Simulation is the research tool of choice for a majority of the mobile ad hoc network (MANET) community. However, while the use of simulation has increased, the credibility of the simulation results has decreased. To determine the state of MANET simulation studies, we surveyed the 2000-2005 proceedings of the ACM International Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc). From our survey, we found significant shortfalls. We present the results of our survey in this paper. We then summarize common simulation study pitfalls found in our survey. Finally, we discuss the tools available that aid the development of rigorous simulation studies. We offer these results to the community with the hope of improving the credibility of MANET simulation-based studies.

No abstract

Three symbolic algorithms for testing the integrability of polynomial systems of partial differential and differential-difference equations are presented. The first algorithm is the well-known Painlevé test, which is applicable to polynomial systems of ordinary and partial differential equations. The second and third algorithms allow one to explicitly compute polynomial conserved densities and higher-order symmetries of nonlinear evolution and lattice equations.The first algorithm is implemented in the symbolic syntax of both Macsyma and Mathematica. The second and third algorithms are available in Mathematica. The codes can be used for computer-aided integrability testing of nonlinear differential and lattice equations as they occur in various branches of the sciences and engineering. Applied to systems with parameters, the codes can determine the conditions on the parameters so that the systems pass the Painlevé test, or admit a sequence of conserved densities or higher-order symmetries.

No abstract

No abstract