In this article we apply the Stenberg criteria to show that the Taylor-Hood P2 − P1 and the Scott-Vogelius P2 − discP1 element pairs satisfy the LBB condition in IR. The Taylor-Hood P2 − P1 pair is shown to be stable on a regular triangulation of the domain. For the ScottVogelius P2−discP1 element pair the mesh is assumed to be a barycenter refinement of a regular triangulation.

The aim of this paper is to study the convergence analysis of three low order Crouzeix-Raviart type nonconforming rectangular finite elements to Maxwell’s equations, on a mixed finite element scheme and a finite element scheme, respectively. The error estimates are obtained for one of above elements with regular meshes and the other two under anisotropic meshes, which are as same as those in th...

Abstract— The purpose of this paper is to give a compact summary of recent results based on the concept of a regular positive-real function. We will list an efficient set of networks which is capable of realising all biquadratics which are realisable by 5-element networks or 6-element networks of seriesparallel type. The structures are simpler than the full BottDuffin synthesis, though there ar...

Let R be a commutative ring and Max (R) be the set of maximal ideals of R. The regular digraph of ideals of R, denoted by −−→ Γreg(R), is a digraph whose vertex set is the set of all non-trivial ideals of R and for every two distinct vertices I and J , there is an arc from I to J whenever I contains a J-regular element. The undirected regular (simple) graph of ideals of R, denoted by Γreg(R), h...

Let G be a multiplicative group, K a commutative ring with unit, and K(G) the group ring of G with respect to K. We say that K(G) is regular if given an x in K(G), there is a y in K(G) such that xyx = x. Using a homological characterization of regular rings which was found independently by M. Harada [2, Theorem 5] and the author, we prove that if G is locally finite, then K(G) is regular if and...