In this Article, we give a simple criterion for the regularity of a tri-linear mapping. We provide if f : X × Y × Z −→ W is a bounded tri-linear mapping and h : W −→ S is a bounded linear mapping, then f is regular if and only if hof is regular. We also shall give some necessary and sufficient conditions such that the fourth adjoint D^∗∗∗∗ of a tri-derivation D is again tri-derivation.

is referred to as the decay rate associated with a. If a is to be introduced in order to absorb an initial disturbance then one naturally wishes to strike upon that a with the least possible (most negative) decay rate. The mathematical attraction here lies in the oftnoted fact that, with respect to damping, ‘more is not better.’ More precisely, for constant a, the decay rate is not a decreasing...

The primary objective of this study was to investigate the degree of influence of Arabic vowel duration in 'emphatic' and 'non-emphatic' contexts on the production of English sequences. The specific questions asked were the following: (i) What is the average Arabic vowel duration in 'emphatic' and 'non-emphatic contexts ? (ii) Is vowel durational variation a function of the complex features of ...

This paper presents a measure of Internet “connectivity” (number of connected companies per capita) normalized by the economic “size ” of areas in the United States. We use cross sectional variation in connectivity to test some hypotheses about technology adoption. We find that areas in the South and Midwest have below average connectivity. Connectivity is also related to the living “attractive...

We investigate the sufficient condition under which each positive b-weakly compact operator is Dunford-Pettis. We also investigate the necessary condition on which each positive b-weakly compact operator is Dunford-Pettis. Necessary condition on which each positive b-weakly compact operator is weakly compact is also considered. We give the operator that is semi-compact, but it is not bweakly. W...