Related papers: Integer superharmonic matrices on the $F$-lattice

We investigate the complexity of the lattice of local clones over a countably infinite base set. In particular, we prove that this lattice contains all algebraic lattices with at most countably many compact elements as complete sublattices,…

We provide the first known upper bounds for the packing dimension of weighted singular and weighted $\omega$-singular matrices. We also prove upper bounds for these sets when intersected with fractal subsets. The latter results, even in the…

We conjecture that quantum Gaudin models in affine types admit families of local higher Hamiltonians, labelled by the (countably infinite set of) exponents, whose eigenvalues are given by functions on a space of meromorphic opers associated…

We present a novel approach for data set scaling based on scale-measures from formal concept analysis, i.e., continuous maps between closure systems, and derive a canonical representation. Moreover, we prove said scale-measures are lattice…

This paper investigates positive harmonic functions on a domain which contains an infinite cylinder, and whose boundary is contained in the union of parallel hyperplanes. (In the plane its boundary consists of two sets of vertical…

We discuss the growth envelopes of Fourier-analytically defined Besov and Triebel-Lizorkin spaces $B^s_{p,q}(\R^n)$ and $F^s_{p,q}(\R^n)$ for $s=\sigma_p=n\max(\frac 1p-1,0)$. These results may be also reformulated as optimal embeddings…

We prove several results on backward orbits of rational functions over number fields. First, we show that if $K$ is a number field, $\phi\in K(x)$ and $\alpha\in K$ then the extension of $K$ generated by the abelian points in the backward…

For a hypergraphic polytope there is a weighted quasisymmetric function which enumerates positive integer points in its normal fan and determines its f-polynomial. This quasisymmetric function invariant of hypergraphs extends the Stanley…

By a famous result, functions in backward shift invariant subspaces in Hardy spaces are characterized by the fact that they admit a pseudocontinuation a.e. on $\T$. More can be said if the spectrum of the associated inner function has holes…

We propose and implement a lattice scheme for coherently manipulating atomic spins. Using the vector light shift and a superlattice structure, we demonstrate experimentally the capability on parallel spin addressing in double-wells and…

We study nested loops in zero sets of sums of Laplace eigenfunctions on closed surfaces. In the real-analytic category, answering a question of Logunov, we prove a uniform bound for the number of rooted double nests in terms of the surface,…

It is known that the $L^{2}$-norms of a harmonic function over spheres satisfies some convexity inequality strongly linked to the Almgren's frequency function. We examine the $L^{2}$-norms of harmonic functions over a wide class of evolving…

We study proportions of consecutive occurrences of permutations of a given size. Specifically, the feasible limits of such proportions on large permutations form a region, called feasible region. We show that this feasible region is a…

This work presents a family of fiber bundles where the total spaces are associated with holomorphic functions on several complex variables and the basis spaces extend the notion of quaternionic slice regular functions of several…

Let $d$ be a square free positive integer and $\mathbb{Q}(\sqrt{d})$ a totally real quadratic field over $\mathbb{Q}$. We show there exists an arithmetic lattice L in $SL(8,\mathbb{R})$ with entries in the ring of integers of…

Let $\Omega \subset \mathbb{R}$ be a compact set with measure $1$. If there exists a subset $\Lambda \subset \mathbb{R}$ such that the set of exponential functions $E_{\Lambda}:=\{e_\lambda(x) = e^{2\pi i \lambda x}|_\Omega :\lambda \in…

Understanding how two tables overlap is useful for many data management tasks, but challenging because tables often differ in row and column orders and lack reliable metadata in practice. Prior work defines the largest rectangular overlap,…

It is shown that every algebra over the chain operad of the little disks operad gives naturally rise to a Hertling-Manin's F-manifold, that is a smooth manifold equipped with an integrable graded commutative associative product on the…

C. Greene introduced the shuffle lattice as an idealized model for DNA mutation and discovered remarkable combinatorial and enumerative properties of this structure. We attempt an explanation of these properties from a lattice-theoretic…

We construct a 2D holographic ionic lattice with hyperscaling-violating infrared geometry and study single-electron spectral functions ("ARPES photoemission curves") on this background. The spectra typically show a three-peak structure,…