Dedekind order completion of C(X) by Hausdorff continuous functions

The concept of Hausdorff continuous interval valued functions, developed within the theory of Hausdorff approximations and originaly defined for interval valued functions of one real variable is extended to interval valued functions defined on a topological space X. The main result is that the set of all finite Hausdorff continuous functions on any topological space X is Dedekind order complete. Hence it contains the Dedekind order completion of the set C(X) of all continuous real functions defined on X as well as the Dedekind order completion of the set C_b(X) of all bounded continuous functions on X. Under some general assumptions about the topological space X the Dedekind order completions of both C(X) and C_b(X) are characterised as subsets of the set of all Hausdorff continuous functions. This solves a long outstanding open problem about the Dedekind order completion of C(X). In addition, it has major applications to the regularity of solutions of large classes of nonlinear PDEs

Exploring the Bimodal Solar System via Sample Return from the Main Asteroid Belt: The Case for Revisiting Ceres

Abstract: Sample return from a main-belt asteroid has not yet been attempted, but appears technologically feasible. While the cost implications are significant, the scientific case for such a mission appears overwhelming. As suggested by the “Grand Tack” model, the structure of the main belt was likely forged during the earliest stages of Solar System evolution in response to migration of the giant planets. Returning samples from the main belt has the potential to test such planet migration models and the related geochemical and isotopic concept of a bimodal Solar System. Isotopic studies demonstrate distinct compositional differences between samples believed to be derived from the outer Solar System (CC or carbonaceous chondrite group) and those that are thought to be derived from the inner Solar System (NC or non-carbonaceous group). These two groups are separated on relevant isotopic variation diagrams by a clear compositional gap. The interface between these two regions appears to be broadly coincident with the present location of the asteroid belt, which contains material derived from both groups. The Hayabusa mission to near-Earth asteroid (NEA) (25143) Itokawa has shown what can be learned from a sample-return mission to an asteroid, even with a very small amount of sample. One scenario for main-belt sample return involves a spacecraft launching a projectile that strikes an object and flying through the debris cloud, which would potentially allow multiple bodies to be sampled if a number of projectiles are used on different asteroids. Another scenario is the more traditional method of landing on an asteroid to obtain the sample. A significant range of main-belt asteroids are available as targets for a sample-return mission and such a mission would represent a first step in mineralogically and isotopically mapping the asteroid belt. We argue that a sample-return mission to the asteroid belt does not necessarily have to return material from both the NC and CC groups to viably test the bimodal Solar System paradigm, as material from the NC group is already abundantly available for study. Instead, there is overwhelming evidence that we have a very incomplete suite of CC-related samples. Based on our analysis, we advocate a dedicated sample-return mission to the dwarf planet (1) Ceres as the best means of further exploring inherent Solar System variation. Ceres is an ice-rich world that may be a displaced trans-Neptunian object. We almost certainly do not have any meteorites that closely resemble material that would be brought back from Ceres. The rich heritage of data acquired by the Dawn mission makes a sample-return mission from Ceres logistically feasible at a realistic cost. No other potential main-belt target is capable of providing as much insight into the early Solar System as Ceres. Such a mission should be given the highest priority by the international scientific community

Optical observations of enhanced activity of the 2005 Draconid meteor shower

Context.The enhanced activity of the Draconid meteor shower was observed on October 8, 2005 using video and photographic cameras. Aims.The aim of this paper is to use a higher than usual number of recorded meteors to look at some physical properties of the Draconid meteoroids, to describe the activity profile, and to infer meteor orbits. Methods.Video data on meteors are used for the determination of the meteor shower activity. Double station data provide precise beginning heights of the meteors as well as their radiants and orbits. Beginning heights and light curves of all meteors are used for investigation of meteoroid properties. Results.Only the descending branch of the enhanced activity was observed between 17:30 and 19 UT. The mass distribution index is similar to the 1998 return. Beginning heights of the Draconid meteors are several kilometres higher in comparison with other meteors of similar velocity. Light curves are nearly symmetrical, with a slight preference of early maxima. Both results are consistent with the very fragile nature of Draconid meteoroids

The influence of changes to abiotic parameters on the fish assemblage structure of a lowland stream

