Maxima of Random Algebraic Curves

Local Maxima of a Random Algebraic Polynomial

We present a useful formula for the expected number of maxima of a normal process ξ(t) that occur below a levelu. In the derivation we assume chiefly that ξ(t), ξ(t), and ξ(t) have, with probability one, continuous 1 dimensional distributions and expected values of zero. The formula referred to above is then used to find the expected number of maxima below the level u for the random algebraic p...

Expected Number of Local Maxima of Some Gaussian Random Polnomials

Maxima of Branching Random Walks

In recent years several authors have obtained limit theorems for Ln, the location of the rightmost particle in a supercritical branching random walk but all of these results have been proved under the assumption that the offspring distribution has (p(O)=.fexp(Ox)dF(x)0. In this paper we investigate what happens when there is a slowly varying function K so that 1-F(x)~x-qK(x) as x...

Algebraic Curves

We consider the problem of tracing algebraic curves by computer, using a numerical technique augmented by symbolic computations. In particular, all singularities are analyzed cOITectly. The methods presented find application in solid modeling and robotics.

Geometry of Algebraic Curves

The canonical divisor on a smooth plane curve 30 6.2. More general divisors on smooth plane curves 31 6.3. The canonical divisor on a nodal plane curve 32 6.4. More general divisors on nodal plane curves 33