Related papers: Stability through non-shadows
We introduce a set of combinatorial techniques for studying the simplicial bounded cohomology of semi-simplicial sets, simplicial complexes and posets. We apply these methods to prove several new bounded acyclicity results for…
We present sufficient conditions for the (strong) statistical stability of some classes of multidimensional piecewise expanding maps. As a consequence we get that a certain natural two-dimensional extension of the classical one-dimensional…
We demonstrate experimentally that in a centrosymmetric paraelectric non-stationary boundary conditions can dynamically halt the intrinsic instability of quasi-steady-state photorefractive self-trapping, driving beam evolution into a stable…
In this note we propose and analyze novel implicit-explicit methods based on second order strong stability preserving multistep time discretizations. Several schemes are developed, and a linear stability analysis is performed to study their…
We consider variational and stability properties of a system of two coupled nonlinear Schr\"{o}dinger equations on the star graph $\Gamma$ with the $\delta$ coupling at the vertex of $\Gamma$. The first part is devoted to the proof of an…
A stability version of the Blaschke-Santal\'o inequality and the affine isoperimetric inequality for convex bodies of dimension n>2 is proved. The first step is the reduction to the case when the convex body is o-symmetric and has axial…
We provide an existence and uniqueness theory for an extension of backward SDEs to the second order. While standard Backward SDEs are naturally connected to semilinear PDEs, our second order extension is connected to fully nonlinear PDEs,…
The problem of approximating the discrete spectra of families of self-adjoint operators that are merely strongly continuous is addressed. It is well-known that the spectrum need not vary continuously (as a set) under strong perturbations.…
FI-graphs were introduced by the second author and White to capture the idea of a family of nested graphs, each member of which is acted on by a progressively larger symmetric group. That work was built on the newly minted foundations of…
We consider an inverse problem for the nonlinear Boltzmann equation with a time-dependent kernel in dimensions $n\ge 2$. We establish a logarithm-type stability result for the collision kernel from measurements under certain additional…
In the first part, we discuss the stability of the strong slope and of the subdifferential of a lower semicontinuous function with respect to Wijsman perturbations of the function, i.e. perturbations described via Wijsman convergence. In…
In this paper, we use character-theoretic techniques to give new nonexistence results for $(n,m,k,\lambda)$-strong external difference families (SEDFs). We also use cyclotomic classes to give two new classes of SEDFs with $m=2$.
In 1966, Kleitman determined the maximum size of a family of subsets of $[n]$ with bounded symmetric difference. Liao, Liu and Yan recently established a vector-space analogue in the cases $n=d+1$ and $n>2d$, and asked for the sharp bound…
We show that there is an absolute $c>0$ such that any subset of $\mathbb{F}_2^\infty$ of size $N$ is $O(N^{1-c})$-stable in the sense of Terry and Wolf. By contrast a size $N$ arithmetic progression in the integers is not $N$-stable.
Motivated by Witten's work (arXiv:hep-th/9312104), we propose the Verlinde/Grassmannian correspondence which relates the GL Verlinde numbers to the K-theoretic quasimap invariants of the Grassmannian. We recover these two types of…
We introduce the idea of *representation stability* (and several variations) for a sequence of representations V_n of groups G_n. A central application of the new viewpoint we introduce here is the importation of representation theory into…
We study the relationship between two notions of pattern avoidance for involutions in the symmetric group and their restriction to fixed-point-free involutions. The first is classical, while the second appears in the geometry of certain…
We consider a family of scalar delay differential equations $x'(t)=f(t,x_t)$, with a nonlinearity $f$ satisfying a negative feedback condition combined with a boundedness condition. We present a global stability criterion for this family,…
We establish a logarithmic stability inequality for the inverse problem of determining the non linear term, appearing in a semilinear BVP, from the corresponding Dirichlet-to-Neumann map (abbreviated to DtN map in the rest of this text).…
We apply spectral stability theory to investigate nonlinear gravity waves in the atmosphere. These waves are determined by modulation equations that result from Wentzel-Kramers-Brillouin theory. First, we establish that plane waves, which…