As our second example we consider the case where TT is a differentiable submersion (in the usual sense) of codimension 1. Thus we assume that X, B are C°°-manifolds of dimensions n + 1 and n, respectively, and that TT is a regular differentiate map. Such a submersion is orientable if the induced line element field on X is orientable, and w will be called simple if w~(b) is connected for all bÇEB.

In this article, we show the existence of certain exact sequences with respect to two homology theories, called d-homology and extended d-homology. We present sufficient conditions for the existence of long exact extended d- homology sequence. Also we give some illustrative examples.

Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Combining the use of our data structure for characterizing feasible packings with our new classes of lower bounds, and other heuristics, we develop a two-level tree search algorithm for solving higher-dimensional packing problems to optimality. Computational re...

In this paper, I show that if p is an odd prime, and if P is a finite p-group, then there exists an exact sequence of abelian groups 0→ T (P )→ D(P )→ lim ←− 1<Q≤P D (

In this paper we focus on problems characterized by an input n-node tree and a collection of subpaths. Motivated by the fact that some of these problems admit a very good approximation (or even a poly-time exact algorithm) when the input tree is a path, we develop a decomposition theorem of trees into paths. Our decomposition allows us to partition the input problem into a collection of O(log l...

This paper presents new bounds, heuristics, and an exact algorithm for the Pallet Loading Problem (PLP). PLP maximizes the number of boxes placed on a rectangular pallet. All boxes have identical rectangular dimensions and, when placed, must be located completely within the pallet. Boxes may be rotated 90 so long as they are placed with edges parallel to the pallet’s edges. The set of all PLP i...