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Perivolaropoulos has recently proposed a position-deformed Heisenberg algebra which includes a maximal length [Phys.Rev.95, 103523 (2017)]. He has shown that this length scale naturally emerges in the context of cosmological particle's horizon or cosmic topology. Following this work, we propose a new deformed algebra and derive the maximal length uncertainty and its corresponding minimal momentum uncertainty from the generalized uncertainty principle. We also construct the corresponding Fourier transform and its inverse representations. Finally, we propose n-dimensional representation of this algebra, Comment: 12pages

We formulate a set of equations that facilitate an exact numerical solution of the Kohn-Sham potential for a finite Hubbard chain with nearest neighbour hopping and arbitrary site potentials. The approach relies on a mapping of the non-interacting Kohn-Sham ground state wave function onto the exact interacting system wavefunction and two interconnected self-consistent cycles. The self-consistent cycles are performed within the framework of the Kohn-Sham non-interacting system without any direct reference to the interacting system. The first self-consistent cycle updates the mapping of the non-interacting wavefunction onto the interacting wavefunction based on a trial input density, while the second self-consistent cycle updates the Kohn-Sham potential to yield the trial density. At the solution point, the exact density, the exact Kohn-Sham potential, the density functional correlation energy and the exact interacting system ground state energy are available., Comment: 8 Pages