We study the level spacing distribution for the spectrum of a point scatterer on a flat torus. In the two-dimensional case, we show that in the weak coupling regime, the eigenvalue spacing distribution coincides with that of the spectrum of the Laplacian (ignoring multiplicities), by showing that the perturbed eigenvalues generically clump with the unperturbed ones on the scale of the mean leve...

In this paper we investigate the asymptotic behavior of the k-th smallest uniform spacing. Among other things, a complete characterization of upper and lower class sequences is obtained. The asymptotic behavior is similar in many respects to that of the minimum of independent uniformly distributed random variables. Let X1 , . . . ,X , be independent identically distributed uniform (0, 1) random...

Recent interest by producers, researchers, and industry personnel concerning the use of grain drills utilizing 7-in. versus 10-in. row spacing have raised questions as to the optimal drill-row spacing for rice. With the increase in hybrid rice produced and the associated low seeding rates, questions arose regarding the response of these cultivars to row widths. The objective of this study was t...

Impact of chevron spacing and asymmetric distribution on supersonic jet acoustics and flow" (2016).

The hypothesis that protein kinase C (PKC) activity is sensitive to phospholipid head group interactions was tested using lipid bilayers of defined composition with PKC purified from rat brain. The head group interactions were modulated by varying phosphatidylcholine cis-unsaturation, vesicle curvature, and by the addition of phosphatidylethanolamine and cholesterol. With unilamellar vesicles (...

Research results at other locations in western U.S. indicate that a plant spacing of approximately 12 inches within rows and 20 or 22 inches between rows is necessary to obtain near maximum yields of sugarbeets (Beta vulgaris 1..) and yet maintain adequate space for machinery operation (4, 6, 10). 3 Increasing row and plant spacings with corresponding decreases in plant population have reduced ...