Related papers: Constructing/analyzing differential distributed la…
The Jacobi system with matrix-valued coefficients and with the spectral parameter depending on a matrix-valued weight factor is considered on the full-line lattice. The scattering from the full-line lattice is expressed in terms of the…
We prove a polynomially effective equidistribution result for expanding translates in the space of $d$-dimensional affine lattices for any $d\ge 2$.
The set of all perfect matchings of a plane (weakly) elementary bipartite graph equipped with a partial order is a poset, moreover the poset is a finite distributive lattice and its Hasse diagram is isomorphic to $Z$-transformation directed…
Let $A$ be a basic finite-dimensional algebra and denote by $\operatorname{tors} A$ the collection of all all torsion classes of $A$. It has been proved in \cite{Demonet} that $\operatorname{tors} A$ is always a completely semidistributive…
We consider the problem of revealing a small hidden lattice from the knowledge of a low-rank sublattice modulo a given sufficiently large integer -- the {\em Hidden Lattice Problem}. A central motivation of study for this problem is the…
In this paper we describe an algorithm for classifying orbits of vectors in Lorentzian lattices. The main point of this is that isomorphism classes of positive definite lattices in some genus often correspond to orbits of vectors in some…
This paper investigates the structure-property relations of thin-walled lattices under dynamic longitudinal compression, characterized by their cross-sections and heights. These relations elucidate the interactions of different geometric…
In the latest developments in the theory of skew lattices, distributivity has been one of the main topics of study. The largest classes of examples of such algebras are distributive. Unlike what happens in lattices, the properties of…
Three-dimensional lattices are fundamental to solid-state physics. The description of a lattice with an atomic basis constitutes the necessary information to predict solid phase properties and evolution. Here, we present a new algorithm for…
We investigate properties of tempered distributions with discrete or countable supports such that their Fourier transforms are distributions with discrete or countable supports as well. We find sufficient conditions for support of the…
We establish a topological duality for bounded lattices. The two main features of our duality are that it generalizes Stone duality for bounded distributive lattices, and that the morphisms on either side are not the standard ones. A…
The distinguished weights form a subset of the weight lattice and are closely tied to the notion of $p$-cells. These weights are defined via iterations of the Lusztig-Vogan bijection. We prove that all distinguished weights exhibit an…
In a preceding article, we have studied a generalization of the problem of finding a martingale on a manifold whose terminal value is known. This article completes the results obtained in the first article by providing uniqueness and…
Lattice structures have great potential for several application fields ranging from medical and tissue engineering to aeronautical one. Their development is further speeded up by the continuing advances in additive manufacturing…
For practical construction of complex synthetic genetic networks able to perform elaborate functions it is important to have a pool of relatively simple "bio-bricks" with different functionality which can be compounded together. To…
This paper describes a new method for classifying a dataset that partitions elements into their categories. It has relations with neural networks but a slightly different structure, requiring only a single pass through the classifier to…
An M-partition of a positive integer m is a partition with as few parts as possible such that any positive integer less than m has a partition made up of parts taken from that partition of m. This is equivalent to partitioning a weight m so…
We describe a short, reproducible workflow for applying finite differences on nonuniform grids determined by a positive weight function g. The grid is obtained by equidistribution, mapping uniform computational coordinates $\xi\in[0,1]$ to…
We study signed differential posets, a signed version of differential posets. These posets satisfy enumerative identities which are signed analogues of those satisfied by differential posets. Our main motivations are the sign-imbalance…
We study the occurrence of number rigidity and deletion singularity in a class of point processes that we call {\it projected perturbed lattices}. These are generalizations of processes of the form…