How large are the level sets of the Takagi function?

Let T be Takagi's continuous but nowhere-differentiable function. This paper considers the size of the level sets of T both from a probabilistic point of view and from the perspective of Baire category. We first give more elementary proofs of three recently published results. The first, due to Z. Buczolich, states that almost all level sets (with respect to Lebesgue measure on the range of T) are finite. The second, due to J. Lagarias and Z. Maddock, states that the average number of points in a level set is infinite. The third result, also due to Lagarias and Maddock, states that the average number of local level sets contained in a level set is 3/2. In the second part of the paper it is shown that, in contrast to the above results, the set of ordinates y with uncountably infinite level sets is residual, and a fairly explicit description of this set is given. The paper also gives a negative answer to a question of Lagarias and Maddock by showing that most level sets (in the sense of Baire category) contain infinitely many local level sets, and that a continuum of level sets even contain uncountably many local level sets. Finally, several of the main results are extended to a version of T with arbitrary signs in the summands.Comment: Added a new Section 5 with generalization of the main results; some new and corrected proofs of the old material; 29 pages, 3 figure

Random walks and polymers in the presence of quenched disorder

After a general introduction to the field, we describe some recent results concerning disorder effects on both `random walk models', where the random walk is a dynamical process generated by local transition rules, and on `polymer models', where each random walk trajectory representing the configuration of a polymer chain is associated to a global Boltzmann weight. For random walk models, we explain, on the specific examples of the Sinai model and of the trap model, how disorder induces anomalous diffusion, aging behaviours and Golosov localization, and how these properties can be understood via a strong disorder renormalization approach. For polymer models, we discuss the critical properties of various delocalization transitions involving random polymers. We first summarize some recent progresses in the general theory of random critical points : thermodynamic observables are not self-averaging at criticality whenever disorder is relevant, and this lack of self-averaging is directly related to the probability distribution of pseudo-critical temperatures $T_c(i,L)$ over the ensemble of samples $(i)$ of size $L$. We describe the results of this analysis for the bidimensional wetting and for the Poland-Scheraga model of DNA denaturation.Comment: 17 pages, Conference Proceedings "Mathematics and Physics", I.H.E.S., France, November 200

Chemical and physical characterization of the isolated protostellar source CB68: FAUST IV

Interstellar matter and star formatio

Further study of the E/f1 (1420) meson in central production

We have studied the reactions {Mathematical expression} where the {Mathematical expression} system is centrally produced, at 85 GeV/c and 300 GeV/c using the CERN Omega spectrometer. A spin-parity analysis of the KS0K±π∓ system shows the presence of a strong JPC=1++ signal which we identify as the E/f1 (1420) meson. We also find evidence for the decay E/f1(1420)→KS0KS0π0 which determines the C-parity of this state to be positive. Alternative explanations of the data have been tested and ruled out. Hence we obtain the quantum numbers of the E/f1 (1420) to be IG(JPC)=0+(1+). © 1992 Springer-Verlag

Has increasing the age for child passengers to wear child restraints improved the extent to which they are used? Results from an Australian focus group and survey study

Acknowledgement that many children in Australia travel in restraints that do not offer them the best protection has led to recent changes in legislation such that the type of restraint for children under 7 years is now specified. This paper reports the results of two studies (observational; focus group/ survey) carried out in the state of Queensland to evaluate the effectiveness of these changes to the legislation. Observations suggested that almost all of the children estimated as aged 0-12 years were restrained (95%). Analysis of the type of restraint used for target-aged children (0-6 year olds) suggests that the proportion using an age-appropriate restraint has increased by an estimated 7% since enactment of the legislation. However, around 1 in 4 children estimated as aged under 7 years were using restraints too large for good fit. Results from the survey and focus group suggested parents were supportive of the changes in legislation. Non-Indigenous parents agreed that the changes had been necessary, were effective at getting children into the right restraints, were easy to understand as well as making it clear what restraint to use with children. Moreover, they did not see the legislation as too complicated or too hard to comply with. Indigenous parents who participated in a focus group also regarded the legislation as improving children’s safety. However, they identified the cost of restraints as an important barrier to compliance. In summary, the legislation appears to have had a positive effect on compliance levels and on raising parental awareness of the need to restrain children child-specific restraints for longer. However, it would seem that an important minority of parents transition their children into larger restraints too early for optimal protection. Intervention efforts should aim to better inform these parents about appropriate ages for transition, especially from forward facing childseats. This could potentially be through use of other important transitions that occur at the same age, such as starting school. The small proportion of parents who do not restrain their children at all are also an important community sector to target. Finally, obtaining restraints presents a significant barrier to compliance for parents on limited incomes and interventions are needed to address this