arXiv subjects

Thomas Ruf

Publications and source records attributed to Thomas Ruf.

9 recordsLinked to original sources

arXiv2026

Some Preliminary Considerations on Energy Behavior in Fluid Dynamics

This work presents a tentative discussion of certain aspects of energy behavior in the context of mathematical fluid dynamics. While some observations are made regarding certain patterns in energy behavior under particular conditions, the broader implications of these findings remain uncertain and should be interpreted with considerable caution. The results are preliminary in nature, and their relevance to analytic properties of solutions is demanding clarification at this stage. These considerations are intended to motivate further inquiry rather than to establish any definitive conclusions. Readers should approach the material presented here as exploratory, with significant open questions left unresolved.

math.AP↗

arXiv2025

Separability and Submetrizability in Locally Convex Spaces

We introduce the property of countable separation for a locally convex Hausdorff space $X$ and relate it to the existence of a metrizable coarser topology. Building on this, we demonstrate how the separability of $X$ is equivalent to the existence of a locally convex topology on the dual $X'$ that is metrizable and coarser than the weak topology $\sigma(X', X)$. This result generalizes known conditions for separability and provides a precise duality between separability and metrizability. We also show how to derive new and known conditions for the separability of $X$ from this characterization.

math.FA↗

arXiv2025

A Rough Divergence Theorem

A generalized divergence theorem is established allowing for domains with inner boundaries. The normal trace of a rough integrand is not a Radon measure; rather, the boundary integral is expressed via a surface functional continuous with respect to the uniform convergence of integrands. We provide necessary and sufficient analytic and geometric conditions on the domain for the validity of the theorem. Central to this characterization is the introduction of the space of functions having bounded fluctuation, whose norm is precisely defined so that the divergence theorem holds if and only if the characteristic function $\chi_U$ of the integration domain $U \subset \R^m$ has finite norm.

math.AP↗

arXiv2024

Orlicz-type Function Spaces and Generalized Gradient Flows with Degenerate Dissipation Potentials in Non-Reflexive Banach Spaces: Theory and Application

This thesis explores two important areas in the mathematical analysis of nonlinear partial differential equations: Generalized gradient flows and vector valued Orlicz spaces. The first part deals with the existence of strong solutions for generalized gradient flows, overcoming challenges such as non-coercive and infinity-valued dissipation potentials and non-monotone subdifferential operators on non-reflexive Banach spaces. The second part focuses on the study of Banach-valued Orlicz spaces, a flexible class of Banach spaces for quantifying the growth of nonlinear functions. Besides improving many known results by imposing minimal assumptions, we extend the theory by handling infinity-valued Orlicz integrands and arbitrary Banach-values in the duality theory. The combination of these results offers a powerful tool for analyzing differential equations involving functions of arbitrary growth rates and leads to a significant improvement over previous results, demonstrated through the existence of weak solutions for a doubly nonlinear initial-boundary value problem of Allen-Cahn-Gurtin type.

math.AP↗

arXiv2022

Non-separably valued Orlicz spaces, part I

For a measure space $\Omega$ we extend the theory of Orlicz spaces generated by an even convex integrand $\varphi \colon \Omega \times X \to \left[ 0, \infty \right]$ to the case when the range Banach space $X$ is arbitrary. Besides settling fundamental structural properties such as completeness, we characterize separability, reflexivity and represent the dual space. This representation includes the cases when $X'$ has no Radon-Nikodym property or $\varphi$ is unbounded. We apply our theory to represent convex conjugates and Fenchel-Moreau subdifferentials of integral functionals, leading to the first general such result on function spaces with non-separable range space. For this, we prove a new interchange criterion between infimum and integral for non-separable range spaces, which we consider of independent interest.

math.FA↗

arXiv2021

Stochastic homogenization of degenerate integral functionals and their Euler-Lagrange equations

We prove stochastic homogenization for integral functionals defined on Sobolev spaces, where the stationary, ergodic integrand satisfies a degenerate growth condition of the form \begin{equation*} c|ξA(ω,x)|^p\leq f(ω,x,ξ)\leq |ξA(ω,x)|^p+Λ(ω,x) \end{equation*} for some $p\in (1,+\infty)$ and with a stationary and ergodic diagonal matrix $A$ such that its norm and the norm of its inverse satisfy minimal integrability assumptions. We also consider the convergence when Dirichlet boundary conditions or an obstacle condition are imposed. Assuming the strict convexity and differentiability of $f$ with respect to its last variable, we further prove that the homogenized integrand is also strictly convex and differentiable. These properties allow us to show homogenization of the associated Euler-Lagrange equations.

math.AP↗

arXiv2021

Unique Minimizers and the Representation of Convex Envelopes in Locally Convex Vector Spaces

It is well known that a strictly convex minimand admits at most one minimizer. We prove a partial converse: Let $X$ be a locally convex Hausdorff space and $f \colon X \mapsto \left( - \infty , \infty \right]$ a function with compact sublevel sets and exhibiting some mildly superlinear growth. Then each tilted minimization problem \begin{equation} \label{eq. minimization problem} \min_{x \in X} f(x) - \langle x' , x \rangle_X \end{equation} admits at most one minimizer as $x'$ ranges over $\text{dom} \left( \partial f^* \right)$ if and only if the biconjugate $f^{**}$ is essentially strictly convex and agrees with $f$ at all points where $f^{**}$ is subdifferentiable. We prove this via a representation formula for $f^{**}$ that might be of independent interest.

math.OC↗

arXiv2014

Observational Aspects of Symmetries of the Neutral B Meson System

We revisit various results, which have been obtained by the BABAR and Belle Collaborations over the last twelve years, concerning symmetry properties of the Hamiltonian, which governs the time evolution and the decay of neutral B mesons.We find that those measurements, which established CP violation in B meson decay, 12 years ago, had as well established T (time-reversal) symmetry violation. They also confirmed CPT symmetry in the decay (T_CPT = 0) and symmetry with respect to time-reversal (epsilon? = 0) and to CPT (delta? = 0) in the B0 ?B0bar oscillation.

hep-ph↗

arXiv2012

Status Report of the DPHEP Study Group: Towards a Global Effort for Sustainable Data Preservation in High Energy Physics

Data from high-energy physics (HEP) experiments are collected with significant financial and human effort and are mostly unique. An inter-experimental study group on HEP data preservation and long-term analysis was convened as a panel of the International Committee for Future Accelerators (ICFA). The group was formed by large collider-based experiments and investigated the technical and organisational aspects of HEP data preservation. An intermediate report was released in November 2009 addressing the general issues of data preservation in HEP. This paper includes and extends the intermediate report. It provides an analysis of the research case for data preservation and a detailed description of the various projects at experiment, laboratory and international levels. In addition, the paper provides a concrete proposal for an international organisation in charge of the data management and policies in high-energy physics.

hep-ex↗