A parallel prefix circuit has n inputs x1, x2, . . . , xn, and computes the n outputs yi = xi • xi−1 • · · ·•x1, 1 ≤ i ≤ n, in parallel, where • is an arbitrary binary associative operator. Snir proved that the depth t and size s of any parallel prefix circuit satisfy the inequality t + s ≥ 2n − 2. Hence, a parallel prefix circuit is said to be of zero-deficiency if equality holds. In this pape...

Whereas the positive equilibrium of a mass-action system with deficiency zero is always globally stable, for deficiency-one networks there are many different scenarios, mainly involving oscillatory behaviour. We present several examples, centers or multiple limit cycles.

Consider a Markovian Petri net with race policy. The marking process has a “product form” stationary distribution if the probability of viewing a given marking can be decomposed as the product over places of terms depending only on the local marking. First we observe that the Deficiency Zero Theorem of Feinberg, developed for chemical reaction networks, provides a structural and simple sufficie...

Chemical Reaction Network theory allows us to decide whether many classes of networks have the capacity for multiple positive equilibria, based on their structural properties. In this way, the deficiency zero theorem asserts that every weakly reversible network of zero deficiency has a unique equilibrium, for any choices of parameter values. We make use of CRNT, aiming not only to discriminate ...

abstract this study was conducted at rudasht research farm in isfahan to evaluate tolerance to zinc (zn) deficiency of 30 spring wheat genotypes, using split plots in a randomized complete blocks design with triplications. main plot consisted of two zn levels (zero and 80 kg zn ha-1 applied as zinc sulfate at planting). the results of anova as well as correlations between tolerance and suscepti...