On second order elliptic equations with a small parameter

The Neumann problem with a small parameter $$(\dfrac{1}{\epsilon}L_0+L_1)u^\epsilon(x)=f(x) \text{for} x\in G, .\dfrac{\partial u^\epsilon}{\partial \gamma^\epsilon}(x)|_{\partial G}=0$$ is considered in this paper. The operators $L_0$ and $L_1$ are self-adjoint second order operators. We assume that $L_0$ has a non-negative characteristic form and $L_1$ is strictly elliptic. The reflection is with respect to inward co-normal unit vector $\gamma^\epsilon(x)$. The behavior of $\lim\limits_{\epsilon\downarrow 0}u^\epsilon(x)$ is effectively described via the solution of an ordinary differential equation on a tree. We calculate the differential operators inside the edges of this tree and the gluing condition at the root. Our approach is based on an analysis of the corresponding diffusion processes.Comment: 28 pages, 1 figure, revised versio

On the prevention of the black spot of shrimp: I. effect of some chemical reagents on the black spot of shrimp. II. the isolation and purification of the enzyme related to the formation of black spot

Foram estudadas, no presente trabalho, as causas do enegrecimento do camarão, tendo-se verificado que o mesmo é causado, fundamentalmente, pela ação da tirosinase, produzida no hepato pâncreas do crustáceo. O isolamento e a purificação da enzima foram realizados. A purificação foi feita, até se obter uma atividade 25 vêzes maior do que o extrato inicial, por meio de cromatografia de absorção, através de Celite 545 e avaliada através da velocidade de formação de dopacromo. O uso de diferentes drogas também foi tratado experimentalmente, tendo-se verificado que o melhor inibidor do processo de enegrecimento é o ácido L-arcórbico que evita a formação da mancha preta durante 9 dias à temperatura de 0 a -2ºC e durante tempo mais longo em temperaturas mais baixas. Tiosulfato de sódio e EDTA também têm boa ação inibidora. As técnicas empregadas são descritas detalhadamente e é apresentada discussão com resultados obtidos por outros autores. Ao que se sabe, esta é aprimeira vez que tirosinase é isolada de um invertebrado.The causes of the black discoloration of three species of shrimp commonly caught off the coast of the State of São Paulo, Brazil, are studied and measures for its prevention are advocated. Landings of shrimp in Santos in 1964 equaled 13% of the total landing, by weight, while economically it is the principal fishery. I - Blackening was effectively prevented by dipping the shrimp in cooled chemical solution for 30 minutes and then storing them at low temperatures. L-ascorbic acid gave the best results, delaying discoloration up to 9 days at 0º to -2ºC and for a longer period at colder temperatures. The effect of Sodium-thiosulfate and EDTA at different temperatures is also discussed. II - Tyrosinase was isolated and assayed by measuring the formation of Dopa-chrome from DL-Dopa at pH 6.8 an 37ºC. Tyrosinase was obtained from the shrimp liver and was purified by approximately 25 times its activity from the initial extract by absorption chromatography through Celite 545, as judged by the rate of dopachrome formation

Renormalization group and continuum limit in Quantum Mechanics

The running coupling constants are introduced in Quantum Mechanics and their evolution is described by the help of the renormalization group equation.Comment: 3 pg., presented at Lattice '94, Bielefel