Every contact manifold can be given a non-fillable contact structure

Recently Francisco Presas Mata constructed the first examples of closed contact manifolds of dimension larger than 3 that contain a plastikstufe, and hence are non-fillable. Using contact surgery on his examples we create on every sphere S^{2n-1}, n>1, an exotic contact structure \xi_- that also contains a plastikstufe. As a consequence, every closed contact manifold M (except S^1) can be converted into a contact manifold that is not (semi-positively) fillable by taking the connected sum of M with (S^{2n-1},\xi_-).Comment: 15 pages, 4 figure

A note on Reeb dynamics on the tight 3-sphere

We show that a nondegenerate tight contact form on the 3-sphere has exactly two simple closed Reeb orbits if and only if the differential in linearized contact homology vanishes. Moreover, in this case the Floquet multipliers and Conley-Zehnder indices of the two Reeb orbits agree with those of a suitable irrational ellipsoid in 4-space.Comment: 20 pages, no figure

Playing with parameters: structural parameterization in graphs

When considering a graph problem from a parameterized point of view, the parameter chosen is often the size of an optimal solution of this problem (the "standard" parameter). A natural subject for investigation is what happens when we parameterize such a problem by various other parameters, some of which may be the values of optimal solutions to different problems. Such research is known as parameterized ecology. In this paper, we investigate seven natural vertex problems, along with their respective parameters: the size of a maximum independent set, the size of a minimum vertex cover, the size of a maximum clique, the chromatic number, the size of a minimum dominating set, the size of a minimum independent dominating set and the size of a minimum feedback vertex set. We study the parameterized complexity of each of these problems with respect to the standard parameter of the others.Comment: 17 page

Compactness results in Symplectic Field Theory

This is one in a series of papers devoted to the foundations of Symplectic Field Theory sketched in [Y Eliashberg, A Givental and H Hofer, Introduction to Symplectic Field Theory, Geom. Funct. Anal. Special Volume, Part II (2000) 560--673]. We prove compactness results for moduli spaces of holomorphic curves arising in Symplectic Field Theory. The theorems generalize Gromov's compactness theorem in [M Gromov, Pseudo-holomorphic curves in symplectic manifolds, Invent. Math. 82 (1985) 307--347] as well as compactness theorems in Floer homology theory, [A Floer, The unregularized gradient flow of the symplectic action, Comm. Pure Appl. Math. 41 (1988) 775--813 and Morse theory for Lagrangian intersections, J. Diff. Geom. 28 (1988) 513--547], and in contact geometry, [H Hofer, Pseudo-holomorphic curves and Weinstein conjecture in dimension three, Invent. Math. 114 (1993) 307--347 and H Hofer, K Wysocki and E Zehnder, Foliations of the Tight Three Sphere, Annals of Mathematics, 157 (2003) 125--255].Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper25.abs.htm

Enough

This collection of short stories follows the themes of trauma and the feeling of not being enough for yourself or others. This includes the pressures we put on ourselves to keep trying to be “right” or what we’re “supposed to be”. The idea is apparent that reaching out instead of self- isolating benefits the characters. What also connects these works is a hint of Southern flair, family, and humor. An irreverent voice connects the work and most of the characters. The inclusion of humor to get through suffering and as a way to talk about tough subjects is a concurrent theme. Body issues, sexual trauma, and aging among other themes are all touched upon and delivered with a side of pole dancing, a GoPro on a fat beagle, a night out with Nana’s ashes and more

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

Rock-Around Orbits

The ability to observe resident space objects (RSOs) is a necessary requirement for space situational awareness. While objects in a Low-Earth Orbit are easily ob- servable by ground-based sensors, diffculties arise when trying to monitor objects with larger orbits far above the Earth's surface, e.g. a Geostationary Orbit. Camera systems mounted on satellites can provide an eff ective way to observe these objects. Using a satellite with a speci c orbit relative to the RSO's orbit, one can passively observe all the objects that share the RSO's orbit over a given time without active maneuvering. An orbit can be defi ned by ve parameters: semi-major axis, eccentricity, right ascension of ascending node, inclination, and argument of perigee (a; e; ; i; !). Using these parameters, one can create an orbit that will surround the target orbit allowing the satellite in the Rock-Around Orbit (RAO) orbit to have a 360 degree view of RSOs in the target orbit. The RAO orbit can be applied to any circular or elliptical target orbit; and for any target orbit, there are many possible RAO orbits. Therefore, diff erent methods are required to narrow down the selection of RAO orbits. These methods use distance limitations, time requirements, orbit perturbations, and other factors to limit the orbit selections. The first step is to determine the range of RAO semi-major axes for any given target orbit by ensuring the RAO orbit does not exceed a prescribed maximum al- lowable distance, dmax from the target orbit. It is then necessary to determine the eccentricity range for each possible RAO semi-major axis. This is done by ensuring the RAO still does not exceed dmax but also ensuring that the RAO orbit travels inside and outside of the target orbit. This comprises one half of the rock-around motion. The final step is to determine the inclination of the RAO orbit. Only a small inclination different from that of the target orbit is required to complete the rock-around motion while the maximum inclination is found by making sure the RAO orbit does not exceed dmax. It is then important to consider orbit perturbations, since they can destroy the synchronization between the RAO and target orbit. By examining the e ffects of the linear J2 perturbations on the right ascension of ascending node and argument of perigee, the correct semi-major axis, eccentricity, and inclination can be chosen to minimize the amount of fuel required for station keeping. The optimal values can be found by finding the Delta v needed for di fferent combinations of the variables and then choosing the values that provide the minimum Delta v. For any target orbit, there are multiple RAO orbit possibilities that can provide 360 degree coverage of a target orbit. Even after eliminating some of them based on the methods already described, there are still many possibilities. The rest of the elimination process would then be based on the mission requirements which could be the range of an on-board sensor, the thruster or reaction wheel controls, or any other number of possibilities

Methods and results of modeling and transmission-line calculations of the superconducting dipole chains of CERN's LHC collider

Electrical modeling and simulation of the LHC magnet strings are being used to determine the key parameters that are needed for the design of the powering and energy extraction equipment. Poles and zeros of the Laplace expression approximating the Bode plot of the measured coil impedance are used to synthesize an R/L/C model of the magnet. Subsequently, this model is used to simulate the behavior of the LHC main dipole magnet string. Lumped transmission line behavior, impedance, resonance, propagation of the power supply ripple, ramping errors, energy extraction transients and their damping are presented in this paper. (3 refs)

A Methodology for Engineering Collaborative and ad-hoc Mobile Applications using SyD Middleware

Today’s web applications are more collaborative and utilize standard and ubiquitous Internet protocols. We have earlier developed System on Mobile Devices (SyD) middleware to rapidly develop and deploy collaborative applications over heterogeneous and possibly mobile devices hosting web objects. In this paper, we present the software engineering methodology for developing SyD-enabled web applications and illustrate it through a case study on two representative applications: (i) a calendar of meeting application, which is a collaborative application and (ii) a travel application which is an ad-hoc collaborative application. SyD-enabled web objects allow us to create a collaborative application rapidly with limited coding effort. In this case study, the modular software architecture allowed us to hide the inherent heterogeneity among devices, data stores, and networks by presenting a uniform and persistent object view of mobile objects interacting through XML/SOAP requests and responses. The performance results we obtained show that the application scales well as we increase the group size and adapts well within the constraints of mobile devices