Revealing the nature of the transient source MAXI J0637-430 through spectro-temporal analysis

We study the spectral and temporal properties of MAXI J0637-430 during its 2019-2020 outburst using NICER, AstroSat and Swift-XRT data. The source was in a disc dominant state within a day of its detection and traces out a ‘c’ shaped profile in the HID, similar to the ‘mini’-outbursts of the recurrent BHB 4U 1630-472. Energy spectrum is obtained in the 0.5 − 10 keV band with NICER and Swift-XRT, and 0.5 − 25 keV with AstroSat. The spectra can be modelled using a multicolour disc emission (diskbb) convolved with a thermal Comptonisation component (thcomp). The disc temperature decreases from 0.6 keV to 0.1 keV during the decay with a corresponding decrease in photon index (Γ) from 4.6 to 1.8. The fraction of Compton scattered photons (fcov) remains < 0.3 during the decay upto mid-January 2020 and gradually increases to 1 as the source reaches hard state. Power Density Spectra (PDS) generated in the 0.01-100 Hz range display no Quasi-periodic Oscillations (QPOs) although band-limited noise (BLN) is seen towards the end of January 2020. During AstroSat observations, Γ lies in the range 2.3 − 2.6 and rms increases from 11 to 20%, suggesting that the source was in an intermediate state till 21 November 2019. Spectral fitting with the relativistic disc model (kerrbb), in conjunction with the soft-hard transition luminosity, favour a black hole with mass 3 − 19 M⊙ with retrograde spin at a distance <15 kpc. Finally, we discuss the possible implications of our findings.

Influence of the cage on the migration and distribution of lubricating oil inside a ball bearing

The migration and distribution of lubricant oil in a rolling bearing strongly affect the elastohydrodynamic lubrication performance between the balls and rings. However, oil re-lubrication is highly dependent on the bearing design, which is different from the ball-on-disc model. This study directly observed the distribution of the lubricant film in a custom-made model-bearing rig, with an outer ring replaced by a glass ring to allow full optical access. The influence of the cage type and surface properties were presented. The physical origin of the re-lubrication mechanism, including capillary flow and mechanical redistribution, was discussed.

Comparative Study of Technologies for Tubule Occlusion and Treatment of Dentin Hypersensitivity

This study aimed to evaluate the occluding/remineralization performance and resistance to acid attacks of the mineralization layer formed by a tooth-desensitizing gel containing amorphous calcium magnesium phosphate (ACMP) particles and compare it to six other desensitizing products available on the market. Similar comprehensive studies are few and there is especially a lack of studies that are up to date. A dentin-disc model was used for in vitro evaluation of the desensitizing toothpastes/gels. Application of the products was performed twice daily for seven days. One set of specimens were evaluated using scanning electron microscopy (SEM) directly after the final treatment and another set was evaluated after an acid challenge, exposing specimens to 2 wt% citric acid. The ACMP desensitizing gel was the only product resulting in complete occlusion by the formation of mineralized material on the dentin surface and inside the tubules. Particle deposition was dominant after treatment with the other desensitizing products, with little or no mineralization, resulting in partial occlusion only. Sensodyne Repair & Protect and Oral-B Pro-Expert showed the highest resistance toward acid attacks. Material inside the tubules remained relatively unaffected by acid attacks in all specimens. The results in this study indicated a great variability among the occluding agents in terms of occlusion and acid resistance of the mineralization layer. The high degree of occlusion and intra-tubular mineralization that could mitigate the effect of acid solubilization indicate that the ACMP desensitizing gel may be a superior option for the treatment of dentin hypersensitivity.

The Beckman–Quarles Theorem in Hyperbolic Geometry

In this paper, we present the counterpart of the Beckman–Quarles theorem in the Poincaré disc model of hyperbolic geometry to characterize the gyroisometries (hyperbolic isometries) with a single nonzero distance a ∈ 0,1 satisfying a 2 ∈ ℚ .

The hyperbolic geometry of financial networks

Based on data from the European banking stress tests of 2014, 2016 and the transparency exercise of 2018 we construct networks of European banks and demonstrate that the latent geometry of these financial networks can be well-represented by geometry of negative curvature, i.e., by hyperbolic geometry. Using two different hyperbolic embedding methods, hydra+ and Mercator, this allows us to connect the network structure to the popularity-vs-similarity model of Papdopoulos et al., which is based on the Poincaré disc model of hyperbolic geometry. We show that the latent dimensions of ‘popularity’ and ‘similarity’ in this model are strongly associated to systemic importance and to geographic subdivisions of the banking system, independent of the embedding method that is used. In a longitudinal analysis over the time span from 2014 to 2018 we find that the systemic importance of individual banks has remained rather stable, while the peripheral community structure exhibits more (but still moderate) variability. Based on our analysis we argue that embeddings into hyperbolic geometry can be used to monitor structural change in financial networks and are able to distinguish between changes in systemic relevance and other (peripheral) structural changes.

The Formulas of Möbius-Bretschneider and Möbius-Cagnoli in the Poincaré Disc Model of Hyperbolic Geometry

In this paper, we present two gyroarea formulas (Möbius-Bretschneider’s formula and Möbius-Cagnoli’s formula) for Möbius gyroquadrilaterals in the Poincaré disc model of hyperbolic geometry.