The linear system of equations Ax = b where A = [aij ] in Cn.n is a crispsingular matrix and the right-hand side is a fuzzy vector is called a singularfuzzy linear system of equations. In this paper, solving singular fuzzy linearsystems of equations using generalized inverses such as Drazin inverse andpseudo-inverse are investigated.

Superintendents know that management of putting greens is an art. Greens are often made of high-porosity sand that does not retain water or nutrients very effectively. Also, putting green grasses are cut extremely short, which does not allow a deep root system to develop and take up nutrients from deep in the soil profile. Therefore, putting greens require frequent irrigation and fertilizer app...

We investigate shift invariant subspaces of $L^2(G)$, where $G$ is a locally compact abelian group. We show that every shift invariant space can be decomposed as an orthogonal sum of spaces each of which is generated by a single function whose shifts form a Parseval frame. For a second countable locally compact abelian group $G$ we prove a useful Hilbert space isomorphism, introduce range funct...

In this paper, we mainly investigate the uniqueness of the entire function sharing a small entire function with its high difference operators. We obtain one results, which can give a negative answer to an uniqueness question relate to the Bruck conjecture dealt by Liu and Yang. Meanwhile, we also establish a difference analogue of the Bruck conjecture for entire functions of order less than 2, ...

Dietary antioxidants play an important role against oxidation, an underlying mechanism in the incidence of chronic diseases. Greens+ is a commercially available preparation containing a variety of plant-derived ingredients. The aim of the current study was to evaluate the antioxidant potential of the methanolic extract of greens+ powder using in vitro and in vivo techniques. In vitro studies we...