Related papers: Numerical study of the local contractivity of the …
Previous results about the non trivial solution of the $\Phi^4$-equations of motion for the Green's functions in the Euclidean\ space (of $0\leq r\leq 4$ dimensions) in the Wightman Quantum Field theory framework, are reviewed in the 0 -…
We show the existence and uniqueness of a solution to a $\Phi_4^4$ non linear renormalized system of equations of motion in Euclidean space. This system represents a non trivial model which describes the dynamics of the $\Phi_4^4$ Green's…
Local scaling of a set means that in a neighborhood of a point the structure of the set can be mapped into a finer scale structure of the set. These scaling transformations are compact sets of locally affine (that is: with uniformly…
The present paper, III, is the third part of a series of papers, under the global title "the non triviality of a $\Phi_4^4$ model". Parts I and II have been previously completed. In them thanks to the properties we dubbed "splitting -tree…
Let $\Phi$ be a concave function on $(0,\infty)$ of strictly lower type $p_{\Phi}\in(0,1]$ and $\omega\in A^{\mathop\mathrm{loc}}_{\infty}(\mathbb{R}^n)$. We introduce the weighted local Orlicz-Hardy space $h^{\Phi}_{\omega}(\mathbb{R}^n)$…
We study the local scaling properties associated with straight line periodic orbits in homogeneous Hamiltonian systems, whose stability undergoes repeated oscillations as a function of one parameter. We give strong evidence of local scaling…
We construct the $\Phi^4_3$ measure on an arbitrary 3-dimensional compact Riemannian manifold without boundary as an invariant probability measure of a singular stochastic partial differential equation. Proving the nontriviality and the…
In this paper, we give lower bounds for the homology of the fibers of a map to a manifold. Using new sheaf theoretic methods, we show that these lower bounds persist over whole open sets of the manifold, and that they are stable under…
We develop a stability theory for contractive local IFSs on compact metric spaces. Unlike the classical global setting, local systems may exhibit a richer symbolic and geometric structure, including code spaces that are not of finite type…
We introduce a weak asymptotic version of nonlinear contraction, termed \emph{asymptotic pointwise contraction}. For a mapping on a metric space, this notion requires the existence of a sequence of functions that dominate the distances…
The mode-locking regions of a dynamical system are the subsets of the parameter space of the system within which there exists an attracting periodic solution. For piecewise-linear continuous maps, these regions have a curious chain…
Suppose R is a Noetherian local ring with prime characteristic p>0. In this article, we show the existence of a local numerical invariant, called the F-signature, which roughly characterizes the asymptotic growth of the number of splittings…
This paper studies the fundamental properties of the high-order forward-backward splitting mapping (HiFBS) and its associated forward-backward envelope (HiFBE) through the lens of high-order regularization for nonconvex composite functions.…
Recently, multi-scale notions of local homology (a variant of persistent homology) have been used to study the local structure of spaces around a given point from a point cloud sample. Current reconstruction guarantees rely on constructing…
We study the topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We consider those maps satisfying the "separation property": different continuity…
Recently, the stability of certain topological phases of matter under weak perturbations was proven. Here, we present a short, alternate proof of the same result. We consider models of topological quantum order for which the unperturbed…
The renormalized trajectory of massless $\phi^4$-theory on four dimensional Euclidean space-time is investigated as a renormalization group invariant curve in the center manifold of the trivial fixed point, tangent to the…
Local protein structure analysis is informative to protein structure analysis and has been used successfully in protein structure prediction and others. Proteins have recurring structural features, such as helix caps and beta turns, which…
We conduct the multifractal analysis of the level sets of the asymptotic behavior of almost additive continuous potentials $(\phi_n)_{n=1}^\infty$ on a topologically mixing subshift of finite type $X$ endowed itself with a metric associated…
This paper investigates fractional torsional rigidity on compact, connected metric graphs, a novel extension of the classical concept to nonlocal operators. The fractional torsional rigidity is defined as the $L^1$-norm of the fractional…