One-third of the people with an age over twenty have some signs of degenerated discs. However, in most of the patients the mere presence of degenerative discs is not a problem leading to pain, neurological compression, or other symptoms. This paper presents an interval type-2 fuzzy hybrid rule-based system to diagnose the abnormal degenerated discs where pain variables are represented by interv...

In this paper we propose a robust genetic algorithm for the multi-mode resourceconstrained project scheduling problem. We present a new representation for the solutions to this problem, which includes an additional bit indicating the scheduling scheme used to construct the schedule, forward or backward. Moreover, we have developed new genetic operators which operate over this representation, ex...

kinetic equations with positive collision operators Abstract We consider " forward-backward " parabolic equations in the abstract form Jdψ/dx+Lψ = 0, 0 < x < τ ≤ ∞, where J and L are operators in a Hilbert space H such that J = J * = J −1 , L = L * ≥ 0, and ker L = 0. The following theorem is proved: if the operator B = JL is similar to a self-adjoint operator, then associated half-range bounda...

Backward motion estimation consists of the class of motion algorithms that do not transmit motion information directly, but rather compute it at the decoder from already transmitted data. Traditional backward algorithms { also known as pel-recursion { rely on continuous image models, and apply resulting parameters onto sampled data. Within the framework of this approach, it is not feasible to i...

We study the backward shift operator on Hilbert spaces Hα (for α ≥ 0) which are norm equivalent to the Dirichlet-type spaces Dα. Although these operators are unitarily equivalent to the adjoints of the forward shift operator on certain weighted Bergman spaces, our approach is direct and completely independent of the standard Cauchy duality. We employ only the classical Hardy space theory and an...