We consider the Bernoulli first-passage percolation on Z (d ≥ 2). That is, the edge passage time is taken independently to be 1 with probability 1− p and 0 otherwise. Let μ(p) be the time constant. We prove in this paper that μ(p1)− μ(p2) ≥ μ(p2) 1− p2 (p2 − p1) for all 0 ≤ p1 < p2 < 1 by using Russo’s formula. AMS classification: 60K 35. 82B 43.

P2 is a new and exciting system that permits declarative implementations of overlay networks. The recently published work cites reasonable implementations and performance for two protocols, Chord and Narada. Our work evaluates P2 through an implementation of a third protocol, the Paxos consensus protocol. P2’s declarative language Overlog, admitted a smooth and readable implementation of the Pa...

DEFINITION: Given a set of points p1, p2, ......., pn, the skyline query returns a set of points P, called as the skyline points, such that any point pi ∈ P is not dominated by any other point in the dataset. A point p1 dominates another point p2, if p1 is not worse than p2 in all dimensions and p1 is better than p2 in at least one dimension. In other words, a point p1 dominates another point p...

Early diagnosis of agenesis of the mandibular second premolar (P2) enhances management of the dental arch in the growing child. The aim of this study was to explore the relationship in the development of the mandibular first molar (M1) and first premolar (P1) at early stages of P2 (second premolar). Specifically, we ask if the likelihood of P2 agenesis can be predicted from adjacent developing ...

Fructose-2,6-P2 and fructose-1,6-P2 are strong activators of muscle phosphofructokinase. They have been shown to be competitive in binding studies, and it is generally thought that they affect the physical and catalytic properties of the enzyme in the same manner. However, there are indications in published data that the effects of the two fructose bisphosphates on phosphofructokinase are not i...

Hydrolysis of phospholipids by plant phospholipase Dbeta (PLDbeta) requires phosphatidylinositol 4,5-bisphosphate [PI(4,5)P2]. Here we show that PLDbeta is stimulated by different polyphosphoinositides, among which PI(4,5)P2 is most effective. On the basis of amino acid sequence analysis, PI(4,5)P2 binding assay, and protein engineering studies, we have identified in the catalytic region of PLD...

The helper component of Cauliflower mosaic virus is encoded by viral gene II. This protein (P2) is dispensable for virus replication but required for aphid transmission. The purification of P2 has never been reported, and hence its biochemical properties are largely unknown. We produced the P2 protein via a recombinant baculovirus with a His tag fused at the N terminus. The fusion protein was p...

Adenosine 5’-triphosphate (ATP) has been shown to be an important extracellular signaling molecule that mediates various physiological activities via the P2 (P2X and P2Y) receptors. However, information on the expression patterns of the P2 receptors during mammalian embryogenesis is limited. We therefore examined the expression patterns of different P2 receptor subtypes in rat embryos. In the h...

A property of graphs is any class of graphs closed under isomorphism. A property of graphs is induced-hereditary and additive if it is closed under taking induced subgraphs and disjoint unions of graphs, respectively. Let P1,P2, . . . ,Pn be properties of graphs. A graph G is (P1,P2, . . . ,Pn)-partitionable (G has property P1◦P2◦ · · · ◦Pn) if the vertex set V (G) of G can be partitioned into ...

Oscillatory behavior of glycolysis in cell-free extracts of rat skeletal muscle involves bursts of phosphofructokinase activity, due to autocatalytic activation by fructose-1,6-P2. Glucose-1,6-P2 similarly might activate phosphofructokinase in an autocatalytic manner, because it is produced in a side reaction of phosphofructokinase and in a side reaction of phosphoglucomutase using fructose-1,6...