相关论文: Lattices, interpolation, and set theory

We introduce the concept of basis for a lattice. This basis plays a vital role to determine the completeness and consistency of the lattice. Weighted lattices are introduced and its complexity is formulated. Some axiomatic systems,…

We survey results devoted to the lattice of varieties of monoids. Along with known results, some unpublished results are given with proofs. A number of open questions and problems are also formulated.

We consider certain scalar product of symmetric functions which is parameterized by a function $r$ and an integer $n$. One the one hand we have a fermionic representation of this scalar product. On the other hand we get a representation of…

In this paper we study possibilities of interpolation and symbol elimination in extensions of a theory $\mathcal{T}_0$ with additional function symbols whose properties are axiomatised using a set of clauses. We analyze situations in which…

Dualization of a monotone Boolean function on a finite lattice can be represented by transforming the set of its minimal 1 to the set of its maximal 0 values. In this paper we consider finite lattices given by ordered sets of their meet and…

This paper investigates the theory of lattices, focusing on extending lattices relative to abstract classes, modular lattices, and torsion lattices. Definitions of type-1 and type-2 extending lattices are provided, along with their weakly…

In this paper, we survey results regarding the interlace polynomial of a graph, connections to such graph polynomials as the Martin and Tutte polynomials, and generalizations to the realms of isotropic systems and delta-matroids.

We consider approximation by functions with finite support and characterize its approximation spaces in terms of interpolation spaces and Lorentz spaces.

This note points out a lemma on closures of monotonic increasing functions and shows how it is applicable to decomposition and modularity for semantics defined as the least fixedpoint of some monotonic function. In particular it applies to…

Given a finite number of samples of a continuous set-valued function F, mapping an interval to compact subsets of the real line, we develop good approximations of F, which can be computed efficiently.

We study the approximation of maps into complex manifolds along with interpolation on certain compact subsets of the plane. Results are also obtained regarding approximation and interpolation of sections of holomorphic submersions.

We propose a unified view of the polarity of functions, that encompasses all specific definitions, generalizes several well-known properties and provides new results. We show that bipolar sets and bipolar functions are isomorphic lattices.…

Asymptotic relations between zeta functions (such as, $\zeta(s),\,\beta(s)$, and other Dirichlet $L$-functions) and interpolation differences of functions like $\vert y\vert^s$ and their interpolating entire functions of exponential type…

We translate notions and results of decomposition and dimension theories for module categories, into the lattice environment. In particular we translate dimension theory in module categories to complete modular upper-continuous lattices.

An updated review is presented of our understanding of color confinement. Lattice results on condensation of magnetic charges are discussed. The role of vortices is analysed.

Radical binomial ideals associated with finite lattices are studied. Gr\"obner basis theory turns out to be an efficient tool in this investigation.

A lattice L is called opc if every monotone function f : L^n -> L is induced by a polynomial. We show here: If L is a lattice with the interpolation property whose cardinality is a strong limit cardinal of uncountable cofinality, then some…

Every lattice is isomorphic to a lattice whose elements are sets of sets, and whose operations are intersection and an operation extending the union of two sets of sets A and B by the set of all sets in which the intersection of an element…

This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…

In our study of electrical networks we develop two themes: finding explicit formulas for special classes of functions defined on the vertices of a transient network, namely monopoles, dipoles, and harmonic functions. Secondly, our interest…