Partial Covering of a Circle by 6 and 7 Congruent Circles

Background: Some medical and technological tasks lead to the geometrical problem of how to cover the unit circle as much as possible by n congruent circles of given radius r, while r varies from the radius in the maximum packing to the radius in the minimum covering. Proven or conjectural solutions to this partial covering problem are known only for n = 2 to 5. In the present paper, numerical solutions are given to this problem for n = 6 and 7. Method: The method used transforms the geometrical problem to a mechanical one, where the solution to the geometrical problem is obtained by finding the self-stress positions of a generalised tensegrity structure. This method was developed by the authors and was published in an earlier publication. Results: The method applied results in locally optimal circle arrangements. The numerical data for the special circle arrangements are presented in a tabular form, and in drawings of the arrangements. Conclusion: It was found that the case of n = 6 is very complicated, whilst the case n = 7 is very simple. It is shown in this paper that locally optimal arrangements may exhibit different types of symmetry, and equilibrium paths may bifurcate.

Application of an active oxygen (blue®m) with free connective graft technique for root coverage – a case report

Gingival recession occurs due to the migration of the gingiva in the apical direction, leading to compromising local aesthetics and root hypersensitivity. Connective tissue graft is the gold standard treatment in these cases improving both functional and aesthetics aspects.The purpose of this case is to report root coverage using the free connective tissue graftingtechnique (CTG) associated with topical application of active oxygen oral gel and mouthwash (blue®m). A 27-year-old female sought care with the main complaint of root hypersensitivity and the presence of gingival recession in the anterior region of the mandible. Clinical examination revealed the presence of type 1 gingival recession in the left mandibular central incisor. The treatment of choice was a modified graft (free connective graft). The graft and recipient bed received applications of blue®m oral gel. The patient was instructed to use blue®m mouthwash and blue®m oral gel after the surgery for 10 days. At 60 days, the patient showed satisfactory healing in the area of the free CTG, with gain of keratinized tissue and partial covering of the gingival recession. Free CTG with the support of the gel and the mouthwash with active oxygen release makes the technique viable, preventing graft necrosis and achieving root coverage and keratinized tissue.

Infrared Nanospectroscopy Reveals DNA Structural Modifications upon Immobilization onto Clay Nanotubes

The growing demand for innovative means in biomedical, therapeutic and diagnostic sciences has led to the development of nanomedicine. In this context, naturally occurring tubular nanostructures composed of rolled sheets of alumino-silicates, known as halloysite nanotubes, have found wide application. Halloysite nanotubes indeed have surface properties that favor the selective loading of biomolecules. Here, we present the first, to our knowledge, structural study of DNA-decorated halloysite nanotubes, carried out with nanometric spatially-resolved infrared spectroscopy. Single nanotube absorption measurements indicate a partial covering of halloysite by DNA molecules, which show significant structural modifications taking place upon loading. The present study highlights the constraints for the use of nanostructured clays as DNA carriers and demonstrates the power of super-resolved infrared spectroscopy as an effective and versatile tool for the evaluation of immobilization processes in the context of drug delivery and gene transfer.

Color–color diagrams as tools for assessment of the variable absorption in high mass X-ray binaries

High mass X-ray binaries hold the promise of allowing us to understand the structure of the winds of their supermassive companion stars by using the emission from the compact object as a backlight to evaluate the variable absorption in the structured stellar wind. The wind along the line of sight can change on timescales as short as minutes and below. However, such short timescales are not available for the direct measurement of absorption through X-ray spectroscopy with the current generation of X-ray telescopes. In this paper, we demonstrate the usability of color–color diagrams for assessing the variable absorption in wind accreting high mass X-ray binary systems. We employ partial covering models to describe the spectral shape of high mass X-ray binaries and assess the implication of different absorbers and their variability on the shape of color–color tracks. We show that in taking into account, the ionization of the absorber, and in particular accounting for the variation of ionization with absorption depth, is crucial to describe the observed behavior well.

