The first new application of the Mathematical Theory of Stochastic Processes to lunar and planetary science: Topography-Profile Diagrams of Mars

The Mathematical Statistics Theory (MST) and the Mathematical Theory of Stochastic Processes (MTSP) are different branches of the more general Mathematical Probability Theory (MPT) that can be used to investigate physical processes through mathematics. Each model of a stochastic process, according to MTSP, can provide one or more interpretations in the MST domain. A large body of work on impact crater statistics according to MST exists, showing cumulative crater frequency (N km⁻²) as a function of age (years) for some particular crater diameter. However, this is only one possible representation in the MST domain of the bombardment of the planetary surface modeled as a stochastic process according to MTSP. The idea that other representations are possible in the MST domain of the same stochastic process from MTSP has been recently presented. The importance of the approach is that each such mathematical-based interpretation can provide a large amount of new information. Coupled with MOLA data, Topography-Profile Diagrams (TPD) are one of the many examples that can provide a large amount of new information regarding the history of Mars. TPD consists of: (1) Topography-Profile Curve (TPC), which is a representation of the planet’s topography, (2) Density-of-Craters Curve (DCC), which represents density of craters, (3) Filtered-DCC (FDCC), which represents DCC filtered by a low-pass filter, included with the purpose of reducing the noise, and (4) Level-of-Substance-Over-Time Curve (LSOTC), which represents interpretation of the influence on the distribution of craters shown by FDCC. TPC uniquely corresponds to the computation of TPD, whereas DCC depends on algorithms for computing the elevation of each crater according to the topography, center coordinates, and radius of impact crater, and FDCC relies on the architecture of the custom designed low-pass filter for filtering DCC. However, all variations of DCC and FDCC, which includes the various impact crater data sets, showed a correlation among the density of craters and elevation over 70–80% of the planet surface. Additionally, if we assume that the ocean primarily caused the noted correlation, LSOTC offers a mathematical approach for estimating topographic change of the ocean’s extent over time. Accordingly, TPD is the first new practical application of MTSP to lunar and planetary sciences, showing correlation of topography to a physical process.     

Hybrid method for crater detection based on topography reconstruction from optical images and the new LU78287GT catalogue of Lunar impact craters

Impact craters are ubiquitous and well-studied structures of high geological relevance on the surfaces of the Earth’s Moon, the terrestrial planets, the asteroids and the satellites of the outer planets. Therefore, it is not surprising that crater detection algorithms (CDAs) are one of the most studied subjects of image processing and analysis in lunar and planetary science. In this paper we are proposing a Hybrid CDA: a modified DEM (digital elevation map) reconstruction method used as a step in an existing CDA based on Hough transform. The new Hybrid CDA consists of: (1) reconstruction of topography from optical images using a shape from shading approach; (2) utilization of the DEM-based CDA; (3) correction of brightness and contrast of optical images used in order to be more suitable for evaluation of detections. An additional result of this work is a new method for evaluation of topography reconstruction algorithms, using a DEM-based CDA and an earlier approach for evaluation of CDAs. The new Hybrid CDA was tested using two Chandrayaan-1 Moon Mineralogy Mapper (M³) images and two excerpts of the Lunar Reconnaissance Orbiter (LRO) Wide Angle Camera (WAC) global optical image mosaic. As a result, the number of craters inside these four regions increased considerably from 1754 (as available in the previous LU60645GT catalogue) to 19 396 craters (as available in the resulting new LU78287GT catalogue). This confirmed the practical applicability of the new Hybrid CDA, which can be used in order to considerably extend current crater catalogues.     

A model for the Balmer pseudocontinuum in spectra of type 1 AGNs

Here we present a new method for subtracting the Balmer pseudocontinuum in the UV part of type 1 AGN spectra. We calculate the intensity of the Balmer pseudocontinuum using the prominent Balmer lines in AGN spectra. We apply the model on a sample of 293 type 1 AGNs from SDSS database, and found that our model of Balmer pseudocontinuum + power law continuum very well fits the majority of AGN spectra from the sample, while in ∼$\sim$15% of AGNs, the model fits reasonable the UV continuum, but a discrepancy between the observed and fitted spectra is noted. Some of the possible reasons for the discrepancy may be a different value for the optical depth in these spectra than used in our model or the influence of the intrinsic reddening.     

Time series analysis of active galactic nuclei: The case of Arp 102B, 3C 390.3, NGC 5548 and NGC 4051

We used the Z-transformed Discrete Correlation Function (ZDCF) and the Stochastic Process Estimation for AGN Reverberation (SPEAR) methods for the time series analysis of the continuum and the Hα$\alpha$ and Hβ$\beta$ line fluxes of a sample of well known type 1 active galactic nuclei (AGNs): Arp 102B, 3C 390.3, NGC 5548, and NGC 4051, where the first two objects are showing double-peaked emission line profiles. The aim of this work is to compare the time lag measurements from these two methods, and check if there is a connection with other emission line properties. We found that the obtained time lags from Hβ are larger than those derived from the Hα analysis for Arp 102B, 3C 390.3 and NGC 5548. This may indicate that the Hβ   line originates at larger radii in these objects. Moreover, we found that the ZDCF and SPEAR time lags are highly correlated (r∼0.87$r\sim 0.87$), and that the error ranges of both ZDCF and SPEAR time lags are correlated with the FWHM of used emission lines (r∼0.7$r\sim 0.7$). This increases the uncertainty of the black hole mass estimates using the virial theorem for AGNs with broader lines.     

Oriented platform for the VEGA-probe to the Halley comet,position detection,working program

Two deep-space probes of the Venera type for the encounter with Halley's comet are being prepared in the Intercosmos program. 150 kg of scientific equipment will be onboard each sonde, including two TV cameras and two spectrometers. These instruments need precise orientation during the fly-by of the comet. For this purpose a stabilised platform is being developed in Czechoslovakia which will be installed onboard both probes and will be able to point to the target with precision 5 minutes of arc and maximum angular velocity 1°/second. A system of position detectors and the working program during the start and the fly-by are described.