Existence criterion for Hall subgroups of finite groups

In the paper we obtain an existence criterion for Hall subgroups of finite groups in terms of a composition series.Comment: We made some editor corrections in the tex

Consequences of Quadratic Frictional Force on the One Dimensional Bouncing Ball Model

Some dynamical properties of the one dimensional Fermi accelerator model, under the presence of frictional force are studied. The frictional force is assumed as being proportional to the square particle's velocity. The problem is described by use of a two dimensional non linear mapping, therefore obtained via the solution of differential equations. We confirm that the model experiences contraction of the phase space area and in special, we characterized the behavior of the particle approaching an attracting fixed point. © 2007 American Institute of Physics

Time-Dependent Framework for Analyzing Emergency Intervention Travel Times and Risk Implications due to Earthquakes. Bucharest Case Study

Earthquakes can generate a significant number of casualties within seconds, as well as high economic losses. The lack of rapid and coordinated emergency intervention can contribute to much greater losses. In this paper we develop a framework taking advantage of the ArcGis Network Analyst extension, able to account for post-earthquake conditions and reflect travel times. By combining 1) network characteristics with 2) direct seismic damage information, 3) models to determine road obstruction potential, 4) traffic information and time-dependent post-earthquake modeling but also 5) emergency intervention facilities (hospitals or fire stations) and considerations regarding their functional limitations, this framework can provide important support for the management of emergency intervention but also for risk reduction planning. Main results consist of maps showing travel times for various scenarios and moments after an earthquake, inaccessible areas, vital roads for access or an identification of important facilities. As case study we chose Bucharest, one of Europe’s most endangered capitals considering the seismic risk level. The city was and could be considerably affected by earthquakes in the Vrancea Seismic Zone, being characterized by a high number of vulnerable buildings and by one of the greatest typical traffic congestion levels in the world. Compared to previous network studies for Bucharest, the new approach is more complex and customable, providing means for real-time integration and time-dependent analysis. Results, for a worst-case scenario, prove that the risks could be even greater than expected, but also what should be done to mitigate them, such as the construction of a new hospital in the western part of the city, ensuring safe delimited routes for emergency vehicles or expanding the treatment capacity of actual hospitals—some of which also need seismic retrofitting. Results of this study will be integrated in the revised version of the National Conception for Post-Earthquake Response—an operational framework which will lead to risk mitigation through the improvement of post-disaster reaction

Dozens of virtual impactor orbits eliminated by the EURONEAR VIMP DECam data mining project

Massive data mining of image archives observed with large etendue facilities represents a great opportunity for orbital amelioration of poorly known virtual impactor asteroids (VIs). There are more than 1000 VIs known today; most of them have very short observed arcs and many are considered lost as they became extremely faint soon after discovery. We aim to improve the orbits of VIs and eliminate their status by data mining the existing image archives. Within the European Near Earth Asteroids Research (EURONEAR) project, we developed the Virtual Impactor search using Mega-Precovery (VIMP) software endowed with a very effective (fast and accurate) algorithm to predict apparitions of candidate pairs for subsequent guided human search. Considering a simple geometric model, the VIMP algorithm searches for any possible intersection in space and time between the positional uncertainty of any VI and the bounding sky projection of any image archive. We applied VIMP to mine the data of 451914 Blanco/DECam images observed between 12 Sep 2012 and 11 Jul 2019, identifying 212 VIs that possibly fall into 1286 candidate images leading to either precovery or recovery events. Following a careful search of candidate images, we recovered and measured 54 VIs in 183 DECam images. About 4000 impact orbits were eliminated from both lists, 27 VIs were removed from at least one list, while 14 objects were eliminated from both lists. The faintest detections were around V~24.0, while the majority fall between 21<V<23. The minimal orbital intersection distances remains constant for 67% detections, increasing for eight objects and decreasing for 10 objects. Most eliminated VIs had short initial arcs of less than 5 days. Some unexpected photometric discovery has emerged regarding the rotation period of 2018 DB, based on the close inspection of longer trailed VIs and the measurement of their fluxes along the trails.Comment: Accepted for publication in Astronomy & Astrophysics (27 July 2020

Hierarchical Self-Assembly of Supramolecular Helical Fibres from Amphiphilic C3-Symmetrical Functional Tris(tetrathiafulvalenes)

The preparation and self-assembly of the enantiomers of a series of C3-symmetric compounds incorporating three tetrathiafulvalene (TTF) residues is reported. The chiral citronellyl and dihydrocitronellyl alkyl chains lead to helical one dimensional stacks in solution. Molecular mechanics and dynamics simulations combined with experimental and theoretical circular dichroism support the observed helicity in solution. These stacks self-assemble to give fibres that have morphologies that depend on the nature of the chiral alkyl group and the medium in which the compounds aggregate. An inversion of macroscopic helical morphology of the citronellyl compound is observed when compared to analogous 2-methylbutyl chains, which is presumably a result of the stereogenic centre being further away from the core of the molecule. This composition still allows both morphologies to be observed, whereas an achiral compound shows no helicity. The morphology of the fibres also depends on the flexibility at the chain ends of the amphiphilic components, as there is not such an apparently persistent helical morphology for the dihydrocitronellyl derivative as for that prepared from citronellyl chains

Collectively optimal routing for congested traffic limited by link capacity

We show that the capacity of a complex network that models a city street grid to support congested traffic can be optimized by using routes that collectively minimize the maximum ratio of betweenness to capacity in any link. Networks with a heterogeneous distribution of link capacities and with a heterogeneous transport load are considered. We find that overall traffic congestion and average travel times can be significantly reduced by a judicious use of slower, smaller capacity links.Comment: 7 pages, 4 figure