Related papers: Mat\'{e}rn Class Tensor-Valued Random Fields and B…
A "tensor space" is a vector space equipped with a finite collection of multi-linear forms. In previous work, we showed that (for each signature) there exists a universal homogeneous tensor space, which is unique up to isomorphism. Here we…
We discuss the appropriate normalization of modes required to generate a homogeneous random field in an open Friedmann-Robertson-Walker universe. We consider scalar random fields and certain tensor random fields that can be obtained by…
A new class of random spatial tessellations is introduced -- the so-called column tessellations of three-dimensional space. The construction is based on a stationary planar tessellation. Each cell of the spatial tessellation is a prism…
Proper classes of extensions of real field was defined and topological properties of these extensions were studied. These extensions can be connected, in this case such set is not closed under binary operations (addition and…
Tensors, or multi-linear forms, are important objects in a variety of areas from analytics, to combinatorics, to computational complexity theory. Notions of tensor rank aim to quantify the "complexity" of these forms, and are thus also…
We propose an explicit way to generate a large class of Operator scaling Gaussian random fields (OSGRF). Such fields are anisotropic generalizations of selfsimilar fields. More specifically, we are able to construct any Gaussian field…
The structure of the coincidence symmetry group of an arbitrary $n$-dimensional lattice in the $n$-dimensional Euclidean space is considered by describing a set of generators. Particular attention is given to the coincidence isometry…
Consider a graphed holomorphic surface $u=F(x,y)$ in $\mathbb{C}^3_{x,y,u}$ under the action of the affine transformation group $A(3)$. In 1999, Eastwood and Ezhov obtained a list of homogeneous models by determining possible tangential…
The fermion gaps are classified into order gap or Mott gap depending on the presence/absence of the order parameter. We construct the holographic model of the Mott gap using the field that is supported by the density only without…
We explicitly present homological residue fields for tensor triangulated categories as categories of comodules in a number of examples across algebra, geometry, and topology. Our results indicate that, despite their abstract nature, they…
The object of this paper is to characterize the third order moments (cumulants) and bispectra of a homogeneous isotropic field defined on a plane. We establish a one to one correspondence between the third order cumulants and the bispectra…
Motivated by questions arising in signal processing, computational complexity, and other areas, we study the ranks and border ranks of symmetric tensors using geometric methods. We provide improved lower bounds for the rank of a symmetric…
Let $K$ be an imaginary quadratic field and $\mathcal{O}_K$ be its ring of integers. Let $h_E$ be the Weber function on certain elliptic curve $E$ with complex multiplication by $\mathcal{O}_K$. We show that if $N$ ($>1$) is an integer…
The mapping class group of a Heegaard splitting is the group of automorphisms of the ambient 3-manifold that take the surface onto itself, modulo isotopies that keep the surface on itself. We characterize the mapping classes that restrict…
We survey recent classification theorems for expansive matrices that generate the same anisotropic homogeneous Triebel-Lizorkin function space or sequence space. The function spaces are classified precisely by those matrices for which their…
We produce an infinite family of imaginary quadratic fields whose ideal class groups have $3$-rank at least $2$.
In this report, the explicit probability density functions of the random Euclidean distances associated with regular hexagons are given, when the two endpoints of a link are randomly distributed in the same hexagon, and two adjacent…
We construct random triangles via uniform sampling of certain families of lines in the plane. Two examples are given. The word "uniform" turns out to be vague; two competing models are examined. Everything we write is well-known to experts.…
An ensemble of random unistochastic (orthostochastic) matrices is defined by taking squared moduli of elements of random unitary (orthogonal) matrices distributed according to the Haar measure on U(N) (or O(N), respectively). An ensemble of…
We present a systematic construction of probes into the dynamics of isospectral ensembles of Hamiltonians by the notion of Isospectral twirling, expanding the scopes and methods of ref.[1]. The relevant ensembles of Hamiltonians are those…