Bijectivity of the canonical map for the noncommutative instanton bundle

It is shown that the quantum instanton bundle introduced in Commun. Math. Phys. 226, 419-432 (2002) has a bijective canonical map and is, therefore, a coalgebra Galois extension.Comment: Latex, 12 pages. Published versio

Non-commutative connections of the second kind

A connection-like objects, termed {\em hom-connections} are defined in the realm of non-commutative geometry. The definition is based on the use of homomorphisms rather than tensor products. It is shown that hom-connections arise naturally from (strong) connections in non-commutative principal bundles. The induction procedure of hom-connections via a map of differential graded algebras or a differentiable bimodule is described. The curvature for a hom-connection is defined, and it is shown that flat hom-connections give rise to a chain complex.Comment: 13 pages, LaTe

Star product formula of theta functions

As a noncommutative generalization of the addition formula of theta functions, we construct a class of theta functions which are closed with respect to the Moyal star product of a fixed noncommutative parameter. These theta functions can be regarded as bases of the space of holomorphic homomorphisms between holomorphic line bundles over noncommutative complex tori.Comment: 12 page

Twisted Hochschild Homology of Quantum Hyperplanes

We calculate the Hochschild dimension of quantum hyperplanes using the twisted Hochschild homology.Comment: 12 pages, LaTe

The 3D Spin Geometry of the Quantum Two-Sphere

We study a three-dimensional differential calculus on the standard Podles quantum two-sphere S^2_q, coming from the Woronowicz 4D+ differential calculus on the quantum group SU_q(2). We use a frame bundle approach to give an explicit description of the space of forms on S^2_q and its associated spin geometry in terms of a natural spectral triple over S^2_q. We equip this spectral triple with a real structure for which the commutant property and the first order condition are satisfied up to infinitesimals of arbitrary order.Comment: v2: 25 pages; minor change

The Hopf algebra structure of the Z3_3-graded quantum supergroup GLq,j(1∣1)_{q,j}(1|1)

In this work, we give some features of the Z$_3$-graded quantum supergroup

Fermion masses, mass-mixing and the almost commutative geometry of the Standard Model

We investigate whether the Standard Model, within the accuracy of current experimental measurements, satisfies the regularity in the form of Hodge duality condition introduced and studied in [9]. We show that the neutrino and quark mass-mixing and the difference of fermion masses are necessary for this property. We demonstrate that the current data supports this new geometric feature of the Standard Model, Hodge duality, provided that all neutrinos are massive. \ua9 2019, The Author(s)

Disorder-Induced First Order Transition and Curie Temperature Lowering in Ferromagnatic Manganites

We study the effect that size disorder in the cations surrounding manganese ions has on the magnetic properties of manganites. This disorder is mimic with a proper distribution of spatially disordered Manganese energies. Both, the Curie temperature and the order of the transition are strongly affected by disorder. For moderate disorder the Curie temperature decreases linearly with the the variance of the distribution of the manganese site energies, and for a disorder comparable to that present in real materials the transition becomes first order. Our results provide a theoretical framework to understand disorder effects on the magnetic behavior of manganites.Comment: 4 pages, three figures include

Impact of temporary desiccation on the mobility of nutrients and metals from sediments of Loskop Reservoir, Olifants River

South Africa is prone to droughts and is heavily dependent on stored water resources. Few studies in South Africa have investigated the impact of drought on water quality when rainfall resumes and reservoir sediments are rewet. Other research has shown that several negative impacts may occur with rewetting, including eutrophication, and acidification with increased metal solubility. In this study, the impact of drying and rewetting sediments on the mobility of nutrients and metals is explored using sediments from Loskop Reservoir. Rarely exposed sediments were collected from three sites, dried at 35°C for 36 days, and then rewet under aerobic conditions. Filtered water samples were collected on Days 1, 2 ,4, 7, 11 and 16 following rewetting, and analysed for NH4+, NO3-, NO2-, total N, total P, PO43-, dissolved Al, Fe, Mn, and SO42-. Results were expressed as mass/m2, and were compared to reference (non-drought) treatments that were maintained under saturated conditions. Acute toxicity tests were performed using Daphnia magna to establish if toxic effects were associated with changes in water quality following sediment rewetting. Following rewetting, elevated SO42- indicated the mobilisation of acid from sulfide oxidation, with an associated reduction in pH. Nitrification was evident as high quantities of organic N and NH4+ were initially released, followed by increases in NO2- + NO3-. Total P increased, but PO43- reduced. This was attributed to complexes formed between PO43- and Fe (FePO4) and Al (AlPO4). Amounts of Fe and Al released were lower following rewetting due to the formation of relatively immobile (hydr)oxides. In contrast, Mn increased substantially reaching maximum values > 2 300 mg/m2 (14 000 μg/L). There were no acute toxic effects observed to D. magna. This study highlights the potential for acidification, mobilisation of nutrients, SO42-, and Mn following rewetting of reservoir sediments under aerobic conditions. This information may be incorporated into reservoir and catchment management plans in the form of revised water quality guidelines and a better ability to predict how drought impacts water quality in our stored water resources.Keywords: sediment, drought, drying, rewetting, nutrient and metal release, Loskop Reservoi