Smoothness of the future and past trapped sets in Kerr-Newman-Taub-NUT spacetimes

We consider the sets of future/past trapped null geodesics in the exterior region of a sub-extremal Kerr-Newman-Taub-NUT spacetime. We show that, from the point of view of any timelike observer outside of such a black hole, trapping can be understood as two smooth sets of spacelike directions on the celestial sphere of the observer

An exact sequence for contact- and symplectic homology

A symplectic manifold $W$ with contact type boundary $M = \partial W$ induces a linearization of the contact homology of $M$ with corresponding linearized contact homology $HC(M)$. We establish a Gysin-type exact sequence in which the symplectic homology $SH(W)$ of $W$ maps to $HC(M)$, which in turn maps to $HC(M)$, by a map of degree -2, which then maps to $SH(W)$. Furthermore, we give a description of the degree -2 map in terms of rational holomorphic curves with constrained asymptotic markers, in the symplectization of $M$.Comment: Final version. Changes for v2: Proof of main theorem supplemented with detailed discussion of continuation maps. Description of degree -2 map rewritten with emphasis on asymptotic markers. Sec. 5.2 rewritten with emphasis on 0-dim. moduli spaces. Transversality discussion reorganized for clarity (now Remark 9). Various other minor modification

Symplectic capacity and short periodic billiard trajectory

We prove that a bounded domain $\Omega$ in $\R^n$ with smooth boundary has a periodic billiard trajectory with at most $n+1$ bounce times and of length less than $C_n r(\Omega)$, where $C_n$ is a positive constant which depends only on $n$, and $r(\Omega)$ is the supremum of radius of balls in $\Omega$. This result improves the result by C.Viterbo, which asserts that $\Omega$ has a periodic billiard trajectory of length less than C'_n \vol(\Omega)^{1/n}. To prove this result, we study symplectic capacity of Liouville domains, which is defined via symplectic homology.Comment: 32 pages, final version with minor modifications. Published online in Mathematische Zeitschrif

An overview of the gravitational spin Hall effect

In General Relativity, the propagation of electromagnetic waves is usually described by the vacuum Maxwell's equations on a fixed curved background. In the limit of infinitely high frequencies, electromagnetic waves can be localized as point particles, following null geodesics. However, at finite frequencies, electromagnetic waves can no longer be treated as point particles following null geodesics, and the spin angular momentum of light comes into play, via the spin-curvature coupling. We will refer to this effect as the gravitational spin Hall effect of light. Here, we review a series of theoretical results related to the gravitational spin Hall effect of light, and we compare the predictions of different models. The analogy with the spin Hall effect in Optics is also explored, since in this field the effect is well understood, both theoretically and experimentally

Symplectic cohomology and q-intersection numbers

Given a symplectic cohomology class of degree 1, we define the notion of an equivariant Lagrangian submanifold. The Floer cohomology of equivariant Lagrangian submanifolds has a natural endomorphism, which induces a grading by generalized eigenspaces. Taking Euler characteristics with respect to the induced grading yields a deformation of the intersection number. Dehn twists act naturally on equivariant Lagrangians. Cotangent bundles and Lefschetz fibrations give fully computable examples. A key step in computations is to impose the "dilation" condition stipulating that the BV operator applied to the symplectic cohomology class gives the identity. Equivariant Lagrangians mirror equivariant objects of the derived category of coherent sheaves.Comment: 32 pages, 9 figures, expanded introduction, added details of example 7.5, added discussion of sign

Verification of loop parallelisations

Writing correct parallel programs becomes more and more difficult as the complexity and heterogeneity of processors increase. This issue is addressed by parallelising compilers. Various compiler directives can be used to tell these compilers where to parallelise. This paper addresses the correctness of such compiler directives for loop parallelisation. Specifically, we propose a technique based on separation logic to verify whether a loop can be parallelised. Our approach requires each loop iteration to be specified with the locations that are read and written in this iteration. If the specifications are correct, they can be used to draw conclusions about loop (in)dependences. Moreover, they also reveal where synchronisation is needed in the parallelised program. The loop iteration specifications can be verified using permission-based separation logic and seamlessly integrate with functional behaviour specifications. We formally prove the correctness of our approach and we discuss automated tool support for our technique. Additionally, we also discuss how the loop iteration contracts can be compiled into specifications for the code coming out of the parallelising compiler

