Optimal Control Realizations of Lagrangian Systems with Symmetry

A new relation among a class of optimal control systems and Lagrangian systems with symmetry is discussed. It will be shown that a family of solutions of optimal control systems whose control equation are obtained by means of a group action are in correspondence with the solutions of a mechanical Lagrangian system with symmetry. This result also explains the equivalence of the class of Lagrangian systems with symmetry and optimal control problems discussed in \cite{Bl98}, \cite{Bl00}. The explicit realization of this correspondence is obtained by a judicious use of Clebsch variables and Lin constraints, a technique originally developed to provide simple realizations of Lagrangian systems with symmetry. It is noteworthy to point out that this correspondence exchanges the role of state and control variables for control systems with the configuration and Clebsch variables for the corresponding Lagrangian system. These results are illustrated with various simple applications

Investigating Fatigue Performance on the Foamed Asphalt Specimens Generated Using Different Foam Properties

An evaluation of fatigue resistance for foamed asphalt mixture is very demanding since the binder is not continuously distributed on the aggregate surface and this mixtures contains water, the content of which dramatically affects the mechanical properties. This paper discusses the results of laboratory fatigue testingon the foamed asphalt mixtures in which the specimens are generated using three different foamed bitumen properties. Foamed bitumen as the binder was produced at three different foaming water content (FWC) at a temperature of 180oC using a 70/100 pen. The aggregates were mechanically mixed with foamed bitumen using a Hobart mixer. The resulting mixtures were then compacted using a gyratory compactor to generatespecimen with diameter of 100 mm. The specimens were fatigue tested at various stress levels at a temperature of 20oC following a curing period of 3 days at 40oC. Overall, fatigue performance of foamed asphalt can be identified based upon both stress and strain for mixtures produced at FWC 1%, 5%, and 10%

A hierarchical Bayesian model to infer PL(Z) relations using Gaia parallaxes

Aims. We aim at creating a Bayesian model to infer the coefficients of PL or PLZ relations that propagates uncertainties in the observables in a rigorous and well founded way. Methods. We propose a directed acyclic graph to encode the conditional probabilities of the inference model that will allow us to infer probability distributions for the PL and PL(Z) relations. We evaluate the model with several semi-synthetic data sets and apply it to a sample of 200 fundamental mode and first overtone mode RR Lyrae stars for which Gaia DR1 parallaxes and literature Ks-band mean magnitudes are available. We define and test several hyperprior probabilities to verify their adequacy and check the sensitivity of the solution with respect to the prior choice. Results. The main conclusion of this work is the absolute necessity of incorporating the existing correlations between the observed variables (periods, metallicities and parallaxes) in the form of model priors in order to avoid systematically biased results, especially in the case of non-negligible uncertainties in the parallaxes. The tests with the semi-synthetic data based on the data set used in Gaia Collaboration et al. (2017) reveal the significant impact that the existing correlations between parallax, metallicity and periods have on the inferred parameters. The relation coefficients obtained here have been superseded by those presented in Muraveva et al. (2018a), that incorporates the findings of this work and the more recent Gaia DR2 measurements.Comment: 14 pages, 12 figures. Submitted to A&

A Meeting with Native American Elders, Activists, Select Funders and Scholars

On June 20-21, 2003, the Marguerite Casey Foundation (MCF) brought together a group of Native people from across the country to participate in a consultative session designed to help the Foundation develop a comprehensive strategy to strengthen and support indigenous families and communities. With the help of CURL, a report was written up documenting the meeting