Let P be a set of n points in the plane, not all on a line. We show that if n is large then there are at least n/2 ordinary lines, that is to say lines passing through exactly two points of P . This confirms, for large n, a conjecture of Dirac and Motzkin. In fact we describe the exact extremisers for this problem, as well as all sets having fewer than n−C ordinary lines for some absolute const...

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Many factors related to the occurrence of browning disorder in ‘Braeburn’ apple were investigated, including harvest maturity, cumulative temperature in growing season, and different orchard locations. The incidence of browning disorder was related to the harvest time of fruit and the activity of superoxide dismutase. Superoxide dismutase activity was lower in late harvested ‘Braeburn’ apple fr...

Timely adoption of new varieties is critical to profitable peach production, and peach quality is a primary factor driving adoption. An adoption model for peach varieties is estimated, incorporating grower evaluations of peach quality. The model identifies the impact of farm characteristics such as the farmer's quality preferences, on-farm agronomic and orchard conditions, as well as geographic...

Since the inception of the freshshipping tree fruit industry shortly after the California Gold Rush (during the 1860s and 1870s) the state’s dominant orchard system has been the open vase, with trees trained into a wide “cone” tree shape at relatively ample spacings within the orchard. Originally, trees were planted on wide, 22-to-25-foot spacings (70 to 90 trees per acre) in both directions to...