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.

In this Wednesday night section for Algebraic Number Theory, we will go through basic facts about one dimensional formal groups and hopefully get to see how they might be useful and interesting. All rings are commutative with identity. The sources of this material are my notes from Elliptic Curves, a course taught by Tom Fisher at Cambridge last year, J. Silverman’s Elliptic Curves Book. A few ...