Remarks on symplectic circle actions, torsion and loops

We study loops of symplectic diffeomorphisms of closed symplectic manifolds. Our main result, which is valid for a large class of symplectic manifolds, shows that the flux of a symplectic loop vanishes whenever its orbits are contractible. As a consequence, we obtain a new vanishing result for the flux group and new instances where the presence of a fixed point of a symplectic circle action is a sufficient condition for it to be Hamiltonian. We also obtain applications to symplectic torsion, more precisely, non-trivial elements of $\mathrm{Symp}_{0}(M,\omega)$ that have finite order.Comment: 16 page

On the Hofer-Zehnder conjecture for semipositive symplectic manifolds

We show that, on a closed semipositive symplectic manifold with semisimple quantum homology, any Hamiltonian diffeomorphism possessing more contractible fixed points, counted homologically, than the total Betti number of the manifold, must have infinitely many periodic points. This generalizes to the semipositive setting the beautiful result of Shelukhin on the Hofer-Zehnder conjecture.Comment: 30 page

An Interactive Tool to Explore and Improve the Ply Number of Drawings

Given a straight-line drawing $\Gamma$ of a graph $G=(V,E)$, for every vertex $v$ the ply disk $D_v$ is defined as a disk centered at $v$ where the radius of the disk is half the length of the longest edge incident to $v$. The ply number of a given drawing is defined as the maximum number of overlapping disks at some point in $\mathbb{R}^2$. Here we present a tool to explore and evaluate the ply number for graphs with instant visual feedback for the user. We evaluate our methods in comparison to an existing ply computation by De Luca et al. [WALCOM'17]. We are able to reduce the computation time from seconds to milliseconds for given drawings and thereby contribute to further research on the ply topic by providing an efficient tool to examine graphs extensively by user interaction as well as some automatic features to reduce the ply number.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Optimal Trajectories for Propellant-Free Rendezvous Missions

The paper provides a new approach to utilizing space environmental forces in time- and energy-optimal, propellant-less spacecraft rendezvous missions. Considering the nonlinear form of the relative dynamic equations, rendezvous missions are posed as optimal control problems subject to input saturation. We conduct a direct optimal control approach to obtain optimal trajectories and control inputs. Initially, we consider the differential drag only and conduct a comprehensive analysis of the effect of altitude on the required control input and achieved cost function. Lorentz forces are then utilized with the differential drag, reducing the time required for time-optimal missions. For energy-optimal missions with combined differential drag and Lorentz forces, a weighting matrix in the cost function is introduced to adjust the relative contributions of these forces

An Agent-Based Computational Bioeconomic Model of Plant Disease Diffusion and Control: Grapevine Leafroll Disease

WP 2013-11 February 2013JEL Classification Codes: C15; C63; D24; Q1

The Effect of Thermal Annealing on the Structural and Optical Properties of CdS Thin Films Deposited by Vacuum Evaporation Method

: Cadmium Sulphide (CdS) thin films were grown on glass substrates by the vacuum evaporation technique. The effect of thermal annealing on the structural and optical properties of the as deposited samples was analyzed. Structure of these films was characterized by X-ray diffraction . CdS films deposited have polycrystalline structure cubic(zinc blende) and hexagonal (demand) .The grain size increases with increasing annealing temperature. The optical properties of CdS films have highly transmittance in visible region of spectrum and reach to more than 84% . Band gap decreases from 2.55 to 2.33 eV with the increasing annealing temperature from 473K to 623 K.

A Control Approach for Nonlinear Stochastic State Uncertain Systems with Probabilistic Safety Guarantees

This paper presents an algorithm to apply nonlinear control design approaches in the case of stochastic systems with partial state observation. Deterministic nonlinear control approaches are formulated under the assumption of full state access and, often, relative degree one. We propose a control design approach that first generates a control policy for nonlinear deterministic models with full state observation. The resulting control policy is then used to build an importance-like probability distribution over the space of control sequences which are to be evaluated for the true stochastic and state-uncertain dynamics. This distribution serves in the sampling step within a random search control optimization procedure, to focus the exploration effort on certain regions of the control space. The sampled control sequences are assigned costs determined by a prescribed finite-horizon performance and safety measure, which is based on the stochastic dynamics. This sampling algorithm is parallelizable and shown to have computational complexity indifferent to the state dimension, and to be able to guarantee safety over the prescribed prediction horizon. A numerical simulation is provided to test the applicability and effectiveness of the presented approach and compare it to a certainty equivalence controller