Quasi-hyperbolic planes in relatively hyperbolic groups

We show that any group that is hyperbolic relative to virtually nilpotent subgroups, and does not admit peripheral splittings, contains a quasi-isometrically embedded copy of the hyperbolic plane. In natural situations, the specific embeddings we find remain quasi-isometric embeddings when composed with the inclusion map from the Cayley graph to the coned-off graph, as well as when composed with the quotient map to "almost every" peripheral (Dehn) filling. We apply our theorem to study the same question for fundamental groups of 3-manifolds. The key idea is to study quantitative geometric properties of the boundaries of relatively hyperbolic groups, such as linear connectedness. In particular, we prove a new existence result for quasi-arcs that avoid obstacles.Comment: v1: 32 pages, 4 figures. v2: 38 pages, 4 figures. v3: 44 pages, 4 figures. An application (Theorem 1.2) is weakened as there was an error in its proof in section 7, all other changes minor, improved expositio

Extending higher dimensional quasi-cocycles

Let G be a group admitting a non-elementary acylindrical action on a Gromov hyperbolic space (for example, a non-elementary relatively hyperbolic group, or the mapping class group of a closed hyperbolic surface, or Out(F_n) for n>1). We prove that, in degree 3, the bounded cohomology of G with real coefficients is infinite-dimensional. Our proof is based on an extension to higher degrees of a recent result by Hull and Osin. Namely, we prove that, if H is a hyperbolically embedded subgroup of G and V is any G-module, then any n-quasi cocycle on H with values in V may be extended to G. Also, we show that our extensions detect the geometry of the embedding of hyperbolically embedded subgroups, in a suitable sense.Comment: Minor revisions. This version has been accepted for publication by the Journal of Topolog

Embedding relatively hyperbolic groups in products of trees

We show that a relatively hyperbolic group quasi-isometrically embeds in a product of finitely many trees if the peripheral subgroups do, and we provide an estimate on the minimal number of trees needed. Applying our result to the case of 3-manifolds, we show that fundamental groups of closed 3-manifolds have linearly controlled asymptotic dimension at most 8. To complement this result, we observe that fundamental groups of Haken 3-manifolds with non-empty boundary have asymptotic dimension 2.Comment: v1: 18 pages; v2: 20 pages, minor change

Maps between relatively hyperbolic spaces and between their boundaries

We study relations between maps between relatively hyperbolic groups/spaces and quasisymmetric embeddings between their boundaries. More specifically, we establish a correspondence between (not necessarily coarsely surjective) quasi-isometric embeddings between relatively hyperbolic groups/spaces that coarsely respect peripherals, and quasisymmetric embeddings between their boundaries satisfying suitable conditions. Further, we establish a similar correspondence regarding maps with at most polynomial distortion. We use this to characterise groups which are hyperbolic relative to some collection of virtually nilpotent subgroups as exactly those groups which admit an embedding into a truncated real hyperbolic space with at most polynomial distortion, generalising a result of Bonk and Schramm for hyperbolic groups.Comment: 51 pages, 3 figure

The production of craters on the mid-sized saturnian satelites by Centaur objects

Context. The Saturnian satellite system has been observed in detail by the Cassini-Huygens mission. These satellites present different surface features, including impact craters caused by small objects probably coming from the trans-Neptunian region. Aims. In this paper we calculate the production of craters on the mid-sized Saturnian satellites produced by Centaurs from the scattered disk (SD) and plutinos in order to determine this contribution, and we compare our estimations with the Cassini observations. Methods. We used a method developed in a previous paper that uses a numerical investigation of the dynamical evolution of Centaur objects to calculate the production of craters. We used a size-frequency distribution (SFD) of scattered disk objects (SDOs) as a power law with a break at diameters d = 60 km considering two cases for the differential power-law index: s2 = 2.5 and s2 = 3.5 for d < 60 km. Results. We calculated the number of craters, the greatest crater produced by Centaurs from the SD and plutinos, and the present cratering rate on each of the mid-sized satellites, for both cases of the SFD of SDOs considered. The contribution of plutinos is negligible compared to SDOs. From our calculations and the comparison with observations we note that the calculated number of craters for s2 = 3.5 is in general nearer the observed number. However, in general for smaller craters, the observed number is less than the calculated one. This trend can be explained by at least two mechanisms. On the one hand, this could be caused by an erasing process that gradually buries the craters, which does not affect large craters. On the other hand, the comparison of the calculated and observed crater size-frequency distribution for different size ranges implies that for d < 60 km, the SFD of SDOs is consistent with the assumed index s2 = 3.5, for d ≳ 0.2−1.4 km and for d ≲ 0.2−1.4 km, it is consistent with s2 = 2.5. Then in the range d ~ 0.2−1.4 km, the SFD of SDOs could have a new break. This change of slope could explain the reduction of small craters, at least for some cases. Conclusions. We found a good agreement when comparing our results with observations. However, independent determination of surface ages and geological processes are needed to determine if there is a new break on the SFD of SDOs, if there is a planetocentric source of craters in the Saturnian system, and which craters are primordial.Fil: Di Sisto, Romina Paula. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Astrofísica de la Plata; ArgentinaFil: Zanardi, M.. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentin

