We give upper bounds on the size of the gap between the constant term and the next non-zero Fourier coefficient of an entire modular form of given weight for Γ0(2). Numerical evidence indicates that a sharper bound holds for the weights h ≡ 2 ( mod 4). We derive upper bounds for the minimum positive integer represented by level two even positive-definite quadratic forms. Our data suggest that, ...

Received ; accepted – 2 – ABSTRACT We report new statistical equilibrium calculations for Fe I and Fe II in the atmosphere of Late-Type stars. We used atomic models for Fe I and Fe II having respectively 256 and 190 levels, as well as 2117 and 3443 radiative transitions. Photoionization cross-sections are from the Iron Project. These atomic models were used to investigate NLTE (non local themod...

We generalize theWeinstein-Moser theorem on the existence of nonlinear normal modes near an equilibrium in a Hamiltonian system to a theorem on the existence of relative periodic orbits near a relative equilibrium in a Hamiltonian system with continuous symmetries. In particular we prove that under appropriate hypotheses there exist relative periodic orbits near relative equilibria even when th...

We formulate according to the quantum mechanical uncertainty relation a new uncertainty relation ∆ ˘ A · ∆l ∼ ¯ h e where ˘ A and ∆l ≥ l B are the electromagnetic pure gauge potential, the position uncertainty and the magnetic length, respectively. Then, we show that the observed potential drops on the edge of QHE samples are varifications of this uncertainty relation, where the quantum potenti...

In this talk the main features of the operator formalism for the b − c systems on general algebraic curves developed in refs. [1]–[2] are reviewed. The first part of the talk is an introduction to the language of algebraic curves. Some explicit techniques for the construction of meromorphic tensors are explained. The second part is dedicated to the discussion of the b−c systems. Some new result...

We prove various results on the notion of ordinal ultrafiters introduced by J. Baumgartner. In particular, we show that this notion of ultrafilter complexity is independent of the more familiar Rudin-Keisler ordering.

We show that (as conjectured by Lin and Wang) when a Vassiliev invariant of type m is evaluated on a knot projection having n crossings, the result is bounded by a constant times nm. Thus the well known analogy between Vassiliev invariants and polynomials justifies (well, at least explains) the odd title of this note.

A closed-form expression is obtained for the generating function of close-packed dimers on a 2M × 2N simple quartic lattice embedded on a Möbius strip. The finite-size corrections are also analyzed and compared with those under cylindrical and free boundary conditions. Particularly, it is found that, for large lattices with a square symmetry and the Möbius boundary condition, the number of dime...

I compare various popular and unpopular techniques for simulating large collisionless stellar systems. I give a quantitative comparison of the raw cpu times required for five separate codes, including tree codes and basis function expansions, which demonstrate that grid codes are most efficient for large numbers of particles. Since efficiency is only one consideration when choosing a code, I di...

A generalization of the classical statistics “maj” and “inv” (the major index and number of inversions) on words is introduced, parameterized by arbitrary graphs on the underlying alphabet. The question of characterizing those graphs that lead to equi-distributed “inv” and “maj” is posed and answered. Résumé: On introduit une généralisation des statistiques classiques que sont “maj” et “inv” (l...