in the transformation semigroup (x, s) we introduce the height of a closed nonempty invariant subset of x, define the transformed dimension of nonempty subset s of x and obtain some results and relations.

this study was focused on the effect of wattle trait on body sizes and scrotal dimensions of traditionally reared wad bucks in the derived savannah environment. data were collected from 153 bucks ranging from 4 months to 2 years of age and this included, scrotal length, scrotal circumference, body weight, height at withers, body length and chest girth. parameters for wattle traits included, wat...

let r be a commutative noetherian ring. we study the behavior of injectiveand at dimension of r-modules under the functors homr(-,-) and -×r-.

We provide a complete picture of the upper quantization dimension in terms Rényi by proving that order r &gt; 0 r&gt;0</mml:annotatio...