Related papers: Constructing $\omega$-free Hardy fields

We resolve the strong Elementary Equivalence versus Isomorphism Problem for finitely generated fields. That is, we show that for every field in this class there is a first-order sentence which characterizes this field within the class up to…

We find sharp conditions on the growth of a rooted regular metric tree such that the Neumann Laplacian on the tree satisfies a Hardy inequality. In particular, we consider homogeneous metric trees. Moreover, we show that a non-trivial…

A consistent, local coordinate formulation of covariant Hamiltonian field theory is presented. Whereas the covariant canonical field equations are equivalent to the Euler-Lagrange field equations, the covariant canonical transformation…

We consider derivations $\partial$ on Conway's field $\mathbf{No}$ of surreal numbers such that the ordered differential field $(\mathbf{No},\partial)$ has constant field $\mathbb{R}$ and is a model of the model companion of the theory of…

In 1975 Szemer\'edi proved that a set of integers of positive upper density contains arbitrarily long arithmetic progressions. Bergelson and Leibman showed in 1996 that the common difference of the arithmetic progression can be a square, a…

We present a general structure theorem for the Hardy field of an o-minimal expansion of the reals by restricted analytic functions and an unrestricted exponential. We proceed to analyze its residue fields with respect to arbitrary convex…

For linear bose field theories, I show that if a classical Hamiltonian function is strictly positive, then there is a canonical transformation making the evolution orthogonal. This structure theorem is used to analyze the corresponding…

Holomorphic fields play an important role in 2d conformal field theory. We generalize them to d>2 by introducing the notion of Cauchy conformal fields, which satisfy a first order differential equation such that they are determined…

We prove that any ordered field can be extended to one for which every decreasing sequence of bounded closed intervals, of any length, has a nonempty intersection; equivalently, there are no Dedekind cuts with equal cofinality from both…

An $H$-field is a type of ordered valued differential field with a natural interaction between ordering, valuation, and derivation. The main examples are Hardy fields and fields of transseries. Aschenbrenner and van den Dries proved…

Using a categorial version of Fra\"iss\'e's theorem due to Droste and G\"obel, we derive a criterion for a comma-category to have universal homogeneous objects. As a first application we give new existence result for universal structures…

We prove several interesting equalities for the integrals of higher order derivatives on the homogeneous groups. As consequences, we obtain the sharp Hardy--Rellich type inequalities for higher order derivatives including both the…

In this paper we present sufficient conditions for the existence of heteroclinic or homoclinic solutions for second order coupled systems of differential equations on the real line. We point out that it is required only conditions on the…

Let $S$ be a sequence of points in $\Omega ,$ where $\Omega$ is the unit ball or the unit polydisc in ${\mathbb{C}}^{n}.$ Denote $H^{p}$($\Omega $) the Hardy space of $\Omega .$ Suppose that $S$ is $H^{p}$ interpolating with $p\geq 2.$ Then…

The work of Adler provides necessary and sufficient conditions for the Wronskian of a given sequence of eigenfunctions of Schr\"odinger's equation to have constant sign in its domain of definition. We extend this result by giving explicit…

An alternative proof of Lie's approach for linearization of scalar second order ODEs is derived using the relationship between $\lambda$-symmetries and first integrals. This relation further leads to a new $\lambda$-symmetry linearization…

We introduce a class of hyperfields which includes several constructions of non-quotient hyperfields. We then use it to partially answer a question posed by M. Baker and T. Zhang: Does a system of homogeneous linear equations with more…

In this note we produce generalized versions of the classical inequalities of Hardy and of Hilbert and we establish their equivalence. Our methods rely on the H^1-BMOA duality. We produce a class of examples to establish that the…

We give an elementary construction of an arbitrary differentially closed field and of a universal differential extension of a differential field in terms of Nash function fields. We also give a characterization of any Archimedean ordered…

We present a method for the Hamiltonian formulation of field theories that are based on Lagrangians containing second derivatives. The new feature of our formalism is that all four partial derivatives of the field variables are initially…