Related papers: Sharp Thresholds for $\epsilon$-Adjoint Singularit…

The abstract boundary has, in recent years, proved a general and flexible way to define the singularities of space-time. In this approach an essential singularity is a non-regular boundary point of an embedding which is accessible by a…

We study GIT stability of divisors in products of projective spaces. We first construct a finite set of one-parameter subgroups sufficient to determine the stability of the GIT quotient. In addition, we characterise all maximal orbits of…

Suppose that you add rigid bars between points in the plane, and suppose that a constant fraction $q$ of the points moves freely in the whole plane; the remaining fraction is constrained to move on fixed lines called sliders. When does a…

Let C be a smooth curve on an index 1 terminal 3-fold. We investigate the existence of extremal terminal divisorial contractions Y-->X that contract an irreducible surface E to C. We consider cases in respect to the singularities of the…

For a real number $0<\epsilon<1/3$, we show that the anti-canonical volume of an $\epsilon$-klt Fano $3$-fold is at most $3200/\epsilon^4$ and the order $O(1/\epsilon^4)$ is sharp.

Recently, the separated fragment (SF) has been introduced and proved to be decidable. Its defining principle is that universally and existentially quantified variables may not occur together in atoms. The known upper bound on the time…

Transonic buffet, self--sustained shock and shear--layer oscillations, imposes hard limits on the cruise envelope of modern transport aircraft, and avoiding it is a primary design driver. State-of-the-art buffet-onset criteria used in…

We study the invariant theory of singular foliations of the projective plane. Our first main result is that a foliation of degree m>1 is not stable only if it has singularities in dimension 1 or contains an isolated singular point with…

We show, in this first part, that the maximal number of singular points of a normal quartic surface $X \subset \mathbb{P}^3_K$ defined over an algebraically closed field $K$ of characteristic $2$ is at most $16$. We produce examples with…

We investigate the effects of a nearby free surface on the stability of a flexible plate in axial flow. Confinement by rigid boundaries is known to affect flag flutter thresholds and fluttering dynamics significantly, and this work…

We compute an upper bound for the dimension of the tangent spaces at classical points of certain eigenvarieties associated with definite unitary groups, especially including the so-called critically refined cases. Our bound is given in…

The extremes of a stationary time series typically occur in clusters. A primary measure for this phenomenon is the extremal index, representing the reciprocal of the expected cluster size. Both a disjoint and a sliding blocks estimator for…

We study the plus-pure threshold (ppt) of hypersurfaces in mixed characteristic. We show that the ppt limits to the $F$-pure threshold (fpt) as we ramify the base DVR. Additionally, we show that analogs of some positive characteristic…

The minimal infinitesimal rigidity of bar-joint frameworks in the non-Euclidean spaces (R^2, ||.||_q) are characterised in terms of (2,2)-tight graphs. Specifically, a generically placed bar-joint framework (G,p) in the plane is minimally…

Mechanical fields over thin elastic surfaces can develop singularities at isolated points and curves in response to constrained deformations (e.g., crumpling and folding of paper), singular body forces and couples, distributions of isolated…

This paper concerns piecewise-smooth maps on $\mathbb{R}^d$ that are continuous but not differentiable on switching manifolds (where the functional form of the map changes). The stability of fixed points on switching manifolds is…

This paper establishes a constructive link between the first slope of Artin-Schreier curves X_f: y^p-y=f(x) and the p-adic weight of the support of f(x). If the maximal p-adic weight element v in Supp(f) is unique, we show that the first…

We study the canonical stability index of nonsingular projective varieties of general type with either large canonical volume or large geometric genus. As applications of a general extension theorem established in the first part, we prove…

In the paper we deal with shells with non-zero Gaussian curvature. We derive sharp Korn's first (linear geometric rigidity estimate) and second inequalities on that kind of shells for zero or periodic Dirichlet, Neumann, and Robin type…

Filamentary structures, or long and narrow streams of material, arise in many areas of astronomy. Here we investigate the stability of such filaments by performing an eigenmode analysis of adiabatic and polytropic fluid cylinders, which are…