Related papers: Circle packing and interpolation in Fock spaces
In theoretical physics, we sometimes have two perturbative expansions of physical quantity around different two points in parameter space. In terms of the two perturbative expansions, we introduce a new type of smooth interpolating function…
We construct a large family of Fourier interpolation bases for functions analytic in a strip symmetric about the real line. Interesting examples involve the nontrivial zeros of the Riemann zeta function and other $L$-functions. We establish…
The evolution of the interface propagation in a slowly rotating half-filled horizontal cylinder is studied using MRI. Initially, the cylinder contains two axially segregated bands of small and large particles with a sharp interface. The…
We consider the problem of packing congruent circles with the maximum radius in a unit square as a mathematical optimization problem. Due to the presence of non-overlapping constraints, this problem is a notoriously difficult nonconvex…
Packings of equal disks in the plane are known to have density at most $\pi/\sqrt{12}$, although this density is never achieved in the square torus, which is what we call the plane modulo the square lattice. We find packings of disks in a…
Three-photon (3P) microscopy is getting traction due to its superior performance in deep tissues. Yet, aberrations and light scattering still pose one of the main limitations in the attainable depth ranges for high-resolution imaging. Here,…
A bounded Apollonian circle packing (ACP) is an ancient Greek construction which is made by repeatedly inscribing circles into the triangular interstices in a Descartes configuration of four mutually tangent circles. Remarkably, if the…
Quartetting ($\alpha$-like clustering) occurs in low density matter ($\le 0.03$ fm$^{-3}$) which exists, e.g., at the surface of nuclei. It is of interest for the $\alpha$ preformation to calculate the $\alpha$ decay of heavy nuclei such as…
We show that if a sample of galaxy clusters is complete above some mass threshold, then hierarchical clustering theories for structure formation predict its autocorrelation function to be determined purely by the cluster abundance and by…
We present a simple, PDE-based proof of the result [M. Johnson, 2001] that the error estimates of [J. Duchon, 1978] for thin plate spline interpolation can be improved by $h^{1/2}$. We illustrate that ${\mathcal H}$-matrix techniques can…
We study the approximation of maps into complex manifolds along with interpolation on certain compact subsets of the plane. Results are also obtained regarding approximation and interpolation of sections of holomorphic submersions.
Given a finite poset $\mathcal P$, we call a family $\mathcal F$ of subsets of $[n]$ $\mathcal P$-saturated if $\mathcal F$ does not contain an induced copy of $\mathcal P$, but adding any other set to $\mathcal F$ creates an induced copy…
In every dimension $d \geq 2$, we give an explicit formula that expresses the values of any Schwartz function on $\mathbb{R}^d$ only in terms of its restrictions, and the restrictions of its Fourier transform, to all origin-centered spheres…
We present a fitting function to describe the statistics of flux modulations caused by interstellar scintillation. The function models a very general quantity: the cross-correlation of the flux observed from a compact radio source of finite…
Carleson measures and interpolating and sampling sequences for weighted Bergman spaces on the unit disk are described for weights that are radial and grow faster than the standard weights $(1-|z|)^{-\alpha}$, $0<\alpha<1$. These results…
The aim of this paper is to give an elementary proof that Hermite expensions of a function $f$ in the modulation space $M^p(R)$ converges to $f$ in $M^p(R)$ when $1< p<+\infty$ and may diverge when $p = 1,\infty$. The result was previously…
We show that for certain triangulations of surfaces, circle packings realising the triangulation can be found by solving a system of polynomial equations. We also present a similar system of equations for unbranched circle packings. The…
For any delta > 1 we construct a periodic and locally finite packing of the plane with ellipses whose delta-enlargement covers the whole plane. This answers a question of Imre B\'ar\'any. On the other hand, we show that if C is a packing in…
Multivariate circular observations, i.e. points on a torus are nowadays very common. Multivariate wrapped models are often appropriate to describe data points scattered on p-dimensional torus. However, statistical inference based on this…
We introduce the novel concept of a non-stationary iterated function system by considering a countable sequence of distinct set-valued maps $\{\mathcal{F}_k\}_{k\in \mathbb{N}}$ where each $\mathcal{F}_k$ maps $\mathcal{H}(X)\to…