Ichthyological monitoring and the assessment of 16 physical and chemical parameters of the water environment were conducted at two localities on the Dyje River, Czech Republic, at different distances downstream from the Znojmo Reservoir (at 12 and 31 km) to reveal habitat alterations. Canonical correspondence analysis confirmed that differences in fish abundance between localities were influenced by different hydrological regimes characterized by discharge and flow velocities and also by water conductivity, which increased with the distance from the reservoir. The influence of chemical parameters of water related to water quality on fish assemblage structure was insignificant. The second locality (further from the reservoir) was characterised by substantial water shortage during the vegetation season. Changes in hydrological regime and the loss of connectivity in the Dyje River both connected with dam building and water shortage for irrigation have led to dramatic changes in the fish assemblage structure since the 1950s and the complete loss of common nase

Catalogue of representative meteor spectra

Aims. We present a library of low-resolution meteor spectra that includes sporadic meteors, members of minor meteor showers, and major meteor showers. These meteors are in the magnitude range from +2 to −3, corresponding to meteoroid sizes from 1 mm to 10 mm. Methods. Parallel double-station video observations allowed us to compute heliocentric orbits for all meteors. Most observations were performed during the periods of activity of major meteor showers in the years between 2006 and 2012. Spectra are classified according to relative intensities of the low-temperature emission lines of Mg, Na, and Fe. Results. Shower meteors were found to be of normal composition, except for Southern δ Aquariids and some members of the Geminid shower, neither of which have Na in the meteor spectra. Variations in Na content are typical for the Geminid shower. Three populations of Na-free mereoroids were identified. The first population are iron meteorites, which have an asteroidal-chondritic origin, but one meteoroid with low perihelion (0.11 AU) was found among the iron meteorites. The second population were Sun-approaching meteoroids in which sodium is depleted by thermal desorption. The third population were Na-free meteoroids of cometary origin. Long exposure to cosmic rays on the surface of comets in the Oort cloud and disintegration of this crust might be the origin of this population of meteoroids

Properties of small meteoroids studied by meteor video observations

Aims. The complex study of millimetre-sized meteoroids can reveal more about the structure and origin of population of these meteoroids. Methods. Double-station video observations, paired with spectroscopic video observations, were used to study small meteoroids. In total 152 sporadic and shower meteors of maximum brightness between magnitude −5 and +3 were analysed. Spectral classification was based on time-integrated intensities of lines of Na, Mg, and Fe. Meteor light curves and deceleration were fitted by the grain erosion model. Heliocentric orbits of all meteors were computed. Monochromatic light curves were constructed in order to study differential ablation. The length of meteor wakes was evaluated as well. Results. The variety of properties among millimetre-sized meteoroids proved different sources and histories of this material. Meteoroids that contain small grains tend to release their sodium early. For given grain sizes, the sodium in Na-poor meteoroids is released earlier than in meteors without sodium depletion. Overall, meteoroids with sodium depletion are revealed to have different structures: they have stronger material without very small grains and they do not show very bright wakes. Two iron meteoroids on Halley-type orbits were observed, thereby supporting the idea of large-scale mixing of material in the early solar system. The distribution of grain sizes of Jupiter-family members was in good agreement with results from the COSIMA instrument on the ROSETTA probe

Search for pairs and groups in the 2006 Geminid meteor shower

Context. The existence of pairs and groups of meteors during meteor showers has been an open question for a long time. The double-station video observation of the 2006 Geminid meteor shower, one of the most active annual showers, is used for the search of such events. Aims. The goal of the paper is to determine whether the observed pairs of Geminid meteors are real events or cases of random coincidence. Methods. The atmospheric trajectories of the observed meteors, photometric masses, and both time and spatial distances of meteoroids in the atmosphere were determined using a double-station video observation. The time gaps between them were analysed statistically. The Monte Carlo simulation was used for the determination of the probability of random pairings. Results. A higher than expected number of candidates for pairs was found among 2006 Geminids. An evaluation of the Poisson distribution shows that a significant fraction of them may be real cases. However, the Monte Carlo simulation did not confirm this result and provided a different view. Analysis of geometrical positions of candidate pairs also did not support the presence of real pairs and groups. Although we cannot exclude that some of them may be physically connected pairs, all the observed cases can be explained as the coincidental appearance of unrelated meteors