First Discovery of the Earliest Angiospermous Megafossils in the World

The first discovery of the earliest angiospermous megafossils, so far in the world,was made by the authors from the Lower Cretaceous Chengzihe Formation of Jixi Basin, eastern Heilongjiang Province,China.Among the angiospermous fossils there are 5 species belonging to 5 genera (including 4 gen.et sp.nov.) reported in this paper.Their microphyllous leaves with irregular venations show the characteristics of some primitive angiosperms whose age is mostly corresponding to the late Hauterivian-early Barremian, partly proved by the underlying conformably marine beds with the Valanginian-Hauterivian dinoflagellates revealed newly also by the authors.     

Approximating earliest arrival flows with flow-dependent transit times

For the earliest arrival flow problem one is given a network G=(V,A) with capacities u(a) and transit times τ(a) on its arcs a∈A, together with a source and a sink vertex s,t∈V. The objective is to send flow from s to t that moves through the network over time, such that for each time θ∈[0,T) the maximum possible amount of flow up to this time reaches t. If, for each θ∈[0,T), this flow is a maximum flow for time horizon θ, then it is called earliest arrival flow. In practical applications a higher congestion of an arc in the network often implies a considerable increase in transit time. Therefore, in this paper we study the earliest arrival problem for the case that the transit time of each arc in the network at each time θ depends on the flow on this particular arc at that time θ.For constant transit times it has been shown by Gale that earliest arrival flows exist for any network. We give examples, showing that this is no longer true for flow-dependent transit times. For that reason we define a relaxed version of this problem where the objective is to find flows that are almost earliest arrival flows. In particular, we are interested in flows that, for each θ∈[0,T), need only α-times longer to send the maximum flow to the sink. We give both constant lower and upper bounds on α; furthermore, we present a constant factor approximation algorithm for this problem.     

Convex comparison of service disciplines in real time queues

We present a comparison of the service disciplines in real time queueing systems (the customers have a deadline before which they should enter the service booth). We state that giving priority to customers having an early deadline minimizes the average stationary lateness. We show this result by comparing adequate random vectors with the Schur convex majorization ordering.     

Performance guarantee for edf under overload

Earliest deadline first (edf) is a widely used algorithm for online deadline scheduling. It has been known for long that edf is optimal for scheduling an underloaded, single-processor system; recent results on the extra-resource analysis of edf further revealed that edf when using moderately faster processors can achieve optimal performance in the underloaded, multi-processor setting. This paper initiates the extra-resource analysis of edf for overloaded systems, showing that edf supplemented with a simple form of admission control can provide a similar performance guarantee in both the single and multi-processor settings.