Related papers: Stability and Grothendieck
Tilt stability is a fundamental concept of variational analysis and optimization that plays a pivotal role in both theoretical issues and numerical computations. This paper investigates tilt stability of local minimizers for a general class…
This paper proves several weak limit theorems for the joint version of extreme order statistics and partial sums of independently and identically distributed random variables. The results are also extended to almost sure limit version.
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.
We generalize various notions of stability of invariant sets of dynamical systems to invariant measures, by defining a topology on the set of measures. The defined topology is similar, but not topologically equivalent to weak* topology, and…
For $0\leqslant \xi\leqslant \omega_1$, we define the notion of $\xi$-weakly precompact and $\xi$-weakly compact sets in Banach spaces and prove that a set is $\xi$-weakly precompact if and only if its weak closure is $\xi$-weakly compact.…
A critical review is presented on the most recent attempt to generally explain the notion of "statistical symmetry". This particular explanation, however, is incomplete and misses one important and essential aspect. The aim of this short…
When a Hamiltonian density is bounded by below, we know that the lowest-energy state must be stable. One is often tempted to reverse the theorem and therefore believe that an unbounded Hamiltonian density always implies an instability. The…
This paper concerns with the compressible two-fluid model with algebraic pressure closure. We prove a conditional weak-strong uniqueness principle, meaning that a finite energy weak solution, with bounded densities, coincides with the…
The weak field limit of the nonminimally coupled Boltzmann equation is studied, and relations between the invariant Bardeen scalar potentials are derived. The Jean's criterion for instabilities is found through the modified dispersion…
This paper is devoted to give a complete unified study of several weak forms of $\ddb-$Lemma on compact complex manifolds.
We refine results of Gannon [G21, Theorem 4.7] and Simon [S15a, Lemma 2.8] on equivalences of convergent Morley sequences. We then introduce the notion of eventual $NIP$, as a property of a model, and give a variant of [KP18, Corollary…
It is proved that the space of differential forms with weak exterior and co-derivative, is compactly embedded into the space of square integrable differential forms. Mixed boundary conditions on weak Lipschitz domains are considered.…
In this paper, we prove a central limit theorem and estabilish a moderate deviation principle for stochastic models of incompressible second fluids. The weak convergence method inreoduced by [4] plays an important role.
In this paper we study the modulus of continuity of weak solutions to a singular elliptic equation in the plane under very weak assumption on the integrability of the elliptic coefficients. Our investigation reveals that the modulus of…
The paper presents a complete (to the best of the author's knowledge) overview on the existing literature concerning the NLS equation with point-concentrated nonlinearity. Precisely, it mainly covers the following topics: definition of the…
Concentration-compactness is used to prove compactness of maximising sequences for a variational problem governing symmetric steady vortex-pairs in a uniform planar ideal fluid flow, where the kinetic energy is to be maximised and the…
We study necessary and sufficient conditions for contraction and incremental stability of dynamical systems with respect to non-Euclidean norms. First, we introduce weak pairings as a framework to study contractivity with respect to…
In this paper, we extend bottleneck stability to the setting of one dimensional constructible persistences module valued in any small abelian category.
In this paper we perform stability analysis for exponential solutions in Einstein-Gauss-Bonnet and cubic Lovelock gravity. We report our findings, provide areas on parameters space and discuss familiarities and differences between cases.…
We investigate the radiative stability of Horndeski scalar-tensor theories with luminally propagating gravitational waves (as extensively discussed in the wake of GW170817) and show that in general there is a tension between obtaining…