Related papers: Bipolarization of posets and natural interpolation
We establish a hierarchy of weighted majorization relations for the singularities of generalized Lam\'e equations and the zeros of their Van Vleck and Heine-Stieltjes polynomials as well as for multiparameter spectral polynomials of higher…
We develop a combinatorial and order-theoretic framework for shuffles, understood as ordered concatenations of indexed families of sequences that induce total orders on the natural numbers. Motivated by the classical \v{S}arkovski\u{i}…
We introduce Craig interpolation and related notions such as uniform interpolation, Beth definability, and theory decomposition in classical propositional logic. We present four approaches to computing interpolants: via quantifier…
A bipartite covering of a (multi)graph $G$ is a collection of bipartite graphs, so that each edge of $G$ belongs to at least one of them. The capacity of the covering is the sum of the numbers of vertices of these bipartite graphs. In this…
So-called polar liquid crystals possess spontaneous long-range mutual orientation of their electric dipole moments, conferring bulk polarity to fluid phases of matter. The combination of polarity and fluidity leads to complex phase…
We show how to develop an expansion of nearly oblate systems in terms of a set of potential-density pairs. A harmonic (multipole) structure is imposed on the potential set at infinity, and the density can be made everywhere regular. We…
Coxeter polynomials are important homological invariants that are defined for a large class of finite-dimensional algebras. It is of particular interest to develop methods to compute these polynomials. We define the notion of insertion of a…
We give an explicit sequence of polarizations such that for every measurable function, the sequence of iterated polarizations converge to the symmetric rearrangement of the initial function.
In this paper we develop a capacities theory connected with the fractional Sobolev spaces with variable exponents. Two kinds of capacities are studied: Sobolev capacity and relative capacity. Basic properties of capacities, including…
We apply a notion of geodesics of plurisubharmonic functions to interpolation of compact subsets of $C^n$. Namely, two non-pluripolar, polynomially closed, compact subsets of $C^n$ are interpolated as level sets $L_t=\{z: u_t(z)=-1\}$ for…
For a given poset, we consider its representations by systems of subspaces of a unitary space ordered by inclusion. We classify such systems for all posets for which an explicit classification is possible.
We consider the equilibrium equations for a linearized Cosserat material and provide two perspectives concerning well-posedness. First, the system can be viewed as the Hodge Laplace problem on a differential complex. On the other hand, we…
A generalization of the polar coding scheme called mixed-kernels is introduced. This generalization exploits several homogeneous kernels over alphabets of different sizes. An asymptotic analysis of the proposed scheme shows that its…
The boolean elements of a Coxeter group have been characterized and shown to possess many interesting properties and applications. Here we introduce "prism permutations," a generalization of those elements, characterizing the prism…
We study the integrability of the general two-dimensional Zakharov-Shabat systems, which appear in application of the inverse scattering transform (IST) to an important class of nonlinear partial differential equations (PDEs) called…
The main purpose of this article is to study from the geometric point of view the problem of limit cycles bifurcation of perturbed completely integrable systems.
We consider an integral operator $\mathcal{I}$, special instances of which was studied in various contexts. Using an appropriate transformation we write this operator in terms of weighted composition operators. Then, we provide a…
Craig interpolation is a fundamental property of classical and non-classic logics with a plethora of applications from philosophical logic to computer-aided verification. The question of which interpolants can be obtained from an…
The polarization of optical fields is a crucial degree of freedom in the all-optical analogue of electromagnetically induced transparency (EIT). However, the physical origins of EIT and polarization induced phenomena have not been well…
We classify finite posets with a particular sorting property, generalizing a result for rectangular arrays. Each poset is covered by two sets of disjoint saturated chains such that, for any original labeling, after sorting the labels along…