A function f : V (G) → {−1, 0, 1} is a minus dominating function if for every vertex v ∈ V (G), ∑ u∈N [v] f(u) ≥ 1. A minus dominating function f of G is called a global minus dominating function if f is also a minus dominating function of the complement G of G. The global minus domination number γ− g (G) of G is defined as γ − g (G) = min{ ∑ v∈V (G) f(v) | f is a global minus dominating functi...

We extend the primal-dual approximation technique of Goemans and Williamson to the Steiner connectivity problem, a kind of Steiner tree problem in hypergraphs. This yields a (k+1)-approximation algorithm for the case that k is the minimum of the maximal number of nodes in a hyperedge minus 1 and the maximal number of terminal nodes in a hyperedge. These results require the proof of a degree pro...

We prove the triviality of the Grothendieck ring of a Z-valued field K under slight conditions on the logical language and on K. We construct a definable bijection from the plane K to itself minus a point. When we specialize to local fields with finite residue field, we construct a definable bijection from the valuation ring to itself minus a point. At the Edinburgh meeting on the model theory ...

Physicists welcomed the news last month of the discovery of a subatomic particle which may bring some order out of the apparent chaos among nuclear particles. The omega-minus, discovered by scientists working with the particle accelerator at Brookhaven National Laboratory in New York, confirms a theory proposed independently, three years ago, by Murray Gell-Mann, professor of theoretical physic...

We show that the linear drift of Brownian motion on universal cover a closed connected smooth Riemannian manifold is C k − 2...

A graph $G$ is $k$-$weighted-list-antimagic$ if for any vertex weighting $\omega\colon V(G)\to\mathbb{R}$ and list assignment $L\colon E(G)\to2^{\mathbb{R}}$ with $|L(e)|\geq |E(G)|+k$ there exists an edge labeling $f$ such that $f(e)\in L(e)$ all $e\in E(G)$, labels of edges are pairwise distinct, the sum on incident to a plus weight distinct from at every other vertex. In this paper we prove ...

Although zygospore (mature zygote) formation in P. blakeslleeanus occurs in liquid glucoseglutamate medium, morphological observations are made more easily when cultures are grown on 1-mm-thick agar medium. Zygophores (sexually differentiated hyphae) develop prior to physical contact in crosses of (plus) and (minus) wild types. Zygophores interlock upon contact and then undergo six successive m...

The relationship between regional blood flow and epicardial S-T segment elevation was studied in 26 open-chest anesthetized dogs with left anterior coronary artery ligations. Changes in myocardial blood flow, measured with 15 plus or minus 5mu (diameter) microspheres labeled with 141-Ce, 85-Sr, and 169-Yb, were correlated with summated S-T segment elevations 15 minutes, 1 hour, and 2 hours afte...