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IAU Commission 19 began in 1919 with the birth of the IAU at the Brussels Conference, where Standing Committee 19 on Latitude Variations was established as one of 32 standing committees. At the first IAU General Assembly in 1922, Standing Committee 19 became Commission 19 “Variation of Latitude”. In the beginning, the main topic of the Commission was the investigation of polar motion. Later, its activities included observations and theory of Earth rotation and connections between Earth orientation variations and geophysical phenomena. As a result, in 1964 at the XII IAU General Assembly, the Commission was renamed “Rotation of the Earth”. The investigation of Earth orientation variations is primarily based on observations of natural and artificial celestial objects. Therefore, maintenance of the international terrestrial and celestial reference frames, as well as the coordinate transformation between the frames and the improvement of the model of precession/nutation, have always been among the primary Commission topics. In 1987, the IAU through Commissions 19 and 31 “Time” established, jointly with the International Union of Geodesy and Geophysics, what is now known as the International Earth Rotation and Reference Systems Service. Commission 19 continued to work to develop methods to improve the accuracy and understanding of Earth orientation variations and related reference systems and frames as well as theoretical studies of Earth rotation. In 2015, Commission 19 was renewed as Commission A2 “Rotation of the Earth” continuing Commission 19’s functions and linking the astronomical community to other scientific organizations such as the International Association of Geodesy, International VLBI Service for Geodesy and Astrometry, International GNSS Service, International Laser Ranging Service and International DORIS Service. During its entire history, IAU Commission 19/A2 has always worked in close cooperation with these and other related services to improve the accuracy and consistency of the Earth orientation parameters and celestial and terrestrial reference frames.
In this paper, we examine a Terminal Formative-period (150 bc–ad 250) bundled offering from the site of Cerro de la Virgen, located on the Pacific coast of Oaxaca, Mexico. The offering was emplaced below a prominent public building in the site's ceremonial centre and contained five stone objects, including a rain deity mask, a fragment of a second mask, a figurine of a deceased ancestor and two miniature table altars, as well as nine small ceramic vessels. Considered together as a ‘sacred bundle’, the stone objects collectively reference agricultural fertility, rulership and ancestor veneration, which we interpret to be a metaphorical invocation of a fundamental tenet of prehispanic Mesoamerican religious belief—the sacred covenant. The offering also played an active part in founding the community of Cerro de la Virgen, connecting its residents with the divine, the ancestors and the outside world and constituting differences in status among its members.
The triennial report of Commission 19 was composed from the contributions of its members. Space does not permit a listing of their names, but their contributions are sincerely appreciated. Unfortunately because of limited space it is also not possible to provide in this report the extensive list of publication of the Commission members. The list of publications is however available on the Commission 19 web site at maia.usno.navy.mil/iauc19.
The definition of the Celestial Ephemeris Pole (CEP) which is the pole of reference for precession and nutation, should be revised taking into account recent advances in observation and theory. This paper reviews the current realization of the CEP and discusses possible extensions of both the conceptual definition and the realization of the CEP. Attention is focused on the corresponding connections between the Earth orientation parameters describing rotational variations and the related excitation parameters expressing dynamics of the geophysical fluids.
With its presence in data integration, chemistry, biological, and geographic systems, eXtensible Markup Language (XML) has become an important standard not only in computer science. A common problem among the mentioned applications involves structural clustering of XML documents—an issue that has been thoroughly studied and led to the creation of a myriad of approaches. In this paper, we present a comprehensive review of structural XML clustering. First, we provide a basic introduction to the problem and highlight the main challenges in this research area. Subsequently, we divide the problem into three subtasks and discuss the most common document representations, structural similarity measures, and clustering algorithms. In addition, we present the most popular evaluation measures, which can be used to estimate clustering quality. Finally, we analyze and compare 23 state-of-the-art approaches and arrange them in an original taxonomy. By providing an up-to-date analysis of existing structural XML clustering algorithms, we hope to showcase methods suitable for current applications and draw lines of future research.
During the XXVIII IAU General Assembly in Beijing IAU Commission 19 - Rotation of the Earth - held a business meeting and a scientific meeting. The business meeting was held on Wednesday, 29 August 2012 during session 1 (08:30-10:00). It was attended by about 35 participants, and six reports were given. First the activities of IAU Commission 19 during the past triennium (2009–2012) were highlighted by the Commission president. Afterwards, the Commission secretary presented the results of the elections for the next triennium (2012–2015) and a list of new members of the Commission. The designated Commission president provided an outlook into the next triennium, before the representatives of the international bodies and services IAG (International Association of Geodesy), IVS (International VLBI Service for Geodesy and Astrometry), and IERS (International Earth Rotation and Reference Systems Service) gave reports about recent activities. A summary of the business meeting is given below in Section 2. The scientific meeting was held on Thursday, 20 August 2012 during sessions 1 and 2 (08:30-12:30). Eleven presentations were given, and about 40 participants attended the sessions. Summaries of the presentations are provided below in Section 3.
