Relative equilibria in the unrestricted problem of a sphere and symmetric rigid body

We consider the unrestricted problem of two mutually attracting rigid bodies, an uniform sphere (or a point mass) and an axially symmetric body. We present a global, geometric approach for finding all relative equilibria (stationary solutions) in this model, which was already studied by Kinoshita (1970). We extend and generalize his results, showing that the equilibria solutions may be found by solving at most two non-linear, algebraic equations, assuming that the potential function of the symmetric rigid body is known explicitly. We demonstrate that there are three classes of the relative equilibria, which we call "cylindrical", "inclined co-planar", and "conic" precessions, respectively. Moreover, we also show that in the case of conic precession, although the relative orbit is circular, the point-mass and the mass center of the body move in different parallel planes. This solution has been yet not known in the literature.Comment: The manuscript with 10 pages, 5 figures; accepted to the Monthly Notices of the Royal Astronomical Societ

Dismantling and decontamination of large-sized radiation-contaminated equipment during Research Building B decommissioning at the Bochvar Institute site

The article presents the results of work on dismantling the large installation equipment of Research Building B at the Bochvar High-technology Research Institute of Inorganic Materials (Bochvar Institute). The works were carried out as part of Building B preparation for decommissioning. The purpose of dismantling the large-sized capacitive equipment was to reconstruct the large installation site for managing radioactive waste generated during Building B decommissioning. The works on decommissioning a radioactively contaminated building within a densely populated district of megalopolis were carried out for the first time. The characteristics of the large-sized capacitive equipment are presented. Radioactive contamination of the capacitive equipment is determined by long-lived a-emitting isotopes: 235U, 238U, 239Pu. The sequence of works on dismantling the radiation-contaminated capacitive equipment includes preparatory work, dismantling the tank piping, localizing radioactive contamination of the external surface of the equipment as well as dismantling and moving it into a transport container. Dismantling and decontamination of the large-sized capacitive equipment was carried out by the Bochvar Institute Decommissioning Department. The following tools were used during the works: (1) a mobile foam decontamination facility to perform decontamination works and (2) a mobile high pressure facility to apply localizing and decontaminating film coatings. The tanks were dismantled by means of low-spark tools, i.e., reciprocating saws. Crane runways were made in order to move the dismantled equipment into transport containers: the movement was carried out with the help of a winch. The main results of dismantling and decontaminating the radioactively contaminated tanks are the dismantling of four units of long-length column-type equipment with heights from 4.2 to 6.4 m and 26 units of capacitive equipment (maximum capacity = 8 m3) as well as decontamination of the internal surfaces of radiation-contaminated equipment (decontamination factor = 25–70). As a result, the activity of the accumulated radioactive waste was reduced (the RW class was changed from 3 to 4). The main conclusion regarding the managment of large-sized radiation-contaminated tanks during Building B decommissioning is as follows: the works were organized and carried out at a high technical level, using modern decontamination and dismantling equipment and modern methods to ensure work safety at the Bochvar Institute site in the city of Moscow

Non-reducible descriptions for conditional Kolmogorov complexity

Assume that a program p on input a outputs b. We are looking for a shorter program q having the same property (q(a) = b). In addition, we want q to be simple conditional to p (this means that the conditional Kolmogorov complexity K (q|p) is negligible). In the present paper, we prove that sometimes there is no such program q, even in the case when the complexity of p is much bigger than K (b|a). We give three different constructions that use the game approach, probabilistic arguments and algebraic arguments, respectively. 1 Definitions and statements Let a and b be binary strings. Consider programs p such that p(a) = b (the program p on input a outputs b). What is the minimal length of such a program? If the programming language is chosen appropriately, this length is close to K (b|a), the conditional Kolmogorov complexity of b given a. We will ignore additive terms of order O(log n) where n is the maximum length of the strings involved. With this precision all the versions of Kolmogorov complexity (the plain one, the prefix one etc.) coincide. For the definition of Kolmogorov complexity K (b) and K (b|a) we refer to the textbook [2]. To avoid references to a specific programming language we will consider “descriptions” instead of programs. A string p is called a conditional description of a string b given a i

Glendonite-Like Carbonate Aggregates from the Lower Ordovician Koporye Formation (Russian Part of the Baltic Klint): Detailed Mineralogical and Geochemical Data and Paleogeographic Implications

Stellate and plate-like carbonate bodies, traditionally called anthraconites, are found throughout the Baltic-Ladoga Klint in bituminous shale of the Koporye Formation (Tremadocian, Lower Ordovician). Although this time interval is usually considered as a greenhouse, there is some evidence for the existence of at least temporary cold conditions during the Cambrian–Ordovician. However, the origin of anthraconites is still strongly debated. We studied the mineralogical, petrographic, cathodoluminescence, geochemical, and isotopic characteristics of anthraconites from five sections of the Russian part of the Baltic paleobasin. A close similarity between the morphological, petrographic, cathodoluminescence, and isotopic characteristics of the studied anthraconites with those of glendonites allow us to suggest that these bodies formed in a similar paleo-environment and should be considered as pseudomorphs of the mineral ikaite. The oxygen and carbon isotope ratios reveal that ikaite precipitation occurred in low-temperature conditions on the seafloor. The carbon isotopic values reveal influence of inorganic seawater carbon along with organic matter decomposition and/or methane oxidation during ikaite-glendonite transformations. The oxygen isotopic composition significantly changed after deposition due to meteoric diagenesis. We propose that the studied Tremadocian anthraconites formed under a region of upwelling, where cold phosphate-rich deep waters rose to the relatively shallow part of the Baltic paleobasin, providing favorable conditions for ikaite precipitation. Based on our cathodoluminescence study, we suggest that ikaite was transformed to calcite over several stages during diagenesis. Mineralogical studies also reveal that primary calcite was transformed to sulfate (gypsum) or dolomite during late superimposed processes