Nonlocal Operational Calculi for Dunkl Operators

The one-dimensional Dunkl operator $D_k$ with a non-negative parameter $k$, is considered under an arbitrary nonlocal boundary value condition. The right inverse operator of $D_k$, satisfying this condition is studied. An operational calculus of Mikusinski type is developed. In the frames of this operational calculi an extension of the Heaviside algorithm for solution of nonlocal Cauchy boundary value problems for Dunkl functional-differential equations $P(D_k)u=f$ with a given polynomial $P$ is proposed. The solution of these equations in mean-periodic functions reduces to such problems. Necessary and sufficient condition for existence of unique solution in mean-periodic functions is found

Projection Methods: Swiss Army Knives for Solving Feasibility and Best Approximation Problems with Halfspaces

We model a problem motivated by road design as a feasibility problem. Projections onto the constraint sets are obtained, and projection methods for solving the feasibility problem are studied. We present results of numerical experiments which demonstrate the efficacy of projection methods even for challenging nonconvex problems

Linear differential operators on contact manifolds

We consider differential operators between sections of arbitrary powers of the determinant line bundle over a contact manifold. We extend the standard notions of the Heisenberg calculus: noncommutative symbolic calculus, the principal symbol, and the contact order to such differential operators. Our first main result is an intrinsically defined "subsymbol" of a differential operator, which is a differential invariant of degree one lower than that of the principal symbol. In particular, this subsymbol associates a contact vector field to an arbitrary second order linear differential operator. Our second main result is the construction of a filtration that strengthens the well-known contact order filtration of the Heisenberg calculus

Relaxation of a Colloidal Particle into a Nonequilibrium Steady State

We study the relaxation of a single colloidal sphere which is periodically driven between two nonequilibrium steady states. Experimentally, this is achieved by driving the particle along a toroidal trap imposed by scanned optical tweezers. We find that the relaxation time after which the probability distributions have been relaxed is identical to that obtained by a steady state measurement. In quantitative agreement with theoretical calculations the relaxation time strongly increases when driving the system further away from thermal equilibrium

Negotiating Concurrently with Unknown Opponents in Complex, Real-Time Domains

We propose a novel strategy to enable autonomous agents to negotiate concurrently with multiple, unknown opponents in real-time, over complex multi-issue domains. We formalise our strategy as an optimisation problem, in which decisions are based on probabilistic information about the opponents' strategies acquired during negotiation. In doing so, we develop the first principled approach that enables the coordination of multiple, concurrent negotiation threads for practical negotiation settings. Furthermore, we validate our strategy using the agents and domains developed for the International Automated Negotiating Agents Competition (ANAC), and we benchmark our strategy against the state-of-the-art. We find that our approach significantly outperforms existing approaches, and this difference improves even further as the number of available negotiation opponents and the complexity of the negotiation domain increases

Micromagnetic Simulation of Nanoscale Films with Perpendicular Anisotropy

A model is studied for the theoretical description of nanoscale magnetic films with high perpendicular anisotropy. In the model the magnetic film is described in terms of single domain magnetic grains with Ising-like behavior, interacting via exchange as well as via dipolar forces. Additionally, the model contains an energy barrier and a coupling to an external magnetic field. Disorder is taken into account in order to describe realistic domain and domain wall structures. The influence of a finite temperature as well as the dynamics can be modeled by a Monte Carlo simulation. Many of the experimental findings can be investigated and at least partly understood by the model introduced above. For thin films the magnetisation reversal is driven by domain wall motion. The results for the field and temperature dependence of the domain wall velocity suggest that for thin films hysteresis can be described as a depinning transition of the domain walls rounded by thermal activation for finite temperatures.Comment: Revtex, Postscript Figures, to be published in J. Appl.Phy

A New Radio Molecular Line Survey of Planetary Nebulae: HNC/HCN as a Diagnostic of Ultraviolet Irradiation

Certain planetary nebulae contain shells, filaments, or globules of cold gas and dust whose heating and chemistry are likely driven by UV and X-ray emission from their central stars and from wind-collision-generated shocks. We present the results of a survey of molecular line emission in the 88-236 GHz range from nine nearby (<1.5 kpc) planetary nebulae spanning a range of UV and X-ray luminosities, using the 30 m telescope of the Institut de Radioastronomie Millimetrique. Rotational transitions of thirteen molecules, including CO isotopologues and chemically important trace species, were observed and the results compared with and augmented by previous studies of molecular gas in PNe. Lines of the molecules HCO+, HNC, HCN, and CN, which were detected in most objects, represent new detections for five planetary nebulae in our study. Specifically, we present the first detections of 13CO (1-0, 2-1), HCO+, CN, HCN, and HNC in NGC 6445; HCO+ in BD+303639; 13CO (2-1), CN, HCN, and HNC in NGC 6853; and 13CO (2-1) and CN in NGC 6772. Flux ratios were analyzed to identify correlations between the central star and/or nebular UV and X-ray luminosities and the molecular chemistries of the nebulae. This analysis reveals a surprisingly robust dependence of the HNC/HCN line ratio on PN central star UV luminosity. There exists no such clear correlation between PN X-rays and various diagnostics of PN molecular chemistry. The correlation between HNC/HCN ratio and central star UV luminosity demonstrates the potential of molecular emission line studies of PNe for improving our understanding of the role that high-energy radiation plays in the heating and chemistry of photodissociation regions.Comment: 17 pages, 17 figures, 6 tables, accepted for publication in Astronomy & Astrophysic