Related papers: The Haar measure in solid mechanics
Let $ Tf =\sum_{ I} \varepsilon_I \langle f,h_{I^+}\rangle h_{I^-}$. Here, $ \lvert \varepsilon _I\rvert=1 $, and $ h_J$ is the Haar function defined on dyadic interval $ J$. We show that, for instance, \begin{equation*} \lVert T \rVert _{L…
The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of…
We study the smoothness of the stationary measure with respect to smooth perturbations of the iterated function scheme and the weight functions that define it. Our main theorems relate the smoothness of the perturbation of: the iterated…
Inertial parameters characterise an object's motion under applied forces, and can provide strong priors for planning and control of robotic actions to manipulate the object. However, these parameters are not available a-priori in situations…
With the increasing growth of technology and the entrance into the digital age, we have to handle a vast amount of information every time which often presents difficulties. So, the digital information must be stored and retrieved in an…
The Fourier transform operation is an important conceptual as well as computational tool in the arsenal of every practitioner of physical and mathematical sciences. We discuss some of its applications in optical science and engineering,…
Experiments and simulations in solid-state high harmonic generation often make use of the distinction between interband and intraband currents. These two contributions to the total current have been associated with qualitatively different…
Fourier Transforms is a first in a series of monographs we present on harmonic analysis. Harmonic analysis is one of the most fascinating areas of research in mathematics. Its centrality in the development of many areas of mathematics such…
We focus on the complex relationship between the shape of dark matter halos and the cosmological models underlying their formation. We used three realistic cosmological models from the Dark Energy Universe Simulation suite. They have…
With the emergence of deep learning, metric learning has gained significant popularity in numerous machine learning tasks dealing with complex and large-scale datasets, such as information retrieval, object recognition and recommendation…
We prove a general result implying the $L^2$ stability of Haar decompositions of $L^2({\bf R}^d)$ functions when the Haar functions are distorted by arbitrary, independent, affine changes of variable that are close to the identity. We apply…
In this paper, we investigate the evaluation problem of the Haar state on the quantum group $O(U_q(n))$ ($n\ge 3$) which is a $q$-deformation of the Haar measure on the Lie group $U(n)$. The relation between the Haar state values of…
The concept of depth has proved very important for multivariate and functional data analysis, as it essentially acts as a surrogate for the notion a ranking of observations which is absent in more than one dimension. Motivated by the rapid…
This paper addresses the question whether a variant of a modal interpretation is conceivable that could accommodate property ascriptions associated with nonorthogonal resolutions of the unity and nonorthogonal families of relative states as…
The paper presents a construction of a quantitative measure of variability for parameter estimates in the data fitting problem under interval uncertainty. It shows the degree of variability and ambiguity of the estimate, and the need for…
The paper overviews and investigates several nonparametric methods of estimating covariograms. It provides a unified approach and notation to compare the main approaches used in applied research. The primary focus is on methods that utilise…
The concept of $p$-adic quincunx Haar MRA was introduced and studied in~\cite{KS10}. In contrast to the real setting, infinitely many different wavelet bases are generated by a $p$-adic MRA. We give an explicit description for all wavelet…
The problem of how mathematics and physics are related at a foundational level is of much interest. One approach is to work towards a coherent theory of physics and mathematics together. Here steps are taken in this direction by first…
I review recent evaluations of the hadronic contribution to the shift in the fine structure constant and to the anomalous magnetic moment of the muon. Substantial progress in a precise determination of these important observables is a…
We prove $\mathrm{H}^1$ and $\mathrm{BMO}$ endpoint inequalities for generic cancellative Haar shifts defined with respect to a possibly non-homogeneous Borel measure $\mu$ satisfying a weak regularity condition. This immediately yields a…