Related papers: A refined transversality theorem on linear perturb…

Perturbation or error bounds of functions have been of great interest for a long time. If the functions are differentiable, then the mean value theorem and Taylor's theorem come handy for this purpose. While the former is useful in…

The purpose of this paper is to present some multidimensional fixed-point theorems and their applications. For this, we provide a multidimensional fixed point theorem and then using this theorem we prove the existence and uniqueness of a…

This work is devoted to dissipative extension theory for dissipative linear relations. We give a self-consistent theory of extensions by generalizing the theory on symmetric extensions of symmetric operators. Several results on the…

We introduce and study properties of certain new harmonic function spaces on products of upper half-spaces.Norm estimates for the so-called expanded Bergman projections are obtained.Sharp theorems on multipliers acting on certain Sobolev…

Singular perturbations have been used to select solutions of (non-convex) variational problems with a multiplicity of minimizers. The prototype of such an approach is the gradient theory of phase transitions by L. Modica, who specialized…

Some sharp discrete inequalities in normed linear spaces are obtained. New reverses of the generalised triangle inequality are also given.

In this paper we establish a general form of the Mass Transference Principle for systems of linear forms conjectured in [1]. We also present a number of applications of this result to problems in Diophantine approximation. These include a…

Deep Learning using the eponymous deep neural networks (DNNs) has become an attractive approach towards various data-based problems of theoretical physics in the past decade. There has been a clear trend to deeper architectures containing…

A non-perturbative method which can go beyond the weak coupling perturbation theory is introduced. Essential idea is to formulate a set of exact differential equations as a function of the coupling strength $g$. Unlike other resummation in…

The use of Variational Autoencoders in different Machine Learning tasks has drastically increased in the last years. They have been developed as denoising, clustering and generative tools, highlighting a large potential in a wide range of…

We describe a quantitative construction of almost-normal diffeomorphisms between embedded orientable manifolds with boundary to be used in the study of geometric variational problems with stratified singular sets. We then apply this…

Kapranov Theorem is a well known generalization of Newton-Puiseux theorem for the case of several variables. This theorem is stated mainly in the context of tropical geometry. We present a new, constructive proof, that also characterizes…

The present paper contains some investigations about a uniform variant of the notion of metric hemiregularity, the latter being a less explored property obtained by weakening metric regularity. The introduction of such a quantitative…

We have one more look at the (homological) perturbation lemma and we point out some non-standard consequences, including the relevance to deformations.

We prove a general version of the homological perturbation lemma which works in the presence of curvature, and without the restriction to strong deformation retracts, building on work of Markl. A key observation is that the notion of strong…

A basic idea in optimal transport is that optimizers can be characterized through a geometric property of their support sets called cyclical monotonicity. In recent years, similar "monotonicity principles" have found applications in other…

In this paper we develop methods to extend the minimal hypersurface approach to positive scalar curvature problems to all dimensions. This includes a proof of the positive mass theorem in all dimensions without a spin assumption. It also…

We consider the problem of learning low-rank tensors from partial observations with structural constraints, and propose a novel factorization of such tensors, which leads to a simpler optimization problem. The resulting problem is an…

We present a covariant and gauge invariant formalism suited to the study of second-order effects associated with higher order tensor perturbations. The analytical method we have developed enables us to characterize pure second-order tensor…

We analyze, mainly using bifurcation methods, an elliptic superlinear problem in one-dimension with periodic boundary conditions. One of the main novelties is that we follow for the first time a bifurcation approach, relying on a…