We study the limiting eigenvalue distribution of n×n banded Toeplitz matrices as n → ∞. From classical results of Schmidt-Spitzer and Hirschman it is known that the eigenvalues accumulate on a special curve in the complex plane and the normalized eigenvalue counting measure converges weakly to a measure on this curve as n → ∞. In this paper, we characterize the limiting measure in terms of an e...

In this paper, we study the underlying geometry in the classical Hamilton-Jacobi theory. The proposed formalism is also valid for nonholonomic systems. We first introduce the essential geometric ingredients: a vector bundle, a linear almost Poisson structure and a Hamiltonian function, both on the dual bundle (a Hamiltonian system). From them, it is possible to formulate the Hamilton-Jacobi the...

We show that conservative distributional solutions to the Semi-Geostrophic systems in a rigid domain are some well-defined sense critical points of time-shifted energy functional involving measure-preserving rearrangements absolute density and momentum, which arise as one-parameter flow maps continuously differentiable, compactly supported divergence free vector fields. also directly, with no r...

We define non-ordinary instanton bundles on Fano threefolds $X$ extending the notion of (ordinary) bundles. determine a lower bound for quantum number bundle, i.e. degree its second Chern class, showing existence such each admissible value when $i_X\ge 2$ or $i_X=1$ and $\mathrm{Pic}(X)$ is cyclic. In these cases we deal with component inside moduli spaces simple containing vector construct stu...