Related papers: Density preserving functions

Periodic Geometry studies isometry invariants of periodic point sets that are also continuous under perturbations. The motivations come from periodic crystals whose structures are determined in a rigid form but any minimal cells can…

An ultrametric preserving function $f$ is said to be strongly ultrametric preserving if ultrametrics $d$ and $f \circ d$ define the same topology on $X$ for each ultrametric space $(X,d)$. The set of all strongly ultrametric preserving…

We provide sufficient density condition for a set of nonuniform samples to give rise to a set of sampling for multivariate bandlimited functions when the measurements consist of pointwise evaluations of a function and its first $k$…

A compression function is a map that slims down an observational set into a subset of reduced size, while preserving its informational content. In multiple applications, the condition that one new observation makes the compressed set change…

Isometries of metric spaces $(X,d)$ preserve all level sets of $d$. We formulate and prove cases of a conjecture asserting if $X$ is a complete Riemannian manifold, then a function $f:X \rightarrow X$ preserving at least one level set…

We construct a H\"older continuous function on the unit interval which coincides in uncountably (in fact continuum) many points with every function of total variation smaller than 1 passing through the origin. We say that a function with…

The density functional theory is extended to account for self-bound systems. To this end the Hohenberg-Kohn theorem is formulated for the intrinsic density and a Kohn-Sham like procedure for an $N$--body system is derived using the…

The principles of density-functional theory are studied for finite lattice systems represented by graphs. Surprisingly, the fundamental Hohenberg-Kohn theorem is found void in general, while many insights into the topological structure of…

The range of the divisor function $\sigma_{-1}$ is dense in the interval $[1,\infty)$. However, the range of the function $\sigma_{-2}$ is not dense in the interval $\displaystyle{\left[1,\frac{\pi^2}{6}\right)}$. We begin by generalizing…

We establish necessary and sufficient conditions for the N-representability of the universal one-electron reduced density matrix functional. Functionals satisfying these conditions are guaranteed to yield variational upper bounds on the…

We construct a function on the real line supported on a set of finite measure whose spectrum has density zero.

Model sets (also called cut and project sets) are generalizations of lattices. Here we show how the self-similarities of model sets are a natural replacement for the group of translations of a lattice. This leads us to the concept of…

This paper concerns a spectral estimation problem in which we want to find a spectral density function that is consistent with estimated second-order statistics. It is an inverse problem admitting multiple solutions, and selection of a…

Sample size criteria are often expressed in terms of the concentration of the posterior density, as controlled by some sort of error bound. Since this is done pre-experimentally, one can regard the posterior density as a function of the…

We consider holomorphic functions on the unit disc whose images are contained in a strip of the complex plane. Under an additional condition, such functions are constants. We also consider appropriate operator valued versions. Applications…

Elementary facts and observations on the cone of supermodular set functions are recalled. The manuscript deals with such operations with set functions which preserve supermodularity and the emphasis is put on those such operations which…

This paper considers the problem of specifying a simple approximating density function for a given data set (x_1,...,x_n). Simplicity is measured by the number of modes but several different definitions of approximation are introduced. The…

In Persistent Homology and Topology, filtrations are usually given by introducing an ordered collection of sets or a continuous function from a topological space to $\R^n$. A natural question arises, whether these approaches are equivalent…

We give the definition of uniform symmetric continuity for functions defined on a nonempty subset of the real line. Then we investigate the properties of uniformly symmetrically continuous functions and compare them with those of…

This article contains a self-contained proof of the stability under convolution of the space of resurgent functions associated with a closed discrete subset of the complex plane (the set of possible singularities), under the assumption that…