A composition operator Tbf = f o b is completely continuous on H1 if and only if \b\ < 1 a.e. If the adjoint operator Tg is completely continuous on VMOA , then 7¿ is completely continuous on Hl . Examples are given to show that the converse fails in general. Two results are given concerning the relationship between the complete continuity of an operator and of its adjoint in the presence of ce...

Scape bending disorder is the most important factor affecting postharvest loss of gerbera cut flowers. One of the ultimate reasons for gerbera stem bending is lignin, with deformation structural functions and defensive mechanisms. This postharvest experiment was conducted to evaluate the role of phenylalanine ammonia lyase (PAL) and peroxidase (POD) enzymes activity in stem bending of two gerbe...

A boolean algebra is shown to be completely representable if and only if it is atomic whereas it is shown that the class of completely representable relation algebras is not elementary.

Let G be a connected and reductive group over the algebraically closed field K. J-P. Serre has introduced the notion of a G-completely reducible subgroup H ≤ G. In this note, we give a notion of G-complete reducibility – G-cr for short – for Lie subalgebras of Lie(G), and we show that if the smooth subgroup H < G is G-cr, then Lie(H) is G-cr as well.

Cryptography the art of secure communications, has been developed at least over 2500 years. Still at present, no perfectly secure as well as practically suitable classical or quantum cryptosystems exist. Statistically encoding the individual bit, here we present a practical key distribution technique which is absolutely secure both for classical and quantum keys. To achieve perfect security, no...

Abstract Anthracnose disease caused by Colletotrichum spp. is one of the most damaging chili diseases. The purpose current study was to determine pathogenicity two important pathogens anthracnose disease, C. gloeosporioides (Penz) Penz. &amp; Sacc. and capsici E.J. Butler Bisby, on several cultivars in laboratory. experimental design used a completely randomized factorial. first factor cultivar...