On a conjecture of Vorst

Let k be an infinite perfect field of positive characteristic such that strong resolution of singularities holds over k. We prove that a localization of a d-dimensional commutative k-algebra R of finite type is K _d+1-regular if and only if it is regular. This partially affirms a conjecture of Vorst.     

A model for crack formation during active solid pyrolysis of a char-forming solid: crack patterns; surface area generation; volatile mass efflux

A model is developed for the formation and propagation of cracks in a material sample that is heated at its top surface, pyrolyses, and then thermally degrades to form char. In this work the sample is heated uniformly over its entire top surface by a hypothetical flame (a heat source). The pyrolysis mechanism is described by a one-step overall reaction that is dependent nonlinearly on the temperature (Arrhenius form). Stresses develop in response to the thermal degradation of the material by means of a shrinkage strain caused by local mass loss during pyrolysis. When the principal stress exceeds a prescribed threshold value, the material forms a local crack. Cracks are found to generally originate at the surface in response to heating, but occasionally they form in the bulk, away from ever-changing material boundaries. The resulting cracks evolve and form patterns whose characteristics are described. Quantities examined in detail are: the crack spacing in the pyrolysis zone; the crack length evolution; the formation and nature of crack loops which are defined as individual cracks that have joined to form loops that are disconnected from the remaining material; the formation of enhanced pyrolysis area; and the impact of all of the former quantities on mass flux. It is determined that the mass flux from the sample can be greatly enhanced over its nominal (non-cracking) counterpart. The mass efflux profile qualitatively resembles those observed in Cone Calorimeter tests.     

Mixture cure models in credit scoring: If and when borrowers default

Mixture cure models were originally proposed in medical statistics to model long-term survival of cancer patients in terms of two distinct subpopulations - those that are cured of the event of interest and will never relapse, along with those that are uncured and are susceptible to the event. In the present paper, we introduce mixture cure models to the area of credit scoring, where, similarly to the medical setting, a large proportion of the dataset may not experience the event of interest during the loan term, i.e. default. We estimate a mixture cure model predicting (time to) default on a UK personal loan portfolio, and compare its performance to the Cox proportional hazards method and standard logistic regression. Results for credit scoring at an account level and prediction of the number of defaults at a portfolio level are presented; model performance is evaluated through cross validation on discrimination and calibration measures. Discrimination performance for all three approaches was found to be high and competitive. Calibration performance for the survival approaches was found to be superior to logistic regression for intermediate time intervals and useful for fixed 12 month time horizon estimates, reinforcing the flexibility of survival analysis as both a risk ranking tool and for providing robust estimates of probability of default over time. Furthermore, the mixture cure model’s ability to distinguish between two subpopulations can offer additional insights by estimating the parameters that determine susceptibility to default in addition to parameters that influence time to default of a borrower.     

Möbius characterization of hemispheres

In this paper we generalize the Möbius characterization of metric spheres as obtained in Foertsch and Schroeder [4] to a corresponding Möbius characterization of metric hemispheres.     

Laser induced forward transfer of SnO2 for sensing applications using different precursors systems

This paper presents the transfer of SnO₂ by laser induced forward transfer (LIFT) for gas sensor applications. Different donor substrates of SnO₂ with and without triazene polymer (TP) as a dynamic release layer were prepared. Transferring these films under different conditions were evaluated by optical microscopy and functionality. Transfers of sputtered SnO₂ films do not lead to satisfactory results and transfers of SnO₂ nanoparticles are difficult. Transfers of SnO₂ nanoparticles can only be achieved when applying a second laser pulse to the already transferred material, which improves the adhesion resulting in a complete pixel. A new approach of decomposing the transfer material during LIFT transfer was developed. Donor films based on UV absorbing metal complex precursors namely, SnCl₂(acac)₂ were prepared and transferred using the LIFT technique. Transfer conditions were optimized for the different systems, which were deposited onto sensor-like microstructures. The conductivity of the transferred material at temperatures of about 400 ^°C are in a range usable for SnO₂ gas sensors. First sensing tests were carried out and the transferred material proved to change conductivity when exposed to ethanol, acetone, and methane.     

The N4 molecule and the N3 + ion

The possibility of the nitrogen molecule forming a stable dimer is investigated. Through ab initio calculations in an extended contracted-gaussian basis, it is demonstrated that N₄ in tetrahedral geometry and N₃ ⁺ in D _3h geometry are local minimum points on their respective internuclear potential energy surfaces. The N₄ molecule is considerably higher in energy than two ground-state N₂ molecules and some study of the barrier for N₄ decomposition has been made. The bond lengths and force constants for the two systems are shown to be similar to their hydrocarbon counterparts, C₄H₄ and C₃H₃ ⁺, tetrahedrane and cyclopropenyl cation. Other related systems are discussed as well.     

Geometric Aspects of Degenerate Modulation Equations

Geometric aspects of degenerate modulation equations associated with spatially reversible systems are considered. Our primary observation is that stationary solutions of such equations always have a Poisson structure that is reminiscent of the equations governing the rigid body in mechanics. The Poisson structure is used to study the geometry of “spatial” phase space: A nontrivial Casimir of the Poisson structure provides a foliation of the phase space, spatially periodic states are given by critical points on level sets of the Casimir and stability type is given by the rate of change of the Casimir function. The bifurcation of spatially periodic states is then studied using singularity theory. The case where branches intersect transversely is treated in detail.     

Nuclear quantum effects in liquid water from path-integral simulations using an ab initio force-matching approach

We have applied path integral simulations, in combination with new ab initio based water potentials, to investigate nuclear quantum effects in liquid water. Because direct ab initio path integral simulations are computationally expensive, a flexible water model is parameterised by force-matching to density functional theory-based molecular dynamics simulations. Static and dynamic properties of liquid water at ambient conditions are presented and the role of nuclear quantum effects, exchange-correlation functionals and dispersion corrections are discussed in regards to reproducing the experimental properties of liquid water.     

Diffusion tensor parameters and principal eigenvector coherence: Relation to b-value intervals and field strength

Diffusion-weighted MRI images acquired at b-value greater than 1000 s mm^− 2 measure the diffusion of a restricted pool of water molecules. High b-value images are accompanied by a reduction in signal-to-noise ratio (SNR) due to the application of large diffusion gradients. By fitting the diffusion tensor model to data acquired at incremental b-value intervals, we determined the effect of SNR on tensor parameters in normal human brains, in vivo. In addition, we also investigated the impact of field strength on the diffusion tensor model. Data were acquired at 1.5 and 3 T, at b-values 0, 1000, 2000 and 3000 s mm^− 2 in twenty diffusion-sensitised directions. Fractional anisotropy (FA), mean diffusivity (MD) and principal eigenvector coherence (κ) were calculated from diffusion tensors fitted between datasets with b-values 0–1000, 0–2000, 0–3000, 1000–2000 and 2000–3000 s mm^− 2. Field strength and b-value effects on diffusion parameters were analysed in white and grey matter regions of interest. Decreases in FA, κ and MD were found with increasing b-value in white matter. Univariate analysis showed a significant increase in FA with increasing field strength in highly organised white matter. These results suggest there are significant differences in diffusion parameters at 1.5 and 3 T and that the optimal results, in terms of the highest values of FA in white matter, are obtained at 3 T with a maximum b = 1000 s mm^− 2.