A novel higher order large-domain hierarchical finite-element technique using curl-conforming vector basis functions constructed from standard Legendre polynomials on generalized curvilinear hexahedral elements is proposed for electromagnetic modeling. The technique combines the inherent modeling flexibility of hierarchical elements with excellent orthogonality and conditioning properties of Le...

Series-parallel orders are deened as the least class of partial orders containing the one-element order and closed by ordinal sum and disjoint union. From this inductive deenition, it is almost immediate that any series-parallel order may be represented by an algebraic expression, which is unique up to the associativity of ordinal sum and to the associa-tivivity and commutativity of disjoint un...

Trotter conjectured that dim P × Q ≥ dimP + dimQ − 2 for all posets P and Q. To shed light on this, we study the k-dimension of products of finite orders. For k ∈ o(ln lnn), the value 2 dimk(P )−dimk(P ×P ) is unbounded when P is an n-element antichain, and 2dim2(mP ) − dim2(mP × mP ) is unbounded when P is a fixed poset with unique maximum and minimum. For products of the “standard” orders Sm ...

We solve an interesting optimization problem motivated by tolerancing metrology, paper position sensing, and facility location: What rectangle fits best a given set of points? This problem has relations to the minimum width annulus problem and also to the largest empty rectangle problem for both of which O(n log n) time solutions are not known. Nevertheless, for our problem there is a linear ti...

The Largest Empty Circle problem seeks the largest circle centered within the convex hull of a set P of n points in R2 and devoid of points from P . In this paper, we introduce a query version of this well-studied problem. In our query version, we are required to preprocess P so that when given a query line Q, we can quickly compute the largest empty circle centered at some point on Q and withi...

Let R be a root system with fixed basis ~' and let W be its Weyl group. For every element w ~ W, there exists a natural correspondence between reduced decompositions of w and some linear orders of the set of inversions of w. We study combinatorial properties of these orders. Furthermore, in the case of a symmetric group, for any permutation w we construct a linear action of the symmetric group ...

A higher order hybrid finite element – method of moments (FEM-MoM) technique for threedimensional analysis and design of radiating and scattering structures is presented. The technique uses generalized parametric hexahedral and quadrilateral elements of arbitrary geometrical orders in conjunction with curland divergence-conforming hierarchical polynomial vector basis functions of arbitrary appr...