A survey on the inverse integrating factor

The relation between limit cycles of planar differential systems and the inverse integrating factor was first shown in an article of Giacomini, Llibre and Viano appeared in 1996. From that moment on, many research articles are devoted to the study of the properties of the inverse integrating factor and its relationwith limit cycles and their bifurcations. This paper is a summary of all the results about this topic. We include a list of references together with the corresponding related results aiming at being as much exhaustive as possible. The paper is, nonetheless, self-contained in such a way that all the main results on the inverse integrating factor are stated and a complete overview of the subject is given. Each section contains a different issue to which the inverse integrating factor plays a role: the integrability problem, relation with Lie symmetries, the center problem, vanishing set of an inverse integrating factor, bifurcation of limit cycles from either a period annulus or from a monodromic ω-limit set and some generalizations.

Canonical Noether symmetries and commutativity properties for gauge systems

For a dynamical system defined by a singular Lagrangian, canonical Noether symmetries are characterized in terms of their commutation relations with the evolution operators of Lagrangian and Hamiltonian formalisms. Separate characterizations are given in phase space, in velocity space, and through an evolution operator that links both spaces. 2000 American Institute of Physics.

(When) would i lie to you? comment on? deception: the role of consequences?

This paper reconsiders the evidence on lying or deception presented in Gneezy (2005,American Economic Review). We argue that Gneezy?s data cannot reject the hipótesis that people are one of two kinds: either a person will never lie, or a person will lie whenever she prefers the outcome obtained by lying over the outcome obtained by telling the truth. This implies that so long as lying induces a preferred outcome over truth-telling, a person?s decisión of whether to lie may be completely insensitive to other changes in the induced outcomes, such as exactly how much she monetarily gains relative to how much she hurts an anonymous partner. We run new but similar experiments to those of Gneezy in order to test this hypothesis. We find that our data cannot reject this hypothesis either, but we also discover substantial differences in behavior between our sub jects and Gneezy?s sub jects.

Strongly non-degenerate Lie algebras

Let A be a semiprime 2 and 3-torsion free non-commutative associative algebra. We show that the Lie algebra Der(A) of(associative) derivations of A is strongly non-degenerate, which is a strong form of semiprimeness for Lie algebras, under some additional restrictions on the center of A. This result follows from a description of the quadratic annihilator of a general Lie algebra inside appropriate Lie overalgebras. Similar results are obtained for an associative algebra A with involution and the Lie algebra SDer(A) of involution preserving derivations of A

Quantum symmetries for exceptional SU(4) modular invariants associated with conformal embeddings

Three exceptional modular invariants of SU(4) exist at levels 4, 6 and 8. They can be obtained from appropriate conformal embeddings and the corresponding graphs have self-fusion. From these embeddings, or from their associated modular invariants, we determine the algebras of quantum symmetries, obtain their generators,and, as a by-product, recover the known graphs E4, E6 and E8 describing exceptional quantum subgroups of type SU(4). We also obtain characteristic numbers (quantum cardinalities, dimensions) for each of them and for their associated quantum groupoïds.

Pairing in a two-component ultracold Fermi gas: Phases with broken-space symmetries

We explore the phase diagram of a two-component ultracold atomic Fermi gas interacting with zero-range forces in the limit of weak coupling. We focus on the dependence of the pairing gap and the free energy on the variations in the number densities of the two species while the total density of the system is held fixed. As the density asymmetry is increased, the system exhibits a transition from a homogenous Bardeen-Cooper-Schrieffer (BCS) phase to phases with spontaneously broken global space symmetries. One such realization is the deformed Fermi surface superfluidity (DFS) which exploits the possibility of deforming the Fermi surfaces of the species into ellipsoidal form at zero total momentum of Cooper pairs. The critical asymmetries at which the transition from DFS to the unpaired state occurs are larger than those for the BCS phase. In this precritical region the DFS phase lowers the pairing energy of the asymmetric BCS state. We compare quantitatively the DFS phase to another realization of superconducting phases with broken translational symmetry: the single-plane-wave Larkin-Ovchinnikov-Fulde-Ferrell phase, which is characterized by a nonvanishing center-of-mass momentum of the Cooper pairs. The possibility of the detection of the DFS phase in the time-of-flight experiments is discussed and quantified for the case of 6Li atoms trapped in two different hyperfine states.

