On the Existence of Solutions of Dynamic Equations on Time Scales in Banach Spaces
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT In this paper we address the question of solvability of dynamic equations on time scales in Banach spaces. In particular, our main theorem extends the result for classical differential equations in Banach spaces of Banaś and Goebel established in [5], to an arbitrary time scale.
Dušan Oberta
wiley +1 more source
A note on Gromov-Hausdorff-Prokhorov distance between (locally) compact measure spaces
, 2013 International audienceWe present an extension of the Gromov-Hausdorff metric on the set of compact metric spaces: the Gromov-Hausdorff-Prokhorov metric on the set of compact metric spaces endowed with a finite measure.
Delmas, Jean-François +2 more
core +1 more source
Renormalization techniques for inflation systems and some of their applications
Acta Crystallographica Section A, EarlyView.In this work, renormalization methods for quantities related to the diffraction of inflation systems are surveyed.Exact renormalization techniques are important and powerful, particularly for inflation‐generated systems. We review recent results in this direction.
Michael Baake +4 more
wiley +1 more source
Global Solutions for Abstract Differential Equations with Non-Instantaneous Impulses
, 2016 CONICYTDICYT-USACHCONICYT: FONDECYT 1130144In this note we study the existence of global solutions for a class of impulsive abstract differential equations with non-instantaneous impulses. Specifically, we establish the existence of mild solutions on and
Hernán R. Henríquez +6 more
core +1 more source
A Hausdorff-measure boundary element method for acoustic scattering by fractal screens [PDF]
Sound-soft fractal screens can scatter acoustic waves even when they have zero surface measure. To solve such scattering problems we make what appears to be the first application of the boundary element method (BEM) where each BEM basis function is ...
Hewett, David P. +12 more
core +2 more sources
One‐Class Autoencoders for Porcelain Art Attribution: The Case of William Billingsley
Archaeometry, EarlyView.ABSTRACT This comprehensive study explores the application of advanced machine learning techniques, specifically one‐class autoencoders, for the authentication and attribution of English porcelain artworks. Focusing primarily on the works of William Billingsley (1758–1828), one of England's most celebrated porcelain decorators, we demonstrate how ...
Hassan Ugail +3 more
wiley +1 more source
Exact dimensionality and projections of random self-similar measures and sets
, 2014 We study the geometric properties of random multiplicative cascade measures defined on self-similar sets. We show that such measures and their projections and sections are almost surely exact dimensional, generalizing a result of Feng and Hu's for self ...
Jin, Xiong +4 more
core +1 more source
SDFs from Unoriented Point Clouds using Neural Variational Heat Distances
Computer Graphics Forum, EarlyView.We propose a novel variational approach for computing neural Signed Distance Fields (SDF) from unoriented point clouds. We first compute a small time step of heat flow (middle) and then use its gradient directions to solve for a neural SDF (right). Abstract We propose a novel variational approach for computing neural Signed Distance Fields (SDF) from ...
Samuel Weidemaier +5 more
wiley +1 more source
Dimension and measure theory of self-similar structures with no separation condition
, 2015 We introduce methods to cope with self-similar sets when we do not assume any separation condition. For a self-similar set K ⊆ ℝᵈ we establish a similarity dimension-like formula for Hausdorff dimension regardless of any separation condition.
Farkas, Ábel
core
Local monotonicity of Hausdorff measures restricted to curves in $\Bbb R^n$ [PDF]
, 2009 summary:We give a sufficient condition for a curve $\gamma: \Bbb R \to \Bbb R^n$ to ensure that the $1$-dimensional Hausdorff measure restricted to $\gamma$ is locally ...
Černý, Robert
core +1 more source