Related papers: Weak Positivity and Dyson's Lemma

Dickson's Lemma is a simple yet powerful tool widely used in termination proofs, especially when dealing with counters or related data structures. However, most computer scientists do not know how to derive complexity upper bounds from such…

We prove a quantitative partial result in support of the Dynamical Mordell-Lang Conjecture (also known as the DML conjecture) in positive characteristic. More precisely, we show the following: given a field $K$ of characteristic $p$, given…

For smoothly bounded, strongly $\mathbb{C}$-convex domains, one can use the Fefferman form or its variants to define projectively invariant norms on sections of holomorphic line bundles, producing a Hardy space. In two variables, we…

We first show the equivalence of two classes of generalized suitable weak solutions to the 3D incompressible Navier-Stokes equations allowing distributional pressure, the class of dissipative weak solutions and local suitable weak…

We derive an explicit formula for global weak solutions of the one dimensional system of pressure-less Euler-Poisson equations. Our variational formulation is an extension of the well-known formula for entropy solutions of the scalar…

We prove a connectedness result for products of weighted projective spaces.

On smooth projective variety, for a reduced effective divisor which is weakly ample in the sense of cohomology, we introduce a Kadaira--Saito vanishing theorem for it.

We extend the weak-strong uniqueness principle to general models of compressible viscous fluids near/on the vacuum. In particular, the physically relevant case of positive density with polynomial decay at infinity is considered.

We study constructively the relations between the finite cases of Dickson's lemma. Although there are many constructive proofs of them, the novel aspect of our proofs is the extraction of a corresponding bound. We provide some new one-step…

We prove the global-in-time existence of nonnegative weak solutions to a class of fourth order partial differential equations on a convex bounded domain in arbitrary spatial dimensions. Our proof relies on the formal gradient flow structure…

In this note, we state various generalisations of the Nakano vanishing theorem under weak positivity assumptions, and compare them with the known results.

Let W be a Weyl group. We can define the notion of positivity of a W-module in terms of the corresponding module over the asymptotic Iwahori-Hecke algebra. We state a conjecture which says that certain explicit W-modules are positive and we…

A form of Williamson's product theorem which applies to Williamson matrices of even order is presented.

We investigate the existence of weak solutions to a multi-component system, consisting of compressible chemically reacting components, coupled with the compressible Stokes equation for the velocity. Specifically, we consider the case of…

We deduce Levinson\'{}s theorem in non-relativistic quantum mechanics in one dimension as a sum rule for the spectral density constructed from asymptotic data. We assume a self-adjoint hamiltonian which guarantees completeness; the…

In this paper, we prove the following "Weak Bounded Negativity Conjecture", which says that given a complex smooth projective surface $X$, for any reduced curve $C$ in $X$ and integer $g$, assume that the geometric genus of each component…

We propose a new approach to models of general compressible viscous fluids based on the concept of dissipative solutions. These are weak solutions satisfying the underlying equations modulo a defect measure. A dissipative solution coincides…

We give a short, self-contained, and elementary proof of the strong law of large numbers under a power law decay hypothesis for joint second moments. The result is related to the classical one by Lyons. However, we also provide a rate of…

This paper is devoted to give a complete unified study of several weak forms of $\ddb-$Lemma on compact complex manifolds.

We give alternative proofs to certain results in the paper "Weak limits of almost invariant projections" by using ultraproducts of operators.