Evaluating the exact infinitesimal values of area of Sierpinski's carpet and volume of Menger's sponge

Very often traditional approaches studying dynamics of self-similarity processes are not able to give their quantitative characteristics at infinity and, as a consequence, use limits to overcome this difficulty. For example, it is well know that the limit area of Sierpinski's carpet and volume of Menger's sponge are equal to zero. It is shown in this paper that recently introduced infinite and infinitesimal numbers allow us to use exact expressions instead of limits and to calculate exact infinitesimal values of areas and volumes at various points at infinity even if the chosen moment of the observation is infinitely faraway on the time axis from the starting point. It is interesting that traditional results that can be obtained without the usage of infinite and infinitesimal numbers can be produced just as finite approximations of the new ones

Processed meat consumption and Lung function: modification by antioxidants and smoking

This article has supplementary material available from www.erj.ersjournals.com: This study was supported by the Medical Research Council, UK. H. Okubo was supported in part by fellowship of the Astellas Foundation for Research on Metabolic Disorders, Japan and the Naito Memorial Grant for Research Abroad from the Naito Foundation, Japan

Data in support of genetic architecture of glucosinolate variations in Brassica napus

The transcriptome-based GWAS approach, Associative Transcriptomics (AT), which was employed to uncover the genetic basis controlling quantitative variation of glucosinolates in Brassica napus vegetative tissues is described. This article includes the phenotypic data of leaf and root glucosinolate (GSL) profiles across a diversity panel of 288 B. napus genotypes, as well as information on population structure and levels of GSLs grouped by crop types. Moreover, data on genetic associations of single nucleotide polymorphism (SNP) markers and gene expression markers (GEMs) for the major GSL types are presented in detail, while Manhattan plots and QQ plots for the associations of individual GSLs are also included. Root genetic association are supported by differential expression analysis generated from root RNA-seq. For further interpretation and details, please see the related research article entitled ‘Genetic architecture of glucosinolate variation in Brassica napus’ [1]

X-ray image reconstruction from a diffraction pattern alone

A solution to the inversion problem of scattering would offer aberration-free diffraction-limited 3D images without the resolution and depth-of-field limitations of lens-based tomographic systems. Powerful algorithms are increasingly being used to act as lenses to form such images. Current image reconstruction methods, however, require the knowledge of the shape of the object and the low spatial frequencies unavoidably lost in experiments. Diffractive imaging has thus previously been used to increase the resolution of images obtained by other means. We demonstrate experimentally here a new inversion method, which reconstructs the image of the object without the need for any such prior knowledge.Comment: 5 pages, 3 figures, improved figures and captions, changed titl

Weak localization of Dirac fermions in graphene beyond the diffusion regime

We develop a microscopic theory of the weak localization of two-dimensional massless Dirac fermions which is valid in the whole range of classically weak magnetic fields. The theory is applied to calculate magnetoresistance caused by the weak localization in graphene and conducting surfaces of bulk topological insulators.Comment: 5 pages, 2 figure

High-resolution ab initio three-dimensional X-ray diffraction microscopy

Coherent X-ray diffraction microscopy is a method of imaging non-periodic isolated objects at resolutions only limited, in principle, by the largest scattering angles recorded. We demonstrate X-ray diffraction imaging with high resolution in all three dimensions, as determined by a quantitative analysis of the reconstructed volume images. These images are retrieved from the 3D diffraction data using no a priori knowledge about the shape or composition of the object, which has never before been demonstrated on a non-periodic object. We also construct 2D images of thick objects with infinite depth of focus (without loss of transverse spatial resolution). These methods can be used to image biological and materials science samples at high resolution using X-ray undulator radiation, and establishes the techniques to be used in atomic-resolution ultrafast imaging at X-ray free-electron laser sources.Comment: 22 pages, 11 figures, submitte

Strain and Electronic Nematicity in La₂₋ₓSrₓCuO₄

Electronic nematicity has previously been observed in La2-xSrxCuO4 thin films by the angle-resolved transverse resistivity method with a director whose orientation is always pinned to the crystal axes when the film is grown on an orthorhombic substrate but not when the substrate is tetragonal. Here we report on measurements of thin films grown on (tetragonal) LaSrAlO4 and subsequently placed in an apparatus that allows the application of uniaxial compressive strain. The apparatus applied enough force to produce a 1% orthorhombicity in LaSrAlO4 and yet no change in the electronic nematicity was observed in films under strain compared to when they were unstrained. The lattice effects are weak, and the origin of nematicity is primarily electronic