The Action Functional for Moyal Planes

Modulo some natural generalizations to noncompact spaces, we show in this Letter that Moyal planes are nonunital spectral triples in the sense of Connes. The action functional of these triples is computed, and we obtain the expected result, i.e. the noncommutative Yang–Mills action associated with the Moyal product. In particular, we show that Moyal gauge theory naturally fits into the rigorous framework of noncommutative geometry.     

A constructive characterization of the split closure of a mixed integer linear program

Two independent proofs of the polyhedrality of the split closure of mixed integer linear program have been previously presented. Unfortunately neither of these proofs is constructive. In this paper, we present a constructive version of this proof. We also show that split cuts dominate a family of inequalities introduced by Köppe and Weismantel.     

Generic Transport Aft-body Drag Reduction using Active Flow Control

Active flow-separation control is an effective and efficient mean for drag reduction and unsteady load alleviation resulting from locally or massively separated flow. Such a situation occurs in configurations where the aerodynamic performance is of secondary importance to functionality. The performance of heavy transport helicopters and aeroplanes, having a large, and almost flat, aft loading ramp suffer from the poor aerodynamics of the aft body. Hence, a combined experimental and numerical investigation was undertaken on a generic transport aeroplane/helicopter configuration. The experimental study provided surface pressures, direct drag measurements, surface and smoke flow visualization. The baseline flow was numerically analyzed, using finite volume solutions of the RANS equations. The baseline flow around the model was insensitive to the Reynolds number in the range it was tested. The flow separating from the aft body was characterized by two main sources of drag and unsteadiness. The first is a separation bubble residing at the lower ramp corner and the second is a pair of vortex systems developing and separating from the sides of the ramp. As the model incidence is decreased, the pair of vortex systems also penetrates deeper towards the centerline of the ramp, decreasing the pressure and increasing the drag. As expected, the ramp lower corner bubble was highly receptive to periodic excitation introduced from four addressable piezo-fluidic actuators situated at the ramp lower corner. Total drag was reduced by 3–11%, depending on the model incidence. There are indications that the flow in the wake of the model is also significantly steadier when the bubble at the lower ramp corner is eliminated. The vortex system is tighter and steadier when the ramp-corner bubble is eliminated.     

A polynomial algorithm for one problem of guillotine cutting

We consider the problem of guillotine cutting a rectangular sheet into two rectangular pieces without rotations. The question is whether there exists a cutting pattern with given numbers of occurrences of both rectangular pieces. A polynomial time algorithm is described to construct the convex hull of solutions to this problem.     

Simplest optimal cutting patterns for equal rectangles

This paper presents branch-and-bound algorithms that can guarantee the simplest optimal cutting patterns of equal rectangles. An existing linear algorithm determines the global upper bound exactly. The branching process ends when a branch of a lower bound equal to the global upper bound is found.     

A Liouville type theorem for polyharmonic elliptic systems

In this paper, we consider the polyharmonic system m(−Δ)U=Vq,m(−Δ)V=Up in RN, for m>1, N>2m, with p?1, q?1, but not both equal to 1, where m(−Δ) is the polyharmonic operator. Set α=2m(q+1)/(pq−1), β=2m(p+1)/(pq−1), for α,β∈[(N−2)/2,N−2m), we prove the nonexistence of positive solutions.     

基于单纯形方法的双层线性规划全局优化算法

通过分析双层线性规划可行域的结构特征和全局最优解在约束域的极点上达到这一特性,对单纯形方法中进基变量的选取法则进行适当修改后,给出了一个求解双层线性规划局部最优解方法,然后引进上层目标函数对应的一种割平面约束来修正当前局部最优解,直到求得双层线性规划的全局最优解.提出的算法具有全局收敛性,并通过算例说明了算法的求解过程.     

A hybrid genetic algorithm-heuristic for a two-dimensional orthogonal packing problem

In this paper we address a two-dimensional (2D) orthogonal packing problem, where a fixed set of small rectangles has to be placed on a larger stock rectangle in such a way that the amount of trim loss is minimized. The algorithm we propose hybridizes a placement procedure with a genetic algorithm based on random keys. The approach is tested on a set of instances taken from the literature and compared with other approaches. The computation results validate the quality of the solutions and the effectiveness of the proposed algorithm.     

Generalised 2-circulant inequalities for the max-cut problem

The max-cut problem is a fundamental combinatorial optimisation problem, with many applications. Poljak and Turzik found some facet-defining inequalities for the associated polytope, which we call 2-circulant inequalities. We present a more general family of facet-defining inequalities, an exact separation algorithm that runs in polynomial time, and some computational results.