Local lower norm estimates for dyadic maximal operators and related Bellman functions

We provide lower $L^q$ and weak $L^p$-bounds for the localized dyadic maximal operator on $R^n$, when the local $L^1$ and the local $L^p$ norm of the function are given. We actually do that in the more general context of homo- geneous tree-like families in probability spaces.Comment: 9 page

Dyadic weights on RnR^n and reverse Holder inequalities

We prove that for any weight $\phi$ defined on $[0,1]^n$ that satisfies a reverse Holder inequality with exponent p > 1 and constant $c\ge1$ upon all dyadic subcubes of $[0,1]^n$, it's non increasing rearrangement satisfies a reverse Holder inequality with the same exponent and constant not more than $2^nc-2^n + 1$, upon all subintervals of $[0; 1]$ of the form $[0; t]$. This gives as a consequence, according to the results in [8], an interval $[p; p_0(p; c)) = I{p,c}$, such that for any $q \in I{p,c}$, we have that $\phi$ is in $L^q$.Comment: 10 page

Sharp Lorentz estimates for dyadic-like maximal operators and related Bellman functions

We precisely evaluate Bellman type functions for the dyadic maximal opeator on $R^n$ and of maximal operators on martingales related to local Lorentz type estimates. Using a type of symmetrization principle, introduced for the dyadic maximal operator in earlier works of the authors we precisely evaluate the supremum of the Lorentz quasinorm of the maximal operator on a function $\phi$ when the integral of $\phi$ is fixed and also the same Lorentz quasinorm of $\phi$ is fixed. Also we find the corresponding supremum when the integral of $\phi$ is fixed and several weak type conditions are given.Comment: 11 page

Occupational Fraud Detection Through Visualization

Occupational fraud affects many companies worldwide causing them economic loss and liability issues towards their customers and other involved entities. Detecting internal fraud in a company requires significant effort and, unfortunately cannot be entirely prevented. The internal auditors have to process a huge amount of data produced by diverse systems, which are in most cases in textual form, with little automated support. In this paper, we exploit the advantages of information visualization and present a system that aims to detect occupational fraud in systems which involve a pair of entities (e.g., an employee and a client) and periodic activity. The main visualization is based on a spiral system on which the events are drawn appropriately according to their time-stamp. Suspicious events are considered those which appear along the same radius or on close radii of the spiral. Before producing the visualization, the system ranks both involved entities according to the specifications of the internal auditor and generates a video file of the activity such that events with strong evidence of fraud appear first in the video. The system is also equipped with several different visualizations and mechanisms in order to meet the requirements of an internal fraud detection system

Estimates for Bellman functions related to dyadic-like maximal operators on weighted spaces

We provide some new estimates for Bellman type functions for the dyadic maximal opeator on $R^n$ and of maximal operators on martingales related to weighted spaces. Using a type of symmetrization principle, introduced for the dyadic maximal operator in earlier works of the authors we introduce certain conditions on the weight that imply estimate for the maximal operator on the corresponding weighted space. Also using a well known estimate for the maximal operator by a double maximal operators on different m easures related to the weight we give new estimates for the above Bellman type functions.Comment: 10 pages. arXiv admin note: text overlap with arXiv:1511.0611

Advances in Wood Composites

Wood composites have shown very good performance, and substantial service lives when correctly specified for the exposure risks present. Selection of an appropriate product for the job should be accompanied by decisions about the appropriate protection, whether this is by design, by preservative treatment or by wood modification techniques. This Special Issue, Advances in Wood Composites presents recent progress in enhancing and refining the performance and properties of wood composites by chemical and thermal modification and the application of smart nanomaterials, which have made them a particular area of interest for researchers. In addition, it reviews some important aspects in the field of wood composites, with particular focus on their materials, applications, and engineering and scientific advances, including solutions inspired biomimetrically by the structure of wood and wood composites. This Special Issue, with a collection of 13 original contributions, provides selected examples of recent Advances in Wood Composite

The effect of lattice periodicity on the electronic configuration near a metal surface

Includes bibliographical references.A method is developed for calculating single electron wave functions in a semi-infinite metal. The effect of the lattice periodicity is explicitly taken into account so that the solution in the far interior is consistent with the band structure of the infinite crystal. The solution is sufficiently general to include surface states. The single electron potentials are reconsidered and some new features are discussed. These include the elimination of the singular zero-order Fourier terms of the ion-electron and Hartree potentials which leads to the surface dipole barrier. Also a simple formula is derived for the exchange potential in the zero-order approximation which allows to calculate the exchange potential for wave vectors which have components of velocity parallel to the surface. The method is finally applied to a semi-infinite sodium crystal with a (001) orientation