Design of a miniature hydrogen fueled gas turbine engine

The design, development, and delivery of a miniature hydrogen-fueled gas turbine engine are discussed. The engine was to be sized to approximate a scaled-down lift engine such as the teledyne CAE model 376. As a result, the engine design emerged as a 445N(100 lb.)-thrust engine flowing 0.86 kg (1.9 lbs.) air/sec. A 4-stage compressor was designed at a 4.0 to 1 pressure ratio for the above conditions. The compressor tip diameter was 9.14 cm (3.60 in.). To improve overall engine performance, another compressor with a 4.75 to 1 pressure ratio at the same tip diameter was designed. A matching turbine for each compressor was also designed. The turbine tip diameter was 10.16 cm (4.0 in.). A combustion chamber was designed, built, and tested for this engine. A preliminary design of the mechanical rotating parts also was completed and is discussed. Three exhaust nozzle designs are presented

Effects of an eccentric inner Jupiter on the dynamical evolution of icy body reservoirs in a planetary scattering scenario

Aims. We analyze the dynamics of small body reservoirs under the effects of an eccentric inner giant planet resulting from a planetary scattering event around a 0.5 M⊙ star. Methods. First, we used a semi-analytical model to define the properties of the protoplanetary disk that lead to the formation of three Jupiter-mass planets. Then, we carried out N-body simulations assuming that the planets are close to their stability limit together with an outer planetesimal disk. In particular, the present work focused on the analysis of N-body simulations in which a single Jupiter-mass planet survives after the dynamical instability event. Results. Our simulations produce outer small body reservoirs with particles on prograde and retrograde orbits, and other ones whose orbital plane flips from prograde to retrograde and back again along their evolution (“Type-F particles”). We find strong correlations between the inclination i and the ascending node longitude Ω of Type-F particles. First, Ω librates around 90° or/and 270°. This property represents a necessary and sufficient condition for the flipping of an orbit. Moreover, the libration periods of i and Ω are equal and they are out to phase by a quarter period. We also remark that the larger the libration amplitude of i, the larger the libration amplitude of Ω. We analyze the orbital parameters of Type-F particles immediately after the instability event (post IE orbital parameters), when a single Jupiter-mass planet survives in the system. Our results suggest that the orbit of a particle can flip for any value of its post IE eccentricity, although we find only two Type-F particles with post IE inclinations i ≲ 17°. Finally, our study indicates that the minimum value of the inclination of the Type-F particles in a given system decreases with an increase in the eccentricity of the giant planet.Fil: Zanardi, Macarena. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; ArgentinaFil: de Elia, Gonzalo Carlos. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; ArgentinaFil: Di Sisto, Romina Paula. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; ArgentinaFil: Naoz, S.. University of California at Los Angeles; Estados UnidosFil: Li, G.. Harvard-Smithsonian Center for Astrophysics; Estados UnidosFil: Guilera, O. M.. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Astrofísica La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas. Instituto de Astrofísica La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Astronómicas y Geofísicas; ArgentinaFil: Brunini, A.. Universidad Nacional de la Patagonia Austral; Argentin

Resilient but Overwhelmed: How do Students in South Sudan Public Universities Cope with the Rising Net Cost?

South Sudan is facing the challenges of transition from a liberation movement to democratic state. The protracted political civil war has increased the country’s fragility, dwindling public allocations to education and other sectors. Should education in fragile states wait for the return of peace? The purpose of this study was to interrogate the influence of net cost on out-of-state students’ access in South Sudan public universities. A total of 378 students were selected through random sampling procedure. Six members of the National Council for Higher Education, four university administrators, four parents and two universities were chosen through purposive sampling. The data collection instruments were questionnaires, interview guide, observation and document analysis guide, Descriptive statistics were presented in form of frequencies, percentages and tables. A one-sample t-test was used to establish whether there was a significant difference in the influence of net cost on students’ decision to access and attend South Sudan public universities between in-state and out-of-state students. Qualitative data was collected and analyzed simultaneously, coded, categorized into themes. The results indicate that although public universities have demonstrated resilience, they are overwhelmed and struggling to provide quality education services to all citizens. Students’ net cost was growing faster than their family income due to the rise in inflation adversely affecting out-ofstate students from low-income families’ access to public universities compared to in-state students. The study recommends that the government fast-track peace and re-engineer its education system to make it more accessible, affordable and equitable to all, particularly those from the marginalized groups. It hopes to contribute to improving policy and practice in educational administration and planning

A VNF modeling approach for verification purposes

Network Function Virtualization (NFV) architectures are emerging to increase networks flexibility. However, this renewed scenario poses new challenges, because virtualized networks, need to be carefully verified before being actually deployed in production environments in order to preserve network coherency (e.g., absence of forwarding loops, preservation of security on network traffic, etc.). Nowadays, model checking tools, SAT solvers, and Theorem Provers are available for formal verification of such properties in virtualized networks. Unfortunately, most of those verification tools accept input descriptions written in specification languages that are difficult to use for people not experienced in formal methods. Also, in order to enable the use of formal verification tools in real scenarios, vendors of Virtual Network Functions (VNFs) should provide abstract mathematical models of their functions, coded in the specific input languages of the verification tools. This process is error-prone, time-consuming, and often outside the VNF developers’ expertise. This paper presents a framework that we designed for automatically extracting verification models starting from a Java-based representation of a given VNF. It comprises a Java library of classes to define VNFs in a more developer-friendly way, and a tool to translate VNF definitions into formal verification models of different verification tools