A Comparative Study of Sulfur Isotope Variations within the Flatreef and Merensky Reef of the Bushveld Complex, South Africa

ABSTRACT The Flatreef, a down-dip, sub-horizontal extension of the Platreef, which underlies the Turfspruit and Macalacaskop farms, represents the future of platinum mining in South Africa. The stratigraphic connection between the Platreef, located at the base of the northern limb of the Bushveld Complex, and the Merensky Reef in the western and eastern limbs of the complex, was disputed for many years due to the heterogeneous nature of the Platreef along strike. However, the discovery of the Flatreef led to a new perspective on the Platreef as the former allowed for the study of a magmatic stratigraphy less affected by footwall interaction. Here, we report whole-rock S isotope (δ34S) compositions across the stratigraphic units of the Flatreef and its footwall and hanging wall as intersected by boreholes UMT-276 and UMT-393, as well as stratigraphic units of the Merensky Reef at Two Rivers Platinum mine in the eastern limb. The units of the Flatreef containing platinum group element mineralization, namely the Main Reef and Upper Reef, have δ34S values that overlap with the range recorded for the Merensky Reef in the western and eastern limbs. In UMT-393, Main Reef δ34S values range between 0.2 and 1.5‰ (with the exception of three outliers, 9.7‰, 11.1‰, and 7.9‰), and 0.52‰ and 11.2‰ for two Upper Reef samples. However, in UMT-276, Main Reef δ34S values range between –0.96 and 2.24‰ and 3.19‰ was recorded for an Upper Reef sample. The S isotope compositions recorded for the Merensky Reef pyroxenite at Two Rivers Platinum mine are relatively higher with δ34S values ranging between 1.24 and 4.83‰. The top unit of the Flatreef, which is a transition zone below the Main Zone, as well as the Footwall Cyclic Unit have heavier S isotope compositions with δ34S values ranging between 6 and 17‰ for the former and 0.7 and 18.6‰ for the latter. At Two Rivers Platinum mine, the hanging-wall anorthosite has a δ34S value of 2.9‰ in contrast to the 5.7‰ measured for the footwall anorthosite and 3.27‰ for the footwall feldspathic pyroxenite. The consistent near-mantle S isotope signature and accompanying metal enrichment in the Main Reef of the Flatreef may be explained by extensive interaction of sulfide minerals in a Lower Zone conduit/pre-Platreef staging chamber with large volumes of uncontaminated magma. The δ34S values of the Merensky Reef at Two Rivers Platinum mine are slightly higher compared to that of the Main Reef at Turfspruit and Macalacaskop possibly due to interaction with underlying carbonate rocks.

ODE-RU: a dynamical system view on recurrent neural networks

<abstract><p>The core of the demonstration of this paper is to interpret the forward propagation process of machine learning as a parameter estimation problem of nonlinear dynamical systems. This process is to establish a connection between the Recurrent Neural Network and the discrete differential equation, so as to construct a new network structure: ODE-RU. At the same time, under the inspiration of the theory of ordinary differential equations, we propose a new forward propagation mode. In a large number of simulations and experiments, the forward propagation not only shows the trainability of the new architecture, but also achieves a low training error on the basis of main-taining the stability of the network. For the problem requiring long-term memory, we specifically study the obstacle shape reconstruction problem using the backscattering far-field features data set, and demonstrate the effectiveness of the proposed architecture using the data set. The results show that the network can effectively reduce the sensitivity to small changes in the input feature. And the error generated by the ordinary differential equation cyclic unit network in inverting the shape and position of obstacles is less than $ 10^{-2} $.</p></abstract>

A note on nil-clean rings

We study a special kind of nil-clean rings, namely those nil-clean rings whose nilpotent elements are difference of two “left-right symmetric” idempotents, and prove that in some various cases they are strongly π-regular. We also show that all nil-clean rings having cyclic unit 2-groups are themselves strongly nil-clean of characteristic 2 (and thus they are again strongly π-regular).

Are protracted timescales of magmatism documented in the Platreef, Bushveld Complex?

