Geochemical Constraints for the Bulk Composition of the Moon

© 2018, Pleiades Publishing, Ltd. Abstract: The bulk composition of the silicate Moon (crust + mantle, BSM) is determined on the basis of inversion of gravitational and seismic data. It is shown that the mantle refractory oxides form two different groups depending on the thermal state. By the bulk Al2O3 content of ~3.0–4.6 wt %, the cold BSM models span the range of Al2O3 content of the silicate Earth (Bulk Silicate Earth, BSE), whereas the hot BSM models are significantly enriched in the Al2O3 content of ~5.1–7.3 wt % (Al2O3 content of ~1.2–1.7 × BSE) relative to BSE. In contrast, apart from the distribution of temperature, both BSM models are characterized by almost constant values of bulk FeO contents (~12.2–13.2 wt %) and MG# values (80.0–81.5), which are strongly distinct from those for BSE (~8 wt % FeO and 89 MG#). The results show that, for the geophysically possible distribution of temperatures, the silicate fraction of the Moon is enriched in FeO and depleted in MgO relative to BSE

Analysis lunar maps using multifractal method

© 2018, International Multidisciplinary Scientific Geoconference. All rights reserved. The aim of the present work is to develop a fractal method for space maps analysis. Although there are accurate theories of lunar motion in the dynamic coordinate system based on lunar laser ranging and space measurements with an accuracy up to multiarcseconds, analysis of various models of the lunar figure is a complicated problem. The reason for it is that the determination of a reference system for coordinate data and assessing its authenticity are difficult. In order to solve the problem, a comparative method, in which the structure of altitude vectors associated with same lunar coordinates is used, may be applied. However, the application of such method requires conduction of a large number of measurements and calculations. Besides, there are a lot of models of the librational zone of the Moon constructed by various methods, so the accuracy of this data is controversial. In other words, the relief of the Moon is of very complicated structure and the application of traditional methods in most cases is unacceptable. At the same time, physical surfaces of celestial bodies are fractal objects. The study of such objects using fractal methods allows not only investigating its structure, but the connection between the structure and processes of its formation as well. Thereby, the development of methods of identifying and analyzing nonlinear complex systems is a subject of great interest. It should be noted that analysis of celestial bodies macrosurfaces based on the study of fractal similarity coefficients has not been conducted in the world practice before. This fully applies to selenography. On the basis of the new method, a comparative analysis of modern lunar maps similarity (maps include altitude isohypses constructed according to ground-based and space observations) was conducted. For 2 models of the lunar librational zone the lunar macrofigure variations were determined using the fractal similarity factors and fractal dimensions. The Moon’s macrofigure models have been built on the basis of harmonic analysis and expansion of altitude data from the dynamic selenocentric catalogue in a series of spherical functions. As a result, the values of fractal dimensions of the lunar relief anomalies for 8 zones of Hayn latitudes are determined. The mean fractal dimension for the lunar librational zone has been obtained. This value is d = 1,345. For the above mentioned areas the fractal similarity factors are obtained. Based on the analysis of the fractal similarity factors for various lunar surface models one may draw a conclusion on how similar these models are when analyzing maps

Analysing the Transverse Structure of the Relativistic Jets of AGN

This paper describes a method of fitting total intensity and polarization profiles in VLBI images of astrophysical jets to profiles predicted by a theoretical model. As an example, the method is used to fit profiles of the jet in the Active Galactic Nucleus Mrk501 with profiles predicted by a model in which a cylindrical jet of synchrotron plasma is threaded by a magnetic field with helical and disordered components. This fitting yields model Stokes Q profiles that agree with the observed profiles to within the 1-2 \sigma uncertainties; the I model and observed profiles are overall not in such good agreement, with the model I profiles being generally more symmetrical than the observed profiles. Consistent fitting results are obtained for profiles derived from 6cm VLBI images at two distances from the core, and also for profiles obtained for different wavelengths at a single location in the VLBI jet. The most striking success of the model is its ability to reproduce the spine-sheath polarization structure observed across the jet. Using the derived viewing angle in the jet rest frame, \delta' approximately 83 degrees, together with a superluminal speed reported in the literature, \beta apparent = 3.3, yields a solution for the viewing angle and velocity of the jet in the observer's frame \delta degrees and \beta approximately 0.96. Although these results for Mrk501 must be considered tentative, the combined analysis of polarization profiles and apparent component speeds holds promise as a means of further elucidating the magnetic field structures and other parameters of parsec-scale AGN jets

