Atmospheric ozone measurements made from B-747 AIRLINERS: Spring 1975

Atmospheric ozone in the upper troposphere and lower stratosphere north of the equator has been registered aboard two commercial B-747 airliners. The composite ozone, flight and meteorological data are reported. Attention is drawn particularly to the vertical profiles of atmospheric ozone mixing ratio as a function of both distance from the tropopause and curvature of the streamlines. The GASP observations suggest that ozone levels typical of the lower stratosphere are often embedded in the upper troposphere, principally during occassions when cyclonic wind curvature was noted

An ERTS-1 investigation for Lake Ontario and its basin

The author has identified the following significant results. Methods of manual, semi-automatic, and automatic (computer) data processing were evaluated, as were the requirements for spatial physiographic and limnological information. The coupling of specially processed ERTS data with simulation models of the watershed precipitation/runoff process provides potential for water resources management. Optimal and full use of the data requires a mix of data processing and analysis techniques, including single band editing, two band ratios, and multiband combinations. A combination of maximum likelihood ratio and near-IR/red band ratio processing was found to be particularly useful

Combinatorics of linear iterated function systems with overlaps

Let $\bm p_0,...,\bm p_{m-1}$ be points in ${\mathbb R}^d$, and let $\{f_j\}_{j=0}^{m-1}$ be a one-parameter family of similitudes of ${\mathbb R}^d$: $$f_j(\bm x) = \lambda\bm x + (1-\lambda)\bm p_j, j=0,...,m-1,$$ where $\lambda\in(0,1)$ is our parameter. Then, as is well known, there exists a unique self-similar attractor $S_\lambda$ satisfying $S_\lambda=\bigcup_{j=0}^{m-1} f_j(S_\lambda)$. Each $\bm x\in S_\lambda$ has at least one address $(i_1,i_2,...)\in\prod_1^\infty\{0,1,...,m-1\}$, i.e., $\lim_n f_{i_1}f_{i_2}... f_{i_n}({\bf 0})=\bm x$. We show that for $\lambda$ sufficiently close to 1, each $\bm x\in S_\lambda\setminus\{\bm p_0,...,\bm p_{m-1}\}$ has $2^{\aleph_0}$ different addresses. If $\lambda$ is not too close to 1, then we can still have an overlap, but there exist $\bm x$'s which have a unique address. However, we prove that almost every $\bm x\in S_\lambda$ has $2^{\aleph_0}$ addresses, provided $S_\lambda$ contains no holes and at least one proper overlap. We apply these results to the case of expansions with deleted digits. Furthermore, we give sharp sufficient conditions for the Open Set Condition to fail and for the attractor to have no holes. These results are generalisations of the corresponding one-dimensional results, however most proofs are different.Comment: Accepted for publication in Nonlinearit

Equilibrium states of the pressure function for products of matrices

Let $\{M_i\}_{i=1}^\ell$ be a non-trivial family of $d\times d$ complex matrices, in the sense that for any $n\in \N$, there exists $i_1... i_n\in \{1,..., \ell\}^n$ such that $M_{i_1}... M_{i_n}\neq {\bf 0}$. Let $P \colon (0,\infty)\to \R$ be the pressure function of $\{M_i\}_{i=1}^\ell$. We show that for each $q>0$, there are at most $d$ ergodic $q$-equilibrium states of $P$, and each of them satisfies certain Gibbs property.Comment: 12 pages. To appear in DCD

Golden gaskets: variations on the Sierpi\'nski sieve

We consider the iterated function systems (IFSs) that consist of three general similitudes in the plane with centres at three non-collinear points, and with a common contraction factor \la\in(0,1). As is well known, for \la=1/2 the invariant set, \S_\la, is a fractal called the Sierpi\'nski sieve, and for \la<1/2 it is also a fractal. Our goal is to study \S_\la for this IFS for 1/2<\la<2/3, i.e., when there are "overlaps" in \S_\la as well as "holes". In this introductory paper we show that despite the overlaps (i.e., the Open Set Condition breaking down completely), the attractor can still be a totally self-similar fractal, although this happens only for a very special family of algebraic \la's (so-called "multinacci numbers"). We evaluate \dim_H(\S_\la) for these special values by showing that \S_\la is essentially the attractor for an infinite IFS which does satisfy the Open Set Condition. We also show that the set of points in the attractor with a unique ``address'' is self-similar, and compute its dimension. For ``non-multinacci'' values of \la we show that if \la is close to 2/3, then \S_\la has a nonempty interior and that if \la<1/\sqrt{3} then \S_\la$ has zero Lebesgue measure. Finally we discuss higher-dimensional analogues of the model in question.Comment: 27 pages, 10 figure

