Related papers: Problems 85 and 87 of Birkhoff's "Lattice theory"

This is a new version of our previous work. In this version, we fill a gap included in the original proof of Theorem 1.1 in our previous paper entitled "An iterative method for Kirchhoff type equations and its applications".

We introduce and examine order convergence and the interval topology on partially ordered sets in general. Problem 76 of Birkhoff's "Lattice Theory" asks whether for complete Boolean algebras the order topology and the interval topology…

This paper concerns the number of lattice points in a circle.

A partial algebra construction of Gr\"atzer and Schmidt from "Characterizations of congruence lattices of abstract algebras" (Acta Sci. Math. (Szeged) 24 (1963), 34-59) is adapted to provide an alternative proof to a well-known fact that…

We discuss initial value problems for time evolution equations in one dimensional space which are expressed by the lattice operators and propose some new equations to which complexity of solutions is of polynomial class. Novel type of…

In this paper we are concerned with three lattice problems: the lattice packing problem, the lattice covering problem and the lattice packing-covering problem. One way to find optimal lattices for these problems is to enumerate all finitely…

This contains Part I of the book: Congruence lattices of finite lattices, which covers about 80 years of research and more than 250 papers.

We present a theory of lazy imperative timing.

Sources of uncertainties in perturbative calculations, tadpole improvement and its role in lattice perturbation theory, and six recent calculations are discussed.

We reconstruct a function by values of its Segal-Bargmann transform at points of a lattice.

We present a method to obtain families of lattice equations. Specifically we focus on two of such families, which include 3-parameters and their members are connected through B\"acklund transformations. At least one of the members of each…

Reducing the NP-problems to the convex/linear analysis on the Birkhoff polytope.

In this paper we study an analogue of the classical Riemann-Hilbert problem stated for the classes of difference and $q$-difference systems. The Birkhoff's existence theorem was generalized in this paper.

Methods are described for the solution of linear inference problems subject to deterministic constraints. The approach builds on work by Backus (1970a,b,c) and Parker (1977), but a range useful advances are suggested to address both…

We here announce and outline a solution of this major and longstanding foundational problem, dealing with all seven of its heavily-interrelated local facets.

We provide infinitely many solutions of a Dirichlet problem on balls.

The following work is an exploration into certain topics in the broad world of integrable models, both classical and quantum, and consists of two main parts of roughly equal length. The first part, consisting of chapters 1-3, concerns…

We study the generalisation of Baxter's three-colour problem to a random lattice. Rephrasing the problem as a matrix model problem we discuss the analyticity structure and the critical behaviour of the resulting matrix model. Based on a set…

We survey the classical results of the Dirichlet Approximation Theorem.

Several open problems in algebraic logic are solved.