Complementarity in classical dynamical systems

The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamical systems with a partitioned phase space. Interpreting partitions in terms of ensembles of epistemic states (symbols) with corresponding classical observables, it is shown that such observables are complementary to each other with respect to particular partitions unless those partitions are generating. This explains why symbolic descriptions based on an \emph{ad hoc} partition of an underlying phase space description should generally be expected to be incompatible. Related approaches with different background and different objectives are discussed.Comment: 18 pages, no figure

Mineral nutrition of vegetable crops: XXV - Mineral nutrition of new zealand spinach plant (Tetragonia expansa Murr.)

The present work was carried out in order to study: a - the effect of omission and presence of the macronutrients and boron on the growth of the plants; b - deficiency symptoms of macronutrients, as well of boron; c - the effect of the deficiency of each nutrient on the chemical composition of the plants. Young spinach plants were grown in pots containing pure quartz sand. Several times a day the plants were irrigated by percolation with nutrient solutions. The treatments were: complete solution and deficient solution, in which each one of the macronutrients was omitted as well boron. Soon as the malnutrition symptoms appered, the plants were harvested and analysed chemically. - symptoms of malnutrition are easily observed for N, K, Ca and B. - symptoms of malnutrition for P, S and Mg are not easily identified. - the nutrient content, in dry matter, in deficient leaves and healthy leaves is:O trabalho teve como objetivo estudar alguns aspectos da nutrição mineral do espinafre (Tetragonia expansa Murr.) no que concerne: 1 - Efeitos da omissão dos macronutrientes e do boro, na obtenção de um quadro sintomatológico; 2 - Efeitos das carências na produção de matéria seca e composição química da planta. Mudas com trinta dias de idade foram transplantadas para soluções nutritivas carentes nos macronutrientes e/ou em boro. A coleta das plantas foi realizada quando os sintomas de deficiência se tornaram evidentes. No material seco procedeu-se a análise química. Os dados mostram que: 1 - os sintomas visuais de deficiência de N, K, Ca e B apresentam-se bem definidos; sendo que os de P, Mg e S são de difícil caracterização ; 2 - os teores dos nutrientes em plantas sadias e deficientes são

Electroweak measurements in electron–positron collisions at w-boson-pair energies at lep

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