On the Movement of Transitive Permutation p-Groups

Let G be a transitive permutation group on a set and m a positive integer. If | – | m for every subset of and all g G, then || 2mp/(p – 1) where p is the least odd prime dividing |G|. It was shown by Mann and Praeger [13] that, for p = 3, the 3-groups G which attain this bound have exponent p. In this paper we will show a generalization of this result for any odd primes.AMS Subject Classification (2000), 20BXX     

A Dynamic Domain Contraction Algorithm for Nonconvex Piecewise Linear Network Flow Problems*

We consider the Nonconvex Piecewise Linear Network Flow Problem (NPLNFP) which is known to be -hard. Although exact methods such as branch and bound have been developed to solve the NPLNFP, their computational requirements increase exponentially with the size of the problem. Hence, an efficient heuristic approach is in need to solve large scale problems appearing in many practical applications including transportation, production-inventory management, supply chain, facility expansion and location decision, and logistics. In this paper, we present a new approach for solving the general NPLNFP in a continuous formulation by adapting a dynamic domain contraction. A Dynamic Domain Contraction (DDC) algorithm is presented and preliminary computational results on a wide range of test problems are reported. The results show that the proposed algorithm generates solutions within 0 to 0.94 % of optimality in all instances that the exact solutions are available from a branch and bound method.     

Universal Amplitude Ratios in the Critical Two-Dimensional Ising Model on a Torus

Using results from conformal field theory, we compute several universal amplitude ratios for the two-dimensional Ising model at criticality on a symmetric torus. These include the correlation-length ratio x =lim _L (L)/L and the first four magnetization moment ratios V _2n = ²ⁿ / ^{2 n} . As a corollary we get the first four renormalized 2n-point coupling constants for the massless theory on a symmetric torus, G*_2n . We confirm these predictions by a high-precision Monte Carlo simulation.     

Stable power laws in variable economies; Lotka-Volterra implies Pareto-Zipf

In recent years we have found that logistic systems of the Generalized Lotka-Volterra type (GLV) describing statistical systems of auto-catalytic elements posses power law distributions of the Pareto-Zipf type. In particular, when applied to economic systems, GLV leads to power laws in the relative individual wealth distribution and in market returns. These power laws and their exponent α are invariant to arbitrary variations in the total wealth of the system and to other endogenously and exogenously induced variations. Received 31 December 2001     

The mechanism of the increase of the generalized dimension of a filtered chaotic time series

The determination of the attractor dimension from an experimental time series may be affected by the influence of filters which are incorporated into many measuring processes. While this is expected from the Kaplan-Yorke conjecture, we show that for one-dimensional maps a weak filter can induce a self-similarity which is responsible for the increase of the Hausdorff dimension. We are able to calculate the increase of the generalized dimensionD _q for the filtered time series of the logistic mapx _i +1=rx _i (1–x _i ) atr=4 analytically.     

Renormalisation group approach to the ideal Bose gas ind dimensions

Critical behaviour of ad-dimensional ideal Bose gas is investigated from the point of view of the renormalisation-group approach. Rescaling of quantum-field amplitudes is avoided by introducing a scaling variable inversely proportional to the thermal momentum of the particles. The scaling properties of various thermodynamic quantities are seen to emerge as a consequence of the irrelevant nature of this variable. Critical behaviour is discussed at fixed particle density as well as at fixed pressure. Connection between susceptibility and correlation function of the order-parameter for a quantum system is elucidated.     

Cluster validity for fuzzy clustering algorithms

The proportion exponent is introduced as a measure of the validity of the clustering obtained for a data set using a fuzzy clustering algorithm. It is assumed that the output of an algorithm includes a fuzzy nembership function for each data point. We show how to compute the proportion of possible memberships whose maximum entry exceeds the maximum entry of a given membership function, and use these proportions to define the proportion exponent. Its use as a validity functional is illustrated with four numerical examples and its effectiveness compared to other validity functionals, namely, classification entropy and partition coefficient.     

Stochastic filtering of multiphase transport phenomena

Whether or not a multiphase mixture is to be considered heterogeneous is a function of scale and hence also a function of the measurement process. Heterogeneities manifested through the measurement process and sampling frequency (extrinsic heterogeneity) are discussed in relationship to the intrinsic heterogeneity associated with the true physical environment. The question of whether or not a multiphase environment may be scaled is partially a function of the scale of the extrinsic heterogeneity of interest. Thus, it is also a function of the instrumental apparatus, which implies that the instrument must also be scaled. We review restrictive scaling constraints in frequency space that an instrument must satisfy for proper scaling of an experiment. Cushman (1984 Water Resour. Res. and 1985 Acta Appl. Math) developed a theory that incorporates the scale and measurement process directly into the multiphase transport equations and which in turn allows for correlation of field properties over scales of motion. We discuss a generalization of this theory which accounts for integral representations of distributional stochastic processes as a function of the scale of the instrument used in the measurement of the field variables. This allows us to solve the stochastic transport equations in an operational setting, i.e., in terms of measurable quantities. Throughout the article examples are presented to illustrate the concepts.     

Heat capacity of MnBr2·4H2O near the antiferromagnetic transition temperature

Heat capacity of MnBr₂·4H₂O has been measured in the critical region around the Neel temperature. The data can be fitted, over a restricted range of |t|⩽10⁻², to the asymptotic power law. The critical exponents and the amplitudesA andA′ are not consistent with any theoretic predictions. However when scaling constraints are imposed, their values agree with the parameters of Ising model. Corrections to scaling are necessary to extend the range of the fit to |t|>10⁻². The correction terms are asymmetric giving −1·15±0·25 as the ratio of the amplitudes of the lowest order correction terms,D andD′ above and belowT _c. This value is in agreement with the recent predictions of the renormalisation group theory.     

Structure function of pion and its compositeness

Using recent data on pion structure function and a rigorous inequality obtained recently using unitarity analyticity and Bjorken scaling a numerical upper bound on the wave-function-renormalisation constant of pion is computed. By the (somewhat drastic) act of neglecting the sea, it is shown that the bare part of the pion can be no more than 38%.