Let A be a principally polarized abelian variety of dimension four and let Θ ⊂ A be a symmetric theta-divisor, which we assume to be smooth. Using the Hodge structure on H(Θ) we associate to A two abelian subvarieties J(K) ⊂ J(H) of the intermediate jacobian J(Θ) of Θ of dimensions five and nine respectively. We show that J(H) is generated by the image under the Abel-Jacobi map of the family F ...

We study the global inversion of a continuous nonsmooth mapping f : R → R, which may be non-locally Lipschitz. To this end, we use the notion of pseudo-Jacobian map associated to f , introduced by Jeyakumar and Luc, and we consider a related index of regularity for f . We obtain a characterization of global inversion in terms of its index of regularity. Furthermore, we prove that the Hadamard i...

It is well-known that a finite graph can be viewed, in many respects, as a discrete analogue of a Riemann surface. In this paper, we pursue this analogy further in the context of linear equivalence of divisors. In particular, we formulate and prove a graph-theoretic analogue of the classical Riemann-Roch theorem. We also prove several results, analogous to classical facts about Riemann surfaces...

Given a formal map F = (F1 . . . , Fn) of the form z + higher order terms, we give tree expansion formulas and associated algorithms for the D-Log of F and the formal flow Ft. The coefficients which appear in these formulas can be viewed as certain generalizations of the Bernoulli numbers and the Bernoulli polynomials. Moreover the coefficient polynomials in the formal flow formula coincide wit...

We consider topological conditions under which a locally invertible map admits a global inverse. Our main theorem states that a local diffeomorphism f : M → R is bijective if and only if Hn−1(M) = 0 and the pre-image of every affine hyperplane is non-empty and acyclic. The proof is based on some geometric constructions involving foliations and tools from intersection theory. This topological re...

Let F (z) = z − H(z) with o(H(z)) ≥ 2 be a formal map from Cn to Cn and G(z) the formal inverse of F (z). In this paper, we give two recurrent formulas for the formal inverse G(z). The first formula not only provides an efficient method for the calculation of G(z), but also reduces the inversion problem to a Cauchy problem of a partial differential equation. The second one is differential free ...

This work is devoted to 2D dispersing billiards with smooth boundary, i.e. periodic Lorentz gases (with and without horizon). We revisit several fundamental properties of these systems and make a number of improvements. The necessity of such improvements became obvious during our recent studies of gases of several particles [CD]. We prove here that local (stable and unstable) manifolds, as well...

In this paper geometric properties of infinitely renormalizable real Hénon-like maps F in R 2 are studied. It is shown that the appropriately defined renormalizations R n F converge exponentially to the one-dimensional renormalization fixed point. The convergence to one-dimensional systems is at a super-exponential rate controlled by the average Jacobian and a universal function a(x). It is als...

This paper discusses analytic methods of acoustic model adaptation for automatic speech recognition and reviews other major methods. The main purpose of this paper is to demonstrate the potential of analytic approach for model adaptation. As an example of analytic methods, Jacobian Adaptation (JA) is intensively discussed and its potential of applicability to speech recognition problems is reve...