Related papers: Unstable arithmetic fracture squares in $\infty$-t…

We generalize the Unstable Formula Theorem characterization of stable theories from \citep{sh78}: that a theory $T$ is stable just in case any infinite indiscernible sequence in a model of $T$ is an indiscernible set. We use a generalized…

We show that a length scale xi can be extracted from the spatial correlations of the "steep cliffs" that appear on fracture surface. Above xi, the slope amplitudes are uncorrelated and the fracture surface is mono-affine. Below xi,…

Sum of Squares programming has been used extensively over the past decade for the stability analysis of nonlinear systems but several questions remain unanswered. In this paper, we show that exponential stability of a polynomial vector…

We develop a new infinite dimensional gluing method for fractional elliptic equations. As a model problem, we construct solutions of the fractional Allen--Cahn equation vanishing on a rotationally symmetric surface which resembles a…

The problem of reconstructing a function from the magnitudes of its frame coefficients has recently been shown to be never uniformly stable in infinite-dimensional spaces [5]. This result also holds for frames that are possibly continuous…

This note investigate some finiteness properties of the category U of unstable modules. One shows finiteness properties for the injective resolution of finitely generated unstable modules. One also shows a stabilization result under…

We give an example of a symplectic manifold with a stable hypersurface such that nearby hypersurfaces are typically unstable.

Let $PL_0(I)$ represent the group of orientation-preserving piecewise-linear homeomorphisms of the unit interval which admit finitely many breaks in slope, under the operation of composition. We find a non-solvable group $W$ and show that…

Let $G$ be a simply connected, connected completely solvable Lie group with Lie algebra $\mathfrak{g}=\mathfrak{p}+\mathfrak{m}.$ Next, let $\pi$ be an infinite-dimensional unitary irreducible representation of $G$ obtained by inducing a…

There exists the Krichever map from the set of quintets (C,p,F,t,e) (where C is an integral and complete algebraic curve, p a smooth rational point, F a rank 2 torsion free coherent sheaf on C, t a local formal parameter in p and e a formal…

An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves the square root of an elliptic operator of second order. Finite element approximation in space is employed.…

A relation between Schur algebras and Steenrod algebra is shown in [Hai10] where to each strict polynomial functor the author associates an unstable module. We show that the restriction of Hai's functor to the subcategory of strict…

We characterize the subscheme of the moduli space of torsion-free sheaves on an elliptic surface which are stable of relative degree zeero (with respect to a polarization of type aH+bf, H being the section and f the elliptic fibre) which is…

Let Z denote the simple limit of prime dimension drop algebras that has a unique tracial state. Let A != 0 be a unital C^*-algebra with A = A tensor Z. Then the homotopy groups of the group U(A) of unitaries in A are stable invariants,…

We define a natural notion of higher order stability and show that subsets of $\mathbb{F}_p^n$ that are tame in this sense can be approximately described by a union of low-complexity quadratic varieties, up to linear error. This generalizes…

We give a stably birational classification for algebraic tori of dimensions $3$ and $4$ over a field $k$. First, we define the weak stably equivalence of algebraic tori and show that there exist $13$ (resp. $128$) weak stably equivalent…

For an equivariant reflexive sheaf over a polarised toric variety, we study slope stability of its reflexive pullback along a toric fibration. Examples of such fibrations include equivariant blow-ups and toric locally trivial fibrations. We…

Let F be a finite subgroup of SL_2 (Z) (necessarily isomorphic to one of Z/2Z, Z/3Z, Z/4Z, or Z/6Z), and let F act on the irrational rotational algebra A_{\theta} via the restriction of the canonical action of SL_2 (Z). Then the crossed…

Usually, in the Black-Scholes pricing theory the volatility is a positive real parameter. Here we explore what happens if it is allowed to be a complex number. The function for pricing a European option with a complex volatility has…

Convection in an infinite fluid layer is often modelled by considering a finite box with periodic boundary conditions in the two horizontal directions. The translational invariance of the problem implies that any solution can be translated…