todos os envolvidos na gestão dos recursos hídricos. Palavras Chave: irrigação, pivô central, uso da água, agricultura irrigada. SAMPAIO NETO, G. D.; BIANCHI, V. R.; PINTO, L. B.; SÁNCHEZ-ROMÁN, R. M. MANAGEMENT OF WATER RESOURCES IN BOI BRANCO SUB-BASIN -SP 2 ABSTRACT Scarcity of water resources due to climatic factors or increase in consumption due to the intensity of some activities has generated conflicts in several regions of Brazil. Agriculture is responsible for 70% of water demand in Brazil, mainly due to the practice of irrigation. On the other hand, irrigated agriculture produces 2.7 times more than rainfed agriculture and employs on average 1.5 direct and indirect jobs per irrigated hectare. Classified in a critical situation, Boi Branco sub-basin, located in Alto Paranapanema region, Itai and Paranapanema municipalities is a strong irrigated agriculture pole. The objective of this work was to raise issues related to the management of water resources, irrigated agriculture and the participation of various sectors of water users in Boi Branco sub-basin. It was observed that quantitative and qualitative data related to water resources in the basins present inconsistency both in actual water demand and in effective availability. There is a need for greater dissemination of information on Boi Branco sub-basin together with investment in research and training of all those involved in water resources management. Keyword: irrigation, central pivot, water use, watershed, irrigated agriculture.