Geometric Approach to Pontryagin's Maximum Principle

Since the second half of the 20th century, Pontryagin's Maximum Principle has been widely discussed and used as a method to solve optimal control problems in medicine, robotics, finance, engineering, astronomy. Here, we focus on the proof and on the understanding of this Principle, using as much geometric ideas and geometric tools as possible. This approach provides a better and clearer understanding of the Principle and, in particular, of the role of the abnormal extremals. These extremals are interesting because they do not depend on the cost function, but only on the control system. Moreover, they were discarded as solutions until the nineties, when examples of strict abnormal optimal curves were found. In order to give a detailed exposition of the proof, the paper is mostly self\textendash{}contained, which forces us to consider different areas in mathematics such as algebra, analysis, geometry.Comment: Final version. Minors changes have been made. 56 page

Spatial infinity in higher dimensional spacetimes

Motivated by recent studies on the uniqueness or non-uniqueness of higher dimensional black hole spacetime, we investigate the asymptotic structure of spatial infinity in n-dimensional spacetimes($n \geq 4$). It turns out that the geometry of spatial infinity does not have maximal symmetry due to the non-trivial Weyl tensor {}^{(n-1)}C_{abcd} in general. We also address static spacetime and its multipole moments P_{a_1 a_2 ... a_s}. Contrasting with four dimensions, we stress that the local structure of spacetimes cannot be unique under fixed a multipole moments in static vacuum spacetimes. For example, we will consider the generalized Schwarzschild spacetimes which are deformed black hole spacetimes with the same multipole moments as spherical Schwarzschild black holes. To specify the local structure of static vacuum solution we need some additional information, at least, the Weyl tensor {}^{(n-2)}C_{abcd} at spatial infinity.Comment: 6 pages, accepted for publication in Physical Review D, published versio

Raditive decay of single charmed baryons

The electromagnetic transitions between ($J^{P}={3/2}^{+}$) and ($J^{P}={1/2}^{+}$) baryons are important decay modes to observe new hadronic states experimentally. For the estimation of these transitions widths, we employ a non-relativistic quark potential model description with color coulomb plus linear confinement potential. Such a description has been employed to compute the ground state masses and magnetic moments of the single heavy flavor baryons. The magnetic moments of the baryons are obtained using the spin-flavor structure of the constituting quark composition of the baryon. Here, we also define an effective constituent mass of the quarks (ecqm) by taking into account the binding effects of the quarks within the baryon. The radiative transition widths are computed in terms of the magnetic moments of the baryon and the photon energy. Our results are compared with other theoretical models.Comment: 06 Pages, Presented at XVIII DAE-BRNS symposium on High energy Physics, Banaras Hindu University, Varansi, INDI

Measurement of the Charged Multiplicities in b, c and Light Quark Events from Z0 Decays

Average charged multiplicities have been measured separately in $b$, $c$ and light quark ($u,d,s$) events from $Z^0$ decays measured in the SLD experiment. Impact parameters of charged tracks were used to select enriched samples of $b$ and light quark events, and reconstructed charmed mesons were used to select $c$ quark events. We measured the charged multiplicities: $\bar{n}_{uds} = 20.21 \pm 0.10 (\rm{stat.})\pm 0.22(\rm{syst.})$, $\bar{n}_{c} = 21.28 \pm 0.46(\rm{stat.}) ^{+0.41}_{-0.36}(\rm{syst.})$ $\bar{n}_{b} = 23.14 \pm 0.10(\rm{stat.}) ^{+0.38}_{-0.37}(\rm{syst.})$, from which we derived the differences between the total average charged multiplicities of $c$ or $b$ quark events and light quark events: $\Delta \bar{n}_c = 1.07 \pm 0.47(\rm{stat.})^{+0.36}_{-0.30}(\rm{syst.})$ and $\Delta \bar{n}_b = 2.93 \pm 0.14(\rm{stat.})^{+0.30}_{-0.29}(\rm{syst.})$. We compared these measurements with those at lower center-of-mass energies and with perturbative QCD predictions. These combined results are in agreement with the QCD expectations and disfavor the hypothesis of flavor-independent fragmentation.Comment: 19 pages LaTex, 4 EPS figures, to appear in Physics Letters

Therapeutic Impact of Cytoreductive Surgery and Irradiation of Posterior Fossa Ependymoma in the Molecular Era: A Retrospective Multicohort Analysis

Posterior fossa ependymoma comprises two distinct molecular variants termed EPN_PFA and EPN_PFB that have a distinct biology and natural history. The therapeutic value of cytoreductive surgery and radiation therapy for posterior fossa ependymoma after accounting for molecular subgroup is not known

Tides in colliding galaxies

Long tails and streams of stars are the most noticeable upshots of galaxy collisions. Their origin as gravitational, tidal, disturbances has however been recognized only less than fifty years ago and more than ten years after their first observations. This Review describes how the idea of galactic tides emerged, in particular thanks to the advances in numerical simulations, from the first ones that included tens of particles to the most sophisticated ones with tens of millions of them and state-of-the-art hydrodynamical prescriptions. Theoretical aspects pertaining to the formation of tidal tails are then presented. The third part of the review turns to observations and underlines the need for collecting deep multi-wavelength data to tackle the variety of physical processes exhibited by collisional debris. Tidal tails are not just stellar structures, but turn out to contain all the components usually found in galactic disks, in particular atomic / molecular gas and dust. They host star-forming complexes and are able to form star-clusters or even second-generation dwarf galaxies. The final part of the review discusses what tidal tails can tell us (or not) about the structure and content of present-day galaxies, including their dark components, and explains how tidal tails may be used to probe the past evolution of galaxies and their mass assembly history. On-going deep wide-field surveys disclose many new low-surface brightness structures in the nearby Universe, offering great opportunities for attempting galactic archeology with tidal tails.Comment: 46 pages, 13 figures, Review to be published in "Tidal effects in Astronomy and Astrophysics", Lecture Notes in Physics. Comments are most welcom

Anemia prevalence in women of reproductive age in low- and middle-income countries between 2000 and 2018

Anemia is a globally widespread condition in women and is associated with reduced economic productivity and increased mortality worldwide. Here we map annual 2000–2018 geospatial estimates of anemia prevalence in women of reproductive age (15–49 years) across 82 low- and middle-income countries (LMICs), stratify anemia by severity and aggregate results to policy-relevant administrative and national levels. Additionally, we provide subnational disparity analyses to provide a comprehensive overview of anemia prevalence inequalities within these countries and predict progress toward the World Health Organization’s Global Nutrition Target (WHO GNT) to reduce anemia by half by 2030. Our results demonstrate widespread moderate improvements in overall anemia prevalence but identify only three LMICs with a high probability of achieving the WHO GNT by 2030 at a national scale, and no LMIC is expected to achieve the target in all their subnational administrative units. Our maps show where large within-country disparities occur, as well as areas likely to fall short of the WHO GNT, offering precision public health tools so that adequate resource allocation and subsequent interventions can be targeted to the most vulnerable populations.Peer reviewe

Search for leptophobic Z ' bosons decaying into four-lepton final states in proton-proton collisions at root s=8 TeV

Peer reviewe