We present the two-loop pure gauge contribution to the gluon-gluon scattering amplitude with maximal helicity violation. Our construction of the amplitude does not rely directly on Feynman diagrams, but instead uses its analytic properties in 4 − 2 dimensions. We evaluate the loop integrals appearing in the amplitude through O( ) in terms of polylogarithms.

MM-Path, an acronym for Method/Message Path, describes the dynamic interactions between methods in object-oriented systems. This paper discusses the classifications of MM-Path, based on the characteristics of object-oriented software. We categorize it according to the generation reasons, the effect scope and the composition of MM-Path. A formalized representation of MM-Path is also proposed, wh...

An enhanced unfolding Inverse Finite Element Method (IFEM) has been used together with an extended strain-based forming limit diagram (EFLD) to develop a fast and reliable approach to predict the feasibility of the deep drawing process of a part and determining where the failure or defects can occur. In the developed unfolding IFEM, the meshed part is properly fold out on the flat sheet and tre...

Several constructions on directed graphs originating in the study of flow equivalence symbolic dynamics (e.g., splittings and delays) are known to preserve Morita class Leavitt path algebras over any coefficient field F. We prove that many these results not only independent F, but largely linear algebra altogether. do this by formulating proving generalisations theorems which category F-vector ...

We are given a transportation line where displacements happen at a bigger speed than in the rest of the plane. A shortest time path is a path between two points which takes less than or equal time to any other. We consider the time to follow a shortest time path to be the time distance between the two points. In this paper, we give a simple algorithm for computing the Time Voronoi Diagram, that...

Robotic systems are usually built as independent agents that collaborate to accomplish a specific task. Analysis of robot path planning consists of route planning and path generation. We will show how to apply the Cell-DEVS formalism and the CD++ toolkit for these tasks. We present a Cell-DEVS model for route planning, which, based on the obstacles, finds different paths available and creates a...

Given k disjoint regions in the plane or space, the bridge problem asks for k − 1 line segments (optimal bridges) which connect these regions so as to minimize the length of the longest path between two points in the final connected region. We present O(n) and O(n2) time algorithms for finding an optimal bridge between two convex regions in the plane and space, respectively. An important proper...

The size of a Reduced Ordered Binary Decision Diagram (ROBDD) is directly influenced by the variables ordering technique used to build the ROBDD. Therefore various variables ordering techniques have been proposed to minimize the size of BDDs. Unfortunately there is no unique method that can be used to obtain the least number of nodes for all BDDs. In this paper we propose two new methods based ...