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In this paper, the notion of weighted Toep-Hank operator G β φ , induced by the symbol φ ∈ L ∞ (β), on the space H 2 (β), β = {βn} n∈Z being a semi-dual sequence of positive numbers with β0 = 1, is introduced. Symbols are identified for the induced weighted Toep-Hank operator to be co-isometry, normal and hyponormal.

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Nitric Oxide (NO), an important biological mediator, is involved in the regulation of the cardiovascular, nervous and immune systems in mammals. Synthesis of NO is catalyzed by its biosynthetic enzyme, Nitric Oxide Synthase (NOS). There are three main isoforms of the enzyme, neuronal NOS, endothelial NOS and inducible NOS, which have very similar structures but differ in their expression and activities. NO is produced in the active site of the enzyme in two distinct cycles from oxidation of the substrate L-arg (L-arginine) in nicotinamide adenine dinucleotide phosphate (NADPH)-dependent reaction. NOS has gained considerable attention of biochemists due to its complexity and unique catalytic mechanism. The review focuses on NOS structure, its function and catalytic reaction mechanism. In particular, the review is concluded with a discussion on the role of all three isoforms of NOS in physiological and pathological conditions and their inhibitors with a focus on the role of computational techniques in their development.

This paper introduces the notion of slant Toep-Hank operator L φ , with symbol φ in L ∞ (T), on the space L 2 (T), T being the unit circle. Along with a matrix characterization for an operator to be slant Toep-Hank , we characterize the symbols for the slant Toep-Hank operator to be compact and hyponormal. Some properties for the compression of slant Toep-Hank operators are also derived.