Comprehensive coherent structures around a surface-mounted low aspect ratio square cylinder in uniform flow with an oblique angle of $45^{\circ }$ were investigated for cylinder-width-based Reynolds numbers of 3000 and 10 000 by direct numerical simulation based on a topology-confined mesh refinement framework. High-resolution simulations and the critical-point concept were scrutinized to reveal for the first time the reasonable and compatible topologies of flow separation and complete near-wall structures, due to their extensive impact on various engineering applications. Large-scale horseshoe vortices are observed at two notable foci in the viscous sublayer. Within this layer, a wall-parallel jet is formed by downflow intruding into the bottom surface at the half-saddle point, then deflecting in the upstream direction and finally penetrating the bottom surface until the half-saddle point. A pair of conical vortices on the cylinder's top surface switch themselves on two sides of the square cylinder, where the switching frequency is identical with that of the sway of the side shear layer. The undulation of the Kelvin–Helmholtz instability is identified in the instantaneous development of a conical vortex and side shear layer, where the scaling of the ratio of the Kelvin–Helmholtz and von Kármán frequencies follows the power-law relation obtained by Lander et al. (J. Fluid Mech., vol. 849, 2018, pp. 1096–1119). Large-scale arch-shaped vortex is often detected in the intermediate wake region of a square cylinder, involving two interconnected portions, such as the leg portion separated from leeward surfaces and head portion rolled up from the top surface. The leg portion of the arch-shaped vortex was rooted by two foci near the bottom-surface plane.

We prove that the restriction of a given orthogonal-complete metric space to the closure of the orbit induced by the origin point with respect to an orthogonal-preserving and orthogonal-continuous map is a complete metric space. Then we show that many existence results on fixed points in orthogonal-complete metric spaces can be proved by using the corresponding existence results in complete metric spaces.

The cao vit gibbon Nomascus nasutus, also known as eastern black crested gibbon, is categorized as Critically Endangered on the IUCN Red List and was considered one of the world's 25 most threatened primates. The only known population occurs along the border between China and Viet Nam. Accurate information on population size and dynamics is critical for the species’ conservation, but population surveys conducted in only one country may over- or underestimate total population size because the home ranges of cao vit gibbon groups often cross the international border. In 2007 and 2016 we conducted two collaborative transboundary censuses of the cao vit gibbon populations in the Trung Khanh Cao Vit Gibbon Species and Habitat Conservation Area in Viet Nam and the Bangliang Gibbon National Nature Reserve in China. The results showed a population size of 102–110 in 2007, which increased to 107–136 in 2016. Our results indicate that previous surveys conducted separately in Viet Nam and China underestimated the global population size of this species. According to our more comprehensive surveys, the gibbon population is increasing slowly. The gibbons and their habitat are legally protected in both countries. Hunting and charcoal making have not been reported in this area since 2007. As habitat carrying capacity is a limiting factor, habitat restoration is required. However, lack of funding to protect the cao vit gibbon remains a challenge.

Based on the metrisation of $b$-metric spaces of Paluszyński and Stempak [‘On quasi-metric and metric spaces’, Proc. Amer. Math. Soc.137(12) (2009), 4307–4312], we prove that every $b$-metric space has a completion. Our approach resolves the limitation in using the quotient space of equivalence classes of Cauchy sequences to obtain a completion of a $b$-metric space.

The mineralogy and crystal chemistry of a new talc ore deposit situated at Thu Ngac commune, Thanh Son district, Phu Tho province, Vietnam, was investigated using X-ray fluorescence, electron microprobe, X-ray diffraction, Fourier transform infrared spectroscopy, solid-state nuclear magnetic resonance (29Si and 1H) and colorimetry.

Both chemical and crystal-chemical analyses showed that the talcs from the Phu Tho province are very pure because they contain few accessory minerals (chlorite, amphibole and goethite) and few substitutions of Si by Fe and Al in their crystal structure. The talc ore may well meet the standards required for a wide range of industrial applications.

In this paper we first give a negative answer to a question of Amini-Harandi [‘Best proximity point theorems for cyclic strongly quasi-contraction mappings’, J. Global Optim.56 (2013), 1667–1674] on a best proximity point theorem for cyclic quasi-contraction maps. Then we prove some new results on best proximity point theorems that show that results of Amini-Harandi for cyclic strongly quasi-contractions are true under weaker assumptions.

Reproduction of Varroa jacobsoni Oudemans has been extensively studied in colonies of the mite's recently acquired host, Apis mellifera Linnaeus. However, data on reproduction in colonies of its original host, A. cerana Fabricius, are still fragmentary. In order to compare reproductive success in naturally infested brood cells of A. cerana and A. mellifera, freshly capped worker and drone cells (0–5 h after capping) were marked and opened 9 days later. When one or more foundress Varroa mites were found, the number and stage of the offspring were recorded. In colonies of A. cerana, V. jacobsoni reproduced almost exclusively in drone cells. Surprisingly, however, these drone cells proved to be better suited for reproduction than drone (and worker) cells of A. mellifera. Firstly, in drone cells of A. cerana, 97–100% of the mites produced daughters and 98–99% of these mites also produced a son. In drone and worker cells of A. mellifera only 70–80% produced daughters and only 74–86% of these mites produced a son. Secondly, if a mite produced daughters, she produced more daughters in drone cells of A. cerana than in drone cells of A. mellifera: 4.5–4.6 vs 2.9–3.7 daughters per mite, respectively. Finally, infestation by two foundress females negatively affected reproduction per mite in drone cells of A. mellifera, but not in drone cells of A. cerana. Thus, V. jacobsoni seems to be better adapted to A. cerana than to A. mellifera, although population growth of mites in A. mellifera colonies is higher due to the exploitation of worker cells besides drone cells.

It is well known that a ring R is semiprime Artinian if and only if every right ideal is an injective right R-module. In this paper we shall be concerned with the following general question: given a ring R all of whose right ideals have a certain property, what implications does this have for the ring R itself? In practice, it is not necessary to insist that all right ideals have the property, usually the maximal or essential right ideals will suffice. On the other hand, Osofsky proved that a ring R is semiprime Artinian if and only if every cyclic right R-module is injective. This leads to the second general question: given a ring R all of whose cyclic right R-modules have a certain property, what can one say about R itself?

In May 1992 the discovery of three pairs of horns in the only remaining area of pristine forest in northern Vietnam led to the description of a new species of ox. A total of 20 specimens have now been found, most of them consisting of only the horns and part of the skull. The Ministry of Forestry in Vietnam is enlarging and upgrading protected areas in the suspected 4000-sq-km range of the Vu Quang ox and surveys are under way in two proposed reserves in neighbouring Laos where the ox is also reported to occur. Meanwhile a local campaign is necessary to inform villagers of the valuable nature of this species and to ban further hunting.

Throughout this paper we consider associative rings with identity and assume that all modules are unitary. As is well known, cyclic modules play an important role in ring theory. Many nice properties of rings can be characterized by their cyclic modules, even by their simple modules. See, for example, [2], [3], [6], [7], [13], [14], [15], [16], [18], [21]. One of the most important results in this direction is the result of Osofsky [14, Theorem] which says: a ring R is semisimple (i.e. right artinian with zero Jacobson radical) if and only if every cyclic right R-module is injective. The other one is due to Vamos [18]: a ring R is right artinian if and only if every cyclic right R-module is finitely embedded.