Is the Ozone Hole Over Your Classroom?

First year university science students are surveyed about their understanding of the ozone layer, ozone depletion and the effect of ozone depletion on Australia. Although students seem to understand the basic function of the ozone layer, over 65% of students incorrectly believe that the ozone hole is over Australia, and over 90% of students incorrectly believe that the ozone hole is present during the summer. Together these ideas seem to explain why nearly 75% of students blame the ozone hole for Australia’s high rate of skin cancer. Survey results also indicate that students seem confused about global warming, and the connection with ozone depletion. Conclusions from this study suggest that better teaching resources for environmental issues such as ozone depletion and global warming are needed before improvements in students’ understanding can be expected

On the scaling property in fluctuation theory for stable L\'evy processes

We find an expression for the joint Laplace transform of the law of $(T_{[x,+\infty[},X_{T_{[x,+\infty[}})$ for a L\'evy process $X$, where $T_{[x,+\infty[}$ is the first hitting time of $[x,+\infty[$ by $X$. When $X$ is an $\alpha$-stable L\'evy process, with $1<\alpha<2$, we show how to recover from this formula the law of $X_{T_{[x,+\infty[}}$; this result was already obtained by D. Ray, in the symmetric case and by N. Bingham, in the case when $X$ is non spectrally negative. Then, we study the behaviour of the time of first passage $T_{[x,+\infty[},$ conditioned to $\{X_{T_{[x,+\infty[}} -x \leq h\}$ when $h$ tends to $0$. This study brings forward an asymptotic variable $T_x^0$, which seems to be related to the absolute continuity of the law of the supremum of $X$

Quantitative evaluation of the piezoelectric response of unpoled ferroelectric ceramics from elastic and dielectric measurements: tetragonal BaTiO3_3

A method for evaluating the piezoelectric response of unpoled ferroelectric ceramics from elastic and dielectric measurements is proposed and tested on BaTiO$_3$. The method is based on the observation that the softening in a ferroelectric phase with respect to the paraelectric phase is of piezoelectric origin. The angular averages of the piezoelectric softening in unpoled ceramics are calculated for ferroelectric phases of different symmetries. The expression of the orientational average with the piezoelectric and dielectric constants of single crystal tetragonal BaTiO$_3$ from the literature reproduces well the softening of the Young's modulus of unpoled ceramic BaTiO$_3$, after a correction for the porosity. The agreement is good in the temperature region sufficiently far from the Curie temperature and from the transition to the orthorhombic phase, where the effect of fluctuations should be negligible, but deviations are found outside this region, and the reason for this is discussed. This validates the determination of the piezoelectric response by means of purely elastic measurements on unpoled samples. The method is indirect and, for quantitative assessments, requires the knowledge of the dielectric tensor. On the other hand, it does not require poling of the sample, and therefore is insensitive to inaccuracies from incomplete poling, and can even be used with materials that cannot be poled, for example due to excessive electrical conductivity. While the proposed example of the Young's modulus of a ceramic provides an orientational average of all the single crystal piezoelectric constants, a Resonant Ultrasound Spectroscopy measurement of a single unpoled ceramic sample through the ferroelectric transition can in principle measure all the piezoelectric constants, together with the elastic ones.Comment: 9 pages, 4 figure

On matrix-valued log-concavity and related Prekopa and Brascamp-Lieb inequalities

We propose a new, self-contained, approach to H. Raufi's extension of Prekopa's theorem for matrix-valued log-concave functions. Along the way, new related inequalities are established, in particular a Brascamp-Lieb variance inequality for matrix weights

Simplifying Inductive Schemes in Temporal Logic

In propositional temporal logic, the combination of the connectives "tomorrow" and "always in the future" require the use of induction tools. In this paper, we present a classification of inductive schemes for propositional linear temporal logic that allows the detection of loops in decision procedures. In the design of automatic theorem provers, these schemes are responsible for the searching of efficient solutions for the detection and management of loops. We study which of these schemes have a good behavior in order to give a set of reduction rules that allow us to compute these schemes efficiently and, therefore, be able to eliminate these loops. These reduction laws can be applied previously and during the execution of any automatic theorem prover. All the reductions introduced in this paper can be considered a part of the process for obtaining a normal form of a given formula