A Hilbert module over a planar algebra is essentially a Hilbert module over a eanonieally defined algebra spanned by the annular tangles in It follows that any planar algebra containing is a module over and in particular, any subfactor planar algebra is a module over the Temperley-Lieb planar...

The nonlinear eigenvalue problem Δ+λ = 0 in the unit square with = 0 on the boundary is often referred to as “the Bratu problem” or “Bratu's problem.” The Bratu problem in 1-dimensional planar coordinates, ″ + λ = 0 with (0) = (1) = 0 has two known, bifurcated, exact solutions for...

Let be any -type Lie algebra with ≥ 2 over an algebraically closed field of characteristic 5. Let be an irreducible -module corresponding to some points and let be its corresponding representation. In this paper, in order to prove that the equality about the versus problem out of the 7 Clay...

We make a study of quasi-Hopf algebras and quasi-Hopf subalgebras over certain commutative rings from the point of view of Frobenius algebras. Separability and strong separability of quasi-Hopf algebras are also studied from this point of view

Let be a proper cone in , let be an × real matrix that satisfies , let be a given vector of , and let λ be a given positive real number. The following two linear equations are considered in this paper: (i) (λ — ) = , ∈ , and (ii) ( — λ) = , ∈ . We obtain several equivalent conditions...

The visco-elastic fluids in computational fluid mechanics (CFM) is an important problem to study. The simulation of the process of shear and elongation material has been successfully carried out in our previous reports (reference [1]). A mixed computational and mathematical approach in...

Two general procedures for computing eigenvalues and error estimates in Sturm-Liouville problems based upon the shooting technique are considered. The proposed methods have a low computational cost and the error estimates can be employed to improve the approximations obtained for the...