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This paper develops a characterisation of when solutions of forced second order linear differential equations converge to the zero solution of the asymptotically stable and unforced second order equation, or when the solution is bounded,…
The Bohl-Perron result on exponential dichotomy for a linear difference equation $$ x(n+1)-x(n) + \sum_{l=1}^m a_l(n)x(h_l(n))=0, h_l(n)\leq n, $$ states (under some natural conditions) that if all solutions of the non-homogeneous equation…
The independence polynomial of a graph is the generating polynomial for the number of independent sets of each size, and its roots are called {\em independence roots}. We investigate the stability of such polynomials, that is, conditions…
The real homology of a compact, n-dimensional Riemannian manifold M is naturally endowed with the stable norm. The stable norm of a homology class is the minimal Riemannian volume of its representatives. If M is orientable the stable norm…
Considering both interspecies and intraspecies fluctuations in ultracold bose-bose mixtures, we derive generalized stability conditions against collapse and phase separation. Furthermore, by examining the energy density of the system, we…
One-dimensional disordered systems with a random potential of a small amplitude and short-range correlations are considered near the initial band edge. The evolution equation is obtained for the mutual ditribution P(\rho,\psi) of the…
In this article we study the expanding properties of random perturbations of contracting Lorenz maps satisfying the summability condition of exponent 1. Under general conditions on the maps and perturbation types, we prove stochastic…
Hooley proved that if $f\in \Bbb Z [X]$ is irreducible of degree $\ge 2$, then the fractions $\{ r/n\}$, $0<r<n$ with $f(r)\equiv 0\pmod n$, are uniformly distributed in $(0,1)$. In this paper we study such problems for reducible…
We consider a 2-dimensional stochastic differential equation in polar coordinates depending on several parameters. We show that if these parameters belong to a specific regime then the deterministic system explodes in finite time, but the…
Bound entanglement, in contrast to free entanglement, cannot be distilled into maximally entangled states by two local observers applying measurements and utilizing classical communication. In this paper we ask whether a relativistic…
We consider continuous relational structures with finite domain $[n] := \{1, \ldots, n\}$ and a many valued logic, $CLA$, with values in the unit interval and which uses continuous connectives and continuous aggregation functions. $CLA$…
R. Shorten, F. Wirth, O. Mason, K. Wulff and C. King have asked whether a linear switched system is guaranteed to be globally uniformly stable under arbitrary switching if it is known that every trajectory induced by a periodic switching…
We study stable conditional measures for a certain equilibrium measure for hyperbolic endomorphisms, on basic sets with overlaps; we show that these conditional measures are geometric probabilities and measures of maximal stable dimension.…
We derive a necessary and sufficient condition for the sum of M independent continuous random variables modulo 1 to converge to the uniform distribution in L^1([0,1]), and discuss generalizations to discrete random variables. A consequence…
We fill the two main remaining gaps in the full classification of non-degenerate planar traveling waves of scalar balance laws from the point of view of spectral and nonlinear stability/instability under smooth perturbations. On one hand we…
In a recent work, Somogyfoki et al. (J. Non-Equilib. Thermodyn. 50, 59-76, 2025) analysed the linear stability of homogeneous equilibrium in third-order non-Fourier heat conduction within the framework of non-equilibrium thermodynamics with…
We prove new results on the stability of the absolutely continuous spectrum for perturbed Stark operators with decaying or satisfying certain smoothness assumption perturbation. We show that the absolutely continuous spectrum of the Stark…
We investigate various forms of (model-theoretic) stability for hypergraphs and their corresponding strengthenings of the hypergraph regularity lemma with respect to partitions of vertices. On the one hand, we provide a complete…
In this article we study the influence of regularly varying probability measures on additive and multiplicative Boolean convolutions. We introduce the notion of Boolean subexponentiality (for additive Boolean convolution), which extends the…
It is well known that while the independence of random variables implies zero correlation, the opposite is not true. Namely, uncorrelated random variables are not necessarily independent. In this note we show that the implication could be…