Abstract We introduce atoms for dyadic atomic $${\mathbb {H}}^1$$ H 1 which the equivalence between and maximal function definitions is dimension independent. give sharp, up to $$\log (d)$$ log ( d</mml:mi...

Three decompositions of a substochastic transition function are shown to yield substochastic parts. These are the Lebesgue decomposition with respect to a finite measure, the decomposition into completely atomic and continuous parts, and on Rn, a decomposition giving a part with continuous distribution function and a part with discontinuous distribution function. Introduction. The present paper...

Utilising self-assembled monolayers (SAMs) to achieve area-selective atomic layer deposition (AS-ALD) as an approach bottom-up nanofabrication has recently gained significant attention from the nanoelectronics industry. With continued downscaling of feature sizes, top-down processing can no longer reach challenging demands industry which requires conformal coating high aspect ratio vias and a r...

We study the stimulated Raman scattering (SRS) of light from an atomic system embedded in a photonic crystal and coherently pumped by a laser field. In our study, the electromagnetic field is treated classically and the atomic system is described quantum mechanically. Considering a decomposition of the pump and Stokes fields into the Bloch modes of the photonic crystals and using a multiscale a...

Determination of atomic-scale crystal structure for nanostructured intermetallic alloys, such as magnetic alloys containing Al, Ni, Co (alnico) and Fe, is crucial for understanding physical properties such as magnetism, but technically challenging due to the small interatomic distances and the similar atomic numbers. By applying energy-dispersive X-ray spectroscopy (EDS) mapping to the study of...

This paper develops a theory for the atomic decomposition of mixtures of translation-invariant signals. Suppose we have a linear combination of shifted copies of a known waveform with unknown shifts and coefficients. These shifts assume continuous values on the real line. We show that one can recover the exact translations and amplitudes by solving a continuous analog of `1 minimization, provid...

0.1. Why Do We Want to Decompose a Space? Basically the goal of mathematics is to classify certain objects. For instance, we are able to classify 2-dimensional manifolds. Then we are trying to classify 3-manifolds while Poincaré conjecture sounds difficult to be solved. In homotopy theory, a general question is how to classify spaces (up to homotopy). The general idea for classifying spaces is:...

The present study outlines an important area in the application of computer modelling to interface phenomena. Being relevant to the fundamental physical problem of competing atomic interactions in systems with reduced dimensionality, these phenomena attract special academic attention. On the other hand, from a technological point of view, detailed knowledge of the fine atomic structure of surfa...

Extracting a subset of a given ontology that captures all the ontology’s knowledge about a specified set of terms is a well-understood task. This task can be based, for instance, on locality-based modules. However, a single module does not allow us to understand neither topicality, connectedness, structure, or superfluous parts of an ontology, nor agreement between actual and intended modeling....