Characterization of knot complements in the 4-sphere

AbstractKnot complements in S4 are characterized as follows: A connected open set W ⊂ S4 is homeomorphic to the complement of some locally flat 2-sphere in S4 if and only if H1(W) is infinite cyclic, W has one end, and the fundamental group of that end is infinite cyclic. Applications include a characterization of weakly flat 2-spheres in S4 and a complement theorem for 2-spheres in S4

Representing homology classes of simply connected 4-manifolds

AbstractThe main theorem asserts that every 2-dimensional homology class of a compact simply connected PL 4-manifold can be represented by a codimension-0 submanifold consisting of a contractible manifold with a single 2-handle attached. One consequence of the theorem is the fact that every map of S2 into a simply connected, compact PL 4-manifold is homotopic to an embedding if and only if the same is true for every homotopy equivalence. The theorem is also the main ingredient in the proof of the following result: If W is a compact, simply connected, PL submanifold of S4, then each element of H2(W;Z) can be represented by a locally flat topological embedding of S2

Constitutive modelling of instabilities and strengths of an unsaturated tailings

Instabilities mostly happen in fully saturated and loose non-cohesive geomaterials like sands or silts or tailings, but it is also possible in unsaturated geomaterials. When unsaturated they can experience a reduction in effective stress and strain soften during water (and air) undrained loading, attaining a very low residual strength. This study focuses on modelling the conditions required to cause instability in unsaturated silty tailings, giving particular consideration to the presence of air and the way it alters the ability for volume change when it remains trapped inside the tailings. A gold tailings is used to calibrate the UNSW boundingsurface plasticity model. The effect of air, including the volumetric change caused by air compression, the alteration of air pressure, the contribution of suction to the effective stress, and suction hardening, are explored. Collapse lines (sometimes referred to as instability lines or flow liquefaction lines which represent boundaries between stable and potentially unstable stress states) in th

The influences of partial saturation on cone penetration tests in silty gold tailings

Laboratory-controlled cone penetration test results of a silty gold tailings in a variety of saturated and unsaturated states, obtained using two calibration chambers, are presented then interpreted using a state parameter-based approach. The research was conducted as part of the TAILLIQ project (tailliq.com), funded by the Australian Research Council and six mining companies, and involving four Australian universities.Cone penetration resistances, which increase due to the presence of suction when the tailings are unsaturated, can be normalised using the initial mean effective stress to establish a relationship with the initial state parameter. The relationship is applicable to saturated and unsaturated conditions, as long as the presence of suction hardening as well as the influence of suction on the mean effective stress are accounted for, and as long as the cone penetrations occur under pseudo drained conditions. The relationships enable state parameters and void ratios to be back-calculated from normalised cone penetration resistances

Selective breeding of saline-tolerant striped catfish (Pangasianodon hypophthalmus) for sustainable catfish farming in climate vulnerable Mekong Delta, Vietnam

peer reviewedStriped catfish (Pangasianodon hypophthalmus), a freshwater species cultured mainly in the Mekong Delta region in Southern Vietnam, is facing a significant challenge due to salinity intrusion as a result of climatic changes. Given these evolving environmental conditions, selecting new strains with a higher salinity tolerance could make production of striped catfish economically feasible in brackish environments. In this study, we carried out a selection program aimed at developing a striped catfish strain able to survive and grow fast in a saline environment. To implement the selection program, we first collected males and females from different provinces in the Mekong delta. We next performed a factorial cross of these breeders to produce half- and full-sib families. When fish reached fry stage (47 dph), we put them in a saline environment (10 ppt) and subsequently kept 50 % of the fastest-growing fish after 143 days post hatching (dph). We repeated this mass selection procedure after 237 dph and 340 dph. We maintained in parallel a randomly selected group in saline conditions and a group of fish reared in freshwater to serve as controls. After crossing the selected individuals, we performed several tests on the next generation of fish to evaluate the effectiveness of selection after one generation in saline conditions. Average direct responses to selection were 18.0 % for growth and 11.4 % for survival rate after one generation of selection. We estimated a moderate realized heritability (0.29) for body weight. The genetic gains obtained in our study for body weight and survival rate after one generation of selection under saline conditions suggest that selection can be effective to improve ability of striped catfish to cope with saline stress. We conclude that our selection program has succeeded in developing a productive strain of striped catfish with better tolerance to salinity. © 2022 The Author

Characterization of knot complements in the n-sphere

Knot complements in the n-sphere are characterized. A connected open subset W of $S^n$ is homeomorphic with the complement of a locally flat (n-2)-sphere in $S^n$, n ≥ 4, if and only if the first homology group of W is infinite cyclic, W has one end, and the homotopy groups of the end of W are isomorphic to those of $S^1$ in dimensions less than n/2. This result generalizes earlier theorems of Daverman, Liem, and Liem and Venema