We develop the plus/minus p-Selmer group theory and plus/minus padic L-function theory for an elliptic curve E with complex multiplication over an abelian extension F of the imaginary quadratic field K given by the complex multiplication of E when p is a prime inert over K/Q (i.e. supersingular). As a result, we prove that the characteristic ideal of the Pontryagin dual of the plus/minus p-Selm...

Watermarking is done in digital images for authentication and to restrict its unauthorized usages. Watermarking is sometimes invisible and can be extracted only by authenticated party. Encrypt a text or information by public – private key from two fuzzy matrix and embed it in image as watermark. In this paper we proposed two fuzzy compositions Product-Mod-Minus, and Compliment-Product-Minus. Em...

Plus- and minus-end vesicle populations from squid axoplasm were isolated from each other by selective extraction of the minus-end vesicle motor followed by 5'-adenylyl imidodiphosphate (AMP-PNP)-induced microtubule affinity purification of the plus-end vesicles. In the presence of cytosol containing both plus- and minus-end motors, the isolated populations moved strictly in opposite directions...