An easy proof of Jensen's theorem on the uniqueness of infinity harmonic functions

We present a new, easy, and elementary proof of Jensen's Theorem on the uniqueness of infinity harmonic functions. The idea is to pass to a finite difference equation by taking maximums and minimums over small balls.Comment: 4 pages; comments added, proof simplifie

Convexity criteria and uniqueness of absolutely minimizing functions

We show that absolutely minimizing functions relative to a convex Hamiltonian $H:\mathbb{R}^n \to \mathbb{R}$ are uniquely determined by their boundary values under minimal assumptions on $H.$ Along the way, we extend the known equivalences between comparison with cones, convexity criteria, and absolutely minimizing properties, to this generality. These results perfect a long development in the uniqueness/existence theory of the archetypal problem of the calculus of variations in $L^\infty.$Comment: 34 page

Electronic structure and ferroelectricity in SrBi2Ta2O9

The electronic structure of SrBi2Ta2O9 is investigated from first-principles, within the local density approximation, using the full-potential linearized augmented plane wave (LAPW) method. The results show that, besides the large Ta(5d)-O(2p) hybridization which is a common feature of the ferroelectric perovskites, there is an important hybridization between bismuth and oxygen states. The underlying static potential for the ferroelectric distortion and the primary source for ferroelectricity is investigated by a lattice-dynamics study using the Frozen Phonon approach.Comment: 17 pages, 7 figures. Phys. Rev. B, in pres

A Placebo‐Controlled Double‐Blinded Randomized Pilot Study of Combination Phytotherapy in Biochemically Recurrent Prostate Cancer

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/136500/1/pros23317_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/136500/2/pros23317.pd

Variational Multiscale Stabilization and the Exponential Decay of Fine-scale Correctors

This paper addresses the variational multiscale stabilization of standard finite element methods for linear partial differential equations that exhibit multiscale features. The stabilization is of Petrov-Galerkin type with a standard finite element trial space and a problem-dependent test space based on pre-computed fine-scale correctors. The exponential decay of these correctors and their localisation to local cell problems is rigorously justified. The stabilization eliminates scale-dependent pre-asymptotic effects as they appear for standard finite element discretizations of highly oscillatory problems, e.g., the poor $L^2$ approximation in homogenization problems or the pollution effect in high-frequency acoustic scattering

An Optimal Protocol to Analyze the Rat Spinal Cord Proteome

Since the function of the spinal cord depends on the proteins found there, better defing the normal Spinal Cord Proteome is an important and challenging task. Although brain and cerebrospinal fluid samples from patients with different central nervous system (CNS) disorders have been studied, a thorough examination of specific spinal cord proteins and the changes induced by injury or associated to conditions such as neurodegeneration, spasticity and neuropathies has yet to be performed. In the present study, we aimed to describe total protein content in the spinal cord of healthy rats, employing different proteomics tools. Accordingly, we have developed a fast, easy, and reproducible sequential protocol for protein extraction from rat spinal cords. We employed conventional two dimensional electrophoresis (2DE) in different pH ranges (eg. 4–7, 3–11 NL) combined with identification by mass spectrometry (MALDI-TOF/TOF), as well as first dimension protein separation combined with Liquid Chromatography Mass Spectrometry/Mass Spectrometry (LC-MS/MS) to maximise the benefits of this technology. The value of these techniques is demonstrated here by the identification of several proteins known to be associated with neuroglial structures, neurotransmission, cell survival and nerve growth in the central nervous system. Furthermore this study identified many spinal proteins that have not previously been described in the literature and which may play an important role as either sensitive biomarkers of dysfunction or of recovery after Spinal Cord Injury