Switching-off in a minimal time a fitzhugh-nagumo system

This paper deals with a system that describes an electrical circuitcomposed by a linear system coupled to a nonlinear one involving a tunneldiode in a flush-and-fill circuit. One of the most comprehensive models for thiskind of circuits was introduced by R. Fitzhugh in 1961, when taking on carebiological tasks. The equation has in its phase plane only two periodic solutions,namely, the unstable singular point S0 and the stable cycle Γ. If the system isat rest on S0, the natural flow of orbits seeks to switch-on the process by going- as time goes by - toward its steady-state, Γ. By using suitable controls it ispossible to reverse such natural tendency going in a minimal time from Γ toS0, switching-off in this way the system. To achieve this goal it is mandatorya minimal enough strength on controls. These facts will be shown by means ofconsiderations on the null control sets in the process.

Classification of handwriting patterns in patients with Parkinson´s disease, using a biometric sensor

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Taylor's power law for ecological communities: an explanation on nonextensive/nonlinear statistical grounds

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A note on permutation regularity

The existence of a small partition of a combinatorial structure into random-like subparts, a so-called regular partition, has proven to be very useful in the study of extremal problems, and has deep algorithmic consequences. The main result in this direction is the Szemeredi Regularity Lemma in graph theory. In this note, we are concerned with regularity in permutations: we show that every permutation of a sufficiently large set has a regular partition into a small number of intervals. This refines the partition given by Cooper (2006) [10], which required an additional non-interval exceptional class. We also introduce a distance between permutations that plays an important role in the study of convergence of a permutation sequence. (C) 2011 Elsevier B.V. All rights reserved.

Lindelof spaces which are indestructible, productive, or D

We discuss relationships in Lindelof spaces among the properties "indestructible". "productive", "D", and related properties. (C) 2011 Elsevier B.V. All rights reserved.

On d- and D-separability

In this article we study relationships between d-separability and D-separability and present conditions under which these concepts are equivalent. We also study their relationship with D+-separability and define a generalization of discrete generability. (C) 2012 Elsevier B.V. All rights reserved.

COMMUTATIVE AUTOMORPHIC LOOPS OF ORDER p(3)

A loop is said to be automorphic if its inner mappings are automorphisms. For a prime p, denote by A(p) the class of all 2-generated commutative automorphic loops Q possessing a central subloop Z congruent to Z(p) such that Q/Z congruent to Z(p) x Z(p). Upon describing the free 2-generated nilpotent class two commutative automorphic loop and the free 2-generated nilpotent class two commutative automorphic p-loop F-p in the variety of loops whose elements have order dividing p(2) and whose associators have order dividing p, we show that every loop of A(p) is a quotient of F-p by a central subloop of order p(3). The automorphism group of F-p induces an action of GL(2)(p) on the three-dimensional subspaces of Z(F-p) congruent to (Z(p))(4). The orbits of this action are in one-to-one correspondence with the isomorphism classes of loops from A(p). We describe the orbits, and hence we classify the loops of A(p) up to isomorphism. It is known that every commutative automorphic p-loop is nilpotent when p is odd, and that there is a unique commutative automorphic loop of order 8 with trivial center. Knowing A(p) up to isomorphism, we easily obtain a classification of commutative automorphic loops of order p(3). There are precisely seven commutative automorphic loops of order p(3) for every prime p, including the three abelian groups of order p(3).

Continuity of Dynamical Structures for Nonautonomous Evolution Equations Under Singular Perturbations

In this paper we study the continuity of invariant sets for nonautonomous infinite-dimensional dynamical systems under singular perturbations. We extend the existing results on lower-semicontinuity of attractors of autonomous and nonautonomous dynamical systems. This is accomplished through a detailed analysis of the structure of the invariant sets and its behavior under perturbation. We prove that a bounded hyperbolic global solutions persists under singular perturbations and that their nonlinear unstable manifold behave continuously. To accomplish this, we need to establish results on roughness of exponential dichotomies under these singular perturbations. Our results imply that, if the limiting pullback attractor of a nonautonomous dynamical system is the closure of a countable union of unstable manifolds of global bounded hyperbolic solutions, then it behaves continuously (upper and lower) under singular perturbations.

A countably compact free Abelian group of size continuum that admits a non-trivial convergent sequence

We show that it is consistent with ZFC that the free Abelian group of cardinality c admits a topological group topology that makes it countably compact with a non-trivial convergent sequence. (C) 2011 Elsevier B.V. All rights reserved.

