Mediterranean journal of mathematics

Vol. 13, num. 6, p. 4109-4128

DOI: 10.1007/s00009-016-0735-3

Date of publication: 2016-12

Abstract:

This paper is devoted to the construction and analysis of a Moser–Steffensen iterative scheme. The method has quadratic convergence without evaluating any derivative nor inverse operator. We present a complete study of the order of convergence for systems of equations, hypotheses ensuring the local convergence, and finally, we focus our attention to its numerical behavior. The conclusion is that the method improves the applicability of both Newton and Steffensen methods having the same order of convergence.]]>

Mediterranean journal of mathematics

Vol. 12, num. 4, p. 1215-1226

DOI: 10.1007/s00009-015-0577-4

Date of publication: 2015-11-01

Abstract:

The dg operad of cellular chains on the operad of spineless cacti of Kaufmann (Topology 46(1):39-88, 2007) is isomorphic to the Gerstenhaber-Voronov dg operad codifying the cup product and brace operations on the Hochschild cochains of an associative algebra, and to the suboperad of the surjection operad of Berger and Fresse (Math Proc Camb Philos Soc 137(1):135-174, 2004), McClure and Smith (Recent progress in homotopy theory (Baltimore, MD, 2000). Contemp Math., Amer. Math. Soc., Providence 293:153-193, 2002) and McClure and Smith (J Am Math Soc 16(3):681-704, 2003). Its homology is the Gerstenhaber dg operad . We construct a map of dg operads such that is commutative and is the canonical map . This formalises the idea that, since the cup product is commutative in homology, its symmetrisation is a homotopy associative operation. Our explicit structure does not vanish on non-trivial shuffles in higher degrees, so does not give a map . If such a map could be written down explicitly, it would immediately lead to a structure on and on Hochschild cochains, that is, to an explicit and direct proof of the Deligne conjecture.

The final publication is available at Springer via http://dx.doi.org/10.1007/s00009-015-0577-4]]>

Mediterranean journal of mathematics

DOI: 10.1007/s00009-013-0360-3

Date of publication: 2013-11

Abstract:

Let G be a graph of order p and size q with loops allowed. A bijective function f:V(G)¿E(G)¿{i}p+qi=1 is an edge-magic labeling of G if the sum f(u)+f(uv)+f(v)=k is independent of the choice of the edge uv. The constant k is called either the valence, the magic weight or the magic sum of the labeling f. If a graph admits an edge-magic labeling, then it is called an edge-magic graph. Furthermore, if the function f meets the extra condition that f(V(G))={i}pi=1 then f is called a super edge-magic labeling and G is called a super edge-magic graph. A digraph D admits a labeling, namely l, if its underlying graph, und(D) admits l. In this paper, we introduce a new construction of super edge-magic labelings which are related to the classical jump of the knight on the chess game. We also use super edge-magic labelings of digraphs together with a generalization of the Kronecker product to get edge-magic labelings of some families of graphs.]]>

Mediterranean journal of mathematics

Vol. 86, num. 4, p. 617-632

DOI: 10.1007/s00009-010-0100-x

Date of publication: 2011-12

Mediterranean journal of mathematics

Vol. 6, num. 4, p. 471-481

DOI: 10.1007/s00009-009-0019-2

Date of publication: 2009-12

Abstract:

Given a pair of matrices (A,B) we study the Lipschitz stability of its controlled invariant subspaces. A sufficient condition is derived from the geometry of the set formed by the quadruples (A,B, F, S) where S is an (A,B)-invariant subspace and F a corresponding feedback.]]>