The main purpose of ...

Isogenies of elliptic curves over finite fields have been well-studied, in part because there are several cryptographic applications. Using Vélu’s formula, isogenies can be constructed explicitly given their kernel. Vélu’s formula applies to elliptic curves given by a Weierstrass equation. In this paper we show how to similarly construct isogenies on Edwards curves and Huff curves. Edwards and ...

A uniform space is a topological space together with some additional structure which allows one to make sense of uniform properties such as completeness or uniform convergence. Motivated by previous work of J. Rivera-Letelier, we give a new construction of the Berkovich analytic space associated to an affinoid algebra as the completion of a canonical uniform structure on the associated rigid-an...

In this article we classify normal forms and unfoldings of linear maps in eigenspaces of (anti)automorphisms of order two. Our main motivation is provided by applications to linear systems of ordinary differential equations, general and Hamiltonian, which have both time-preserving and time-reversing symmetries. However the theory gives a uniform method to obtain normal forms and unfoldings for ...

We study bifurcations between the normal and superconducting states, and between superconducting states with different winding numbers, in a thin loop of superconducting wire, of uniform thickness, to which a magnetic field is applied. We then consider the response of a loop with small thickness variations. We find that close to the transition between normal and superconducting states lies a re...

In this paper, we introduce the modified general iterative methods for finding a common fixed point of asymptotically nonexpansive semigroups, which is a unique solution of some variational inequality. We prove the strong convergence theorems of such iterative scheme in a real Banach space which has a uniformly Gâteaux differentiable norm and admits the duality mapping jφ and uniform normal str...