On $p$-adic intermediate Jacobians

Mixed Intermediate Jacobians

Dynamics of Special Points on Intermediate Jacobians

We prove some general density statements about the subgroup of invertible points on intermediate jacobians; namely those points in the Abel-Jacobi image of nullhomologous algebraic cycles on projective algebraic manifolds.

p-adic Shearlets

The field $Q_{p}$ of $p$-adic numbers is defined as the completion of the field of the rational numbers $Q$ with respect to the  $p$-adic norm $|.|_{p}$. In this paper, we study the continuous and discrete $p-$adic shearlet systems on $L^{2}(Q_{p}^{2})$. We also suggest discrete $p-$adic shearlet frames. Several examples are provided.

On p-adic Classification

A p-adic modification of the split-LBG classification method is presented in which first clusterings and then cluster centers are computed which locally minimise an energy function. The outcome for a fixed dataset is independent of the prime number p with finitely many exceptions. The methods are applied to the construction of p-adic classifiers in the context of learning.

p-approximation of Jacobians

The paper investigates the nonlinear function spaces introduced by Giaquinta, Modica and Souček. It is shown that a function from Cart(Ω,Rm) is approximated by C functions strongly in A(Ω,R) whenever q < p. An example is shown of a function which is in cart(Ω,R) but not in cart(Ω,R).