We study the existence, uniqueness and stability properties of solutions to the integral equation q,=Q[q] with q,(-)=l, q,()=0. Here Q[u](x)=f K(x-y)g(y,u(y))dy is defined on functions bounded between 0 and 1, K is a probability density function and g(x,u)=[s(x)u +u]/[l+s(x)u2+ o(x)(1-u)2] according to a population genetics model. The hypotheses on g are based on the biological assumption that ...

We refine the definition of the fractional Galois ideal introduced in [Paul Buckingham. The canonical fractional Galois ideal at s = 0. J. Number Theory, 128(6):1749–1768, 2008] which was based on Snaith’s fractional ideal, allowing us to give a general relationship of this object with the Stark elements appearing in Rubin’s integral sharpening of Stark’s Conjecture. We motivate this by using t...

We refine the definition of the fractional Galois ideal introduced in [Paul Buckingham. The canonical fractional Galois ideal at s = 0. J. Number Theory, 128(6):1749–1768, 2008] which was based on Snaith’s fractional ideal, allowing us to give a general relationship of this object with the Stark elements appearing in Rubin’s integral sharpening of Stark’s Conjecture. We motivate this by using a...

A general expression for the correlation time of the decay of the magnetization of an assembly of singledomain noninteracting ferromagnetic particles is given in terms of the inverse of the Fokker-Planck operator. The results of Moro and Nordio @G. Moro and P. L. Nordio, Mol. Phys. 56, 255 ~1985!#, given in the context of dielectric relaxation, are recovered when the Fokker-Planck operator is a...

A well known resuk from complex analysis allows us, under suitable drcumstances, to compute the number of roots of an analytic function, f(z), that lie inside a counterclockwise, simple dosed curve, C, by computing the integral, We employ interval arithmetic and automatic differentiation m give an auminatic and guaranteed bound on the integral. Furthermore, we explore the interplay of the choic...

Miniature x-ray sources present unique challenges due to the cost, power and space constraints placed upon them. One of the key functional differences from larger traditional x-ray tubes is that the x-ray spot is comprised of the entirety of the electrons produced by the filament without the benefit of active focusing elements in most cases. The result is an x-ray spot that is not well describe...

Example 1. An exponential curve. My topic is best introduced by an example. I take it from the correspondence between Leibniz and Huygens in 1690-1691. Leibniz wrote about his new differential and integral calculus. Huygens was very skeptical and proposed problems for Leibniz to solve. In the course of this exchange Leibniz came to use an exponential equation to represent a curve. This was enti...

We present a curve matching framework for planar open curves under similarity transform based on a new scale invariant signature. The signature is derived from the concept of integral of unsigned curvatures. If one input curve as a whole can be aligned with some part in the second curve then the algorithm will find the requisite starting and end positions and will estimate the similarity transf...