The article discusses the interrelationships of the loxodrome or rhumb line, isometric latitude, and the Mercator projection of the rotational ellipsoid. It is shown that by applying the isometric latitude, a very simple equation of the rhumb line on the ellipsoid is obtained. The consequence of this is that the isometric latitude can be defined using the generalized geodetic longitude and not only using the geodetic latitude, as was usual until now. Since the image of the rhumb line in the plane of the Mercator projection is a straight line, the isometric latitude can also be defined using this projection. Finally, a new definition of the normal aspect of the Mercator projection of the ellipsoid is given. It is a normal aspect cylindrical projection in which the images of the rhumb line on the ellipsoid are straight lines in the plane of projection that, together with the images of the meridians in the projection, form equal angles as the rhumb line forms with the meridians on the ellipsoid. The article provides essential knowledge to all those who are interested in the use of maps in navigation. It will be useful for teachers and students studying cartography and GIS, maritime, or applied mathematics. The author uses mathematical methods, especially differential geometry. The assumption is that the readers are no strangers to mathematical cartography.

A total of 25 SSR primers were screened on 37 putative F₁s derived from the five different crosses. Identified cross specific highly informative SSRs primers, i.e., 14 for the first cross, 10 for the second, 12 for the third and 6 each for fourth and fifth crosses. For the first cross Bhagwa × Daru 17, four primers (HvSSRT_375, NRCP_SSR9, NRCP_SSR12 and NRCP_SSR92) were found to be highly informative with higher 100% hybrid purity index (HPI), PIC (~0.52), and observed heterozygosity (Ho, range 0.87–0.93) values, and two F₁s namely H₁ and H₂ were found to be highly heterotic with a heterozygosity index (HI) of 92.85%. Similarly, for Bhagwa × Nana, three primers (HvSSRT_375, HvSSRT_605 and NRCP_SSR19) had higher HPI (70%–100%), PIC (0.52–0.69), and Ho (0.75–0.33) values, and three F₁s H₁, H₂, and H₄ had 70% (HI). For Bhagwa × IC318712, four SSRs (HvSSRT_254, HvSSRT_348, HvSSRT_826 and NRCP_SSR95) had higher Ho (~0.83), HPI (100%) and PIC (~0.52) values, and four F₁s H₂, H₇, H₉, and H₁₀ showed 91.66% (HI). For Bhagwa × Nayana, HvSSRT_605, HvSSRT_826, and HvSSRT_432, and for Ganesh × Nayana, HVSSRT_375, HVSSRT_605, and HvSSRT_826 were found informative. These markers will be highly useful in developing maps of populations.

Introduction: In Colombia, the last oral health study showed that about 70% of the population has partial edentulism while 5.2% will have lost all their teeth between the age of 65 and 79. Rehabilitation with implants is an increasingly used option, which requires clinical and radiographic follow-up. Panoramic radiography is a low-cost option, in which it is possible to observe areas of bone loss, mesiodistal angulation of the implant, relationship with anatomical structures and lesions suggestive of peri-implantitis. Reports and analysis of relevant data on radiographic findings associated with dental implants are required to determine the risk factors for their success in patients who use them. Objective: To determine the prevalence and characterize the findings associated with osseointegration implants in panoramic radiographs. Methods: A descriptive cross-sectional observational study was carried out with 10,000 digital panoramic radiographs selected by convenience from radiological centers in the city of Bogota, Colombia, of which 543 corresponded to the sample analyzed for the presence of implants. The following were evaluated for each implant: location, position, angulation and distances to adjacent structures, using the Clínicalview® program (Orthopantomograph OP200D, Instrumentarium, USA). Results: The frequency of radiographs with implants was 5.43% with a total of 1,791 implants, with an average of 3.2 per radiograph. They were found in greater proportion in the upper jaw with a supracrestal location and an angulation of 10.3 degrees. 32% had implant/tooth or implant/implant distances that were less than optimal. 40.9% were restored and 1.2% showed lesions compatible with periimplantitis. Conclusions: A high percentage of the implants reviewed have a risk factor that affects their long-term viability, either due to angulation, supracrestal or crestal position, proximity to teeth or other implants, or because they are not restorable.

Based on the characteristics of liquid lens sparse aperture imaging, a radiative multiplet array structure is proposed; a simplified model of sparse aperture imaging is given, and the analytical expression of the modulation transfer function is derived from the optical pupil function of the multiplet array structure; the specific distribution form of this multiplet array structure is given, and the structure parameters are approximated by the dimensionless method; the two types of radiative multiplet array structures are discussed, and the filling factor, redundancy, modulation transfer function and other characteristic parameters are calculated. The physical phenomena exhibited by the parametric scan are discussed, and the structural features and imaging characteristics of these two arrays are compared. The results show that the type-II structure with larger actual equivalent aperture and actual cutoff frequency and lower redundancy is selected when the average modulation transfer function and the IF characteristics of the modulation transfer function of the two structures are close to each other; the type-II structure has certain advantages in imaging; the conclusion is suitable for arbitrary enclosing circle size because the liquid lens-based multiplet array structure adopts dimensionless approximation parameters; compared with the composite toroidal structure, the radiative multiplet mirror structure has a larger actual cut-off frequency and actual equivalent aperture when the filling factor is the same.

In this paper, a classification of low-dimensional nanomaterials is given, and new type of these nanomaterials — subnanophase coatings are proposed. Experimental results on the formation of a wetting layer of a transition metal on a silicon substrate by physical deposition in vacuum and results of this layer identification by the EELS method are given. Based on these results, a new approach to the formation of subnanophase coatings has been proposed by creation of an interface stresses structuring WL. The possible properties and application prospects of subnanophase coatings are considered.