Uniqueness of SRB measures for transitive diffeomorphisms on surfaces

We give a description of ergodic components of SRB measures in terms of ergodic homoclinic classes associated to hyperbolic periodic points. For transitive surface diffeomorphisms, we prove that there exists at most one SRB measure.Comment: 18 pages, 4 figure

λ\lambda-symmetries for discrete equations

Following the usual definition of $\lambda$-symmetries of differential equations, we introduce the analogous concept for difference equations and apply it to some examples.Comment: 10 page

Multivariable control of a twin lift helicopter system using the LQG/LTR design methodology

Guidelines for developing a multivariable centralized automatic flight control system (AFCS) for a twin lift helicopter system (TLHS) are presented. Singular value ideas are used to formulate performance and stability robustness specifications. A linear Quadratic Gaussian with Loop Transfer Recovery (LQG/LTR) design is obtained and evaluated

Offensive alliances in cubic graphs

An offensive alliance in a graph $\Gamma=(V,E)$ is a set of vertices $S\subset V$ where for every vertex $v$ in its boundary it holds that the majority of vertices in $v$'s closed neighborhood are in $S$. In the case of strong offensive alliance, strict majority is required. An alliance $S$ is called global if it affects every vertex in $V\backslash S$, that is, $S$ is a dominating set of $\Gamma$. The global offensive alliance number $\gamma_o(\Gamma)$ (respectively, global strong offensive alliance number $\gamma_{\hat{o}}(\Gamma)$) is the minimum cardinality of a global offensive (respectively, global strong offensive) alliance in $\Gamma$. If $\Gamma$ has global independent offensive alliances, then the \emph{global independent offensive alliance number} $\gamma_i(\Gamma)$ is the minimum cardinality among all independent global offensive alliances of $\Gamma$. In this paper we study mathematical properties of the global (strong) alliance number of cubic graphs. For instance, we show that for all connected cubic graph of order $n$, $$\frac{2n}{5}\le \gamma_i(\Gamma)\le \frac{n}{2}\le \gamma_{\hat{o}}(\Gamma)\le \frac{3n}{4} \le \gamma_{\hat{o}}({\cal L}(\Gamma))=\gamma_{o}({\cal L}(\Gamma))\le n,$$ where ${\cal L}(\Gamma)$ denotes the line graph of $\Gamma$. All the above bounds are tight

Topological defects and misfit strain in magnetic stripe domains of lateral multilayers with perpendicular magnetic anisotropy

Stripe domains are studied in perpendicular magnetic anisotropy films nanostructured with a periodic thickness modulation that induces the lateral modulation of both stripe periods and inplane magnetization. The resulting system is the 2D equivalent of a strained superlattice with properties controlled by interfacial misfit strain within the magnetic stripe structure and shape anisotropy. This allows us to observe, experimentally for the first time, the continuous structural transformation of a grain boundary in this 2D magnetic crystal in the whole angular range. The magnetization reversal process can be tailored through the effect of misfit strain due to the coupling between disclinations in the magnetic stripe pattern and domain walls in the in-plane magnetization configuration

Music for Integration Research Briefing (Poster)

Music as an inclusion tool for children has been proven useful because music is a non-discriminatory way of engaging people with little command of the local language. This A0 poster offers policy and education professionals at all levels tools to integrate newly-arrived children, including a theoretical framework, practical examples and strategies to develop new activities