We consider a system of fermions with a quasi-random almost-Mathieu disorder interacting through a many-body short range potential. We establish exponential decay of the zero temperature correlations, indicating localization of the interacting ground state, for weak hopping and interaction and almost everywhere in the frequency and phase; this extends the analysis in [17] to chemical potentials...

We consider the Schrr odinger equation for a class of two-level atoms in a quasi-periodic external eld for large coupling, i.e., for which the energy diierence 2 between the unperturbed levels is suuciently small. We show that this equation has a solution in terms of a formal power series in , with coeecients which are quasi-periodical functions of the time, in analogy to the Lindstedt-Poincar ...

It is proved that if an algebra R over a field can be endowed with a pointed and finite-dimensional .nfiltration such that the associated .n-graded algebra T is semi-commutative, then R is left and right finitely partitive. In order to do this, a multi-variable Poincare! series for every finitely generated graded T-module is considered and it is shown that this Poincare! series is a rational fu...

To continue a branch of homoclinic solutions starting from a Bogdanov–Takens (BT) point in parameter and state space, one needs a predictor based on asymptotics for the bifurcation parameter values and the corresponding small homoclinic orbits in the phase space. We derive two explicit asymptotics for the homoclinic orbits near a generic BT point. A recent generalization of the Lindstedt–Poinca...

This article reviews the construction and some applications of twisted Poincare-covariant quantum fields on Moyal plane. The Drinfeld twist, which plays a key mathematical role in this construction, is then applied to case discrete groups, with view geons gravity. Poincare-twisted can also be study CMB anisotropies, corrections power spectrum are used put constraints spacetime noncommutativity....

For M and N closed oriented connected smooth manifolds of the same dimension, we consider the mapping space Map(M, N ; f) of continuous maps homotopic to f : M → N . We will show that the evaluation map from the space of maps to the manifold N induces a nontrivial homomorphism on the fundamental group only if the self coincidence number of f , denoted Λf,f , equals zero. Since Λf,f is equal to ...

In this paper, the existence of limit cycles for the specific bilinear systems is explored. Based on the BellmanGronwall inequality approach, not only the exponentially stable limit cycles phenomenon of such systems can be certified but also the oscillation behaviors of such systems can be correctly predicted. Finally, a numerical example is provided to illustrate the feasibility and effectiven...

BACKGROUND Atrial fibrillation (AFib) is one of the prominent causes of stroke, and its risk increases with age. We need to detect AFib correctly as early as possible to avoid medical disaster because it is likely to proceed into a more serious form in short time. If we can make a portable AFib monitoring system, it will be helpful to many old people because we cannot predict when a patient wil...

We are interested in the motion of a small particle in some regions of the Earth Moon system As a rst model we will use the spatial Restricted Three Body Problem RTBP see for de nition and main properties It is well known that in synodic coordinates this model has ve equilibrium points We will focus on the one that is behind the Moon usually called the L point Our purpose is to describe the dyn...