Related papers: The Brouwer invariance theorems in reverse mathema…
We prove the inverse conjecture for the Gowers U^{s+1}[N]-norm for all s >= 3; this is new for s > 3, and the cases s<3 have also been previously established. More precisely, we establish that if f : [N] -> [-1,1] is a function with || f…
We consider Brouwer's fixed point theorem and Sperner's lemma in one dimension. We present a proof of the Brouwer theorem using the Sperner lemma, and vice versa. However, we also show that they are not equivalent, because the Sperner lemma…
Kronecker observed that either all roots or only one root of a solvable irreducible equation of odd prime degree with integer coefficients are real. This gives a possibility to construct specific examples of equations not solvable by…
We prove a version of Wordingham's theorem for left regular representations in the setting of Fell bundles of inverse semigroups and use this result to discuss the various associated cross sectional C*-algebras.
The aim of Reverse Mathematics(RM for short)is to find the minimal axioms needed to prove a given theorem of ordinary mathematics. These minimal axioms are almost always equivalent to the theorem, working over the base theory of RM, a weak…
In this paper we study a new approach to classify mathematical theorems according to their computational content. Basically, we are asking the question which theorems can be continuously or computably transferred into each other? For this…
This paper proposes a new and efficient numerical algorithm for recovering the damping coefficient from the spectrum of a damped wave operator, which is a classical Borg-Levinson inverse spectral problem. The algorithm is based on inverting…
We consider a linearised inverse conductivity problem for electromagnetic waves in a three dimensional bounded domain at a high time-harmonic frequency. Increasing stability bounds for the conductivity coefficient in the full Maxwell system…
We present some results and conjectures on a generalization to the noncommutative setup of the Brouwer fixed-point theorem from the Borsuk-Ulam theorem perspective.
Given a countable o-minimal theory T, we characterize the Borel complexity of isomorphism for countable models of T up to two model-theoretic invariants. If T admits a nonsimple type, then it is shown to be Borel complete by embedding the…
Weak coalgebra-Galois extensions are studied. A notion of an invertible weak entwining structure is introduced. It is proven that, within an invertible weak entwining structure, the surjectivity of the canonical map implies bijectivity…
We prove that the Cohesiveness Principle (COH) is $\Pi^1_1$ conservative over $RCA_0 + I\Sigma^0_n$ and over $RCA_0 + B\Sigma^0_n$ for all $n \geq 2$ by recursion-theoretic means. We first characterize COH over $RCA_0 + B\Sigma^0_2$ as a…
Usually such area of mathematics as differential equations acts as a consumer of results given by functional analysis. This article will give an example of the reverse interaction of these two fields of knowledge. Namely, the derivation and…
In this paper, we investigate a model describing induction hardening of steel. The related system consists of an energy balance, an ODE for the different phases of steel, and Maxwell's equations in a potential formulation. The existence of…
We develop an obstruction theory for Hirsch extensions of cbba's with twisted coefficients. This leads to a variety of applications, including a structural theorem for minimal cbba's, a construction of relative minimal models with twisted…
This paper uses the framework of reverse mathematics to investigate the strength of two recurrence theorems of topological dynamics. It establishes that one of these theorems, the existence of an almost periodic point, lies strictly between…
We consider the inverse resonance problem in one-dimensional scattering theory. The scattering matrix consists of $2\times 2$ entries of meromorphic functions, which are quotients of certain Fourier transform. The resonances are expressed…
In this paper, we prove the non-uniqueness of stationary solutions to steady incompressible Euler equations with source terms. Based on the convex integration scheme developed by De Lellis and Sz\'{e}kelyhidi, the Euler system is…
Estimating nonlinear functionals of probability distributions from samples is a fundamental statistical problem. The "plug-in" estimator obtained by applying the target functional to the empirical distribution of samples is biased.…
We develop some techniques for studying various versions of the function space BMO. Special cases of one of our results give alternative proofs of the celebrated John- Nirenberg inequality and of related inequalities due to John and to Wik.…