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When a solution to the Cauchy problem for nonlinear dispersive equations is obtained by a fixed point argument using auxiliary function spaces, it is non-trivial to ensure uniqueness of solutions in a natural space such as the class of…

An important quantity associated with a complex polynomial $p(z)$ is $\Vert p \Vert_\infty$, the maximum of its modulus over the unit disc $D$. We prove, $z_* \in D$ is a local maximum of $|p(z)|$ if and only if $a_*$ satisfies,…

In this paper we present a new bound obtained with the probabilistic method for the solution of the Set Covering problem with unit costs. The bound is valid for problems of fixed dimension, thus extending previous similar asymptotic…

In recent work, Harman and Snowden introduced a notion of measure on a Fra\"iss\'e class $\mathfrak{F}$, and showed how such measures lead to interesting tensor categories. Constructing and classifying measures is a difficult problem, and…

We consider fast algorithms for monotone submodular maximization with a general matroid constraint. We present a randomized $(1 - 1/e - \epsilon)$-approximation algorithm that requires $\tilde{O}_{\epsilon}(\sqrt{r} n)$ independence oracle…

The Constant Degree Hypothesis was introduced by Barrington et. al. (1990) to study some extensions of $q$-groups by nilpotent groups and the power of these groups in a certain computational model. In its simplest formulation, it…

We establish a higher-dimensional irrationality criterion for periods which are presented as Mellin integrals depending on many parameters. The criterion is stated as an upper bound on the multi-variate transfinite diameter of the image of…

Let (M,g) be a smooth compact, n dimensional Riemannian manifold, n=3,4 with smooth n-1 dimensional boundary. We search the positive solutions of the singularly perturbed Klein Gordon Maxwell Proca system with homogeneous Neumann boundary…

This paper studies the extreme singular values of non-harmonic Fourier matrices. Such a matrix of size $m\times s$ can be written as $\Phi=[ e^{-2\pi i j x_k}]_{j=0,1,\dots,m-1, k=1,2,\dots,s}$ for some set $\mathcal{X}=\{x_k\}_{k=1}^s$.…

Asymptotic behavior of the singular value decomposition (SVD) of blown up matrices and normalized blown up contingency tables exposed to Wigner-noise is investigated.It is proved that such an m\times n matrix almost surely has a constant…

In a series of papers, we will develop systematically the basic spectral theory of (self-adjoint) boundary value problems for operators of Dirac type. We begin in this paper with the characterization of (self-adjoint) boundary conditions…

This article proposes an initiation to \'Ecalle's mould calculus, a powerful combinatorial tool which yields surprisingly explicit formulas for the normalising series attached to an analytic germ of singular vector field. This is…

For a self mapping $f:\mathbb{D}\to \mathbb{D}$ of the unit disk in $\mathbb{C}$ which has finite distortion, we give a separation condition on the components of the set where the distortion is large - say greater than a given constant -…

Let $\{X_n\}_{n\geq 1}$ be either a sequence of arbitrary random variables, or a martingale difference sequence, or a centered sequence with a suitable level of negative dependence. We prove Baum-Katz type theorems by only assuming that the…

We continue the study in [21] of the linearizability near an indif- ferent fixed point of a power series f, defined over a field of prime characteristic p. It is known since the work of Herman and Yoccoz [13] in 1981 that Siegel's…

The problem of expressing a specific polynomial as the determinant of a square matrix of affine-linear forms arises from algebraic geometry, optimisation, complexity theory, and scientific computing. Motivated by recent developments in this…

We revisit the stability issue of determining the conductivity at the boundary from the corresponding Dirichlet-to-Neumann map. We discuss both the method based on singular solutions and the one built on the localized oscillating solutions.…

We give a simple proof of a well-known theorem of G\'al and of the recent related results of Aistleitner, Berkes and Seip [1] regarding the size of GCD sums. In fact, our method obtains the asymptotically sharp constant in G\'al's theorem,…

Our work proves rigidity theorems for initial data sets associated with compact smooth spin manifolds with boundary and with compact convex polytopes, subject to the dominant energy condition. For manifolds with smooth boundary, this is…

In this paper we study the so-called large solutions of elliptic semilinear equations with non null sources term, thus solutions blowing up on the boundary of the domain for which reason they are greater than any other solution whenever…