New Achievements in Manufacturing of Church Bells

Analysis, modelling and design of the bells are a topical issue for manufacturers of bells, in general, and for church bells manufacturers in particular. The transition from manual design of a bell to that achieved with the computer led to  fabrication of bells capable to produce sounds of bells controlled close to those of musical instruments. It is mentioned a number of specialized software such as AUTODESK, for sizing profile of a bell; RESHAPE for analyzing and adjusting tones and WAVANAL for processing issued sound. The performances of a bell are closely related to the material used, casting technologies, possibly heat treatment and their grinding, processes that can be controlled automatically by computer

An Enzyme-Enhanced Extraction of Anthocyanins from Red Cabbage and Their Thermal Degradation Kinetics

There is a great demand for developing efficient anthocyanins extraction related to each plant material. Conventional methods have been replaced by novel techniques, but they might remain attractive when combined with the latter. Anthocyanins extraction from fresh and dried red cabbage was investigated by maceration, ultrasonication, and with enzymes. Pre-treatments through drying determined an improved extraction with respect to fresh samples, freeze-drying emerging as the best method. Combined enzyme-assisted extraction with maceration resulted in higher yield by conducting several extractions (1078.8±12.5 mg/100 g DW). The kinetic studies revealed good stability of anthocyanins at 50 °C, while constant degradation at 80 °C. The rate constant k at 80 °C and pH 3.5 was 1.7 10–3 min–1 and the half-life time t1/2 was 6.7 h. Thermal analysis evidenced heat-induced changes in particular for extracts undergoing pre-heating. These results are valuable for optimal processing conditions of anthocyanins-containing products

Échange international et distorsions internes:Comment gouverner la globalisation ?

La concurrence des pays émergents de la taille de la Chine ou de l’Inde fait resurgir avec force le débat qui oppose partisans et adversaires du libre-échange au sein même des pays développés. Pour les premiers, la croissance du commerce international est forcément bénéficiaire pour tous. Pour les seconds, elle est la cause de tous les maux et en particulier du chômage. Les choses sont pourtant bien différentes et beaucoup moins simples. Les changements dans le commerce international, comme d’ailleurs le progrès technique, créent inévitablement des distorsions qui perturbent le fonctionnement de l’économie. Ces distorsions ne sont pas réductibles à des dysfonctionnements des marchés des biens ou du travail. Elles ne peuvent donc pas être éliminées ab initio en choisissant des institutions optimales. Pour autant, des restrictions au commerce international ne sont pas une solution car elles risquent de créer d’autres distorsions qui viennent s’ajouter aux premières. Des distorsions avant tout intérieures appellent des solutions intérieures. Pour explorer ces solutions, il faut retenir une analyse conçue pour étudier, non les propriétés des positions d’équilibre avant et après l’ouverture à l’échange, mais les caractéristiques d’un processus de transition dont le succès n’est pas assuré. Ce type d’analyse permet de mettre en évidence la nécessité d’introduire une forme d’inertie dans les mécanismes d’ajustement. Si une relative flexibilité des salaires est encore possible quand l’intensité du changement est limitée, une certaine viscosité est requise dans le cas contraire, et un accès facilité aux ressources financières externes est nécessaire. Ce résultat pourrait aider à formuler les choix institutionnels et organisationnels à mettre en œuvre dans les économies qui veulent tirer avantage du commerce international et de la globalisation.Changes in the pattern of international trade inevitably create distortions that perturb the functioning of the economy. These distortions may not be reduced to malfunctioning goods or labour markets, and hence cannot be eliminated by simply choosing the optimal institutions. Domestic distortions call for domestic solutions. To explore these solutions it is useless to analyze the properties of equilibria before and after the opening to trade. Rather, we need to build an analytical framework suited to investigate the characteristics of a transition process whose success is not guaranteed ex ante. it appears that wage rigidity and an easy access to external financial resources are necessary in presence of fast pace of change, while if change is sufficiently slow the standard recipe of wage flexibility may be appropriate. These results may help in the institutional and organizational choices to be implemented in economies willing to profit from international trade and globalization