We construct an algebraic distributive lattice D that is not isomorphic to the congruence lattice of any lattice. This solves a long-standing open problem, traditionally attributed to R. P. Dilworth, from the forties. The lattice D has compact top element and אω+1 compact elements. Our results extend to any algebra possessing a polynomially definable structure of a joinsemilattice with largest ...

A priority queue is a data type where the element with the smallest key value can be found and deleted, and new elements can be inserted. It is also called a priority queue when the element with the largest key value is wanted, instead of the smallest. In some cases, it is interesting to find and delete both the smallest and the largest element, as well as to be able to insert new elements. A s...

We focus here on a class of fourth-order parabolic equations that can be written as system second-order by introducing an auxiliary variable. design novel fully discrete mixed finite element method to approximate these equations. In our approach, we propose new techniques using the backward differentiation formula for time derivative and special technique approximation nonlinear terms. The use ...

In this series of papers, we construct operators that extend certain given functions on the boundary of a tetrahedron into the interior of the tetrahedron, with continuity properties in appropriate Sobolev norms. These extensions are novel in that they have certain polynomial preservation properties important in the analysis of high order finite elements. This part of the series is devoted to i...

Raven’s Progressive Matrices (RPMs) are a popular family of general intelligence tests, and provide a non-verbal measure of a test subject’s reasoning abilities. Traditionally RPMs have been manually designed. To make them readily available for both practice and examination, we tackle the problem of automatically synthesizing RPMs. Our goal is to efficiently generate a large number of RPMs that...