Generalised dimensions of measures on almost self-affine sets

We establish a generic formula for the generalised q-dimensions of measures supported by almost self-affine sets, for all q>1. These q-dimensions may exhibit phase transitions as q varies. We first consider general measures and then specialise to Bernoulli and Gibbs measures. Our method involves estimating expectations of moment expressions in terms of `multienergy' integrals which we then bound using induction on families of trees

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

Small union with large set of centers

Let $T\subset{\mathbb R}^n$ be a fixed set. By a scaled copy of $T$ around $x\in{\mathbb R}^n$ we mean a set of the form $x+rT$ for some $r>0$. In this survey paper we study results about the following type of problems: How small can a set be if it contains a scaled copy of $T$ around every point of a set of given size? We will consider the cases when $T$ is circle or sphere centered at the origin, Cantor set in ${\mathbb R}$, the boundary of a square centered at the origin, or more generally the $k$-skeleton ($0\le k<n$) of an $n$-dimensional cube centered at the origin or the $k$-skeleton of a more general polytope of ${\mathbb R}^n$. We also study the case when we allow not only scaled copies but also scaled and rotated copies and also the case when we allow only rotated copies

Sixty Years of Fractal Projections

Sixty years ago, John Marstrand published a paper which, among other things, relates the Hausdorff dimension of a plane set to the dimensions of its orthogonal projections onto lines. For many years, the paper attracted very little attention. However, over the past 30 years, Marstrand's projection theorems have become the prototype for many results in fractal geometry with numerous variants and applications and they continue to motivate leading research.Comment: Submitted to proceedings of Fractals and Stochastics

Self-Similar Corrections to the Ergodic Theorem for the Pascal-Adic Transformation

Let T be the Pascal-adic transformation. For any measurable function g, we consider the corrections to the ergodic theorem sum_{k=0}^{j-1} g(T^k x) - j/l sum_{k=0}^{l-1} g(T^k x). When seen as graphs of functions defined on {0,...,l-1}, we show for a suitable class of functions g that these quantities, once properly renormalized, converge to (part of) the graph of a self-affine function. The latter only depends on the ergodic component of x, and is a deformation of the so-called Blancmange function. We also briefly describe the links with a series of works on Conway recursive $10,000 sequence.Comment: version to appear in Stochastics and Dynamics. We added a discussion on the links with Conway 10,000$ recursive sequenc

LVII. On the sivatherium giganteum, a new fossil ruminant Genus, from the valley of the markanda, in the siválik branch of the sub-himálayan mountains

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X. On additional fossil species of the order quadrumana from the Sewálík Hills

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Higher-dimensional multifractal value sets for conformal infinite graph directed Markov systems

We give a description of the level sets in the higher dimensional multifractal formalism for infinite conformal graph directed Markov systems. If these systems possess a certain degree of regularity this description is complete in the sense that we identify all values with non-empty level sets and determine their Hausdorff dimension. This result is also partially new for the finite alphabet case.Comment: 20 pages, 1 figur

Contact Tank Design Impact on Process Performance

In this study three-dimensional numerical models were refined to predict reactive processes in disinfection contact tanks (CTs). The methodology departs from the traditional performance assessment of contact tanks via hydraulic efficiency indicators, as it simulates directly transport and decay of the disinfectant, inactivation of pathogens and accumulation of by-products. The method is applied to study the effects of inlet and compartment design on contact tank performance, with special emphasis on turbulent mixing and minimisation of internal recirculation and short-circuiting. In contrast to the conventional approach of maximising the length-to-width ratio, the proposed design changes are aimed at addressing and mitigating adverse hydrodynamic structures, which have historically led to poor hydraulic efficiency in many existing contact tanks. The results suggest that water treatment facilities can benefit from in-depth analyses of the flow and kinetic processes through computational fluid dynamics, resulting in up to 38 % more efficient pathogen inactivation and 14 % less disinfection by-product formation

The Freezeout Hypersurface at LHC from particle spectra: Flavor and Centrality Dependence

We extract the freezeout hypersurface in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=$ 2760 GeV at the CERN Large Hadron Collider by analysing the data on transverse momentum spectra within a unified model for chemical and kinetic freezeout. The study has been done within two different schemes of freezeout, single freezeout where all the hadrons freezeout together versus double freezeout where those hadrons with non-zero strangeness content have different freezeout parameters compared to the non-strange ones. We demonstrate that the data is better described within the latter scenario. We obtain a strange freezeout hypersurface which is smaller in volume and hotter compared to the non-strange freezeout hypersurface for all centralities with a reduction in $\chi^2/N_{df}$ around $40\%$. We observe from the extracted parameters that the ratio of the transverse size to the freezeout proper time is invariant under expansion from the strange to the non-strange freezeout surfaces across all centralities. Moreover, except for the most peripheral bins, the ratio of the non-strange and strange freezeout proper times is close to $1.3$.Comment: Final version accepted for publicatio