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.

A process ∆ is regular if it is bisimilar to a process ∆′ with finitely many states. We prove that regularity of normed PA processes is decidable and we present a practically usable polynomial-time algorithm. Moreover, if the tested normed PA process ∆ is regular then the process ∆′ can be effectively constructed. It implies decidability of bisimulation equivalence for any pair of processes suc...

The D-eigenvalues {µ1,…,µp} of a graph G are the eigenvalues of its distance matrix D and form its D-spectrum. The D-energy, ED(G) of G is given by ED (G) =∑i=1p |µi|. Two non cospectral graphs with respect to D are said to be D-equi energetic if they have the same D-energy. In this paper we show that if G is an r-regular graph on p vertices with 2r ≤ p - 1, then the complements of iterated lin...

A normally regular digraph with parameters (v, k, λ, μ) is a directed graph on v vertices whose adjacency matrix A satisfies the equation AAt = kI + λ(A + At) + μ(J − I − A − At). This means that every vertex has out-degree k, a pair of nonadjacent vertices have μ common out-neighbours, a pair of vertices connected by an edge in one direction have λ common out-neighbours and a pair of vertices ...

We study germs of pairs of codimension one regular foliations in R. We show that the discriminant of the pair determines the topological type of the pair. We also consider various classifications of the singularities of the discriminant.

r is called commuting regular ring (resp. semigroup) if for each x,y $in$ r thereexists a $in$ r such that xy = yxayx. in this paper, we introduce the concept of commuting$pi$-regular rings (resp. semigroups) and study various properties of them.

We describe particular paths in the flip-graph of regular triangulations in any dimension. It is shown that any pair of regular triangulations is connected by a path along which none of their common faces are destroyed. As a consequence, we obtain the connectivity of the flip-graph of regular triangulations that share the same vertex set. © 2006 Elsevier B.V. All rights reserved.

The class of completely regular codes includes not only some of the most important error-correcting codes, such as perfect codes and uniformly packed codes, but also a number of substructures fundamental to the study of distance-regular graphs themselves. In a companion paper, we study products of completely regular codes and codes whose parameters form arithmetic progressions. This family of c...

Let   a family of monomorphisms in the category A ‎To study mathematical notions in a category  A‎, ‎such as injectivity‎, ‎tensor products‎, ‎flatness‎, ‎with respect to a class M of its (mono)morphisms‎, ‎one should know some of the categorical properties of the pair (A ‎,M ‎)‎. ‎In this paper we take A to be the‎‎category  Pos-S  of S-partially ordered sets  and   to be a particular‎ class o...