Related papers: Problems concerning Diophantine exponents of latti…

This paper discusses some topics of enquiry concerning fractals, functions on them, and so on.

This article introduces and studies Minkowski Bisectors, Minkowski Cells, and Lattice Coverings.

Some Open Problems Concerning Orthogonal Polynomials.

We extend the key formula which intertwines multiplicative Markoff-Lagrange spectrum and symbolic dynamics. The proof uses complex analysis and elucidates the strategy of the problem. Moreover, the new method applies to a wide variety of…

We consider a variety of settings involving chains with one or more defects stemming from the introduction of nodes bearing internal resonators. Motivated by experimental results in woodpile elastic lattices with one or two defects, we…

We study quadratic approximations for two families of hyperquadratic continued fractions in the field of Laurent series over a finite field. As the first application, we give the answer to a question of the second author concerning…

We elaborate on a problem raised by Schmidt in 1967 which generalizes the theory of classical Diophantine approximation to subspaces of $\R^n$. We consider Diophantine exponents for linear subspaces of $\R^n$ which generalize the…

The aim of this paper is to study the profiniteness of compact topological residuated lattices and the existence of Hausdorff topological residuated lattices. Firstly, we study profinite residuated lattices and obtain sufficient and…

In this paper we give a simple proof of an inequality for intermediate Diophantine exponents obtained recently by W. M. Schmidt and L. Summerer.

In this survey, we discuss some basic problems concerning random matrices with discrete distributions. Several new results, tools and conjectures will be presented.

In this paper we investigate the problem of which Lie algebras appear as the derived algebra of a Lie algebra. We present new results that further develop this study and address two questions raised in a paper concerned with the…

One of the longstanding problems in universal algebra is the question of which finite lattices are isomorphic to the congruence lattices of finite algebras. This question can be phrased as which finite lattices can be represented as…

The structure of a previously developed representation of the Leech lattice, $\Lambda_{24}$, is exposed to further light with this unified and very simple construction.

In a previous article [N. Delice, F.W. Nijhoff and S. Yoo-Kong, J. Phys. A: Math. Theor. 48(3) (2015), 035206] a novel class of elliptic Lax pairs for integrable lattice equations was introduced. The present article proposes a…

We give a broad survey of inequalities for the number of linear extensions of finite posets. We review many examples, discuss open problems, and present recent results on the subject. We emphasize the bounds, the equality conditions of the…

These lecture notes discuss classical models of liquid crystals, and the different ways in which defects are described according to the different models.

We study the lattices of algebraic and transcendental cycles of cubic fourfolds.

In this paper, we prove an inequality regarding the differential polynomial. This improves some recent results.

We prove several rigorous results about the asymptotic behaviour of the numbers of tadpoles (or lassos) embedded in a lattice, including cases where the head is subject to a constraint like being unknotted, or where the tail pierces the…

In this article we introduce theory and algorithms for learning discrete representations that take on a lattice that is embedded in an Euclidean space. Lattice representations possess an interesting combination of properties: a) they can be…