3,714 research outputs found
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 be a fixed set. By a scaled copy of around
we mean a set of the form for some .
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 around every point
of a set of given size? We will consider the cases when is circle or sphere
centered at the origin, Cantor set in , the boundary of a square
centered at the origin, or more generally the -skeleton () of an
-dimensional cube centered at the origin or the -skeleton of a more
general polytope of .
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 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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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 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
around . 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 .Comment: Final version accepted for publicatio
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