The incidence of strawberry flower infection by Botrytis cinerea was monitored in unsprayed field plots in three successive years together with meteorological data and numbers of conidia in the air. There were large differences in conidia numbers and weather conditions in the 3 years. Three sets of models were derived to relate inoculum and weather conditions to the incidence of flower infection; by inoculum only, by weather variables only, and by both inoculum and weather variables. All the models fitted the observed incidence satisfactorily. High inoculum led to more infection. Models using weather variables only gave more accurate predictions than models using inoculum only. Models using both weather variables and inoculum gave the best predictions, but the improvement over the models based on weather variables only was small. The relationship between incidence of flower infection and inoculum and weather variables was generally consistent between years. Of the weather variables examined, daytime vapor pressure deficit and nighttime temperature had the greatest effect in determining daily incidence of flower infection. Infection was favored by low day vapor pressure deficit and high night temperature. The accuracy and consistency of the weather-based models suggest they could be explored to assist in management of gray mold.

ABSTRACT. Let G be a Vilenkin group. Let E C G be closed with Haar measure zero. We show there is a continuous function whose Vilenkin-Fourier series diverges at every point in E.

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