Propionic acid (PA) is a fungicide and bactericide, registered to control fungi and bacteria in stored grains, hay, grain storage areas, poultry litter, and drinking water for livestock and poultry. European Union (EU) certifies PA as the great of grain preserver and most efficient in controlling Salmonella and other pathogens. Recently it is used as feed additive in poultry and non-ruminant pr...

For a rank-1 matrix A = a ⊗ b over max algebra, we define the perimeter of A as the number of nonzero entries in both a and b. We characterize the linear operators which preserve the rank and perimeter of rank-1 matrices over max algebra. That is, a linear operator T preserves the rank and perimeter of rank-1 matrices if and only if it has the form T (A) = U ⊗ A ⊗ V , or T (A) = U ⊗ A ⊗ V with ...

IN THEIR PERSPECTIVE “The trouble with negative emissions” (14 October, p. 182), K. Anderson and G. Peters assert that negative-emissions technologies are an “unjust and high-stakes gamble.” This characterization would sideline negativeemissions technologies and remove potentially important options from the portfolio for mitigating and ameliorating climate change. As Anderson and Peters acknowl...

In this paper we prove new results about the extremal structure of paths in directed graphs. Say we are given a directed graph G = (V,E) on n nodes, a set of sources S ⊆ V of size |S| = n, and a subset P ⊆ S × V of pairs (s, t) where s ∈ S, of size O(n), such that for all pairs (s, t) ∈ P , there is a path from s to t. Our goal is to remove as many edges from G as possible while maintaining the...

Given a domain $I\subset\Bbb{C}$ and an integer $N>0$, function $f: I\to\Bbb{C}$ is said to be {\it entrywise positivity preserving} on positive semidefinite $N\times N$ matrices $A=(a_{jk})\in I^{N\times N}$, if the application $f[A]=(f(a_{jk}))$ of $f$ $A$ for all such $A$. Such preservers in dimensions have been classified by Schoenberg Rudin as being absolutely monotonic. In fixed dimension...