Towards Computing Inferences from English News Headlines

Newspapers are a popular form of written discourse, read by many people, thanks to the novelty of the information provided by the news content in it. A headline is the most widely read part of any newspaper due to its appearance in a bigger font and sometimes in colour print. In this paper, we suggest and implement a method for computing inferences from English news headlines, excluding the information from the context in which the headlines appear. This method attempts to generate the possible assumptions a reader formulates in mind upon reading a fresh headline. The generated inferences could be useful for assessing the impact of the news headline on readers including children. The understandability of the current state of social affairs depends greatly on the assimilation of the headlines. As the inferences that are independent of the context depend mainly on the syntax of the headline, dependency trees of headlines are used in this approach, to find the syntactical structure of the headlines and to compute inferences out of them.Comment: PACLING 2019 Long paper, 15 page

The impact of Stieltjes' work on continued fractions and orthogonal polynomials

Stieltjes' work on continued fractions and the orthogonal polynomials related to continued fraction expansions is summarized and an attempt is made to describe the influence of Stieltjes' ideas and work in research done after his death, with an emphasis on the theory of orthogonal polynomials

Near-Field Scanning Optical Microscope Combined with Digital Holography for Three-Dimensional Electromagnetic Field Reconstruction

International audienceNear-field scanning optical microscopy (NSOM) has proven to be a very powerful imaging technique that allows overcoming the diffraction limit and obtaining information on a scale much smaller than what can be achieved by classical optical imaging techniques. This is achieved using nanosized probes that are placed in close proximity to the sample surface, and thus allow the detection of evanescent waves that contain important information about the properties of the sample on a subwavelength scale. In particular, some aperture-based probes use a nanometer-sized hole to locally illuminate the sample. The far-field radiation of such probes is essential to their imaging properties, but cannot be easily estimated since it highly depends on the environment with which it interacts. In this chapter, we tackle this problem by introducing a microscopy method based on full-field off-axis digital holography that allows us to study in details the three-dimensional electromagnetic field scattered by a NSOM probe in different environments. We start by describing the NSOM and holography techniques independently, and continue by highlighting the advantage of combining both methods. We present a comparative study of the reconstructed light from a NSOM tip located in free space or coupled to transparent and plasmonic media. While far-field methods, such as back focal plane imaging, can be used to infer the directionality of angular radiation patterns, the advantage of our technique is that a single hologram contains information on both the amplitude and phase of the scattered light, allowing to reverse numerically the propagation of the electromagnetic field towards the source. We also present Finite Difference Time Domain (FDTD) simulations to model the radiation of the NSOM tip as a superposition of a magnetic and an electric dipole. We finally propose some promising applications that could be performed with this combined NSOM-holography technique

Geochemical Constraints for the Bulk Composition of the Moon

© 2018, Pleiades Publishing, Ltd. Abstract: The bulk composition of the silicate Moon (crust + mantle, BSM) is determined on the basis of inversion of gravitational and seismic data. It is shown that the mantle refractory oxides form two different groups depending on the thermal state. By the bulk Al2O3 content of ~3.0–4.6 wt %, the cold BSM models span the range of Al2O3 content of the silicate Earth (Bulk Silicate Earth, BSE), whereas the hot BSM models are significantly enriched in the Al2O3 content of ~5.1–7.3 wt % (Al2O3 content of ~1.2–1.7 × BSE) relative to BSE. In contrast, apart from the distribution of temperature, both BSM models are characterized by almost constant values of bulk FeO contents (~12.2–13.2 wt %) and MG# values (80.0–81.5), which are strongly distinct from those for BSE (~8 wt % FeO and 89 MG#). The results show that, for the geophysically possible distribution of temperatures, the silicate fraction of the Moon is enriched in FeO and depleted in MgO relative to BSE