in this paper, the concept of k-regular fuzzy matrix as a general- ization of regular matrix is introduced and some basic properties of a k-regular fuzzy matrix are derived. this leads to the characterization of a matrix for which the regularity index and the index are identical. further the relation between regular, k-regular and regularity of powers of fuzzy matrices are dis- cussed.

We present a new AFEM for the Laplace-Beltrami operator with arbitrary polynomial degree on parametric surfaces, which are globally W 1 ∞ and piecewise in a suitable Besov class embedded in C1,α with α ∈ (0, 1]. The idea is to have the surface sufficiently well resolved in W 1 ∞ relative to the current resolution of the PDE in H1. This gives rise to a conditional contraction property of the PDE...

Szemerédi’s regularity lemma is an important tool in graph theory which has applications throughout combinatorics. In this paper we prove an analogue of Szemerédi’s regularity lemma in the context of abelian groups and use it to derive some results in additive number theory. The simplest is a structure theorm for sets which are almost sum-free. If A ⊆ {1, . . . , N} has δN2 triples (a1, a2, a3)...

In this paper we analyze the practical implications of Szemerédi’s regularity lemma in the preservation of metric information contained in large graphs. To this end, we present a heuristic algorithm to find regular partitions. Our experiments show that this method is quite robust to the natural sparsification of proximity graphs. In addition, this robustness can be enforced by graph densification.

The regularity lemma of Szemerédi gives a concise approximate description of a graph via a so called regular partition of its vertex set. In this paper we address the following problem: can a graph have two “distinct” regular partitions? It turns out that (as observed by several researchers) for the standard notion of a regular partition, one can construct a graph that has very distinct regular...

We study the general partitioning problem and the discrepancy problem in dense hypergraphs. Using the regularity lemma [16] and its algorithmic version proved in [5], we give polynomial time approximation schemes for the general partitioning problem and for the discrepancy problem.

Szemerédi’s regularity lemma proved to be a fundamental result in modern graph theory. It had a number of important applications and is a widely used tool in extremal combinatorics. For some applications variants of the regularity lemma were considered. Here we discuss several of those variants and their relation to each other.

in this paper we study optimization problems with infinite many inequality constraints on a banach space where the objective function and the binding constraints are locally lipschitz‎. ‎necessary optimality conditions and regularity conditions are given‎. ‎our approach are based on the michel-penot subdifferential.

in this paper, we investigate the existence of positive solutions for the ellipticequation $delta^{2},u+c(x)u = lambda f(u)$ on a bounded smooth domain $omega$ of $r^{n}$, $ngeq2$, with navier boundary conditions. we show that there exists an extremal parameter$lambda^{ast}>0$ such that for $lambda< lambda^{ast}$, the above problem has a regular solution butfor $lambda> lambda^{ast}$, the probl...

Let F be a fixed graph of chromatic number r + 1. We prove that for all large n the degree sequence of any F -free graph of order n is, in a sense, close to being dominated by the degree sequence of some r-partite graph. We present two different proofs: one goes via the Regularity Lemma and the other uses a more direct counting argument. Although the latter proof is longer, it gives better esti...