Vacuum polarization by a global monopole with finite core

We investigate the effects of a $(D+1)$-dimensional global monopole core on the behavior of a quantum massive scalar field with general curvature coupling parameter. In the general case of the spherically symmetric static core, formulae are derived for the Wightman function, for the vacuum expectation values of the field square and the energy-momentum tensor in the exterior region. These expectation values are presented as the sum of point-like global monopole part and the core induced one. The asymptotic behavior of the core induced vacuum densities is investigated at large distances from the core, near the core and for small values of the solid angle corresponding to strong gravitational fields. In particular, in the latter case we show that the behavior of the vacuum densities is drastically different for minimally and non-minimally coupled fields. As an application of general results the flower-pot model for the monopole's core is considered and the expectation values inside the core are evaluated.Comment: 22 pages, 4 figures, misprint is corrected, discussion is added, figures are change

Cultivo de Brachiaria brizantha Stapf. cv. Marandu em solução nutritiva com omissões de macronutrientes

In a greenhouse experiment Brachiaria brizantha Stapf, cv. Marandu was grown in a nutrient solution. The treatments were a complete nutrient solution, nutrient solutions with the omissions of each macronutrient (N, P, K, Ca, Mg and S) and a control (with the omission of all macronutrients). Plants were harvested 50 days after transplanting. Dry matter yield, tiller number and plant height were recorded, and nutrient concentrations in shoot and root were determined. Omissions of N and P were the most limiting for plant growth, whereas K and Ca did not affect grass growth and tillering. Mg and S omissions resulted in significant decreases in the plant parameters. Great decreases in plant nutrient concentrations were verified in the treatments with nutrient omissions in solution. Visual symptoms of deficiencies were observed for each nutrient omission treatment, with those of N and P being the first and that of Ca being the latest shown by the plants. Studies on forms and sources of nutrients for nutrient solution to be used with this grass are suggested.Em experimento de casa de vegetação, cultivou-se Brachiaria brizantha Stapf. cv. Marandu em solução nutritiva, tendo como tratamentos a solução completa, as omissões individuais de N, P, K, Ca, Mg, S e a testemunha (com omissão dos macronutrientes). Fez-se o acompanhamento da manifestação dos sintomas visuais de deficiência e, 50 dias após o transplante, avaliou-se a produção de matéria seca (MS), número de perfilhos (NP), a altura das plantas (H), bem como a composição mineral da parte aérea e das raízes. As omissões de N e P limitaram o crescimento, ao passo que a omissão de K não afetou a produção de MS e NP. A omissão de Ca não trouxe, para o período considerado, restrições na produção de MS, NP e H. Nas omissões de Mg e S as plantas tiveram fraco desempenho, superando apenas os tratamentos onde foram omitidos o N e o P. A composição mineral da parte aérea só apresentou diferenças acentuadas nos teores para os nutrientes omitidos. Sintomas visuais de deficiência foram observados para todas as omissões, sendo os primeiros manifestados através da omissão do N e do P e os últimos, através da omissão do Ca. São sugeridos estudos para melhor definição do balanço entre formas e fontes de nutrientes para a solução nutritiva quando utilizada no cultivo de plantas de Brachiaria brizantha cv. Marandu