We analyze the impact of interior symmetries on the multiplicity of the eigenvalues of the Jacobian matrix at a fully synchronous equilibrium for the coupled cell systems associated to homogeneous networks. We consider also the special cases of regular and uniform networks. It follows from our results that the interior symmetries, as well as the reverse interior symmetries and quotient interior...

In previous work the authors considered the asymmetric simple exclusion process on the integer lattice in the case of step initial condition, particles beginning at the positive integers. There it was shown that the probability distribution for the position of an individual particle is given by an integral whose integrand involves a Fredholm determinant. Here we use this formula to obtain three...

We consider the Sobolev space X = W s,p(Sm;Sk−1). We prove the existence of a robust distributional Jacobian Ju for u ∈ X provided sp ≥ k−1; this generalizes a result of Bourgain, Brezis and the second author [10], where the case m = k is considered. In the critical case where sp = k − 1, we identify the image of the map X 3 u 7→ Ju. This extends a result of Alberti, Baldo and Orlandi [2] for s...

We associate with a plane meromorphic curve f a tree model T (f) based on its contact structure. Then we give a description of the y-derivative of f (resp. the Jacobian J(f, g)) in terms of T (f) (resp. T (fg)). We also characterize the regularity of f in terms of its tree.

Generalizing a result for the binary lens, similar alternative expressions are also given for the Jacobian determinant for a gravitational lens consisting of an arbitrary number of discrete lensing centres, with arbitrary masses and locations in a plane. The results for a binary lens are recovered, agreeing with some already known results, and correcting errors in others.

Article history: Received 9 April 2014 Accepted 3 June 2015 Available online 17 June 2015

In this paper we survey the role of D-module theory in the comparison between logarithmic and meromorphic de Rham complexes of integrable logarithmic connections with respect to free divisors, and we present some new linearity conditions on the Jacobian ideal which arise in this setting. MSC: 32C38; 14F40; 32S40

An explicit construction of pairing-friendly hyperelliptic curves with ordinary Jacobians was firstly given by D. Freeman. In this paper, we give other explicit constructions of pairing-friendly hyperelliptic curves with ordinary Jacobians based on the closed formulae for the order of the Jacobian of a hyperelliptic curve of type y = x + ax. We present two methods in this paper. One is an analo...

We describe how to prove the Mordell-Weil theorem for Jacobians of hyperelliptic curves over Q and how to compute the rank and generators for the Mordell-Weil group.

In this note, we present a condition which guarantees spatial uniformity for the asymptotic behavior of the solutions of a reaction-diffusion PDE with Neumann boundary conditions in one dimension, using the Jacobian matrix of the reaction term and the first Dirichlet eigenvalue of the Laplacian operator on the given spatial domain. We also derive an analog of this PDE result for the synchroniza...