Lifting the curtain: The Seyfert galaxy Mrk 335 emerges from deep low-state in a sequence of rapid flare events

Context. The narrow-line Seyfert 1 galaxy Mrk 335 was one of the X-ray brightest active galactic nuclei, but it has systematically faded since 2007. Aims. We report the discovery with Swift of a sequence of bright and rapid X-ray flare events that reveal the emergence of Mrk 335 from its ultra-deep multiyear low state. Methods. Results are based on our dedicated multiyear monitoring of Mrk 335 with Swift. Results. Unlike other bright active galactic nuclei, the optical–UV is generally not correlated with the X-rays in Mrk 335 on a timescale of days to months. This fact either implies the absence of a direct link between the two emission components; or else implies that the observed X-rays are significantly affected by (dust-free) absorption along our line of sight. The UV and optical, however, are closely correlated at the 99.99% confidence level. The UV is leading the optical by Δt = 1.5 ± 1.5 d. The Swift X-ray spectrum shows strong deviations from a single power law in all brightness states of the outbursts, indicating that significant absorption or reprocessing is taking place. Mrk 335 displays a softer-when-brighter variability pattern at intermediate X-ray count rates, which has been seen in our Swift data since 2007 (based on a total of 590 observations). This pattern breaks down at the highest and lowest count rates. Conclusions. We interpret the 2020 brightening of Mrk 335 as a decrease in column density and covering factor of a partial-covering absorber along our line of sight in the form of a clumpy accretion-disk wind that reveals an increasing portion of the intrinsic emission of Mrk 335 from the disk and/or corona region, while the optical emission-line regions receive a less variable spectral energy distribution. This then also explains why Mrk 335 was never seen to change its optical Seyfert type (not “changing look”) despite its factor ∼50 X-ray variability with Swift.

Production of Vanadium Concentrate from a Small-Scale Lead Vanadate Deposit by Gravity Concentration: A Pilot Plant Study

The renewable energy revolution calls for high-performing materials and makes metallic compounds like lithium, cobalt, nickel and vanadium more and more critical. Innovations contribute to inventions and developments like vanadium redox flow batteries for large-scale energy storage systems with numerous technological advantages. Potential shortages of vanadium and its sources will contribute to turbulence in vanadium pricing. Nowadays, main sources and production sites of vanadium are located in Russia, China and South Africa. About 85% of vanadium applications are ferroalloys and high-performance alloys, which make production and price of vanadium dependent on the iron ore market. Partial covering of a potential vanadium demand may be achieved by an exploitation of lead vanadate ore deposits as alternative vanadium source. In the present work, the processing of a lead vanadate ore, mainly containing vanadinite and descloizite was investigated. Based on ore characterizations and preliminary beneficiation tests, a flowsheet was developed to design a small-scale processing plant, including comminution, dewatering and gravity separation. Preliminary laboratory tests and samples from the small-scale processing plant show promising results for the recovery of vanadium in a lead vanadate concentrate with a grade of 12 to 16% V2O5 and a recovery of 68 to 75%.

Elucidating the global distribution of reprocessing gas in NGC 1194

ABSTRACT A joint XMM–Newton and NuSTAR observation was conducted for the bright, local Seyfert 1.9 galaxy, NGC 1194. The hard spectral form of this active galactic nucleus (AGN) was modelled using the toroidal reprocessor mytorus. The decoupled model form provides a good description of the spectrum, with reflection arising from gas with a global average column density >4 × 1024 cm−2 and transmission of the continuum through an order-of-magnitude lower column. In this model, the reflection strength is a factor of ∼3 higher than expected from a simple torus. Such a result may indicate that much of the intrinsic X-ray continuum is hidden from view. An alternative model is that of a patchy torus, where 85 per cent of sightlines are obscured by Compton-thick gas and the remaining 15 per cent by Compton-thin gas. The patchy torus model is based on a solar abundance of Fe and is consistent with X-ray partial-covering results found in other AGN. That a patchy torus model would relieve the issue with the strength of the reflection signature is not an intuitive result: such an insight regarding the geometry of the global reprocessing gas could not have been obtained using ad hoc model components to describe the spectral form.

Physicochemical Aspects of the Performance of Hair-Conditioning Formulations

Most of the currently used products for repairing and conditioning hair rely on the deposition of complex formulations, based on mixtures involving macromolecules and surfactants, onto the surface of hair fibers. This leads to the partial covering of the damaged areas appearing in the outermost region of capillary fibers, which enables the decrease of the friction between fibers, improving their manageability and hydration. The optimization of shampoo and conditioner formulations necessitates a careful examination of the different physicochemical parameters related to the conditioning mechanism, e.g., the thickness of the deposits, its water content, topography or frictional properties. This review discusses different physicochemical aspects which impact the understanding of the most fundamental bases of the conditioning process.