We derive closed-form expressions for the poles and zeros of approximate fractional integrator/differentiator filters, which correspond to spectral roll-off filters having any desired log-log slope to a controllable degree of accuracy over any bandwidth. The filters can be described as a uniform exponential distribution of poles along the negative-real axis of the s plane, with zeros interleavi...

Here, the exponent of q in the upper bound is optimal because, when ξ has bounded partial quotients, there is also a constant c > 0 such that |ξ − p/q| ≥ cq for all rational numbers p/q (see Chapter I of [14]). Define the height H(P ) of a polynomial P ∈ R[T ] as the largest absolute value of its coefficients, and the height H(α) of an algebraic number α as the height of its irreducible polynom...

In this paper we continue the study of the method of approximations in Boolean complexity. We introduce a framework which naturally generalizes previously known ones. The main result says that in this framework there exist approximation models providing in principle exponential lower bounds for almost all Boolean functions, and such that the number of testing functionals is only singly exponent...

The phase transition of two-dimensional Ising model on random point patterns is investigated using Monte Carlo simulation and the critical temperature is calculated using the Bethe approximation. We find a linear relation between the critical temperature and the structural characteristics of the random point pattern, as described by Aboav's parameter. Numerical results and analytical calculatio...

Internal waves describe the (linear) response of an incompressible stably stratified fluid to small perturbations. The inclination their group velocity with respect vertical is completely determined by frequency. Therefore reflection on a sloping boundary cannot follow Descartes' laws, and it expected be singular if slope has same as velocity. In this paper, we prove that in critical geometry w...

Several investigators have fit psychometric functions to data from adaptive procedures for threshold estimation. Although the threshold estimates are in general quite correct, one encounters a slope bias that has not been explained up to now. The present paper demonstrates slope bias for parametric and nonparametric maximum-likelihood fits and for Spearman-Kärber analysis of adaptive data. The ...

An analysis of the conditions under which range registration was previously performed using a piecewise linear approximation to a comparametric function is presented. Stricter constraints are introduced which result in a better estimation of the exposure difference between two images of the same scene. Specifically, a positive slope constraint is imposed on each linear segment. Also, the knot l...