Search results for "Functional analysis"

Torus computed tomography

2020

We present a new computed tomography (CT) method for inverting the Radon transform in 2D. The idea relies on the geometry of the flat torus, hence we call the new method Torus CT. We prove new inversion formulas for integrable functions, solve a minimization problem associated to Tikhonov regularization in Sobolev spaces and prove that the solution operator provides an admissible regularization strategy with a quantitative stability estimate. This regularization is a simple post-processing low-pass filter for the Fourier series of a phantom. We also study the adjoint and the normal operator of the X-ray transform on the flat torus. The X-ray transform is unitary on the flat torus. We have i…

2018

Background: The relation between training load, especially internal load, and the recovery-stress state is of central importance for avoiding negative adaptations in high-performance sports like swimming. The aim of this study was to analyze the individual time-delayed linear effect relationship between training load and recovery-stress state with single case time series methods and to monitor the acute recovery-stress state of high-performance swimmers in an economical and multidimensional manner over a macro cycle. The Acute Recovery and Stress Scale (ARSS) was used for daily monitoring of the recovery-stress state. The methods session-RPE (sRPE) and acute:chronic workload-ratio (ACWR) we…

Image Compression by 2D Motif Basis

2011

Approaches to image compression and indexing based on extensions to 2D of some of the Lempel-Ziv incremental parsing techniques have been proposed in the recent past. In these approaches, an image is decomposed into a number of patches, consisting each of a square or rectangular solid block. This paper proposes image compression techniques based on patches that are not necessarily solid blocks, but are affected instead by a controlled number of undetermined or don't care pixels. Such patches are chosen from a set of candidate motifs that are extracted in turn from the image 2D motif basis, the latter consisting of a compact set of patterns that result from the autocorrelation of the image w…

Regularity properties for quasiminimizers of a $(p,q)$-Dirichlet integral

2021

Using a variational approach we study interior regularity for quasiminimizers of a $(p,q)$-Dirichlet integral, as well as regularity results up to the boundary, in the setting of a metric space equipped with a doubling measure and supporting a Poincar\'{e} inequality. For the interior regularity, we use De Giorgi type conditions to show that quasiminimizers are locally H\"{o}lder continuous and they satisfy Harnack inequality, the strong maximum principle, and Liouville's Theorem. Furthermore, we give a pointwise estimate near a boundary point, as well as a sufficient condition for H\"older continuity and a Wiener type regularity condition for continuity up to the boundary. Finally, we cons…

Pointwise characterizations of Hardy-Sobolev functions

2006

We establish simple pointwise characterizations of functions in the Hardy-Sobolev spaces within the range n/(n+1)<p <=1. In addition, classical Hardy inequalities are extended to the case p <= 1.

Higher Order Sobolev-Type Spaces on the Real Line

2014

This paper gives a characterization of Sobolev functions on the real line by means of pointwise inequalities involving finite differences. This is also shown to apply to more general Orlicz-Sobolev, Lorentz-Sobolev, and Lorentz-Karamata-Sobolev spaces.

Characterization of Orlicz–Sobolev space

2007

We give a new characterization of the Orlicz–Sobolev space W1,Ψ(Rn) in terms of a pointwise inequality connected to the Young function Ψ. We also study different Poincaré inequalities in the metric measure space.

On Compacta K for Which C(K) Has Some Good Renorming Properties

2019

By renorming it is usually meant obtaining equivalent norms in a Banach space with better properties, like being local uniformly rotund (LUR) or Kadets. In these notes we are concerned with C(K) spaces and pointwise lower semicontinuous Kadets or LUR renormings on them. If a C(K) space admits some of such equivalent norms then this space, endowed with the pointwise topology, has a countable cover by sets of small local norm-diameter (SLD). This property may be considered as the topological baseline for the existence of a pointwise lower semicontinuous Kadets, or even LUR renorming, since in many concrete cases it is the first step to obtain such a norm. In these notes we survey some methods…

Pointwise Inequalities for Sobolev Functions on Outward Cuspidal Domains

2019

Abstract We show that the 1st-order Sobolev spaces $W^{1,p}(\Omega _\psi ),$$1&amp;lt;p\leq \infty ,$ on cuspidal symmetric domains $\Omega _\psi $ can be characterized via pointwise inequalities. In particular, they coincide with the Hajłasz–Sobolev spaces $M^{1,p}(\Omega _\psi )$.

Conformations, Transverse Fluctuations and Crossover Dynamics of a Semi-Flexible Chain in Two Dimensions

2014

We present a unified scaling description for the dynamics of monomers of a semiflexible chain under good solvent condition in the free draining limit. We consider both the cases where the contour length $L$ is comparable to the persistence length $\ell_p$ and the case $L\gg \ell_p$. Our theory captures the early time monomer dynamics of a stiff chain characterized by $t^{3/4}$ dependence for the mean square displacement(MSD) of the monomers, but predicts a first crossover to the Rouse regime of $t^{2\nu/{1+2\nu}}$ for $\tau_1 \sim \ell_p^3$, and a second crossover to the purely diffusive dynamics for the entire chain at $\tau_2 \sim L^{5/2}$. We confirm the predictions of this scaling descr…