A well known path-planning technique for mobile robots or planar aerial vehicles is to use Dubins paths, which are minimum-distance paths between two configurations subject to the constraints of the Dubins car model. An extension of this method to a three-dimensional Dubins airplane model has recently been proposed. This chapter builds on that work showing a complete architecture for implementi...

We solve the problem of one-dimensional peg solitaire. In particular, we show that the set of configurations that can be reduced to a single peg forms a regular language, and that a linear-time algorithm exists for playing the game.

The SEIR model for the transmission dynamics of measles is extended by the addition of second-order space derivatives to enable the geographic spread of the disease in a population which has not been vaccinated against it. The resulting system of three reaction-diffusion equations is solved by a convergent finite-difference technique which is second-order accurate in space and time. A parallel ...

• For a discrete RV the mass function is pX(x) = P (X = x). The continuous analog is the probability density function (pdf) that may be interpreted as fX(x) ≈ P (x < X < x+ ∆)/∆ as 0 < ∆→ 0. • The cumulative distribution function (cdf) FX(x) = P (X ≤ x) is the probability that X is less than or equal to a specific value. In the continuous case we have fX(x) = dFX(x)/dx and FX(x) = ∫ x −∞ fX(r)d...

We review the progress in the theory of one-dimensional (1D) Fermi liquids which has occurred over the past decade. The usual Fermi liquid theory based on a quasi-particle picture, breaks down in one dimension because of the Peierls divergence in the particlehole bubble producing anomalous dimensions of operators, and because of charge-spin separation. Both are related to the importance of scat...

One-dimensional Dithering

This paper studies T -preorders by using their Representation Theorem that states that every T -preorder on a set X can be generated in a natural way by a family of fuzzy subsets of X . Especial emphasis is made on the study of onedimensional T -preorders (i.e.: T -preorders that can be generated by only one fuzzy subset). Strong complete T -preorders are characterized.