We give a formula for the component at p of the p-adic height pairing of a divisor of degree 0 on a hyperelliptic curve. We use this to give a Chabauty-like method for finding p-adic approximations to p-integral points on such curves when the Mordell-Weil rank of the Jacobian equals the genus. In this case we get an explicit bound for the number of such p-integral points, and we are able to use...

In this article we show how to generalize to the Darbouxian, Liouvillian and Riccati case the extactic curve introduced by J. Pereira. With this approach, we get new algorithms for computing , if it exists, a rational, Darbouxian, Liouvillian or Riccati first integral with bounded degree of a polynomial planar vector field. We give probabilistic and deterministic algorithms. The arithmetic comp...

We are concerned with the existence of smooth time functions on connected time–oriented Lorentzian manifolds. The problem is tackled in a more general abstract setting, namely in a manifold M where is just defined a field of tangent convex cones (Cx)x∈M enjoying mild continuity properties. Under some conditions on its integral curves, we will construct a time function. Our approach is based on ...

1. Introduction. By a famous theorem of Siegel [S], the number of integral points on an elliptic curve E over an algebraic number field K is finite. A conjecture of Lang and Demyanenko (see [L3], p. 140) states that, for a quasiminimal model of E over K, this number is bounded by a constant depending only on the rank of E over K and on K (see also [HSi], [Zi4]). This conjecture was proved by Si...

The objective of reconstructive integral geometry is to recover a function from its integrals over a set of subvarieties. A parametrix is a method of reconstruction of a function from its integral data up to a smoothing operator. In the simplest case, a parametrix recovers a function with a jump singularity along a curve (surface) up to a continuous function, which can be quite informative in m...

Given a quasisymmetric automorphism γ of the unit circle T we define and study a modification Pγ of the classical Poisson integral operator in the case of the unit disk D. The modification is done by means of the generalized Fourier coefficients of γ. For a Lebesgue’s integrable complexvalued function f on T, Pγ [f ] is a complex-valued harmonic function in D and it coincides with the classical...

This paper puts forth the notion that explicitly speciied transition bands have been introduced in the lter design literature in part as an indirect approach for dealing with discontinu-ities in the desired frequency response. We suggest that the use of explicitly speciied transition bands is sometimes inappropriate because, to satisfy a meaningful optimality criterion, their use implicitly ass...

We derive a simple, fast one-dimensional integral for the equatorial rotation curve of a thin disk with surface density Σ(R) modeled as a spheroid with axis ratio q. The result is simpler than standard expressions even in the limit of an infinitely thin disk (q → 0). Subject headings: galaxies: kinematics and dynamics

The aim of this paper is to establish the existence, behavior and approximation of certain classes of solutions of the quasilinear systems of differential equations. Behavior of integral curves in neighborhoods of an arbitrary or certain curve is considered. The approximate solutions with precise error estimates are determined. The theory of qualitative analysis of differential equations and to...

We present a slicing-based coherence measure for clusters of DTI integral curves. For a given cluster, we probe samples from the cluster by “slicing” it with a plane at regularly spaced locations parameterized by curve arclengths. Then we compute a stability measure based on the spatial relations between the projections of the curve points in individual slices and their change across the slices...