Related papers: A remark on Whitehead's Lemma

Regularisation allows one to handle ill-posed inverse problems. Here we focus on discrete unfolding problems. The properties of the results are characterised by the consistency between measurements and unfolding result and by the posterior…

Some occurrences of $n$ can be replaced by $n-1$ in a special case of the Shapley-Folkman lemma.

[1] investigates advanced connotations of Hardy and Rellich-type inequalities on complete noncompact Riemannian manifolds, delving on deriving inequalities that incorporate poignant weight functions. These inequalities prolongate classical…

Due to the omission of a hypothesis from an elementary lemma in the author's paper "Gleason parts and point derivations for uniform algebras with dense invertible group", some of the proofs presented in that paper are flawed. We prove here…

An elementary application of Fatou's lemma gives a strengthened version of the monotone convergence theorem. We call this the convergence from below theorem. We make the case that this result should be better known, and deserves a place in…

We derive the Helmholtz theorem for stochastic Hamiltonian systems. Precisely, we give a theorem characterizing Stratonovich stochastic differential equations, admitting a Hamiltonian formulation. Moreover, in the affirmative case, we give…

This is a short expository account of the regularity lemma for stable graphs proved by the authors, with some comments on the model theoretic context, written for a general logical audience.

We prove that under certain assumptions holomorphic functions which are Azukawa isometries at one point are in fact biholomorphisms.

By carrying out refined point-wise estimates for the mean curvature, we prove better rigidity theorems of Lagrangian and symplectic translating solitons.

We give a direct proof of Schensted's lemma asserting that row and column insertion in a tableau commute.

We give a new proof of Brooks' theorem that immediately implies a strengthening of Brooks' theorem, known as Catlin's theorem.

In this article, we prove an analog of the classical collar lemma in the setting of Hitchin representations.

Selection lemmas are classical results in discrete geometry that have been well studied and have applications in many geometric problems like weak epsilon nets and slimming Delaunay triangulations. Selection lemma type results typically…

We provide proofs for the fact that certain orders have no descending chains and no antichains.

Firstly, we provide a different proof of an important lemma in Buzzard and Calegari's work on slopes of overconvergent 2-adic modular forms via nonarchimedean linear Hodge-Newton decomposition. The lemma shows that two equivalent matrices…

We give the theorem of coincidence of a class of functions defined by a generalised modulus of smoothness with a class of functions defined by the order of the best approximation by algebraic polynomials. We also prove the appropriate…

One (actually, almost the only effective) way to prove formality of a differentiable manifold is to be able to produce a suitable derivation $\delta$ such that $d\delta$-lemma holds. We first show that such derivation $\delta$ generates a…

In this paper we give some new consequences that follow from our formula for increments of the Hardy-Littlewood integral. The main of these ones are $\mathcal{T}_1$ and $\mathcal{T}_2$ equivalents of the Fermat-Wiles theorem.

We describe the projectives in the category of functors from a graded poset to abelian groups. Based on this description we define a related condition, pseudo-projectivity, and we prove that this condition is enough for the vanishing of the…

This paper proves the existence of a dichotomy which being formally derived from the topological successiveness of w-order leads to the same absurdity of Zeno's Dichotomy II. It also derives a contradictory result from the first Zeno's…