Cover crops are increasingly being used for weed management, and planting them as diverse mixtures has become an increasingly popular strategy for their implementation. While ecological theory suggests that cover crop mixtures should be more weed suppressive than cover crop monocultures, few experiments have explicitly tested this for more than a single temporal niche. We assessed the effects of cover crop mixtures (5- or 6-species and 14-species mixtures) and monocultures on weed abundance (weed biomass) and weed suppression at the time of cover crop termination. Separate experiments were conducted in Madbury, NH, from 2014 to 2017 for each of three temporal cover-cropping niches: summer (spring planting–summer termination), fall (summer planting–fall termination), and spring (fall planting–subsequent spring termination). Regardless of temporal niche, mixtures were never more weed suppressive than the most weed-suppressive cover crop grown as a monoculture, and the more diverse mixture (14 species) never outperformed the less diverse mixture. Mean weed-suppression levels of the best-performing monocultures in each temporal niche ranged from 97% to 98% for buckwheat (Fagopyrum esculentum Moench) in the summer niche and forage radish (Raphanus sativus L. var. niger J. Kern.) in the fall niche, and 83% to 100% for triticale (×Triticosecale Wittm. ex A. Camus [Secale × Triticum]) in the winter–spring niche. In comparison, weed-suppression levels for the mixtures ranged from 66% to 97%, 70% to 90%, and 67% to 99% in the summer, fall, and spring niches, respectively. Stability of weed suppression, measured as the coefficient of variation, was two to six times greater in the best-performing monoculture compared with the most stable mixture, depending on the temporal niche. Results of this study suggest that when weed suppression is the sole objective, farmers are more likely to achieve better results planting the most weed-suppressive cover crop as a monoculture than a mixture.

In terms of the normal cone and the coderivative,we provide some necessary and/or sufficient conditions of metric subregularity for(not necessarily closed) convex multifunctions in normed spaces. As applications, we present someerror bound results for (not necessarily lower semicontinuous) convex functions on normedspaces. These results improve and extend some existing error bound results.

Some new random coincidence point and random fixed point theorems for multivalued mappings in separable complete metric spaces are proved. The results presented in this paper are the stochastic versions of corresponding results of Chang and Peng and extend the result of the author.

The aim of this paper is to explore some properties of quasiuniform multifunction spaces. Various kinds of completeness of the quasiuniform multifunction space (YmX, UmX) are characterized in terms of suitable properties of the range space (Y, U). We also discuss the local compactness of quasiuniform multifunction spaces. By using the notion of small-set symmetry, the classic result of Hunsaker and Naimpally is extended to the quasiuniform setting.

We give several general implicit function and closed graph theorems for ser-valued functions. Let Z be a normed space, X, Y metric spaces with X complete. Let f: X ⇉ Z, F: X × Y ⇉ Z be multifunctions with z0 ∈ f(x0) ∩ F(x0, y0) such that f is open at (x0, y0) and f ‘approximates’ F in an appropriate sense. Suppose that f−1(z) is closed, F(x, y) is compact for each x, y and z and suppose that F(x0, ·) is lower semi-continuous at y0. Then F(·, y) is of closed graph ‘locally’, is open at x0, and there exists a function x(·) with x(y) → x0 for y → y0 such that z0 ∈ F(x(y), (y)) for all y near y0. A more general form dealing with the non-linear rate situation is also established.

In this paper the notion of inverse cluster set, which was recently introduced and studied for functions by T. R. Hamlett and P. E. Long (Proc. Amer. Math. Soc, 53 (1975), 470-476), is extended to and investigated for multifunctions. We generalize the notion of inverse cluster set, extend to multifunctions and generalize some known results for inverse cluster sets of functions and offer some new results. In the latter sections, compactness generalizations are characterized in terms of inverse cluster sets and some results on connected and conectivity functions are extended to multifunctions.