相关论文: Stability and deformation of F-singularities

We study Bridgeland stability conditions on smooth surfaces arising from birational morphisms $S \to T$ to a singular surface. Assuming that $T$ has only ADE singularities or certain cyclic quotient singularities, we produce pre-stability…

Let (R,m) -> (S,n) be a flat local homomorphism of excellent local rings. We investigate the conditions under which the weak or strong F-regularity of R passes to S. We show that is suffices that the closed fiber S/mS be Gorenstein and…

This paper studies the polynomial stabilization of an elastic plate with dynamical boundary conditions on a non-smooth domain. To deal with the possible loss of solution regularity induced by boundary singularities, we formulate the problem…

In this paper it is established that all two-dimensional polynomial automorphisms over a regular ring R are stably tame. In the case R is a Dedekind Q-algebra, some stronger results are obtained. A key element in the proof is a theorem…

This paper explores the Hyers-Ulam stability of generalized Jensen additive and quadratic functional equations in \(\beta\)-homogeneous \(F\)-space, showing that approximately satisfying mappings have a unique exact approximating…

We investigate errors in tangents and adjoints of implicit functions resulting from errors in the primal solution due to approximations computed by a numerical solver. Adjoints of systems of linear equations turn out to be unconditionally…

Given a normal $\mathbb{Q}$-Gorenstein complex variety $X$, we prove that if one spreads it out to a normal $\mathbb{Q}$-Gorenstein scheme $\mathcal{X}$ of mixed characteristic whose reduction $\mathcal{X}_p$ modulo $p$ has normal $F$-pure…

We examine the dynamics of neutral black rings, and identify and analyze a selection of possible instabilities. We find the dominating forces of very thin black rings to be a Newtonian competition between a string-like tension and a…

A theory for stabilization of quantum resonances by a mechanism similar to one leading to classical resonances in nonlinear systems is presented. It explains recent surprising experimental results, obtained for cold Cesium atoms when driven…

We study the spaces of locally-finite stability conditions on the derived categories of coherent sheaves on the minimal resolutions of $A_n$-singularities supported at the exceptional sets. Our main theorem is that they are connected and…

We investigate the stability properties of an abstract class of semi-linear systems. Our main result establishes rational rates of decay for classical solutions assuming a certain non-uniform observability estimate for the linear part and…

We study $\epsilon$-representations of discrete groups by unitary operators on a Hilbert space. We define the notion of Ulam stability of a group which loosely means that finite-dimensional $\epsilon$-represendations are uniformly close to…

Let $E\subset \mathbb R^n$, $n\ge 2$, be a set of finite perimeter with $|E|=|B|$, where $B$ denotes the unit ball. When $n=2$, since convexification decreases perimeter (in the class of open connected sets), it is easy to prove the…

For a reduced F-finite ring R of characteristic p >0 and q=p^e one can write R^{1/q} = R^{a_q} \oplus M_q, where M_q has no free direct summands over R. We investigate the structure of F-finite, F-pure rings R by studying how the numbers…

We show that if the rotation set of a homeomorphism of the torus is stable under small perturbations of the dynamics, then it is a convex polygon with rational vertices. We also show that such homeomorphisms are $C^0$-generic and have…

We prove a general result implying the $L^2$ stability of Haar decompositions of $L^2({\bf R}^d)$ functions when the Haar functions are distorted by arbitrary, independent, affine changes of variable that are close to the identity. We apply…

Given a prime number $p$ and a positive integer $m$, we provide a family of diagonal hypersurfaces $\{ f_n \}_{n = 1}^{\infty}$ in $m$ variables, for which the denominator of $\text{ fpt } (f_{n})$ (in lowest terms) is always $p$ and whose…

We consider a rational map f:S->S of a complex projective surface together with an invariant meromorphic two form. Under a mild topological assumption on the map, we show that the zeroes of the invariant form can be eliminated by birational…

We extend the definition of $n$-dimensional difference equations to complex order $\alpha\in \mathbb{C} $. We investigate the stability of linear systems defined by an $n$-dimensional matrix $A$ and derive conditions for the stability of…

We investigate the stability of an Fermi ball(F-ball) within the next-to-leading order approximation in the thin wall expansion. We find out that an F-ball is unstable in case that it is electrically neutral. We then find out that an…