Related papers: Stable $\A^1$-connectedness
This paper demonstrates some connections between the coefficients of a Taylor series $f(z)=\ds\sum_{n=0}^\infty a_n z^n$ and singularities of the function. There are many known results of this type, for example, counting the number of poles…
The stability number of a graph G is the cardinality of a stability system of G (that is of a stable set of maximum size of G). A graph is alpha-stable if its stability number remains the same upon both the deletion and the addition of any…
The Deligne-Mumford stable reduction theorem asserts that for a family of stable curves over the punctured disk, after a finite base change, the family can be completed in a unique way to a family of stable curves over the disk. In this…
In the theory of the moduli-stacks of n-pointed stable curves, there are two fundamental functors, contraction and stabilization. These functors are constructed in [4], where they are used to show that the various \bar{M_{g,n}}'s are…
A new notion of independence relation is given and associated to it, the class of flat theories, a subclass of strong stable theories including the superstable ones is introduced. More precisely, after introducing this independence…
We argue that string theory should have a formulation for which stability and causality are evident. Rather than regard strings as fundamental objects, we suggest they should be regarded as composite systems of more fundamental point-like…
We analyze stabilization with respect to ${\mathbb P}^1$ in the Morel--Voevodsky unstable motivic homotopy theory. We introduce a refined notion of cellularity (a.k.a., biconnectivity) in various motivic homotopy categories taking into…
We consider networks of infinite-dimensional port-Hamiltonian systems $\mathfrak{S}_i$ on one-dimensional spatial domains. These subsystems of port-Hamiltonian type are interconnected via boundary control and observation and are allowed to…
We initiate a systematic investigation of the abstract elementary classes that have amalgamation, satisfy tameness (a locality property for orbital types), and are stable (in terms of the number of orbital types) in some cardinal. Assuming…
We study the stable behaviour of discrete dynamical systems where the map is convex and monotone with respect to the standard positive cone. The notion of tangential stability for fixed points and periodic points is introduced, which is…
This paper concerns a question that frequently occurs in various applications: Is any diffusive coupling of stable linear systems, also stable? Although it has been known for a long time that this is not the case, we shall identify a…
This paper concerns piecewise-smooth maps on $\mathbb{R}^d$ that are continuous but not differentiable on switching manifolds (where the functional form of the map changes). The stability of fixed points on switching manifolds is…
In the stable marriage problem, a set of men and a set of women are given, each of whom has a strictly ordered preference list over the acceptable agents in the opposite class. A matching is called stable if it is not blocked by any pair of…
Conjecture F from [VW12] states that the complements of closures of certain strata of the symmetric power of a smooth irreducible complex variety exhibit rational homological stability. We prove a generalization of this conjecture to the…
The classical one-phase Stefan problem (without surface tension) allows for a continuum of steady state solutions, given by an arbitrary (but sufficiently smooth) domain together with zero temperature. We prove global-in-time stability of…
Brief development of the idea of the very important notion of continuity is given. Continuity is often confused with contiguity, "drawing the graph in one go," "no gaps," etc. The author argues in support of using correct notions of…
We propose a framework for model-theoretic stability and simplicity in an approximate first-order setting and generalize some classical results.
Networks of interacting nodes connected by edges arise in almost every branch of scientific enquiry. The connectivity structure of the network can force the existence of invariant subspaces, which would not arise in generic dynamical…
A criterion is established for the transitivity of connectedness in a transfinite graph. Its proof is much shorter than a prior argument published previously for that criterion.
The stable reduction theorem says that a family of curves of genus $g\geq 2$ over a punctured curve can be uniquely completed (after possible base change) by inserting certain stable curves at the punctures. We give a new proof of this…