Symmetries and fixed point stability of stochastic differential equations modeling self-organized criticality

A stochastic nonlinear partial differential equation is constructed for two different models exhibiting self-organized criticality: the Bak-Tang-Wiesenfeld (BTW) sandpile model [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] and the Zhang model [Phys. Rev. Lett. 63, 470 (1989)]. The dynamic renormalization group (DRG) enables one to compute the critical exponents. However, the nontrivial stable fixed point of the DRG transformation is unreachable for the original parameters of the models. We introduce an alternative regularization of the step function involved in the threshold condition, which breaks the symmetry of the BTW model. Although the symmetry properties of the two models are different, it is shown that they both belong to the same universality class. In this case the DRG procedure leads to a symmetric behavior for both models, restoring the broken symmetry, and makes accessible the nontrivial fixed point. This technique could also be applied to other problems with threshold dynamics.

Remote Synchronization Reveals Network Symmetries and Functional Modules

We study a Kuramoto model in which the oscillators are associated with the nodes of a complex network and the interactions include a phase frustration, thus preventing full synchronization. The system organizes into a regime of remote synchronization where pairs of nodes with the same network symmetry are fully synchronized, despite their distance on the graph. We provide analytical arguments to explain this result, and we show how the frustration parameter affects the distribution of phases. An application to brain networks suggests that anatomical symmetry plays a role in neural synchronization by determining correlated functional modules across distant locations.

Symmetries of the free Schrödinger equation in the non-commutative plane

We study all the symmetries of the free Schr odinger equation in the non-commu- tative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schröodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.

Symmetries of the free Schrödinger equation in the non-commutative plane

We study all the symmetries of the free Schrödinger equation in the non-commu- tative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schröodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.

One more lie: the Monday effect in Spain’s retail petrol market

Empirical evidence drawn from the economic literature points to a low level of competition in the retail petrol market. Similar evidence can be found for the Spanish market. In fact, both Spain’s antitrust authority -Comisión Nacional de la Competencia- and its energy regulator -Comisión Nacional de la Energía- have recently initiated disciplinary proceedings against the majors on the grounds of suspected price manipulation in the retail petrol market. They are accused of cutting retail prices on Mondays so as to distort the rank position of Spain in European Union statistics in a practice that has received the name of the Monday effect. Here, we analyze this effect by constructing a database that includes daily retail prices for all petrol stations in Spain in the period 2009-2012, and a more detailed database for the city of Barcelona in 2013. Our estimations confirm that: 1- in 2011 and 2012 prices fell on Mondays at retailers branded by majors; 2- prices were unchanged at stations in our two control groups; 3- prices were also seen to fall when a more detailed analysis was conducted, and this price cut was also found in 2013. In short, one more indicator of collusion in this sector and … one more lie.

Aplicacions contínues entre espais classificadors de grups p-locals finits

Projecte de recerca elaborat a partir d’una estada a la Universitat d'Aberdeen, Irlanda, entre abril i maig del 2007. Un dels objectius de la topologia algebraica és la de classificar espais topològics i aplicacions continues mitjançant estructures algebraiques associades a ells. És a dir, mitjançant diferents maneres d'associar un objecte algebraic a un espai, es pretén reflectir el màxim de la seva estructura topològica. D'altra banda, donat un grup G, se li pot associar un espai topològic BG anomenat l'espai classificador del grup que és l'espai que classifica els G-fibrats vectorials. El programa d'estudiar el tipus d'homotopia d'espais i aplicacions contínues ha donat molts fruits quan els espais que s'estudien són espais classificadors (en particular, grups finits i grups de Lie). En particular, a causa del fet que moltes propietats algebraiques del grup queden reflectides en l'espai classificador, aquest tipus d'espais juguen un paper molt important en la interelació entre l'àlgebra i la topologia. Per exemple, els treballs de Dwyer, Zabrodsky i Mislin identifiquen les aplicacions contínues entre espais classificadors d'un p-grup i un grup qualsevol amb els morfismes entre grups llevat conjugació. L’objectiu d’aquest projecte és el de descriure les aplicacions contínues entre p-completats d’espais classificadors a partir d’informació algebraica referent a l’estructura de p-subgrups de cadascun d’ells.