Dichotomy of Solar Coronal Jets: Standard Jets and Blowout Jets

By examining many X-ray jets in Hinode/XRT coronal X-ray movies of the polar coronal holes, we found that there is a dichotomy of polar X-ray jets. About two thirds fit the standard reconnection picture for coronal jets, and about one third are another type. We present observations indicating that the non-standard jets are counterparts of erupting-loop H alpha macrospicules, jets in which the jet-base magnetic arch undergoes a miniature version of the blowout eruptions that produce major CMEs. From the coronal X-ray movies we present in detail two typical standard X-ray jets and two typical blowout X-ray jets that were also caught in He II 304 Angstrom snapshots from STEREO/EUVI. The distinguishing features of blowout X-ray jets are (1) X-ray brightening inside the base arch in addition to the outside bright point that standard jets have, (2) blowout eruption of the base arch's core field, often carrying a filament of cool (T ~10(exp 4) - 10(exp 5) K) plasma, and (3) an extra jet-spire strand rooted close to the bright point. We present cartoons showing how reconnection during blowout eruption of the base arch could produce the observed features of blowout X-ray jets. We infer that (1) the standard-jet/blowout-jet dichotomy of coronal jets results from the dichotomy of base arches that do not have and base arches that do have enough shear and twist to erupt open, and (2) there is a large class of spicules that are standard jets and a comparably large class of spicules that are blowout jets

Engaging stakeholders in research to address water-energy-food (WEF) nexus challenges

The water–energy–food (WEF) nexus has become a popular, and potentially powerful, frame through which to analyse interactions and interdependencies between these three systems. Though the case for transdisciplinary research in this space has been made, the extent of stakeholder engagement in research remains limited with stakeholders most commonly incorporated in research as end-users. Yet, stakeholders interact with nexus issues in a variety of ways, consequently there is much that collaboration might offer to develop nexus research and enhance its application. This paper outlines four aspects of nexus research and considers the value and potential challenges for transdisciplinary research in each. We focus on assessing and visualising nexus systems; understanding governance and capacity building; the importance of scale; and the implications of future change. The paper then proceeds to describe a novel mixed-method study that deeply integrates stakeholder knowledge with insights from multiple disciplines. We argue that mixed-method research designs—in this case orientated around a number of cases studies—are best suited to understanding and addressing real-world nexus challenges, with their inevitable complex, non-linear system characteristics. Moreover, integrating multiple forms of knowledge in the manner described in this paper enables research to assess the potential for, and processes of, scaling-up innovations in the nexus space, to contribute insights to policy and decision making

Fractional and noncommutative spacetimes

We establish a mapping between fractional and noncommutative spacetimes in configuration space. Depending on the scale at which the relation is considered, there arise two possibilities. For a fractional spacetime with log-oscillatory measure, the effective measure near the fundamental scale determining the log-period coincides with the non-rotation-invariant but cyclicity-preserving measure of \kappa-Minkowski. At scales larger than the log-period, the fractional measure is averaged and becomes a power-law with real exponent. This can be also regarded as the cyclicity-inducing measure in a noncommutative spacetime defined by a certain nonlinear algebra of the coordinates, which interpolates between \kappa-Minkowski and canonical spacetime. These results are based upon a braiding formula valid for any nonlinear algebra which can be mapped onto the Heisenberg algebra.Comment: 15 pages. v2: typos correcte

Contour lines of the discrete scale invariant rough surfaces

We study the fractal properties of the 2d discrete scale invariant (DSI) rough surfaces. The contour lines of these rough surfaces show clear DSI. In the appropriate limit the DSI surfaces converge to the scale invariant rough surfaces. The fractal properties of the 2d DSI rough surfaces apart from possessing the discrete scale invariance property follow the properties of the contour lines of the corresponding scale invariant rough surfaces. We check this hypothesis by calculating numerous fractal exponents of the contour lines by using numerical calculations. Apart from calculating the known scaling exponents some other new fractal exponents are also calculated.Comment: 9 Pages, 12 figure