Investigating the Potentials of Sluice Box Angle of Tilt on the Beneficiation of Birnin-Gwari Gold Deposit

The potentials of sluice box angle of tilt on the beneficiation of Birin-Gwari gold deposit was investigated. The sample was sourced from twenty (20) pits on the mine site and homogenized towards chemical characterization. Particle size analysis using 100 g head sample over the sieve range of 500 µm and 45 µm. 100 g each of the homogenized samples was charged into the sluice box at varied tilt angles ranging from 10º to 60º and also at a varying feed rate of 50 kg/hr to 100 kg/hr at 1000 mls flow rate. The Energy Dispersive X-ray Fluorescence Spectrometry (ED-XRFS) revealed 10.15 ppm Au, 0.43% Fe, 0.05% Pb, and other constituent elements in trace form. Particle size analysis showed the liberation size to be -125+90 µm. The highest yield in mass was given as 32.70 g assaying 43.20 ppm at an angle of 10º and varied feed rate while keeping other parameters/constituent constant and also, 56.32 g was the highest yield in mass assaying 12.83 ppm at 50 kg/hr feed rate.Keywords: Birnin-Gwari gold, Beneficiation, Characterization, Sluice box.

Integral trace form of extensions of degree pq

In this work, we present the integral trace form [Formula: see text] of a cyclic extension [Formula: see text] with degree [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] are distinct odd primes, the conductor of [Formula: see text] is a square free integer, and [Formula: see text] belongs to the ring of algebraic integers [Formula: see text] of [Formula: see text]. The integral trace form of [Formula: see text] allows one to calculate the packing radius of lattices constructed via the canonical (or twisted) homomorphism of submodules of [Formula: see text].

Constructions of Dense Lattices of Full Diversity

A lattice construction using Z-submodules of rings of integers of number fields is presented. The construction yields rotated versions of the laminated lattices A_n for n = 2,3,4,5,6, which are the densest lattices in their respective dimensions. The sphere packing density of a lattice is a function of its packing radius, which in turn can be directly calculated from the minimum squared Euclidean norm of the lattice. Norms in a lattice that is realized by a totally real number field can be calculated by the trace form of the field restricted to its ring of integers. Thus, in the present work, we also present the trace form of the maximal real subfield of a cyclotomic field. Our focus is on totally real number fields since their associated lattices have full diversity. Along with high packing density, the full diversity feature is desirable in lattices that are used for signal transmission over both Gaussian and Rayleigh fading channels.

The Trace Form Over Cyclic Number Fields

In the mid 80’s Conner and Perlis showed that for cyclic number fields of prime degree p the isometry class of integral trace is completely determined by the discriminant. Here we generalize their result to tame cyclic number fields of arbitrary degree. Furthermore, for such fields, we give an explicit description of a Gram matrix of the integral trace in terms of the discriminant of the field.

Trace form associated to cyclic number fields of ramified odd prime degree

In this work, we computate the trace form [Formula: see text] associated to a cyclic number field [Formula: see text] of odd prime degree [Formula: see text], where [Formula: see text] ramified in [Formula: see text] and [Formula: see text] belongs to the ring of integers of [Formula: see text]. Furthermore, we use this trace form to calculate the expression of the center density of algebraic lattices constructed via the Minkowski embedding from some ideals in the ring of integers of [Formula: see text].

Cohomological operations for the Brauer group and Witt kernels of a quartic field extension

Let [Formula: see text] be a field, [Formula: see text], [Formula: see text][Formula: see text], [Formula: see text] a quartic field extension. We investigate the divided power operation [Formula: see text] on the group [Formula: see text]. In particular, we show that any element of [Formula: see text] is a symbol [Formula: see text], where [Formula: see text], [Formula: see text], and [Formula: see text] is the quadratic trace form associated with the extension [Formula: see text]. As an application, we obtain certain results on the Stifel–Whitney maps [Formula: see text].