Boundary regularity for the Poisson equation in reifenberg-flat domains

This paper is devoted to the investigation of the boundary regularity for the Poisson equation {{cc} -\Delta u = f & \text{in} \Omega u= 0 & \text{on} \partial \Omega where $f$ belongs to some $L^p(\Omega)$ and $\Omega$ is a Reifenberg-flat domain of $\mathbb R^n.$ More precisely, we prove that given an exponent $\alpha\in (0,1)$, there exists an $\varepsilon>0$ such that the solution $u$ to the previous system is locally H\"older continuous provided that $\Omega$ is $(\varepsilon,r_0)$-Reifenberg-flat. The proof is based on Alt-Caffarelli-Friedman's monotonicity formula and Morrey-Campanato theorem

A Generalization of Connes-Kreimer Hopf Algebra

``Bonsai'' Hopf algebras, introduced here, are generalizations of Connes-Kreimer Hopf algebras, which are motivated by Feynman diagrams and renormalization. We show that we can find operad structure on the set of bonsais. We introduce a new differential on these bonsai Hopf algebras, which is inspired by the tree differential. The cohomologies of these are computed here, and the relationship of this differential with the appending operation $*$ of Connes-Kreimer Hopf algebras is investigated

A flow disturbance estimation and rejection strategy for multirotors with round-trip trajectories

This paper presents a round-trip strategy of multirotors subject to unknown flow disturbances. During the outbound flight, the vehicle immediately utilizes the wind disturbance estimations in feedback control, as an attempt to reduce the tracking error. During this phase, the disturbance estimations with respect to the position are also recorded for future use. For the return flight, the disturbances previously collected are then routed through a feedforward controller. The major assumption here is that the disturbances may vary over space, but not over time during the same mission. We demonstrate the effectiveness of this feedforward strategy via experiments with two different types of wind flows; a simple jet flow and a more complex flow. To use as a baseline case, a cascaded PD controller with an additional feedback loop for disturbance estimation was employed for outbound flights. To display our contributions regarding the additional feedforward approach, an additional feedforward correction term obtained via prerecorded data was integrated for the return flight. Compared to the baseline controller, the feedforward controller was observed to produce 43% less RMSE position error at a vehicle ground velocity of 1 m/s with 6 m/s of environmental wind velocity. This feedforward approach also produced 14% less RMSE position error for the complex flows as well

Effect of fibronectin on the binding of antithrombin III to immobilized heparin

An objective of this research is to verify the mechanism of anticoagulant activity of surface-immobilized heparin in the presence of plasma proteins. The competition and binding interaction between immobilized heparin and antithrombin III (ATIII)/thrombin have been described in vitro. However, the strong ionic character of heparin leads to its specific and nonspecific binding with many other plasma proteins. Most notably, fibronectin contains six active binding sites for heparin which may interfere with the subsequent binding of heparin with ATIII or thrombin. \ud Heparin was covalently immobilized through polyethylene oxide (PEO) hydrophilic spacer groups onto a model surface synthesized by random copolymerization of styrene and p-aminostyrene. The binding interaction of immobilized heparin with ATIII was then determined in the presence of different fibronectin concentrations. The binding interaction was studied by first binding immobilized heparin with ATIII, followed by the introduction of fibronectin; heparin binding with fibronectin, followed by incubation with ATIII, and simultaneous incubation of surface immobilized heparin with ATIII and fibronectin. The extent of ATIII binding to heparin in each experiment was assayed using a chromogenic substrate for ATIII, S-2238. \ud The results of this study demonstrate that the displacement of ATIII from immobilized heparin was proportional to the fibronectin concentration, and was reversible. Furthermore, the binding sequence did not play a role in the final concentration of ATIII bound to immobilized heparin

Modeling, system identification, and control of ASTREX

The modeling, system identification and controller design aspects of the ASTREX precision space structure are presented in this work. Modeling of ASTREX is performed using NASTRAN, TREETOPS and I-DEAS. The models generated range from simple linear time-invariant models to nonlinear models used for large angle simulations. Identification in both the time and frequency domains are presented. The experimental set up and the results from the identification experiments are included. Finally, controller design for ASTREX is presented. Simulation results using this optimal controller demonstrate the controller performance. Finally the future directions and plans for the facility are addressed

The EPOCH Project: I. Periodic variable stars in the EROS-2 LMC database

The EPOCH (EROS-2 periodic variable star classification using machine learning) project aims to detect periodic variable stars in the EROS-2 light curve database. In this paper, we present the first result of the classification of periodic variable stars in the EROS-2 LMC database. To classify these variables, we first built a training set by compiling known variables in the Large Magellanic Cloud area from the OGLE and MACHO surveys. We crossmatched these variables with the EROS-2 sources and extracted 22 variability features from 28 392 light curves of the corresponding EROS-2 sources. We then used the random forest method to classify the EROS-2 sources in the training set. We designed the model to separate not only $\delta$ Scuti stars, RR Lyraes, Cepheids, eclipsing binaries, and long-period variables, the superclasses, but also their subclasses, such as RRab, RRc, RRd, and RRe for RR Lyraes, and similarly for the other variable types. The model trained using only the superclasses shows 99% recall and precision, while the model trained on all subclasses shows 87% recall and precision. We applied the trained model to the entire EROS-2 LMC database, which contains about 29 million sources, and found 117 234 periodic variable candidates. Out of these 117 234 periodic variables, 55 285 have not been discovered by either OGLE or MACHO variability studies. This set comprises 1 906 $\delta$ Scuti stars, 6 607 RR Lyraes, 638 Cepheids, 178 Type II Cepheids, 34 562 eclipsing binaries, and 11 394 long-period variables. A catalog of these EROS-2 LMC periodic variable stars will be available online at http://stardb.yonsei.ac.kr and at the CDS website (http://vizier.u-strasbg.fr/viz-bin/VizieR).Comment: 18 pages, 20 figures, suggseted language-editing by the A&A editorial office is applie