Narrating urban entrepreneurship: a matter of imagineering?

The battle between cities with regard to their creative possibilities has evolved into a process of multiplying ever-new images and variegated stories of urban attractiveness and success. Engineering “cool” images and “hot” stories about one’s city is now a central endeavor in the narratives of urban policy-making that center more and more on the idea of the entrepreneurial city. The making of an entrepreneurial image is enacted through various narrative genres that lie somewhere between place making and place marketing, between branding and boosting, between restoration and revanchism, between iconic architecture and mega-spectacle. This “imagineering” is not only part of the way cities try to (re)present themselves as entrepreneurial to various audiences through a real “image inflation” (Zukin, 2008, p. xii) but is 1 Forthcoming in: B. Lange,.A. Kalandides, B. Stoeber, I. Wellmann (Hrsg.) (2009): Governance der Kreativwirtschaft. Diagnosen und Handlungsoptionen. Transcript-Verlag, Bielefeld. 2 also inscribed in the various ways urban creativity and entrepreneurship can be studied, researched and imagined. In this chapter we aim to differentiate the political narratives of the entrepreneurial city as we emphasize the need to understand the politics of narration and make a plea for critical reflexivity in our forms of researching and theorizing. We will thus try to investigate how the politics of narration is intertwined with the narration of political concepts and will argue that the narrating of urban entrepreneurship can raise very different images and discourses of city life beyond those that are currently engineered. We will distinguish between a grand narrative, a counter-narrative, and an assemblage of more ambivalent little narratives, which we call prosaic narration. While the distinction between these three types might be seen as a bit too simple and “straight”, we believe that by juxtaposing these different forms of narration and alternating between them, we can help problematize the engineering of the city as entrepreneurial and imagine alternative views both of city life and of what is understood as its creativity.

Symmetric planar central configurations of five bodies: Euler plus two

We study planar central configurations of the five-body problem where three of the bodies are collinear, forming an Euler central configuration of the three-body problem, and the two other bodies together with the collinear configuration are in the same plane. The problem considered here assumes certain symmetries. From the three bodies in the collinear configuration, the two bodies at the extremities have equal masses and the third one is at the middle point between the two. The fourth and fifth bodies are placed in a symmetric way: either with respect to the line containing the three bodies, or with respect to the middle body in the collinear configuration, or with respect to the perpendicular bisector of the segment containing the three bodies. The possible stacked five-body central configurations satisfying these types of symmetries are: a rhombus with four masses at the vertices and a fifth mass in the center, and a trapezoid with four masses at the vertices and a fifth mass at the midpoint of one of the parallel sides.

International regimes as knowledge syndicates? Energy and trends of global governance

El poder de l'Estat i la sobirania tradicional s'està deteriorant de manera constant, sobretot en termes de la provisió de certs béns públics fonamentals. Els Estats, en particular, són incapaços de manejar el coneixement i la informació que és essencial per mantenir la competitivitat i la sostenibilitat en una economia interdependent. Estructures fiables de la governança mundial i la cooperació internacional estan lluny de ser establertes. Energia com a problema a les agendes p dels governs, les empreses privades i la societat civil és un exemple manifest d'aquesta dinàmica.. L'actual sistema de governança mundial d'energia implica accions polítiques disperses per actors divers. L'Agència Internacional de l'Energia té un paper destacat, però està debilitat per la seva composició limitada i basada en el coneixement- epistèmic en lloc del material o executiu. Aquest treball sosté que ni la mida ni nombre de membres disponibles estan dificultant la governabilitat mundial d'energia. Més aviat, l'energia és una sèrie de béns públics que es troben als llimbs, on els estats no poden pagar la seva disposició, així com els diversos interessos impedir l'establiment d'una autoritat internacional. Després de la introducció de la teoria del règim internacional i el concepte de coneixement basats en les comunitats epistèmiques, l'article revisa l'estat actual de la governabilitat de l'energia mundia. A continuació es presenta una comparació d'aquesta estructura amb els règims de govern nacional i regional, d'una banda, i amb règims globals ambientals i de salut, de l'altra