The Commission supports and coordinates scientific investigations about Earth rotation and related reference frames. Above all C19 encourages and develops cooperation and collaboration in observation and theoretical studies of Earth orientation (the motions of the pole in the terrestrial and celestial reference systems and the rotation about the pole). The Commission serves the astronomical community by linking it to the official organizations providing the International Terrestrial and Celestial Reference Systems/Frames (ITRS/ITRF and ICRS/ICRF) and Earth orientation parameters (EOP): International Association of Geodesy (IAG), International Earth Rotation and Reference System Service (IERS), International VLBI Service for Geodesy and Astrometry (IVS), International GNSS Service (IGS), International Laser Ranging Service (ILRS), International DORIS Service (IDS). Among the most important activities are the development of methods for improving the accuracy and understanding of Earth orientation and related reference systems/frames. Further, C19 ensures the agreement and continuity of the reference frames used for Earth orientation with other astronomical reference frames and their densifications and provides means of comparing observational and analysis methods and results to ensure accuracy of data and models.
The IAU Commission 19 meeting during the XXVII IAU General Assembly in Rio de Janeiro was held on Wednesday 5 August 2009, sessions 3 (14:00–15:30) and 4 (16:00–17:30). It was attended by about 40 participants. The meeting was split into three sessions.
There were four 1.5-hour sessions of Division I business meetings during the XXVIIth IAU General Assembly. The first three were devoted to the reports of Commissions, Working Groups and services associated with the Division, discussion about plans for the next triennium and future structure of the Division. Scientific presentations on the future space astrometric mission Gaia were made at the fourth session.
The axial component of Earth rotation, which is conventionally expressed by Universal Time (UT1), contains small physical signals with diurnal and subdiurnal periods. This part of the spectrum is dominated by the tidal effects which are regular and predictable. The largest components express the influence of the gravitationally forced ocean tides with diurnal and semidiurnal periods and amplitudes up to 0.02 milliseconds (ms) in UT1 corresponding to an angular displacement of 0.30 milliarcseconds (mas); see Table 8.3 of the IERS Conventions (IERS, 2003). There are also smaller subdiurnal components (amplitudes up to 0.03 mas), designated as “spin libration” by Chao et al. (1991), due to direct influence of the tidal gravitation on those features of the Earth's density distribution which are expressed by the non-zonal terms of the geopotential. These components are not included in the models recommended by the IERS Conventions, in contrast to the corresponding effect in polar motion (ibid., Table 5.1).
Here we consider in detail the subdiurnal libration in UT1. We derive an analytical solution for the structural model of the Earth consisting of an elastic mantle and a liquid core which are not coupled to each other. The reference solution for the rigid Earth is computed by using the satellite-determined coefficients of geopotential and the recent developments of the tide generating potential (TGP). We arrived to the conclusion that the set of terms with amplitudes exceeding the truncation level of 0.005 mas consists of 11 semidiurnal harmonics due to the influence of the TGP term u22 on the equatorial flattening of the Earth expressed by the Stokes coefficients C22, S22. There is an excellent agreement between our estimates for the rigid Earth and the amplitudes derived by Wünsch (1991). The only important difference is the term with the tidal code ν2, which seems to be overlooked in the development of Wünsch. Our amplitudes computed for an elastic Earth with liquid core appear to be in reasonable agreement with those derived by Chao et al. (1991), but the latter model was not complete. The estimated effect is superimposed on the ocean tide influences having the same frequencies but 9 to 11 times larger amplitudes. Nevertheless, its maximum peak-to-peak size is about 0.105 mas, hence definitely above the current uncertainty of UT1 determinations. Comparison with the corresponding model of prograde diurnal polar motion associated with the Earth's triaxiality (IERS Conventions, Table 5.1) shows that: 1) the two effects are of similar size, 2) there is consistency between the underlying dynamical models, parameters employed, etc. In conclusion, we recommend adding the model developed here to the set of procedures provided by the IERS Conventions.
