The semi-inner product, in the sense of Lumer, on weighted Hardy space which generate the norm is unique. Also we will discuss some properties of the numerical range of bounded linear operators on weighted Hardy spaces.

The residual effect of a commercial spray containing 2.0% benzyl benzoate against Dermatophagoides pteronyssinus was evaluated in the laboratory. Filter papers treated with benzyl benzoate were dried for 2 hours and placed in Petri dishes. Adult mites were then added and mortality was assessed following 24 hour contact and at succeeding 4 weeks intervals up to week 28 post-treatment using the s...

Abstract We introduce a new metric homology theory, which we call Moderately Discontinuous Homology, designed to capture Lipschitz properties of singular subanalytic germs. The main novelty our approach is allow “moderately discontinuous” chains, are specially advantageous for capturing the subtleties outer phenomena. Our invariant finitely generated graded abelian group any and homomorphisms ....

Vitis vinifera grapevines are highly susceptible to downy mildew caused by the host-specific oomycete Plasmopara viticola. In humid climates like New York, where the unchecked pathogen will defoliate vines and destroy young fruit clusters, growers depend upon multiple fungicide applications for disease management. However, management of P. viticola by fungicides is tenuous, because the pathogen...