Related papers: Stability and Arithmetic
We consider several classes of degenerate hyperbolic equations involving delay terms and suitable nonlinearities. The idea is to rewrite the problems in an abstract way and, using semigroup theory and energy method, we study well posedness…
Some invariances under perturbations of the spin glass phase are introduced, their proofs outlined and their consequences illustrated as factorisation rules for the overlap distribution. A comparison between the state of the art for mean…
We prove two general results concerning spectral sequences of $\mathbf{FI}$-modules. These results can be used to significantly improve stable ranges in a large portion of the stability theorems for $\mathbf{FI}$-modules currently in the…
We consider the nonlinear Schr\"odinger equation with a focusing cubic term and a defocusing quintic nonlinearity in dimensions two and three. The core of this article is the notion of stability of solitary waves. We recall the two standard…
The goal of this note two-fold. First, I draw attention to the way that semistability (in the sense of King) gives us a geometrical picture of (some of) the extension-closed abelian subcategories of a finite-dimensional algebra. Second, I…
Nonlinear partial differential equations are central to physics, engineering, and finance. Except in a limited number of integrable cases, their solution generally requires numerical methods whose cost becomes prohibitive in…
We prove a general homological stability theorem for certain families of groups equipped with product maps, followed by two theorems of a new kind that give information about the last two homology groups outside the stable range. (These…
As attribution-based explanation methods are increasingly used to establish model trustworthiness in high-stakes situations, it is critical to ensure that these explanations are stable, e.g., robust to infinitesimal perturbations to an…
We will see that key concepts of number theory can be defined for arbitrary operations. We give a generalized distributivity for hyperoperations (usual arithmetic operations and operations going beyond exponentiation) and a generalization…
In this work stability of polygonal configurations on a plane and sphere is investigated. The conditions of linear stability are obtained. A nonlinear analysis of the problem is made with the help of Birkhoff normalization. Some problems…
This paper deals with stability in the numerical solution of the prominent Heston partial differential equation from mathematical finance. We study the well-known central second-order finite difference discretization, which leads to large…
We develop several aspects of local and global stability in continuous first order logic. In particular, we study type-definable groups and genericity.
We complete a full classification of non-degenerate traveling waves of scalar balance laws from the point of view of spectral and nonlinear stability/instability under (piecewise) smooth perturbations. A striking feature of our analysis is…
Under some assumptions, we compute the Picard group of moduli of stable sheaves on Abelian surfaces. Considering relative moduli spaces, it is sufficient to consider the moduli of stable sheaves on the product of elliptic curves. By using…
We study semi-stable ideal lattices coming from real quadratic number fields. Specifically, we demonstrate infinite families of semi-stable and unstable ideal lattices of trace type, establishing explicit conditions on the canonical basis…
Leibniz algebras are a non-anticommutative version of Lie algebras. They play an important role in different areas of mathematics and physics and have attracted much attention over the last thirty years. In this paper we investigate whether…
We introduce a notion of stability for non-autonomous Hamiltonian flows on two-dimensional annular surfaces. This notion of stability is designed to capture the sustained twisting of particle trajectories. The main Theorem is applied to…
The two-phase horizontally periodic quasistationary Stokes flow in $\mathbb{R}^2$, describing the motion of two immiscible fluids with equal viscosities that are separated by a sharp interface, which is parameterized as the graph of a…
We investigate the standard stable manifold theorem in the context of a partially hyperbolic singu-larity of a vector field depending on a parameter. We prove some estimates on the size of the neighbourhood where the local stable manifold…
This is a short expository account of the regularity lemma for stable graphs proved by the authors, with some comments on the model theoretic context, written for a general logical audience.