The False Claims Act\u27s First-to-File Bar: Jurisdictional or Not?

While the general theory behind the First-to-File bar may appear relatively simple, properly and practically applying it is a difficult task. Though there are many complexities involved with First-to-File litigation, this Article focuses on the current disagreement among the various circuit courts of appeals as to whether the First-to-File bar is a jurisdictional bar to litigation. This Article is not intended to offer an exhaustive analysis or resolution to this issue, but rather, will simply introduce the current debate and offer initial thoughts on why the authors believe the First-to-File bar is a non-jurisdictional provision

Limit theorems for Lévy flights on a 1D Lévy random medium

We study a random walk on a point process given by an ordered array of points (ωk, k ∈ Z) on the real line. The distances ωk+1 − ωk are i.i.d. random variables in the domain of attraction of a β-stable law, with β ∈ (0, 1) ∪ (1, 2). The random walk has i.i.d. jumps such that the transition probabilities between ωk and ωℓ depend on ℓ − k and are given by the distribution of a Z-valued random variable in the domain of attraction of an α-stable law, with α ∈ (0, 1) ∪ (1, 2). Since the defining variables, for both the random walk and the point process, are heavy-tailed, we speak of a Lévy flight on a Lévy random medium. For all combinations of the parameters α and β, we prove the annealed functional limit theorem for the suitably rescaled process, relative to the optimal Skorokhod topology in each case. When the limit process is not càdlàg, we prove convergence of the finite-dimensional distributions. When the limit process is deterministic, we also prove a limit theorem for the fluctuations, again relative to the optimal Skorokhod topology

Solutions of elliptic equations with a level surface parallel to the boundary: stability of the radial configuration

Positive solutions of homogeneous Dirichlet boundary value problems or initial-value problems for certain elliptic or parabolic equations must be radially symmetric and monotone in the radial direction if just one of their level surfaces is parallel to the boundary of the domain. Here, for the elliptic case, we prove the stability counterpart of that result. In fact, we show that if the solution is almost constant on a surface at a fixed distance from the boundary, then the domain is almost radially symmetric, in the sense that is contained in and contains two concentric balls Bre and Bri, with the difference re 12ri (linearly) controlled by a suitable norm of the deviation of the solution from a constant. The proof relies on and enhances arguments developed in a paper by Aftalion, Busca and Reichel

Combining astrometry and JUICE -- Europa Clipper radio science to improve the ephemerides of the Galilean moons

The upcoming JUICE and Europa Clipper missions to Jupiter's Galilean satellites will provide radio science tracking measurements of both spacecraft. Such data are expected to significantly help estimating the moons' ephemerides and related dynamical parameters. However, the two missions will yield an imbalanced dataset, with no flybys planned at Io, condensed over less than six years. Current ephemerides' solutions for the Galilean moons, on the other hand, rely on ground-based astrometry collected over more than a century which, while being less accurate, bring very valuable constraints on the long-term dynamics of the system. An improved solution for the Galilean satellites' complex dynamics could however be achieved by exploiting the existing synergies between these different observation sets. To quantify this, we merged simulated JUICE and Clipper radio science data with existing ground-based astrometric and radar observations, and performed the inversion. Our study specifically focusses on the resulting formal uncertainties in the moons' states, as well as Io's and Jupiter's tidal dissipation parameters. Adding astrometry stabilises the moons' state solution, especially beyond the missions' timelines. It furthermore reduces the uncertainties in $1/Q$ (inverse of the tidal quality factor) by a factor two to four for Jupiter, and about 30-35\% for Io. Among all data types, classical astrometry data prior to 1960 proved particularly beneficial. We also show that ground observations of Io add the most to the solution, confirming that ground observations can fill the lack of radio science data for this specific moon. We obtained a noticeable solution improvement when exploiting the complementarity between all different observation sets. These promising simulation results thus motivate future efforts to achieve a global solution from actual JUICE and Clipper radio science data

Combining astrometry and JUICE-Europa Clipper radio science to improve the ephemerides of the Galilean moons

