T>0 properties of the infinitely repulsive Hubbard model for arbitrary number of holes

Based on representations of the symmetric group $S_N$, explicit and exact Schr\"odinger equation is derived for $U=\infty$ Hubbard model in any dimensions with arbitrary number of holes, which clearly shows that during the movement of holes the spin background of electrons plays an important role. Starting from it, at T=0 we have analyzed the behaviour of the system depending on the dimensionality and number of holes. Based on the presented formalism thermodynamic quantities have also been expressed using a loop summation technique in which the partition function is given in terms of characters of $S_N$. In case of the studied finite systems, the loop summation have been taken into account exactly up to the 14-th order in reciprocal temperature and the results were corrected in higher order based on Monte Carlo simulations. The obtained results suggest that the presented formalism increase the efficiency of the Monte Carlo simulations as well, because the spin part contribution of the background is automatically taken into account by the characters of $S_N$.Comment: 26 pages, 1 embedded ps figure; Phil. Mag. B (in press

A provisional effective evaluation when errors are present in independent variables

Algorithms are examined for evaluating the parameters of a regression model when there are errors in the independent variables. The algorithms are fast and the estimates they yield are stable with respect to the correlation of errors and measurements of both the dependent variable and the independent variables