Solutions of xqk+⋯+xq+x=ax^{q^k}+\cdots+x^{q}+x=a in GF2nGF{2^n}

Though it is well known that the roots of any affine polynomial over a finite field can be computed by a system of linear equations by using a normal base of the field, such solving approach appears to be difficult to apply when the field is fairly large. Thus, it may be of great interest to find an explicit representation of the solutions independently of the field base. This was previously done only for quadratic equations over a binary finite field. This paper gives an explicit representation of solutions for a much wider class of affine polynomials over a binary prime field

Magnetic reversals in a simple model of MHD

We study a simple magnetohydrodynamical approach in which hydrodynamics and MHD turbulence are coupled in a shell model, with given dynamo constrains in the large scales. We consider the case of a low Prandtl number fluid for which the inertial range of the velocity field is much wider than that of the magnetic field. Random reversals of the magnetic field are observed and it shown that the magnetic field has a non trivial evolution linked to the nature of the hydrodynamics turbulence.Comment: 4 pages, submitted to PR

Dynamical behavior across the Mott transition of two bands with different bandwidths

We investigate the role of the bandwidth difference in the Mott metal-insulator transition of a two-band Hubbard model in the limit of infinite dimensions, by means of a Gutzwiller variational wave function as well as by dynamical mean-field theory. The variational calculation predicts a two-stage quenching of the charge degrees of freedom, in which the narrower band undergoes a Mott transition before the wider one, both in the presence and in the absence of a Hund's exchange coupling. However, this scenario is not fully confirmed by the dynamical mean-field theory calculation, which shows that, although the quasiparticle residue of the narrower band is zero within our numerical accuracy, low-energy spectral weight still exists inside the Mott-Hubbard gap, concentrated into two peaks symmetric around the chemical potential. This spectral weight vanishes only when the wider band ceases to conduct too. Although our results are compatible with several scenarios, e.g., a narrow gap semiconductor or a semimetal, we argue that the most plausible one is that the two peaks coexist with a narrow resonance tied at the chemical potential, with a spectral weight below our numerical accuracy. This quasiparticle resonance is expected to vanish when the wider band undergoes the Mott transition.Comment: 11 pages, 12 figure

Database Engines for Geographical Information Systems

Our ability to identify, acquire, store, enquire on and analyse data is increasing as never before, especially in the GIS field. Technologies are becoming available to manage a wider variety of data and to make intelligent inferences on that data. The mainstream arrival of large-scale database engines is not far away. The experience of using the first such products tells us that they will radically change data management in the GIS field

Fly on the wall: can students' learning be enhanced by allowing them to witness their own summative assessment and feedback event?

The Design studio learning system within New Zealand Tertiary Design Schools has a unique critique method, (often called 'The Crit'); The Crit event itself is rather a 'veiled' process and has been analyzed and written about extensively. There has also been some negative feedback from students that this form of critiquing process is not necessarily a good type of feedback process. Is there a method that protects the student's privacy related to his or her own design work and at the same time maintains the Design School's integrity of supplying reasoned and fair assessment within the wider Profession? A field trial scenario was designed and arranged with a group of volunteer design students, so each in turn, could sit-in and witness their own assessment / feedback session. This paper reports on this field trial, (timed to occur after the critique). This paper analyses this experiment, exploring the field trial responses, looking for links within a wider Educational literature base to the ground this 'Fly on the Wall' scenario within known pedagogies. NB. This scenario is not proposing to supplant 'The Crit,' rather the intention being in addition to it

How to Solve Quantum Nonlinear Abelian Gauge Theory in Two Dimension in the Heisenberg Picture

The new method based on the operator formalism proposed by Abe and Nakanishi is applied to the quantum nonlinear abelian gauge theory in two dimension. The soluble models in this method are extended to wider class of quantum field theories. We obtain the exact solution in the canonical-quantization operator formalism in the Heisenberg picture. So this analysis might shed some light on the analysis of gravitational theory and non-polynomial field theories.Comment: LaTeX, 12 pages, to be published in IJMP