In this paper we consider the classical system of matrix equationsover , an arbitrary regular ring with identity. Necessary and sufficient conditions for the existence and the expression of the general solution to the system are derived. As an application, the linear matrix equation + = over is...

Non-Hermitian matrix Schrödinger equation obtained by the Bäcklund- Darboux transformation (BDT) is treated. The potentials, fundamental solutions, and Weyl functions are constructed explicitly. Λ symmetric reduction of the BDT is introduced and this case is studied in greater detail:...

We present some formal systems in the language of linearly ordered rings with finite sets whose nonlogical axioms are strictly mathematical, which correspond to polynomially bounded arithmetic. With an additional strictly mathematical axiom, the systems correspond to exponentially bounded arithmetic

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...

This note uses some recent powerful tools related with semidirect products * of pseu-dovarieties of semigroups, particularly when the second factor is the pseudovariety of all finite groups, to give syntactic proofs of equalities of the form , where denotes the pseudovariety consisting of the...

For a prime let be the Brown-Peterson spectrum with homotopy ring . Using the arithmetical properties of the coe cients in the Brown-Peterson -series, we obtain the complete structure of the -module generated by the canonical elements

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...