Given a family $${\mathcal {F}}$$ of k-element sets, $$S_1,\ldots ,S_r\in {\mathcal form an r-sunflower if $$S_i \cap S_j =S_{i'} S_{j'}$$ for all $$i \ne j$$ and $$i' j'$$ . According to famous conjecture Erdős Rado (JAMA 35: 85–90, 1960), there is constant $$c=c(r)$$ such that $$|{\mathcal {F}}|\ge c^k$$ , then contains r-sunflower. We come close proving this families bounded Vapnik-Chervonen...

The relevance of the study is due to need reduce energy intensity process cutting sunflower stalks by choosing a rational profile knives. research based on comparative analysis experimental values forces for proposed and manufactured design knife system known systems. studies have shown that implementation retaining main knives header in form curved spiral Archimedes allowed force. It was also ...

BACKGROUND Field-scale changes in the water footprint during crop growth play an important role in formulating sustainable water utilisation strategies. This study aimed to explore field-scale variation in the water footprint of growing sunflowers in the western Jilin Province, China, during a 3-year field experiment. The goals of this study were to (1) determine the components of the 'blue' an...

1: Seeds of sunflowers are often modelled by the map n 7−→ φθ(n) = √ ne2iπnθ leading to a roughly uniform repartition with two consecutive seeds separated by the divergence angle 2πθ for θ the golden ratio. We associate to an arbitrary real divergence angle 2πθ a geodesic path γθ : R>0 −→ PSL2(Z)\H of the modular curve and use it for local descriptions of the image φθ(N) of the phyllotactic map...

Nectar-related traits influence the number of bee visits to sunflowers, but effects floret size on diversity and composition communities are unknown. In 4 year × planting date combinations, bees were collected from sunflowers with small (< 7.5 mm), medium (7.5–9 or large (> 9 mm) florets, counts foraging used clarify responses plant traits. No effect was found, associations tongue length led di...

Sunflower (Helianthus annuus L.) is one of the most important vegetable oil sources in world and our country. The preference for sunflower consumption increases importance sunflowers Rust, downy mildew, Verticillium wilt, Sclerotinia stalk head rot, charcoal blight, leaf spot are some diseases commonly seen sunflowers. In years, depending on climatic conditions, Downy mildew (Plasmopara halsted...