Planetary geometry handbook: Venus positional data, 1988 - 2020, volume 2

Graphical data necessary for the analysis of planetary exploration missions to Venus are presented. Positional and geometric information spanning the time period from 1988 through 2020 is provided. The data and the usage are explained

Planetary geometry handbook: Mars positional data, 1990 - 2020, volume 3

Graphical data necessary for the analysis of planetary exploration missions to Mars are presented. Positional and geometric information spanning the time period from 1990 through 2020 is provided. The data and usage are explained

Planetary geometry handbook: Saturn positional data, 1985 - 2020, volume 5

Graphical data necessary for the analysis of planetary exploration missions to Saturn are presented. Positional and geometric information spanning the time period from 1985 through 2020 is provided. The data and their usage are explained

Planetary geometry handbook: Jupiter positional data, 1985 - 2020, volume 4

Graphical data necessary for the analysis of planetary exploration missions to Jupiter are presented. Positional and geometric information spanning the time period from 1985 through 2020 is provided. The data and their usage are explained

Bayesian optimisation for premise selection in automated theorem proving (student abstract)

Modern theorem provers utilise a wide array of heuristics to control the search space explosion, thereby requiring optimisation of a large set of parameters. An exhaustive search in this multi-dimensional parameter space is intractable in most cases, yet the performance of the provers is highly dependent on the parameter assignment. In this work, we introduce a principled probabilistic framework for heuristic optimisation in theorem provers. We present results using a heuristic for premise selection and the Archive of Formal Proofs (AFP) as a case study.</jats:p

Formalising Mathematics in Simple Type Theory

Despite the considerable interest in new dependent type theories, simple type theory (which dates from 1940) is sufficient to formalise serious topics in mathematics. This point is seen by examining formal proofs of a theorem about stereographic projections. A formalisation using the HOL Light proof assistant is contrasted with one using Isabelle/HOL. Harrison's technique for formalising Euclidean spaces is contrasted with an approach using Isabelle/HOL's axiomatic type classes. However, every formal system can be outgrown, and mathematics should be formalised with a view that it will eventually migrate to a new formalism

The Psychological and Physiological Effects of Music on Athletic Performance

Please view abstract in the attached PDF file

Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation

Optical constant spectra for silicon and thermally grown silicon dioxide have been simultaneously determined using variable angle of incidence spectroscopic ellipsometry from 0.75 to 6.5 eV. Spectroscopic ellipsometric data sets acquired at multiple angles of incidence from seven samples with oxide thicknesses from 2 to 350 nm were analyzed using a self-contained multi-sample technique to obtain Kramers–Kronig consistent optical constant spectra. The investigation used a systematic approach utilizing optical models of increasing complexity in order to investigate the need for fitting the thermal SiO2 optical constants and including an interface layer between the silicon and SiO2 in modeling the data. A detailed study was made of parameter correlation effects involving the optical constants used for the interface layer. The resulting thermal silicon dioxide optical constants were shown to be independent of the precise substrate model used, and were found to be approximately 0.4% higher in index than published values for bulk glasseous SiO2. The resulting silicon optical constants are comparable to previous ellipsometric measurements in the regions of overlap, and are in agreement with long wavelength prism measurements and transmission measurements near the band gap

Phase Transitions in liquid Helium 3

The phase transitions of liquid Helium 3 are described by truncations of an exact nonperturbative renormalization group equation. The location of the first order transition lines and the jump in the order parameter are computed quantitatively. At the triple point we find indications for partially universal behaviour. We suggest experiments that could help to determine the effective interactions between fermion pairs.Comment: 4 pages, 6 figures, LaTe

A Possible Stellar Metallic Enhancement in Post-T Tauri Stars by a Planetesimal Bombardment

The photospheres of stars hosting planets have larger metallicity than stars lacking planets. In the present work we study the possibility of an earlier metal enrichment of the photospheres by means of impacting planetesimals during the first 20-30Myr. Here we explore this contamination process by simulating the interactions of an inward migrating planet with a disc of planetesimal interior to its orbit. The results show the percentage of planetesimals that fall on the star. We identified the dependence of the planet's eccentricity ($e_p$) and time scale of migration ($\tau$) on the rate of infalling planetesimals. For very fast migrations ($\tau=10^2$yr and $\tau=10^3$yr) there is no capture in mean motion resonances, independently of the value of $e_p$. Then, due to the planet's migration the planetesimals suffer close approaches with the planet and more than 80% of them are ejected from the system. For slow migrations ($\tau=10^5$yr and $\tau=10^6$yr) the percentage of collisions with the planet decrease with the increase of the planet's eccentricity. For $e_p=0$ and $e_p=0.1$ most of the planetesimals were captured in the 2:1 resonance and more than 65% of them collided with the star. Whereas migration of a Jupiter mass planet to very short pericentric distances requires unrealistic high disc masses, these requirements are much smaller for smaller migrating planets. Our simulations for a slowly migrating 0.1 $M_{\rm Jupiter}$ planet, even demanding a possible primitive disc three times more massive than a primitive solar nebula, produces maximum [Fe/H] enrichments of the order of 0.18 dex. These calculations open possibilities to explain hot Jupiters exoplanets metallicities.Comment: Accepted for publication by Monthly Notices of the Royal Astronomical Societ