L^0-CONVEX COMPACTNESS AND RANDOM NORMAL STRUCTURE IN L^0(F,B)

Let(B,||·||)be a Banach space,(?,F,P)a probability space,and L^0(F,B)the set of equivalence classes of strong random elements(or strongly measurable functions)from(?,F,P)to(B,||·||).It is well known that L^0(F,B)becomes a complete random normed module,which has played an important role in the process of applications of random normed modules to the theory of Lebesgue-Bochner function spaces and random operator theory.Let V be a closed convex subset of B and L^0(F,V)the set of equivalence classes of strong random elements from(?,F,P)to V.The central purpose of this article is to prove the following two results:(1)L^0(F,V)is L^0-convexly compact if and only if V is weakly compact;(2)L^0(F,V)has random normal structure if V is weakly compact and has normal structure.As an application,a general random fixed point theorem for a strong random nonexpansive operator is given,which generalizes and improves several well known results.We hope that our new method,namely skillfully combining measurable selection theorems,the theory of random normed modules,and Banach space techniques,can be applied in the other related aspects.

Anti-clogging ability of the labyrinth emitter and its evaluation method

Emitter clogging is one of the most serious factors that restrict the drip irrigation system operation and water use efficiency.To scientifically characterize and evaluate emitter clogging risk,a literature review,short-period emitter anti-clogging tests,and CFD(Computational Fluid Dynamics)hydraulic performance tests were conducted.Results showed that the emitter anti-clogging ability is related to its structure,material,and processing technology,not external factors.This was evidenced in the irrigation tests,as with the different water qualities,the same emitters were repeatedly prone to clog or to avoid clogging.A predictive model of structural resistance coefficient(Cs),a quantitative indicator of the emitter anti-clogging ability,whose value ranges between 0 and 1,was utilized.Larger Cs values indicate a lower anti-clogging ability and thus a higher risk of clogging.A good linear relationship between Cs and the relative flow rate was detected,and the Cs relationship with the fluidity index(x)was determined to be a power function.The Cs should be controlled within the range of 0.146-0.461 when designing new emitters to ensure that they have good anti-clogging properties.This research will provide theoretical guidance for the anti-clogging management of drip irrigation systems and for the design of optimal emitter structures.