Minimum Restraint Functions for unbounded dynamics: general and control-polynomial systems

We consider an exit-time minimum problem with a running cost, $l\geq 0$ and unbounded controls. The occurrence of points where $l=0$ can be regarded as a transversality loss. Furthermore, since controls range over unbounded sets, the family of admissible trajectories may lack important compactness properties. In the first part of the paper we show that the existence of a $p_0$-minimum restraint function provides not only global asymptotic controllability (despite non-transversality) but also a state-dependent upper bound for the value function (provided $p_0>0$). This extends to unbounded dynamics a former result which heavily relied on the compactness of the control set. In the second part of the paper we apply the general result to the case when the system is polynomial in the control variable. Some elementary, algebraic, properties of the convex hull of vector-valued polynomials' ranges allow some simplifications of the main result, in terms of either near-affine-control systems or reduction to weak subsystems for the original dynamics.Comment: arXiv admin note: text overlap with arXiv:1503.0344

Transport properties of armchair graphene nanoribbon junctions between graphene electrodes

The transmission properties of armchair graphene nanoribbon junctions between graphene electrodes are investigated by means of first-principles quantum transport calculations. First the dependence of the transmission function on the size of the nanoribbon has been studied. Two regimes are highlighted: for small applied bias transport takes place via tunneling and the length of the ribbon is the key parameter that determines the junction conductance; at higher applied bias resonant transport through HOMO and LUMO starts to play a more determinant role, and the transport properties depend on the details of the geometry (width and length) of the carbon nanoribbon. In the case of the thinnest ribbon it has been verified that a tilted geometry of the central phenyl ring is the most stable configuration. As a consequence of this rotation the conductance decreases due to the misalignment of the $pi$ orbitals between the phenyl ring and the remaining part of the junction. All the computed transmission functions have shown a negligible dependence on different saturations and reconstructions of the edges of the graphene leads, suggesting a general validity of the reported results

The value function of an asymptotic exit-time optimal control problem

We consider a class of exit--time control problems for nonlinear systems with a nonnegative vanishing Lagrangian. In general, the associated PDE may have multiple solutions, and known regularity and stability properties do not hold. In this paper we obtain such properties and a uniqueness result under some explicit sufficient conditions. We briefly investigate also the infinite horizon problem

Prevention and non-pharmacological management of pain in newborns

Objective: to describe the main non-pharmacological interventions for pain relief in newborns available in Neonatal Intensive Care Unit. Method: an exploratory search of the MedLine, Lilacs and Scielo online databases was conducted to retrieve references of studies published from 2004 to 2013. Results: several non-pharmacological interventions were shown to be effective, to represent low risk for neonates and to have a low operational cost. The ones most often discussed in the literature were: oral administration of glucose/sucrose, non-nutritive sucking, breastfeeding, skin-to-skin contact, facilitated tucking and swaddling. Conclusion: healthcare teams should be familiar with these methods and use them more effectively in Neonatal Intensive Care Unit daily routines, so as to ensure that newborns receive qualified and more human care

Stability Estimates for an Inverse Problem for the Linear Boltzmann Equation

In this paper we consider the inverse problem of recovering the total extinction coefficient and the collision kernel for the time-dependent Boltzmann equation via boundary measurements. We obtain stability estimates for the extinction coefficient in terms of the albedo operator and also an identification result for the collision kernel.In this paper we consider the inverse problem of recovering the total extinction coefficient and the collision kernel for the time-dependent Boltzmann equation via boundary measurements. We obtain stability estimates for the extinction coefficient in terms of the albedo operator and also an identification result for the collision kernel

The Brightest Cluster Galaxy in Abell 85: The Largest Core Known so far

We have found that the brightest cluster galaxy (BCG) in Abell~85, Holm 15A, displays the largest core so far known. Its cusp radius, $r_{\gamma} = 4.57 \pm 0.06$ kpc ($4.26^{\prime\prime}\pm 0.06^{\prime\prime}$), is more than 18 times larger than the mean for BCGs, and $\geq1$ kpc larger than A2261-BCG, hitherto the largest-cored BCG (Postman, Lauer, Donahue, et al. 2012) Holm 15A hosts the luminous amorphous radio source 0039-095B and has the optical signature of a LINER. Scaling laws indicate that this core could host a supermassive black hole (SMBH) of mass $M_{\bullet}\thicksim (10^{9}-10^{11})\,M_{\odot}$. We suggest that cores this large represent a relatively short phase in the evolution of BCGs, whereas the masses of their associated SBMH might be set by initial conditions.Comment: 14 pages, 3 figure, 2 tables, accepted for publication in ApJ Letters on October 6th, 2014, replacement of previous manuscript submitted on May 30th, 2014 to astro-p