We describe an algorithm for counting points on an arbitrary hyperelliptic curve over a finite field Fpn of odd characteristic, using Monsky-Washnitzer cohomology to compute a p-adic approximation to the characteristic polynomial of Frobenius. For fixed p, the asymptotic running time for a curve of genus g over Fpn with a rational Weierstrass point is O(g4+ǫn3+ǫ).

Point processes are a useful mathematical tool for describing events over time, and so there many recent approaches representing learning them. One notable open question is how to precisely describe the flexibility of point process models whether exists general model that can represent all processes. Our work bridges this gap. Focusing on widely used event intensity function representation proc...

Introducing a higher order modulus of smoothness based on qintegers, in this paper first we obtain Jackson-type estimates in approximation by Jackson-type generalizations of the q-Picard and q-Gauss-Weierstrass singular integrals and give their global smoothness preservation property with respect to the uniform norm. Then, we study approximation and geometric properties of the complex variants ...

A bstract We consider 18 families of elliptic Calabi-Yaus which arise in constructing F -theory compactifications string vacua, and show each case that the upper Hodge diamond a crepant resolution associated Weierstrass model coincides with (blown up) projective bundle is naturally embedded. Such results are unexpected, as we does not satisfy hypotheses Lefschetz hyperplane theorem. In light su...

The approximation operators provided by classical Approximation Theory use exclusively as underlying algebraic structure the linear structure of the reals. Also they are all linear operators. We address in the present paper the following problems: Need all the approximation operators be linear? Is the linear structure the only one which allows us to construct particular approximation operators?...

In this paper, we consider the width invariant trapezoidal and triangularapproximations of fuzzy numbers. The presented methods avoid the effortful computation of Karush-Kuhn-Tucker Theorem. Some properties of the new approximation methods are presented and the applicability of the methods is illustrated by examples. In addition, we show that the proposed approximations of fuzzy numbers preserv...