The Commission supports and coordinates scientific investigations in the Earth rotation and related reference frames. Several changes had been introduced to the structure of Commission 19 since the IAU XXVI General Assembly in Prague, 2006. The Organizing Committee of Commission 19 has been substantially reduced. It consists now of six ex-officio members, the Commission president, vice-president, past president and representatives from the International Association of Geodesy (IAG), International Earth Rotation and Reference Systems Service (IERS), International VLBI Service for Geodesy and Astrometry (IVS), and five members at-large who are nominated by the OC, selected by the Commission members and elected by the IAU GA for a maximum of two terms. The modified terms of reference of Commission 19, the list of members and other details can be found at the Commission website <iau-comm19.cbk.waw.pl/>.
Division I provides a focus for astronomers studying a wide range of problems related to fundamental physical phenomena such as time, the inertial reference frame, positions and proper motions of celestial objects and precise dynamical computation of the motions of bodies in stellar or planetary systems in the Universe.
The aim of this paper is to study sequences of integers for which the second differences between their squares are constant. We show that there are infinitely many nontrivial monotone sextuples having this property and discuss some related problems.
The activities in scientific research related to Commission 19 are mostly developed in the different institutions that have sent their reports here enclosed, in the different meetings that have been organized in related themes, and in the WGs of the Division 1. An important additional activity has been developed in the frame of precession and nutation. This research has been initiated by the Descartes Prize received by the Nutation Consortium in 2003.
Coalgebras and comodules are dualisations of algebras and modules. In this chapter we introduce the basic definitions and study several properties of these notions. The theory of coalgebras over fields and their comodules is well presented in various textbooks (e.g., Sweedler , Abe , Montgomery , Dǎscǎlescu, Nǎstǎsescu and Raianu ). Since the tensor product behaves differently over fields and rings, not all the results for coalgebras over fields can be extended to coalgebras over rings. Here we consider base rings from the very beginning, and part of our problems will be to find out which module properties of a coalgebra over a ring are necessary (and sufficient) to ensure the desired properties. In view of the main subject of this book, this chapter can be treated as a preliminary study towards corings. Also for this reason we almost solely concentrate on those properties of coalgebras and comodules that are important from the module theory point of view. The extra care paid to module properties of coalgebras will pay off in Chapter 3.
Throughout, R denotes a commutative and associative ring with a unit.
Intuitively, a coalgebra over a ring can be understood as a dualisation of an algebra over a ring. Coalgebras by themselves are equally fundamental objects as are algebras. Although probably more difficult to understand at the beginning, they are often easier to handle than algebras.
In this chapter we introduce and analyse the main new class of examples of corings, that is, corings associated to entwining structures. An entwining structure can be understood as a generalisation of a bialgebra. In many applications, in particular in mathematical physics and noncommutative geometry, it can be viewed as a symmetry of a noncommutative manifold. From the Hopf algebra point of view, the introduction of an entwining structure leads to the unification of various categories of Hopf modules studied for over 30 years. Various properties of such modules can be then understood on a more fundamental level once they are formulated in terms of associated corings. Thus in this chapter we introduce the notion of an entwining structure, give numerous examples and study properties of associated corings and comodules. All aspects of the general theory of corings and comodules discussed in the previous chapters are thus illustrated and used in deriving properties of entwined modules.
Throughout this chapter, R is a commutative ring, A is an R-algebra and C is an R-coalgebra. The coproduct of C and any other coalgebra (including bialgebras and Hopf algebras) is denoted by Δ and its counit by ε. The product in A is denoted by µ, and the unit as a map is ⍳ : R → A. If no confusion arises, we also write 1 for the element 1A = ⍳(1R).
Corings and comodules are fundamental algebraic structures that can be thought of as both dualisations and generalisations of rings and modules. Corings were introduced by Sweedler in 1975 as a generalisation of coalgebras and as a means of presenting a semi-dual version of the Jacobson-Bourbaki Theorem, but their origin can be traced back to 1968 in the work of Jonah on cohomology of coalgebras in monoidal categories. In the late seventies they resurfaced under the name of bimodules over a category with a coalgebra structure, BOCSs for short, in the work of Rojter and Kleiner on algorithms for matrix problems. For a long time, essentially only two types of examples of corings truly generalising coalgebras were known – one associated to a ring extension, the other to a matrix problem. The latter example was also studied in the context of differential graded algebras and categories. This lack of examples hindered the full appreciation of the fundamental role of corings in algebra and obviously hampered their progress in general coring theory.
On the other hand, from the late seventies and throughout the eighties and nineties, various types of Hopf modules were studied. Initially these were typically modules and comodules of a common bialgebra or a Hopf algebra with some compatibility condition, but this evolved to modules of an algebra and comodules of a coalgebra with a compatibility condition controlled by a bialgebra.