相关论文: A-stabilization and the ranges of complex polynomi…
The stability problem of a class of nonlinear switched systems defined on compact sets with state-dependent switching is considered. Instead of the Caratheodory solutions, the general Filippov solutions are studied. This encapsulates…
Grunewald, Mennicke and Vaserstein proved that the Bass stable rank of $\mathbb{Z}[x]$, the ring of the univariate polynomials over $\mathbb{Z}$, is $3$. This note addresses minor errors found in their proof. Using their method, we show in…
We give a complete characterization of polynomials in two complex variables that are cyclic with respect to the coordinate shifts acting on Dirichlet-type spaces in the bidisk, which include the Hardy space and the Dirichlet space of the…
For any complex polynomial P having all its zeros in the unit disk, we estimate the rate of change of the argument P (z) when the point z runs through the boundary of this disk.
In this paper we present new results on the preservation of polynomial stability of damped wave equations under addition of perturbing terms. We in particular introduce sufficient conditions for the stability of perturbed two-dimensional…
The problem of the dynamical stability of anistropic systems is studied, by proposing a criterion in terms of the adiabatic local index $\gamma$. The result has general validity and can be applied to several physical situations.…
We prove a homological stabilization theorem for Hurwitz spaces: moduli spaces of branched covers of the complex projective line. This has the following arithmetic consequence: let l>2 be prime and A a finite abelian l-group. Then there…
A set of generalized squeezed-coherent states for the finite u(2) oscillator is obtained. These states are given as linear combinations of the mode eigenstates with amplitudes determined by matrix elements of exponentials in the su(2)…
We give an introduction to renormalisation, focusing first on a pedagogical description of fundamental concepts of the procedure and its features, then we introduce the renormalisation group and its equations. We discuss then the case of…
Identification of the parameters of stable linear dynamical systems is a well-studied problem in the literature, both in the low and high-dimensional settings. However, there are hardly any results for the unstable case, especially…
We present the formalism of q-stars with local or global U(1) symmetry. The equations we formulate are solved numerically and provide the main features of the soliton star. We study its behavior when the symmetry is local in contrast to the…
Stability is a key property of dynamical systems. In some cases, we want to change unstable system into stable one to achieve certain goals in engineering. Here, we present an example of a $3$ dimensional switched system that alternates…
We investigate the stationary-state fluctuations of a growing one-dimensional interface described by the KPZ dynamics with a noise featuring smooth spatial correlations of characteristic range $\xi$. We employ Non-perturbative Functional…
We illustrate how to extend the concept of structural stability through applying it to the front propagation speed selection problem. This consideration leads us to a renormalization group study of the problem. The study illustrates two…
We study stationary solutions in the differential kinetic equation, which was introduced in for description of a local dual cascade wave turbulence. We give a full classification of single-cascade states in which there is a finite flux of…
We study the unitary relaxation dynamics of disordered spin chains following a sudden quench of the Hamiltonian. We give analytical arguments, corroborated by specific numerical examples, to show that the existence of a stationary state…
A short survey of the renormalization problem in QCD and its non-perturbative solution by means of numerical simulations on the lattice is given. Most emphasis is on scale dependent renormalizations, which can be reliably addressed via a…
In this paper, we investigate the existence and the global stability of periodic solution for dynamical systems with periodic interconnections, inputs and self-inhibitions. The model is very general, the conditions are quite weak and the…
We consider discrete-time switching systems composed of a finite family of affine sub-dynamics. First, we recall existing results and present further analysis on the stability problem, the existence and characterization of compact…
The stabilization of one-dimensional solitons by a nonlinear lattice against the critical collapse in the focusing quintic medium is a challenging issue. We demonstrate that this purpose can be achieved by combining a…