&lt;p&gt;Models for the formation of the Rustenberg Layered Suite of the Bushveld Igneous Complex continue to be debated. The consensus timescale over which magmatism took place has reduced hand in hand with advancements in geochronological techniques and data precision. The most recent studies by double spiked (&lt;sup&gt;202&lt;/sup&gt;Pb-&lt;sup&gt;205&lt;/sup&gt;Pb) zircon CA-ID-TIMS U-Pb have indicated emplacement in less than 1 Myrs [1][2]. Increasing analytical precision has also seemingly permitted individual magmatic layers to be resolved, leading to the &amp;#8220;out of sequence sill&amp;#8221; emplacement model [2], albeit contested [3].&lt;/p&gt;&lt;p&gt;We present two new high-precision zircon dates obtained from two continuous core intervals collected &amp;#160;&lt;4m apart in a single Ni-Cu-PGE rich pyroxenite unit in the Turfspruit section of the Platreef, Northern Limb of the Bushveld Complex [4]. Grobler et al. [5] correlate this pyroxenite with the Merensky Cyclic Unit of the Upper Critical Zone in eastern and western limbs. Assuming the recommended zircon &lt;sup&gt;238&lt;/sup&gt;U/&lt;sup&gt;235&lt;/sup&gt;U of Hiess et al. [6] without uncertainties propagated as per previous studies e.g. [1][2], the age interpretations of these two samples define a minimum and maximum temporal interval between 1.01 &amp;#177;0.16 Myrs and 1.28 &amp;#177;0.22 Myrs that brackets, or overlaps with, the entirety of previous dates from all preceding studies. The pyroxenite is continuous, without intrusive contacts, and the stratigraphically lower sample produces an apparently younger zircon age than the overlying sample. &amp;#160;It seems highly unlikely the entire longevity of the Bushveld&amp;#8217;s magmatic evolution was apparently captured within this 4 m section. Therefore, it now seems highly improbable that the Bushveld was emplaced and cooled in less than 1 Myrs, as the current paradigm states [1].&lt;/p&gt;&lt;p&gt;The older date from the Platreef now aligns the isotopic age relationships with the field observations of the overlying Main Zone, in contrast to the interpretation of Mungall et al. [2]. The new dates alone neither support nor contradicts the &amp;#8220;out of sequence&amp;#8221; sill emplacement model. Rather they merely indicate that melt related process that crystallised zircon was protracted within narrow vertical intervals, and that future work should acknowledge this potential complexity. It raises questions which age of event(s) introduced or modified sulfides within the ore bearing horizon. This requires greater integration of the geochronological record with ore textures at a high sampling density.&lt;/p&gt;&lt;p&gt;However, there also remains a substantial, yet previously overlooked caveat to all geochronological interpretations presented thus far; &amp;#8220;out of sequence&amp;#8221; sills in particular. This caveat is that the variations in the &lt;sup&gt;238&lt;/sup&gt;U/&lt;sup&gt;235&lt;/sup&gt;U between samples over observed magnitudes of variations in zircon [4] could account for any offsets in &lt;sup&gt;207&lt;/sup&gt;Pb/&lt;sup&gt;206&lt;/sup&gt;Pb dates interpreted as real temporal differences. This issue remains to be tested.&lt;/p&gt;&lt;p&gt;References:&lt;/p&gt;&lt;p&gt;[1] Zeh A et al. (2015) EPSL 418:103-114; [2] Mungall J et al. (2016) Nat. Coms. 13385; [3] Latypov R et al. (2017) South African Jour of Geol. 120.4, 565-574; [4] Nodder SM (2015) MESci dissertation, Cardiff University, 257pp; [5] Grobler D et al. (2019) Min Dep 54, 3-28; [6] Hiess J et al. (2012) Science 418,103-114&lt;/p&gt;

BASS CYCLIC UNITS AS FACTORS IN A FREE GROUP IN INTEGRAL GROUP RING UNITS

Marciniak and Sehgal showed that if u is a non-trivial bicyclic unit of an integral group ring then there is a bicyclic unit v such that u and v generate a non-abelian free group. A similar result does not hold for Bass cyclic units of infinite order based on non-central elements as some of them have finite order modulo the center. We prove a theorem that suggests that this is the only limitation to obtain a non-abelian free group from a given Bass cyclic unit. More precisely, we prove that if u is a Bass cyclic unit of an integral group ring ℤG of a solvable and finite group G, such that u has infinite order modulo the center of U(ℤG) and it is based on an element of prime order, then there is a non-abelian free group generated by a power of u and a power of a unit in ℤG which is either a Bass cyclic unit or a bicyclic unit.