Related papers: On the stability of periodic binary sequences with…
This paper investigates the robustness of exponential stability of a class of switched systems described by linear functional differential equations under arbitrary switching. We will measure the stability robustness of such a system,…
The Sitnikov problem is a special case of the restricted three-body problem where the primaries moves in elliptic orbits of the two-body problem with eccentricity $e\in [0,1[$ and the massless body moves on a straight line perpendicular to…
We propose an informal test for stationarity in a time series which checks for the compatibility of nonlinear approximations to the dynamics made in different segments of the sequence. The segments are compared directly, rather than via…
This article is devoted to the stability of error bounds (local and global) for semi-infinite convex constraint systems in Banach spaces. We provide primal characterizations of the stability of local and global error bounds when systems are…
Confidence intervals are a standard technique for analyzing data. When applied to time series, confidence intervals are computed for each time point separately. Alternatively, we can compute confidence bands, where we are required to find…
Through multiple-scales and symmetry arguments we derive a model set of amplitude equations describing the interaction of two steady-state pattern-forming instabilities, in the case that the wavelengths of the instabilities are nearly in…
We consider the general spatial three body problem and study the dynamics of planetary systems consisting of a star and two planets which evolve into 2/1 mean motion resonance and into inclined orbits. Our study is focused on the periodic…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…
We consider an inverse problem for the nonlinear Boltzmann equation with a time-dependent kernel in dimensions $n\ge 2$. We establish a logarithm-type stability result for the collision kernel from measurements under certain additional…
This paper jointly addresses the challenges of non-stationarity and high dimensionality in analysing multivariate time series. Building on the classical concept of cointegration, we introduce a more flexible notion, called stability space,…
Two nested classes of discrete-time linear time-invariant systems, which differ by the set of periodic signals that they leave invariant, are studied. The first class preserves the property of periodic monotonicity (period-wise…
The estimation of periodicity is a fundamental task in many scientific areas of study. Existing methods rely on theoretical assumptions that the observation times have equal or i.i.d. spacings, and that common estimators, such as the…
We derive an exact formula for the complex frequency in spatio-temporal stability analysis that is valid for arbitrary complex wave numbers. The usefulness of the formula lies in the fact that it depends only on purely temporal quantities,…
In this paper, the construction of finite-length binary sequences whose nonlinear complexity is not less than half of the length is investigated. By characterizing the structure of the sequences, an algorithm is proposed to generate all…
In this paper, we see several basic properties of graded linear series. We firstly see that, if a graded linear series contains an ample series, then so are the pullbacks of the system under birational morphisms. Using this proposition, we…
We prove nonlinear stability of line soliton solutions of the KP-II equation with respect to transverse perturbations that are exponentially localized as $x\to\infty$. We find that the amplitude of the line soliton converges to that of the…
We investigate stability properties of a type of periodic solutions of the $N$-vortex problem on general domains $\Omega\subset \mathbb{R}^2$. The solutions in question bifurcate from rigidly rotating configurations of the whole-plane…
Consider a string of $n$ positions, i.e. a discrete string of length $n$. Units of length $k$ are placed at random on this string in such a way that they do not overlap, and as often as possible, i.e. until all spacings between neighboring…
The presence of mean motion resonances (MMRs) complicates analysis and fitting of planetary systems observed through the radial velocity (RV) technique. MMR can allow planets to remain stable in regions of phase space where strong…
We identify a binary sequence $\mathcal{S}=(s_n)_{n=0}^\infty$ with the $2$-adic integer $G_\mathcal{S}(2)=\sum\limits_{n=0}^\infty s_n2^n$. In the case that $G_\mathcal{S}(2)$ is algebraic over $\mathbb{Q}$ of degree $d\ge 2$, we prove…