Regularized trace on separable Banach spaces

If H is a separable Hilbert space, Gül (2008) has shown that a regularized trace formula can be computed on L² (H, [0, π]) for a second order differential operator with bounded operator-valued coefficients, where H is a separable Hilbert space. Kuelbs (1970) has shown that every separable Banach space can be continuously and densely embedded into a separable Hilbert space, while Gill (2016) has used Kuelbs result to show that the dual of a Banach space does not have a unique representation. In this paper, we use the results of Kuelbs and Gill to study the regularized trace formula on L2 (B, [0, π]), where B is an arbitrary separable Banach space.Publisher's Versio

Electronic structure of unidirectional superlattices in crossed electric and magnetic fields and related terahertz oscillations

We have studied Bloch electrons in a perfect unidirectional superlattice subject to crossed electric and magnetic fields, where the magnetic field is oriented ``in-plane'', i.e. in parallel to the sample plane. Two orientation of the electric field are considered. It is shown that the magnetic field suppresses the intersubband tunneling of the Zener type, but does not change the frequency of Bloch oscillations, if the electric field is oriented perpendicularly to both the sample plane and the magnetic field. The electric field applied in-plane (but perpendicularly to the magnetic field) yields the step-like electron energy spectrum, corresponding to the magnetic-field-tunable oscillations alternative to the Bloch ones.Comment: 7 pages, 1 figure, accepted for publication in Phys. Rev.

Thermal extraction of volatiles from the lunar regolith simulant NU-LHT-2M: preparations for in-situ analyses on the Moon

The present work describes the end-to-end demonstration of enriching the lunar highland regolith simulant NU-LHT-2M with loosely adsorbed water, releasing this and other volatile compounds by thermal treatment in high-vacuum, and identifying the released volatile species through mass spectrometry. This demonstration was performed to characterise how different sample conditions will affect the in-situ measurements performed by the ProSPA gas analysis instrument that is to operate at the lunar south pole on board the Russian Luna-27 lander. A laboratory breadboard was set up that allows testing of variable parameter combinations, such as different initial water contents, particle sizes, quantities, and bulk densities of the sample, as well as different heating rates. Three distinct temperature-dependent phases of outgassing were identified. Between -50 °C and 300 °C loosely adsorbed volatiles, mainly water in a mass fraction of around 0.1 % to 0.2 %, were released from the samples. Above that the samples showed mineral decomposition which led to the release of trapped water, carbon dioxide, and hydrogen sulfide. It was shown that the gas pressure produced by outgassing of the volatile species in a continuously pumped system is noticeably higher if the sample is larger, contains smaller particles, or if a higher heating rate is applied

Clinical Characteristics and Outcomes Among Individuals With Spinal Implant Infections: A Descriptive Study.

Little is known about the clinical presentation and outcomes associated with spinal implant infections. Here, we describe a single center's experience in a retrospective cohort of 109 individuals with spinal implant infections, including clinical, microbiological, therapeutic, and outcome data

Thermalisation time and specific heat of neutron stars crust

We discuss the thermalisation process of the neutron stars crust described by solving the heat transport equation with a microscopic input for the specific heat of baryonic matter. The heat equation is solved with initial conditions specific to a rapid cooling of the core. To calculate the specific heat of inner crust baryonic matter, i.e., nuclear clusters and unbound neutrons, we use the quasiparticle spectrum provided by the Hartree-Fock-Bogoliubov approach at finite temperature. In this framework we analyse the dependence of the crust thermalisation on pairing properties and on cluster structure of inner crust matter. It is shown that the pairing correlations reduce the crust thermalisation time by a very large fraction. The calculations show also that the nuclear clusters have a non-negligible influence on the time evolution of the surface temperature of the neutron star.Comment: 7 pages, 5 figures, submitted to Phys. Rev.

Frameworks for Estimating Causal Effects in Observational Settings: Comparing Confounder Adjustment and Instrumental Variables

To estimate causal effects, analysts performing observational studies in health settings utilize several strategies to mitigate bias due to confounding by indication. There are two broad classes of approaches for these purposes: use of confounders and instrumental variables (IVs). Because such approaches are largely characterized by untestable assumptions, analysts must operate under an indefinite paradigm that these methods will work imperfectly. In this tutorial, we formalize a set of general principles and heuristics for estimating causal effects in the two approaches when the assumptions are potentially violated. This crucially requires reframing the process of observational studies as hypothesizing potential scenarios where the estimates from one approach are less inconsistent than the other. While most of our discussion of methodology centers around the linear setting, we touch upon complexities in non-linear settings and flexible procedures such as target minimum loss-based estimation (TMLE) and double machine learning (DML). To demonstrate the application of our principles, we investigate the use of donepezil off-label for mild cognitive impairment (MCI). We compare and contrast results from confounder and IV methods, traditional and flexible, within our analysis and to a similar observational study and clinical trial

Dust Bowl Days: A Study of Women\u27s Lives and Experiences

A thesis exploring the lives and conditions of white women on small family farms in the Dust Bowl