A note on weakly hyperbolic equations with analytic principal part

In this note we show how to include low order terms in the C^∞$C^{\infty }$ well-posedness results for weakly hyperbolic equations with analytic time-dependent coefficients. This is achieved by doing a different reduction to a system from the previously used one. We find the Levi conditions such that the C^∞$C^{\infty }$ well-posedness continues to hold.     

On the spectrum of stiffness matrices arising from isogeometric analysis

We study the spectral properties of stiffness matrices that arise in the context of isogeometric analysis for the numerical solution of classical second order elliptic problems. Motivated by the applicative interest in the fast solution of the related linear systems, we are looking for a spectral characterization of the involved matrices. In particular, we investigate non-singularity, conditioning (extremal behavior), spectral distribution in the Weyl sense, as well as clustering of the eigenvalues to a certain (compact) subset of \(\mathbb C\) . All the analysis is related to the notion of symbol in the Toeplitz setting and is carried out both for the cases of 1D and 2D problems.     

Hamiltonian linear type centers of linear plus cubic homogeneous polynomial vector fields

We provide normal forms and the global phase portraits in the Poincaré disk for all the Hamiltonian linear type centers of linear plus cubic homogeneous planar polynomial vector fields.     

Auslander–Reiten Components with Sectional Bypasses

In this work, we will prove that the modules lying in a sectional bypass of an arrow in the Auslander–Reiten quiver of an artin algebra, are either all left stable or all right stable, but not τ-periodic. Moreover, if such a bypass exists, then the Auslander–Reiten quiver has an infinite left or right stable component which contains a section with a bypass.     

Self-interacting scalar field trapped in a DGP brane: The dynamical systems perspective

We apply the dynamical systems tools to study the linear dynamics of a self-interacting scalar field trapped on a DGP brane. The simplest kinds of self-interaction potentials are investigated: (a) constant potential, and (b) exponential potential. It is shown that the dynamics of DGP models can be very rich and complex. One of the most interesting results of this study shows that dynamical screening of the scalar field self-interaction potential, occurring within the Minkowski cosmological phase of the DGP model and that mimics 4D phantom behaviour, is an attractor solution for a constant self-interaction potential but not for the exponential one. In the latter case gravitational screening is not even a critical point of the corresponding autonomous system of ordinary differential equations.