相关论文: A-stabilization and the ranges of complex polynomi…
This note is an introduction to the properties of stable polynomials in several variables with real or complex coefficients. These polynomials are defined in terms of where the polynomial is non-vanishing. We do not cover well-known topics…
We study the problem of stabilization for the acoustic system with a spatially distributed damping. With imposing hypothesis on the structural properties of the damping term, we identify exponential decay of solutions with growing time.
Several recently discovered properties of multiple families of special polynomials (some orthogonal and some not) that satisfy certain differential, difference or q-difference equations are reviewed. A general method of construction of…
Complex scalar fields charged under a global U(1) symmetry can admit non-topological soliton configurations called Q-balls which are stable against decay into individual particles or smaller Q-balls. These Q-balls are interesting objects…
In this paper, we study the stability of the concentration inequality for one-dimensional complex polynomials. We provide the stability of the local concentration inequality and a global version using a Wehrl-type entropy.
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
This paper studies the polynomial optimization problem whose feasible set is a union of several basic closed semialgebraic sets. We propose a unified hierarchy of Moment-SOS relaxations to solve it globally. Under some assumptions, we prove…
Q-ball is a non-topological soliton whose stability is ensured by global U(1) symmetry. We study a Q-ball which arises in the Affleck-Dine mechanism for baryogenesis and consider its possible instability due to U(1) breaking term ($A$-term)…
A finitely generated quadratic module or preordering in the real polynomial ring is called stable, if it admits a certain degree bound on the sums of squares in the representation of polynomials. Stability, first defined explicitly by…
Let $\nu$ be a rank one valuation on $K[x]$ and $\Psi_n$ the set of key polynomials for $\nu$ of degree $n\in\N$. We discuss the concepts of being $\Psi_n$-stable and $(\Psi_n,Q)$-fixed. We discuss when these two concepts coincide. We use…
This paper deals with stability of a certain class of fractional order linear and nonlinear systems. The stability is investigated in the time domain and the frequency domain. The general stability conditions and several illustrative…
We investigate the dynamics of $U(1)$ gauged Q-balls using fully three-dimensional numerical simulations. We consider two different scenarios: first, the classical stability of gauged Q-balls with respect to generic three-dimensional…
In this paper, we consider a matroid generalization of the stable matching problem. In particular, we consider the setting where preferences may contain ties. For this generalization, we propose a polynomial-time algorithm for the problem…
This article presents some interesting and novel results concerning the average modulus of random polynomials on the unit circle and the unit disc, with coefficients distributed as standard normal variates. The paper also introduces new…
In this paper, we conduct a numerical analysis of the strong stabilization and polynomial decay of solutions for the initial boundary value problem associated with a system that models the dynamics of a mixture of two rigid solids with…
Linear systems of neutral type are considered using the infinite dimensional approach. The main problems are asymptotic, non-exponential stability, exact controllability and regular asymptotic stabilizability. The main tools are the moment…
The study of dynamical systems on complex networks is of paramount importance in engineering, given that many natural and artificial systems find a natural embedding on discrete topologies. For instance, power grids, chemical reactors and…
Scalars carrying a conserved global charge $Q$ can form stable localized field configurations composed of a large number of particles. These non-topological solitons are spherically symmetric and are called Q-balls. While usually analyzed…
We give refined bounds for the regularity of FI-modules and the stable ranges of FI-modules for various forms of their stabilization studied in the representation stability literature. We show that our bounds are sharp in several cases. We…
We investigate the conditions for a QCD axion to coexist with stabilised moduli in string compactifications. We show how the simplest approaches to moduli stabilisation give unacceptably large masses to the axions. We observe that solving…