In this paper, we shall give an explicit Gauss diagram formula for the Kontsevich integral of links up to degree four. This practical formula enables us to actually compute the Kontsevich integral in a combinatorial way.

Earned Value Management Method (EVM), widely used in the world, is a project management method of costschedule integrated control. But the traditional EVM sometimes cannot provide an accurate result. In this paper, a practical method is given to analyze the project performance, in which the Network Diagram Method and the Critical Path Method have been introduced into EVM system that can better ...

We first note that block diagrams have been important for the learning of GPSS and have been used in most GPSS text books. The full value of block diagrams is obtained first when they can be automatically generated from program code and that block diagrams in turn can generate code. The computer generation of block diagrams requires, however, very exact rules for the block diagrams. This is lac...

We construct an involution on set partitions which keeps track of the numbers of crossings, nestings and alignments of two edges. We derive then the symmetric distribution of the numbers of crossings and nestings in partitions, which generalizes a recent result of Klazar and Noy in perfect matchings. By factorizing our involution through bijections between set partitions and some path diagrams ...

This paper shows that a macroscopic fundamental diagram (MFD) relating flow and average density must exist on any street with blocks of diverse widths and lengths, but no turns, even if all or some of the intersections are controlled by arbitrarily timed traffic signals. The timing patterns are assumed to be fixed in time. Exact expressions in terms of a shortest path recipe are given, both, fo...

In typical 2D Voronoi diagrams, the distance from a site to a point in the plane is unaffected by the existance of other sites. In 2D pursuit/evasion Voronoi diagrams, the distance from an evader to a point is the length of the shortest path to that point that avoids all pursuers. Since pursuers can move, the paths that evaders follow to reach certain points in the plane can be quite complicate...

In the last quarter of the twentieth century, an innovative three-dimensional graphical technique was introduced into biological oceanography and ecology, where it spread rapidly. Used to improve scientists' understanding of the importance of scale within oceanic ecosystems, this influential diagram addressed biological scales from phytoplankton to fish, physical scales from diurnal tides to oc...

We analyze the impact of the recent Feynman-diagrammatic (FD) two-loop results for the mass of the lightest CP-even Higgs boson in the MSSM on the theoretical upper bound for mh as a function of tanβ. The results are compared with previous results obtained by renormalization group (RG) methods. The incorporation of dominant FD two-loop corrections into the decay width Γ(h → f f̄) is also discuss...

In this study, an extended stress-based forming limit diagram (FLD) for prediction of necking based on the Marciniak and Kucznski (M-K) model is represented and applied in tube hydroforming. The bulge forming of a straight tube is simulated by finite element method and verified with published experimental data. This adaptive simulation technique is based on the ability to detect the onset an...

A Bratteli diagram is a type of graph in which the vertices are split into finite subsets occupying an infinite sequence of levels, starting with a bottom level and moving to successively higher levels along edges connecting consecutive levels. An information source on a Bratteli diagram consists of a sequence of PMFs on the vertex sets at each level that are compatible under edge transport. By...