XLI. A Note on beta rays and atomic number

A note on the Roman domatic number of a digraph

Roman dominating function} on a digraph $D$ with vertex set $V(D)$ is a labeling$fcolon V(D)to {0, 1, 2}$such that every vertex with label $0$ has an in-neighbor with label $2$. A set ${f_1,f_2,ldots,f_d}$ ofRoman dominating functions on $D$ with the property that $sum_{i=1}^d f_i(v)le 2$ for each $vin V(D)$,is called a {em Roman dominating family} (of functions) on $D$....

The Relative Effects of X-Rays, Gamma Rays and Beta Rays on Chromosomal Breakage in Tradescantia.

OR some time it has been generally considered that the production of F chromosomal aberrations in Tradescantia and many other materials is essentially independent of the wave length of the exciting radiation in the region shorter than 1.5 A. This view has not been seriously questioned in recent years and to date has remained one of the fundamental tenets of radiobiology. A number of isolated in...

A note on random number generation

A note on generators of number fields

We establish upper bounds for the smallest height of a generator of a number field k over the rational field Q. Our first bound applies to all number fields k having at least one real embedding. We also give a second conditional result for all number fields k such that the Dedekind zeta-function associated to the Galois closure of k/Q satisfies GRH. This provides a partial answer to a question ...

A Note on Waring ’ s Number Modulo

The Waring number of the integers modulo m with respect to k-th powers, denoted by ρ(m, k), is the smallest r such that every integer is a sum of r k-th powers modulo m. This number is also the diameter of an associated Cayley graph, called the Waring graph. In this paper this number is computed when m is a power of 2. More precisely the following result is obtained: Let n, s and b be natural n...