A minimal Kurepa line

We show it is consistent with \ZFC that there is an everywhere Kurepa line which is order isomorphic to all of its dense $\aleph_2$-dense suborders. Moreover, this Kurepa line does not contain any Aronszajn suborder. We also show it is consistent with \ZFC that there is a minimal Kurepa line which does not contain any Aronszajn suborder

X-ray micro-computed tomography imaging for coal characterization

An Australian bituminous coal is imaged at high resolution of 16.1 μm with (wet) and without (dry) X-ray attenuating fluids present in the pore space using a large-field three-dimensional microfocus helical X-ray computed tomography (micro-CT) instrument. Scanning Electron Microscope (SEM) is conducted on slices of the specimen to visualize coal micro-features up to resolution of about 15 nm. Two- and three-dimensional image registration techniques are used to precisely overlay micro-CT tomograms of the core plug in dry and wet conditions and SEM images to yield detailed threedimensional visualizations of the geometry and topology of the fracture systems in coal. SEM images are also used to produce a calibration curve based on the relationship between the micro-CT intensity values and the true apertures of fractures within coal. This eliminates the need for two sets of imaging. Advanced filtering algorithms are applied to segment the micro-CT image into four distinct phases: resolved fractures, sub-resolution pores and fractures, macerals, and minerals. The application of micro-CT in determination of relative age relationships between adjacent geological features is presented. The distribution of resolved aperture size within the coal sample is investigated and the variation of permeability and porosity in several sub-samples of the coal is plotted. The analysis suggests that coal permeability is independent of porosity and is likely affected by other petrophysical properties such as lithotype. To include the effects of mineral phase on coal properties, we remove the segmented mineral phase and merge it to the resolved fracture phase. This analysis affirms that minerals are deposited in highly connected regions

Can You Take Komjath's Inaccessible Away?

In this paper we aim to compare Kurepa trees and Aronszajn trees. Moreover, we analyze the affect of large cardinal assumptions on this comparison. Using the the method of walks on ordinals, we will show it is consistent with ZFC that there is a Kurepa tree and every Kurepa tree contains a Souslin subtree, if there is an inaccessible cardinal. This is stronger than Komjath's theorem that asserts the same consistency from two inaccessible cardinals. We will show that our large cardinal assumption is optimal, i.e. if every Kurepa tree has an Aronszajn subtree then $\omega_2$ is inaccessible in the constructible universe \textsc{L}. Moreover, we prove it is consistent with ZFC that there is a Kurepa tree $T$ such that if $U \subset T$ is a Kurepa tree with the inherited order from $T$, then $U$ has an Aronszajn subtree. This theorem uses no large cardinal assumption. Our last theorem immediately implies the following: assume $\textrm{MA}_{\omega_2}$ holds and $\omega_2$ is not a Mahlo cardinal in \textsc{L}. Then there is a Kurepa tree with the property that every Kurepa subset has an Aronszajn subtree. Our work entails proving a new lemma about Todorcevic's $\rho$ function which might be useful in other contexts.Comment: 20 page