Search results for "Function"
showing 10 items of 14432 documents
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…
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 $V_3$.…
Isometric embeddings of snowflakes into finite-dimensional Banach spaces
2016
We consider a general notion of snowflake of a metric space by composing the distance by a nontrivial concave function. We prove that a snowflake of a metric space $X$ isometrically embeds into some finite-dimensional normed space if and only if $X$ is finite. In the case of power functions we give a uniform bound on the cardinality of $X$ depending only on the power exponent and the dimension of the vector space.
Executive functions in kindergarten children at risk for developmental coordination disorder
2018
Executive functioning (EF) is a key cognitive process for development. Little is known about EF in Kindergarten children at risk for developmental coordination disorder (DCD), despite this age being one of the most critical and intensive period of motor and cognitive development. In our investigation we compared EF in kindergarten children at risk for DCD with Typically Developing (TD) children. Participants were 36 Italian children, 18 at risk for DCD (9 boys and 9 girls) who had a mean age of 4.6 years and 18 TD (9 boys and 9 girls) who had a mean age of 4.6. Executive functions were measured by tasks targeting cold executive functioning (working memory, fluency, inhibitory control) and t…
A Geometrical Three-Ring-Based Model for MIMO Mobile-to-Mobile Fading Channels in Cooperative Networks
2011
Published version of an article published in the journal: Eurasip Journal on Advances in Signal Processing. Also available from the publisher at: http://dx.doi.org/10.1155/2011/892871. OA This paper deals with the modeling and analysis of narrowband multiple-input multiple-output (MIMO) mobile-to-mobile (M2M) fading channels in relay-based cooperative networks. In the transmission links from the source mobile station to the destination mobile station via the mobile relay, non-line-of-sight (NLOS) propagation conditions are taken into account. A stochastic narrowband MIMO M2M reference channel model is derived from the geometrical three-ring scattering model, where it is assumed that an infi…
Automatic crack detection results using a novel device for survey and analysis of road pavement condition
2019
To accurately schedule maintenance operations, it is crucial to monitor the pavement state and, thus, evaluate the structural and functional indices during its entire service life. In particular, surface conditions (cracks, potholes, patches, rutting, etc.) must be properly checked – especially in terms of detection, identification, and classification of distresses – for avoiding reaching dangerous values for users (overpassing safety thresholds). However, monitoring and survey activities can be so costly (not only in economic terms, but further considering the execution time) to discourage their execution, with evident drawbacks for a proper maintenance management and the related intervent…
On the Almost Everywhere Convergence of Multiple Fourier-Haar Series
2019
The paper deals with the question of convergence of multiple Fourier-Haar series with partial sums taken over homothetic copies of a given convex bounded set $$W\subset\mathbb{R}_+^n$$ containing the intersection of some neighborhood of the origin with $$\mathbb{R}_+^n$$ . It is proved that for this type sets W with symmetric structure it is guaranteed almost everywhere convergence of Fourier-Haar series of any function from the class L(ln+L)n−1.
Estimates for the differences of positive linear operators and their derivatives
2019
The present paper deals with the estimate of the differences of certain positive linear operators and their derivatives. Oxur approach involves operators defined on bounded intervals, as Bernstein operators, Kantorovich operators, genuine Bernstein-Durrmeyer operators, and Durrmeyer operators with Jacobi weights. The estimates in quantitative form are given in terms of the first modulus of continuity. In order to analyze the theoretical results in the last section, we consider some numerical examples.
Exact Fourier expansion in cylindrical coordinates for the three-dimensional Helmholtz Green function
2009
A new method is presented for Fourier decomposition of the Helmholtz Green Function in cylindrical coordinates, which is equivalent to obtaining the solution of the Helmholtz equation for a general ring source. The Fourier coefficients of the Helmholtz Green function are split into their half advanced+half retarded and half advanced-half retarded components. Closed form solutions are given for these components in terms of a Horn function and a Kampe de Feriet function, respectively. The systems of partial differential equations associated with these two-dimensional hypergeometric functions are used to construct a fourth-order ordinary differential equation which both components satisfy. A s…