Hemihelical local minimizers in prestrained elastic bi-strips

We consider a double layered prestrained elastic rod in the limit of vanishing cross section. For the resulting limit Kirchoff-rod model with intrinsic curvature we prove a supercritical bifurcation result, rigorously showing the emergence of a branch of hemihelical local minimizers from the straight configuration, at a critical force and under clamping at both ends. As a consequence we obtain the existence of nontrivial local minimizers of the $3$-d system.Comment: 16 pages, 2 figure

Domain formation in magnetic polymer composites: an approach via stochastic homogenization

We study the magnetic energy of magnetic polymer composite materials as the average distance between magnetic particles vanishes. We model the position of these particles in the polymeric matrix as a stochastic lattice scaled by a small parameter $\varepsilon$ and the magnets as classical $\pm 1$ spin variables interacting via an Ising type energy. Under surface scaling of the energy we prove, in terms of $\Gamma$-convergence that, up to subsequences, the (continuum) $\Gamma$-limit of these energies is finite on the set of Caccioppoli partitions representing the magnetic Weiss domains where it has a local integral structure. Assuming stationarity of the stochastic lattice, we can make use of ergodic theory to further show that the $\Gamma$-limit exists and that the integrand is given by an asymptotic homogenization formula which becomes deterministic if the lattice is ergodic.Comment: 31 page

Ground states of a two phase model with cross and self attractive interactions

We consider a variational model for two interacting species (or phases), subject to cross and self attractive forces. We show existence and several qualitative properties of minimizers. Depending on the strengths of the forces, different behaviors are possible: phase mixing or phase separation with nested or disjoint phases. In the case of Coulomb interaction forces, we characterize the ground state configurations

(Total) Vector Domination for Graphs with Bounded Branchwidth

Given a graph $G=(V,E)$ of order $n$ and an $n$-dimensional non-negative vector $d=(d(1),d(2),\ldots,d(n))$, called demand vector, the vector domination (resp., total vector domination) is the problem of finding a minimum $S\subseteq V$ such that every vertex $v$ in $V\setminus S$ (resp., in $V$) has at least $d(v)$ neighbors in $S$. The (total) vector domination is a generalization of many dominating set type problems, e.g., the dominating set problem, the $k$-tuple dominating set problem (this $k$ is different from the solution size), and so on, and its approximability and inapproximability have been studied under this general framework. In this paper, we show that a (total) vector domination of graphs with bounded branchwidth can be solved in polynomial time. This implies that the problem is polynomially solvable also for graphs with bounded treewidth. Consequently, the (total) vector domination problem for a planar graph is subexponential fixed-parameter tractable with respectto $k$, where $k$ is the size of solution.Comment: 16 page

Verbi locativi in italiano come varianti di verbi supporto

In questo articolo discuteremo la nozione di "carrier verbs" (secondo la definizione del linguista americano Zellig Harris) o di "light verbs" (come denominata all'inizio del XX secolo da Otto Jespersen). La nostra cornice teorica è rappresentata dal lessico-grammatica di Maurice Gross, una teoria iniziata negli anni settanta a partire dalla sintassi del francese sulle basi matematiche già individuate per la lingua inglese da Zellig Harris. In particolare, discuteremo di come alcuni verbi locativi dell'italiano possano essere usati come verbi supporto (secondo la definizione data da Gross dei "light verbs" harrisiani) e assumano il ruolo sintattico una volta attribuito dai grammatici greci e latini alla copula esse.En aquest article discutirem la noció de "carrier verbs" (segons la definició del lingüista americà Zellig Harris) o de "light verbs" (segons la denominació que Otto Jespersen n'havia donat a principi del segle XX). El nostre marc teòric de referència és el lèxic-gramàtica de Maurice Gross, una teoria començada els anys setanta a partir de la sintaxi del francès en les bases matemàtiques ja individuades per a la llengua anglesa per Zelling Harris. Concretament, tractarem de com alguns verbs locatius de l'italià es poden emprar com a verbs de suport (tal com Gross va definir els "light verbs" harrisians) i de com assumeixen el paper sintàctic que els gramàtics grecs i llatins atribuïen a la còpula esse.In this article we aim at discussing the notion of carrier verbs (according to the definition provided by the American linguist Zellig Harris) or of light verbs (as defined at the beginning of the twentieth century by Otto Jespersen). Our theoretical framework is represented by Maurice Gross' lexicon-grammar, a theory developed during the seventies on the French syntax and directly inspired by Zellig Harris' mathematical grammar of English. Particularly, we are going to discuss of how some Italian locative verbs can be used as support verbs (according to the definition which Maurice Gross has given of the harrisian light verbs) and can play the syntactic role traditionally given to the copula esse by the Greek and Latin grammarians

Parameterized Inapproximability of Target Set Selection and Generalizations

In this paper, we consider the Target Set Selection problem: given a graph and a threshold value $thr(v)$ for any vertex $v$ of the graph, find a minimum size vertex-subset to "activate" s.t. all the vertices of the graph are activated at the end of the propagation process. A vertex $v$ is activated during the propagation process if at least $thr(v)$ of its neighbors are activated. This problem models several practical issues like faults in distributed networks or word-to-mouth recommendations in social networks. We show that for any functions $f$ and $\rho$ this problem cannot be approximated within a factor of $\rho(k)$ in $f(k) \cdot n^{O(1)}$ time, unless FPT = W[P], even for restricted thresholds (namely constant and majority thresholds). We also study the cardinality constraint maximization and minimization versions of the problem for which we prove similar hardness results