Properly coloured copies and rainbow copies of large graphs with small maximum degree

Let G be a graph on n vertices with maximum degree ?. We use the Lovasz local lemma to show the following two results about colourings ? of the edges of the complete graph Kn. If for each vertex v of Kn the colouring ? assigns each colour to at most (n - 2)/(22.4?2) edges emanating from v, then there is a copy of G in Kn which is properly edge-coloured by ?. This improves on a result of Alon, Jiang, Miller, and Pritikin [Random Struct. Algorithms 23(4), 409433, 2003]. On the other hand, if ? assigns each colour to at most n/(51?2) edges of Kn, then there is a copy of G in Kn such that each edge of G receives a different colour from ?. This proves a conjecture of Frieze and Krivelevich [Electron. J. Comb. 15(1), R59, 2008]. Our proofs rely on a framework developed by Lu and Szekely [Electron. J. Comb. 14(1), R63, 2007] for applying the local lemma to random injections. In order to improve the constants in our results we use a version of the local lemma due to Bissacot, Fernandez, Procacci, and Scoppola [preprint, arXiv:0910.1824]. (c) 2011 Wiley Periodicals, Inc. Random Struct. Alg., 40, 425436, 2012

Almost p-compact groups

We show that if p is a selective ultrafilter, then for each cardinal alpha <= omega(1), there exists a topological group G such that G(beta) is almost p-compact (in particular, countably compact), for beta < alpha, but G(alpha) is not countably compact. If in addition, we assume Martin's Axiom, then the result above holds for every alpha < c. (C) 2012 Elsevier By. All rights reserved.

Architectures, stability and optimization for clock distribution networks

Synchronous telecommunication networks, distributed control systems and integrated circuits have its accuracy of operation dependent on the existence of a reliable time basis signal extracted from the line data stream and acquirable to each node. In this sense, the existence of a sub-network (inside the main network) dedicated to the distribution of the clock signals is crucially important. There are different solutions for the architecture of the time distribution sub-network and choosing one of them depends on cost, precision, reliability and operational security. In this work we expose: (i) the possible time distribution networks and their usual topologies and arrangements. (ii) How parameters of the network nodes can affect the reachability and stability of the synchronous state of a network. (iii) Optimizations methods for synchronous networks which can provide low cost architectures with operational precision, reliability and security. (C) 2011 Elsevier B. V. All rights reserved.

Towards automated first-order abduction: the cut-based approach

Traditional abduction imposes as a precondition the restriction that the background information may not derive the goal data. In first-order logic such precondition is, in general, undecidable. To avoid such problem, we present a first-order cut-based abduction method, which has KE-tableaux as its underlying inference system. This inference system allows for the automation of non-analytic proofs in a tableau setting, which permits a generalization of traditional abduction that avoids the undecidable precondition problem. After demonstrating the correctness of the method, we show how this method can be dynamically iterated in a process that leads to the construction of non-analytic first-order proofs and, in some terminating cases, to refutations as well.

The sigma-isotypic decomposition and the sigma-index of reversible-equivariant systems

This work is concerned with dynamical systems in presence of symmetries and reversing symmetries. We describe a construction process of subspaces that are invariant by linear Gamma-reversible-equivariant mappings, where Gamma is the compact Lie group of all the symmetries and reversing symmetries of such systems. These subspaces are the sigma-isotypic components, first introduced by Lamb and Roberts in (1999) [10] and that correspond to the isotypic components for purely equivariant systems. In addition, by representation theory methods derived from the topological structure of the group Gamma, two algebraic formulae are established for the computation of the sigma-index of a closed subgroup of Gamma. The results obtained here are to be applied to general reversible-equivariant systems, but are of particular interest for the more subtle of the two possible cases, namely the non-self-dual case. Some examples are presented. (C) 2011 Elsevier BM. All rights reserved.

A NOTE ON OPEN 3-MANIFOLDS SUPPORTING FOLIATIONS BY PLANES

We show that if N, an open connected n-manifold with finitely generated fundamental group, is C-2 foliated by closed planes, then pi(1)(N) is a free group. This implies that if pi(1)(N) has an abelian subgroup of rank greater than one, then F has at least a nonclosed leaf. Next, we show that if N is three dimensional with fundamental group abelian of rank greater than one, then N is homeomorphic to T-2 x R. Furthermore, in this case we give a complete description of the foliation.