Search results for "FOS"
showing 10 items of 15075 documents
Geometric rough paths on infinite dimensional spaces
2022
Similar to ordinary differential equations, rough paths and rough differential equations can be formulated in a Banach space setting. For $\alpha\in (1/3,1/2)$, we give criteria for when we can approximate Banach space-valued weakly geometric $\alpha$-rough paths by signatures of curves of bounded variation, given some tuning of the H\"older parameter. We show that these criteria are satisfied for weakly geometric rough paths on Hilbert spaces. As an application, we obtain Wong-Zakai type result for function space valued martingales using the notion of (unbounded) rough drivers.
Advances in plant materials, food by-products, and algae conversion into biofuels: use of environmentally friendly technologies
2019
Green technologies have emerged as useful tools for the generation of clean fuels with the potential to minimize the effect of human activity on the environment. Currently, these fuels are mainly composed of hydrocarbons obtained from crude oil. Over the past two decades, biomass has gained significant attention as a renewable feedstock for more sustainable biofuel production and has been a great candidate to replace fossil fuels. The principal components of most of the available biomass are cellulose, hemi-cellulose, and lignin. Although the available green technologies for biofuel production are progressing rapidly, productivity and chemical yield from these techniques are still below the…
Relative proton and γ widths of astrophysically important states in 30S studied in the β-delayed decay of 31Ar
2013
Resonances just above the proton threshold in 30S affect the 29P(p,gamma)30S reaction under astrophysical conditions. The (p,gamma)-reaction rate is currently determined indirectly and depends on the properties of the relevant resonances. We present here a method for finding the ratio between the proton and gamma partial widths of resonances in 30S. The widths are determined from the beta-2p and beta-p-gamma decay of 31Ar, which is produced at the ISOLDE facility at the European research organization CERN. Experimental limits on the ratio between the proton and gamma partial widths for astrophysical relevant levels in 30S have been found for the first time. A level at 4688(5) keV is identif…
Space-filling vs. Luzin's condition (N)
2013
Let us assume that we are given two metric spaces, where the Hausdorff dimension of the first space is strictly smaller than the one of the second space. Suppose further that the first space has sigma-finite measure with respect to the Hausdorff measure of the corresponding dimension. We show for quite general metric spaces that for any measurable surjection from the first onto the second space, there is a set of measure zero that is mapped to a set of positive measure (both measures are the Hausdorff measures corresponding to the Hausdorff dimension of the first space). We also study more general situations where the measures on the two metric spaces are not necessarily the same and not ne…
Integrability of orthogonal projections, and applications to Furstenberg sets
2022
Let $\mathcal{G}(d,n)$ be the Grassmannian manifold of $n$-dimensional subspaces of $\mathbb{R}^{d}$, and let $\pi_{V} \colon \mathbb{R}^{d} \to V$ be the orthogonal projection. We prove that if $\mu$ is a compactly supported Radon measure on $\mathbb{R}^{d}$ satisfying the $s$-dimensional Frostman condition $\mu(B(x,r)) \leq Cr^{s}$ for all $x \in \mathbb{R}^{d}$ and $r > 0$, then $$\int_{\mathcal{G}(d,n)} \|\pi_{V}\mu\|_{L^{p}(V)}^{p} \, d\gamma_{d,n}(V) \tfrac{1}{2}$ and $t \geq 1 + \epsilon$ for a small absolute constant $\epsilon > 0$. We also prove a higher dimensional analogue of this estimate for codimension-1 Furstenberg sets in $\mathbb{R}^{d}$. As another corollary of our method,…
Visible parts of fractal percolation
2009
We study dimensional properties of visible parts of fractal percolation in the plane. Provided that the dimension of the fractal percolation is at least 1, we show that, conditioned on non-extinction, almost surely all visible parts from lines are 1-dimensional. Furthermore, almost all of them have positive and finite Hausdorff measure. We also verify analogous results for visible parts from points. These results are motivated by an open problem on the dimensions of visible parts.
Mapping an electron wave function by a local electron scattering probe
2015
A technique is developed which allows for the detailed mapping of the electronic wave function in two-dimensional electron gases with low-temperature mobilities up to $15\times {10}^{6}\;{\mathrm{cm}}^{2}\;{{\rm{V}}}^{-1}\;{{\rm{s}}}^{-1}$. Thin ('delta') layers of aluminium are placed into the regions where the electrons reside. This causes electron scattering which depends very locally on the amplitude of the electron wave function at the position of the Al δ-layer. By changing the distance of this layer from the interface we map the shape of the wave function perpendicular to the interface. Despite having a profound effect on the electron mobiliy, the δ-layers do not cause a widening of …
The richest superclusters : I Morphology
2007
We study the morphology of the richest superclusters from the catalogues of superclusters of galaxies in the 2dF Galaxy Redshift Survey and compare the morphology of real superclusters with model superclusters in the Millennium Simulation. We use Minkowski functionals and shapefinders to quantify the morphology of superclusters: their sizes, shapes, and clumpiness. We generate empirical models of simple geometry to understand which morphologies correspond to the supercluster shapefinders. We show that rich superclusters have elongated, filamentary shapes with high-density clumps in their core regions. The clumpiness of superclusters is determined using the fourth Minkowski functional $V_3$.…
Multi-scale morphology of the galaxy distribution
2006
Many statistical methods have been proposed in the last years for analyzing the spatial distribution of galaxies. Very few of them, however, can handle properly the border effects of complex observational sample volumes. In this paper, we first show how to calculate the Minkowski Functionals (MF) taking into account these border effects. Then we present a multiscale extension of the MF which gives us more information about how the galaxies are spatially distributed. A range of examples using Gaussian random fields illustrate the results. Finally we have applied the Multiscale Minkowski Functionals (MMF) to the 2dF Galaxy Redshift Survey data. The MMF clearly indicates an evolution of morpho…