Related papers: Kolmogorov--Arnold stability
An exact semiclassical version of the classical KAM theorem about small perturbations of vector fields on the torus is given. Moreover, a renormalization theorem based on counterterms for some semiclassical systems that are close to being…
The substitution lemma is a renowned theorem within the realm of lambda-calculus theory and concerns the interactional behaviour of the metasubstitution operation. In this work, we augment the lambda-calculus's grammar with an uninterpreted…
Minimax optimization problems are an important class of optimization problems arising from both modern machine learning and from traditional research areas. We focus on the stability of constrained minimax optimization problems based on the…
Motivated by Maulik-Okounkov stable maps associated to quiver varieties, we define and construct algebraic stable maps on tensor products of representations in the category O of the Borel subalgebra of an arbitrary untwisted quantum affine…
This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The case of a nominal linear quantum system is considered with non-quadratic…
This note consists of three unrelated remarks. First, we demonstrate how roughly speaking $*$-homomorphisms between matrix stable $C^*$-algebras are exactly the uniformly continuous $*$-preserving group homomorphisms between their genral…
The stability of higher-order time derivative theories using the polymer extension of quantum mechanics is studied. First, we focus on the well-known Pais-Uhlenbeck model and by casting the theory into the sum of two decoupled The…
This article establishes the existence of Lyapunov functions for analyzing the stability of a class of state-constrained systems, and it describes algorithms for their numerical computation. The system model consists of a differential…
The ain of this note is to make available the unpublished proof of Scorichenko of the isomorphism between stable K-theory and functor homology for polynomial coefficients over an arbitrary ring.
The Koopman Operator (KO) provides an analytical solution of dynamical systems in terms of orthogonal polynomials. This work exploits this representation to include the propagation of uncertainties, where the polynomials are modified to…
This paper aims to provide various applications for second-order variational analysis of extended-real-valued piecewise liner functions recently obtained in [1]. We mainly focus here on establishing relationships between full stability of…
We generalize the Oka extension theorem, and obtain bounds on the norm of the extension, by using operator theory.
Reynold's parametricity theory captures the property that parametrically polymorphic functions behave uniformly: they produce related results on related instantiations. In dependently-typed programming languages, such relations and…
We embed polarised orbifolds with cyclic stabiliser groups into weighted projective space via a weighted form of Kodaira embedding. Dividing by the (non-reductive) automorphisms of weighted projective space then formally gives a moduli…
For $\delta$ an $m$-tuple of analytic functions, we define an algebra $\hidg$, contained in the bounded analytic functions on the analytic polyhedron $ {|\delta^l(z)| < 1, \ 1 \leq l \leq m}$, and prove a representation formula for it. We…
In 2007 Phillips and Weaver showed that, assuming the Continuum Hypothesis, there exists an outer automorphism of the Calkin algebra. (The Calkin algebra is the algebra of bounded operators on a separable complex Hilbert space, modulo the…
A trichotomy theorem for countable, stable, unsuperstable theories is offered. We develop the notion of a `regular ideal' of formulas and study types that are minimal with respect to such an ideal.
Representation stability is a phenomenon whereby the structure of certain sequences $X_n$ of spaces can be seen to stabilize when viewed through the lens of representation theory. In this paper I describe this phenomenon and sketch a…
We extend the notion of numerical stability of finite difference approximations to include hyperbolic systems that are first order in time and second order in space, such as those that appear in Numerical Relativity. By analyzing the symbol…
One possible way to fix partly a ``canonical definition'' of $\tau$-functions beyond the conventional KP/Toda framework could be to postulate that evolution operators are {\it always} group elements. We discuss implications of this…