Two loops calculation in chiral perturbation theory and the unitarization program of current algebra

In this paper we compare two loop Chiral Perturbation Theory (ChPT) calculation of pion-pion scattering with the unitarity second order correction to the current algebra soft-pion theorem. It is shown that both methods lead to the same analytic structure for the scattering amplitude.Comment: 13 pages, Revtex 3.0, no figures, submitted to Phys. Lett.

Families of nested completely regular codes and distance-regular graphs

In this paper infinite families of linear binary nested completely regular codes are constructed. They have covering radius $\rho$ equal to $3$ or $4$, and are $1/2^i$-th parts, for $i\in\{1,\ldots,u\}$ of binary (respectively, extended binary) Hamming codes of length $n=2^m-1$ (respectively, $2^m$), where $m=2u$. In the usual way, i.e., as coset graphs, infinite families of embedded distance-regular coset graphs of diameter $D$ equal to $3$ or $4$ are constructed. In some cases, the constructed codes are also completely transitive codes and the corresponding coset graphs are distance-transitive

Zipf's Law for web surfers

One of the main activities of Web users, known as 'surfing', is to follow links. Lengthy navigation often leads to disorientation when users lose track of the context in which they are navigating and are unsure how to proceed in terms of the goal of their original query. Studying navigation patterns of Web users is thus important, since it can lead us to a better understanding of the problems users face when they are surfing. We derive Zipf's rank frequency law (i.e., an inverse power law) from an absorbing Markov chain model of surfers' behavior assuming that less probable navigation trails are, on average, longer than more probable ones. In our model the probability of a trail is interpreted as the relevance (or 'value') of the trail. We apply our model to two scenarios: in the first the probability of a user terminating the navigation session is independent of the number of links he has followed so far, and in the second the probability of a user terminating the navigation session increases by a constant each time the user follows a link. We analyze these scenarios using two sets of experimental data sets showing that, although the first scenario is only a rough approximation of surfers' behavior, the data is consistent with the second scenario and can thus provide an explanation of surfers' behavior

Unitarized pion-nucleon scattering amplitude from inverse amplitude method

In a recent work on low energy pion-nucleon scattering, instead of using chiral perturbation theory (ChPT) amplitude, we started from a pion-nucleon {\it soft-pion} result and used elastic unitarity directly as a dynamical constraint to construct first-order unitarity corrected amplitudes. The resulting amplitudes are crossing symmetric but, as the ChPT ones, satisfy only approximate unitarity relation. In the present work, we reconsider our approach and we apply the inverse amplitude method (IAM) in order to access the energy resonance region. We present the resulting S- and P-wave phase shifts that are shown to be in qualitative agreement with experimental data.Comment: 6 pages, 3 figure

Symmetry breaking patterns of the 3-3-1 model at finite temperature

We consider the minimal version of an extension of the standard electroweak model based on the $SU(3)_c \times SU(3)_L \times U(1)_X$ gauge symmetry (the 3-3-1 model). We analyze the most general potential constructed from three scalars in the triplet representation of $SU(3)_L$, whose neutral components develop nonzero vacuum expectation values, giving mass for all the model's massive particles. {}For different choices of parameters, we obtain the particle spectrum for the two symmetry breaking scales: one where the $SU(3)_L \times U(1)_X$ group is broken down to $SU(2)_L\times U(1)_Y$ and a lower scale similar to the standard model one. Within the considerations used, we show that the model encodes two first-order phase transitions, respecting the pattern of symmetry restoration. The last transition, corresponding to the standard electroweak one, is found to be very weak first-order, most likely turning second-order or a crossover in practice. However, the first transition in this model can be strongly first-order, which might happen at a temperature not too high above the second one. We determine the respective critical temperatures for symmetry restoration for the model.Comment: 13 pages, 8 figures. Minor changes to match published versio

On the number of nonequivalent propelinear extended perfect codes

The paper proves that there exist an exponential number of nonequivalent propelinear extended perfect binary codes of length growing to infinity. Specifically, it is proved that all transitive extended perfect binary codes found by Potapov are propelinear. All such codes have small rank, which is one more than the rank of the extended Hamming code of the same length. We investigate the properties of these codes and show that any of them has a normalized propelinear representation