M. and M.   Abstract: Existence and uniqueness of solution for singular 2-D systems depends on regularity condition. Simple regularity implies regularity and under this assumption, the generalized wave model (GWM) is introduced to cast singular 2-D system of equations as a family of non-singular 1-D models with variable structure.These index dependent models, along with a set of boundary co...

Based on a recently proposed parametric approach for eigenstructure assignment in descriptor linear systems via output feedback, the robust eigenvalue assignment problem in descriptor linear systems via output feedback is solved. The problem aims to assign a set of finite closed-loop eigenvalues which have minimum sensitivities with respect to perturbations in the closed-loop coefficient matric...

Regular languages are closed under a wealth of formal language operators. Incorporating such operators in regular expressions leads to concise language specifications, but the transformation of such enhanced regular expressions to finite automata becomes more involved. We present an approach that enables the direct construction of finite automata from regular expressions enhanced with further o...

Continuation-passing style (CPS) is often criticized to be more expensive than the usual direct style of functional programming. By structure, CPS functions indeed are passed one extra argument (the continuation), and each intermediate result indeed occurs in a function call (to the continuation). As higher-order functions, continuations are also more expensive. However, by structure also, CPS ...

On December 3, 2012, following the Third Abel conference, in honor of Endre Szemerédi, Terence Tao posted on his blog a proof of the spectral version of Szemerédi’s regularity lemma. This, in turn, proves the original version.

By using the Szemerédi Regularity Lemma [10], Alon and Sudakov [1] recently extended the classical Andrásfai-Erdős-Sós theorem [2] to cover general graphs. We prove, without using the Regularity Lemma, that the following stronger statement is true. Given any (r+1)-partite graph H whose smallest part has t vertices, there exists a constant C such that for any given ε > 0 and sufficiently large n...

Let H be a fixed graph with h vertices. The graph removal lemma states that every graph on n vertices with o(n) copies of H can be made H-free by removing o(n) edges. We give a new proof which avoids Szemerédi’s regularity lemma and gives a better bound. This approach also works to give improved bounds for the directed and multicolored analogues of the graph removal lemma. This answers question...

The asymptotics of 2-colour Ramsey numbers of loose and tight cycles in 3-uniform hypergraphs were recently determined [16, 17]. We address the same problem for Berge cycles and for 3 colours. Our main result is that the 3-colour Ramsey number of a 3-uniform Berge cycle of length n is asymptotic to 5n 4 . The result is proved with the Regularity Lemma via the existence of a monochromatic connec...

Recently, Mikołaj Bojańczyk introduced a class of max-regular languages, an extension of regular languages of infinite words preserving many of its usual properties. This new class can be seen as a different way of generalizing the notion of regularity from finite to infinite words. This paper compares regular and max-regular languages in terms of topological complexity. It is proved that up to...

Szemerédi’s Regularity Lemma is an important tool for analyzing the structure of dense graphs. There are versions of the Regularity Lemma for sparse graphs, but these only apply when the graph satisfies some local density condition. In this paper, we prove a sparse Regularity Lemma that holds for all graphs. More generally, we give a Regularity Lemma that holds for arbitrary real matrices.