Existence criterion for Hall subgroups of finite groups

In the paper we obtain an existence criterion for Hall subgroups of finite groups in terms of a composition series.Comment: We made some editor corrections in the tex

Hierarchical Self-Assembly of Supramolecular Helical Fibres from Amphiphilic C3-Symmetrical Functional Tris(tetrathiafulvalenes)

The preparation and self-assembly of the enantiomers of a series of C3-symmetric compounds incorporating three tetrathiafulvalene (TTF) residues is reported. The chiral citronellyl and dihydrocitronellyl alkyl chains lead to helical one dimensional stacks in solution. Molecular mechanics and dynamics simulations combined with experimental and theoretical circular dichroism support the observed helicity in solution. These stacks self-assemble to give fibres that have morphologies that depend on the nature of the chiral alkyl group and the medium in which the compounds aggregate. An inversion of macroscopic helical morphology of the citronellyl compound is observed when compared to analogous 2-methylbutyl chains, which is presumably a result of the stereogenic centre being further away from the core of the molecule. This composition still allows both morphologies to be observed, whereas an achiral compound shows no helicity. The morphology of the fibres also depends on the flexibility at the chain ends of the amphiphilic components, as there is not such an apparently persistent helical morphology for the dihydrocitronellyl derivative as for that prepared from citronellyl chains

Distributed flow optimization and cascading effects in weighted complex networks

We investigate the effect of a specific edge weighting scheme $\sim (k_i k_j)^{\beta}$ on distributed flow efficiency and robustness to cascading failures in scale-free networks. In particular, we analyze a simple, yet fundamental distributed flow model: current flow in random resistor networks. By the tuning of control parameter $\beta$ and by considering two general cases of relative node processing capabilities as well as the effect of bandwidth, we show the dependence of transport efficiency upon the correlations between the topology and weights. By studying the severity of cascades for different control parameter $\beta$, we find that network resilience to cascading overloads and network throughput is optimal for the same value of $\beta$ over the range of node capacities and available bandwidth

Integrating fluctuations into distribution of resources in transportation networks

We propose a resource distribution strategy to reduce the average travel time in a transportation network given a fixed generation rate. Suppose that there are essential resources to avoid congestion in the network as well as some extra resources. The strategy distributes the essential resources by the average loads on the vertices and integrates the fluctuations of the instantaneous loads into the distribution of the extra resources. The fluctuations are calculated with the assumption of unlimited resources, where the calculation is incorporated into the calculation of the average loads without adding to the time complexity. Simulation results show that the fluctuation-integrated strategy provides shorter average travel time than a previous distribution strategy while keeping similar robustness. The strategy is especially beneficial when the extra resources are scarce and the network is heterogeneous and lowly loaded.Comment: 14 pages, 4 figure

Optimal transport on wireless networks

We present a study of the application of a variant of a recently introduced heuristic algorithm for the optimization of transport routes on complex networks to the problem of finding the optimal routes of communication between nodes on wireless networks. Our algorithm iteratively balances network traffic by minimizing the maximum node betweenness on the network. The variant we consider specifically accounts for the broadcast restrictions imposed by wireless communication by using a different betweenness measure. We compare the performance of our algorithm to two other known algorithms and find that our algorithm achieves the highest transport capacity both for minimum node degree geometric networks, which are directed geometric networks that model wireless communication networks, and for configuration model networks that are uncorrelated scale-free networks.Comment: 5 pages, 4 figure

Consequences of Quadratic Frictional Force on the One Dimensional Bouncing Ball Model

Some dynamical properties of the one dimensional Fermi accelerator model, under the presence of frictional force are studied. The frictional force is assumed as being proportional to the square particle's velocity. The problem is described by use of a two dimensional non linear mapping, therefore obtained via the solution of differential equations. We confirm that the model experiences contraction of the phase space area and in special, we characterized the behavior of the particle approaching an attracting fixed point. © 2007 American Institute of Physics