Quadratic Maps in Two Variables on Arbitrary Fields

Let $\mathbb{F}$ be a field of characteristic different from $2$ and $3$, and let $V$ be a vector space of dimension $2$ over $\mathbb{F}$. The generic classification of homogeneous quadratic maps $f\colon V\to V$ under the action of the linear group of $V$, is given and efficient computational criteria to recognize equivalence are provided.Comment: 12 pages, no figure

Cauchy–Riemann equations and J-symplectic forms

AbstractLet (Σ,j) be a Riemann surface. The almost complex manifolds (M,J) for which the J-holomorphic curves ϕ:Σ→M are of variational type, are characterized. This problem is related to the existence of a vertically non-degenerate closed complex 3-form on Σ×M (see Theorem 4.3 below), which determines a family of J-symplectic structures on (M,J) parametrized by Σ

Safer parameters for the Chor–Rivest cryptosystem

AbstractVaudenay’s cryptanalysis against Chor–Rivest cryptosystem is applicable when the parameters, p and h, originally proposed by the authors are used. Nevertheless, if p and h are both prime integers, then Vaudenay’s attack is not applicable. In this work, a choice of these parameters resistant to the existing cryptanalytic attacks, is presented. The parameters are determined in a suitable range guaranteeing its security and the computational feasibility of implementation. Regrettably, the obtained parameters are scarce in practice

Cryptanalysis of a novel cryptosystem based on chaotic oscillators and feedback inversion

An analysis of a recently proposed cryptosystem based on chaotic oscillators and feedback inversion is presented. It is shown how the cryptosystem can be broken when Duffing's oscillator is considered. Some implementation problems of the system are also discussed.Comment: 9 pages, 3 figures, latex forma

Non-Hamiltonian Actions and Lie-Algebra Cohomology of Vector Fields

Two examples of Diff⁺S¹-invariant closed two-forms obtained from forms on jet bundles, which does not admit equivariant moment maps are presented. The corresponding cohomological obstruction is computed and shown to coincide with a nontrivial Lie algebra cohomology class on H²(X(S¹))

Structure of diffeomorphism-invariant Lagrangians on the product bundle of metrics and linear connections

Abstract. Let p C : C = CN → N be the bundle of linear connections on a smooth manifold N and let p M : M → N be the bundle of pseudo-Riemannian metrics of a given signature (n + , n − ), n + + n − = n = dim N on N. The structure of the first-order Lagrangians defined on the bundle M × N C → N that are invariant under the natural action of the diffeomorphisms of N, is determined