Related papers: Odd index of the amended potential implies linear …
For system of two ordinary differential equations of the second order representing autonomous non-conservative holonomic mechanical system, in case of dynamics such as one-frequency periodical oscillations, is found integrated invariant of…
We identify the kinks of a deformed O(3) linear Sigma model as the solutions of a set of first-order systems of equations; the above model is a generalization of the MSTB model with a three-component scalar field. Taking into account…
It is shown that small distortions on the boundaries are amplified in the core of a magnetized plasma if the system is close to marginal stability for the ideal magnetohydrodynamic interchange mode. It is also shown that such marginal…
In one-dimensional anharmonic lattices, we construct nonlinear standing waves (SWs) reducing to harmonic SWs at small amplitude. For SWs with spatial periodicity incommensurate with the lattice period, a transition by breaking of…
We consider a model for systemic risk comprising of a system of diffusion processes, interacting through their empirical mean. Each process is subject to a confining double-well potential with some uncertainty in the coefficients,…
We study the branch of semi-stable and unstable solutions (i.e., those whose Morse index is at most one) of the Dirichlet boundary value problem $-\Delta u=\frac{\lambda f(x)}{(1-u)^2}$ on a bounded domain $\Omega \subset \R^N$, which…
Dynamic perturbation equations are derived for a generic stationary state of an elastic string model -- of the kind appropriate for representing a superconducting cosmic string -- in a flat background. In the case of a circular equilibrium…
We study a singular Hamiltonian system with an $\al$-homogeneous potential that contains, as a particular case, the classical $N$--body problem. We introduce a variational Morse--like index for a class of collision solutions and, using the…
For a class of linear switched systems in continuous time a controllability condition implies that state feedbacks allow to achieve almost sure stabilization with arbitrary exponential decay rates. This is based on the Multiplicative…
The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schroedinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and…
Given a homogeneous linear discrete or continuous dynamical system, its stability index is given by the dimension of the stable manifold of the zero solution. In particular, for the $n$ dimensional case, the zero solution is globally…
We investigate errors in tangents and adjoints of implicit functions resulting from errors in the primal solution due to approximations computed by a numerical solver. Adjoints of systems of linear equations turn out to be unconditionally…
We consider a non-relativistic quantum particle interacting with a singular potential supported by two parallel straight lines in the plane. We locate the essential spectrum under the hypothesis that the interaction asymptotically…
An invertible dynamical system with some hyperbolic structure is considered. Upper estimates for the correlations of continuous observables is given in terms of modulus of continuity. The result is applied to certain H\'enon maps and…
Exponential stability of the nonlinear filtering equation is revisited, when the signal is a finite state Markov chain. An asymptotic upper bound for the filtering error due to incorrect initial condition is derived in the case of slowly…
When time reversal is broken the viscosity tensor can have a non vanishing odd part. In two dimensions, and only then, such odd viscosity is compatible with isotropy. Elementary and basic features of odd viscosity are examined by…
In this paper, we first explore exponential stability by using Monotonicity inequality and use this information to obtain the existence of Invariant measure for linear Stochastic PDEs with potential in the space of tempered distributions.…
A zero-energy mid-band singularity has been found in the energy spectrum of random matrices with correlations between diagonal and off-diagonal elements typical of vibrational problems. Two representative classes of matrices, characterizing…
We introduce the concept of $\epsilon$-uncontrollability for random linear systems, i.e. linear system in which the usual matrices have been replaced by random matrices. We also estimate the $\epsilon$-uncontrollability in the case where…
Unitarity is the fundamental property of the S-matrix while its usage for a scattering of unstable particles has been subtle as unstable particles do not appear in the asymptotic states. Defining unstable-particle amplitudes as residues of…