Context. The upcoming JUICE and Europa Clipper missions targeting Jupiter s Galilean satellites will provide radio science tracking measurements of both spacecraft. Such data are expected to significantly help estimating the moons ephemerides and related dynamical parameters (e.g. tidal dissipation parameters). However, the two missions will yield an imbalanced dataset, with no flybys planned at Io, condensed over less than six years. Current ephemerides solutions for the Galilean moons, on the other hand, rely on ground-based astrometry collected over more than a century which, while being less accurate, bring very valuable constraints on the long-term dynamics of the system. Aims. An improved solution for the Galilean satellites complex dynamics could however be achieved by exploiting the existing synergies between these different observation sets. Methods. To quantify this, we merged simulated radio science data from both JUICE and Europa Clipper spacecraft with existing ground-based astrometric and radar observations, and performed the inversion in different configurations: either adding all available ground observations or individually assessing the contribution of different data subsets. Our discussion specifically focusses on the resulting formal uncertainties in the moons states, as well as Io s and Jupiter s tidal dissipation parameters. Results. Adding astrometry stabilises the moons state solution, especially beyond the missions timelines. It furthermore reduces the uncertainties in 1/Q (inverse of the tidal quality factor) by a factor two to four for Jupiter, and about 30- 35% for Io. Among all data types, classical astrometry data prior to 1960 proved particularly beneficial. Overall, we also show that ground observations of Io add the most to the solution, confirming that ground observations can fill the lack of radio science data for this specific moon. Conclusions. We obtained a noticeable solution improvement when making use of the complementarity between all different observation sets. The promising results obtained with simulations thus motivate future efforts to achieve a global solution from actual JUICE and Clipper radio science measurements

Recent advances in modelling and simulation of surface integrity in machining - A review

Machining is one of the final steps in the manufacturing value chain, where the dimensional tolerances are fine-tuned, and the functional surfaces are generated. Many factors such as the process type, cutting parameters, tool geometry and wear can influence the surface integrity (SI) in machining. Being able to predict and monitor the influence of different parameters on surface integrity provides an opportunity to produce surfaces with predetermined properties. This paper presents an overview of the recent advances in computational and artificial intelligence methods for modelling and simulation of surface integrity in machining and the future research and development trends are highlighted

Part Variation Modeling to Avoid Scrap Parts in Multi-stage Production Systems

Manufacturing systems for today's products are complex systems requiring a variety of different processes in order to be able to manufacture all necessary part features. This also applies to the production of rotating components, which have experienced increasing demand at the latest due to the growth in mobility. As in almost every manufacturing process, quality-reducing defects can occur due to deviations for example tool wear, which cannot always be avoided. Those, that have accumulated from previous process steps can cause the occurrence of superimposed defects. This leads to complex relationships between quality defects in the end product and the numerous parameters of the manufacturing processes. To remain competitive, production must be optimized in order to identify defects as early as possible, as well as their dependencies and variation patterns. The paper presents an approach to identify and model part variations within multi-stage production systems. Subsequently, based on a detected deviation, a downstream compensation strategy can be proposed at an early stage of the manufacturing process, which uses the capability of the overall system to fundamentally eliminate rejects

The influence of lower-limb prostheses technology on Paracanoeing time-trial performance

Within the Paracanoeing discipline, it is important to ensure appropriate control is achieved by a paddler with a disability. However, this Paralympic Games discipline has seen very little attention to date. The aims of this study were to understand the kinematic impact to a paracanoeist when not utilising the use of a prosthetic lowerlimb. A kayaker with a uni-lateral transfemoral amputation completed several 200m maximal efforts both with and without their prosthesis. When the prosthetic limb was removed, there were significant differences found in stroke rate, stroke speed, stroke length and overall power output. Sagittal and frontal video analysis demonstrated the residual limb movements when paddling and indicated where support would be required to improve the kayak’s control. It is recommended that those with lower-limb absence wishing to paddle a kayak competitively utilise the use of a prostheses designed for the kayaking environment that supports the residual limb at both the upper and inner thigh and the distal end

Harmonic fields on the extended projective disc and a problem in optics

The Hodge equations for 1-forms are studied on Beltrami's projective disc model for hyperbolic space. Ideal points lying beyond projective infinity arise naturally in both the geometric and analytic arguments. An existence theorem for weakly harmonic 1-fields, changing type on the unit circle, is derived under Dirichlet conditions imposed on the non-characteristic portion of the boundary. A similar system arises in the analysis of wave motion near a caustic. A class of elliptic-hyperbolic boundary-value problems is formulated for those equations as well. For both classes of boundary-value problems, an arbitrarily small lower-order perturbation of the equations is shown to yield solutions which are strong in the sense of Friedrichs.Comment: 30 pages; Section 3.3 has been revise