Elliptic boundary value problems with Gaussian white noise loads

Linear second order elliptic boundary value problems (BVP) on bounded Lipschitz domains are studied in the case of Gaussian white noise loads. The challenging cases of Neumann and Robin BVPs are considered.The main obstacle for usual variational methods is the irregularity of the load. In particular, the Neumann boundary values are not well-defined.In this work, the BVP is formulated by replacing the continuity of boundary trace mappings with measurability. Instead of variational methods alone, the novel BVP derives also from Cameron–Martin space techniques.The new BVP returns the study of irregular white noise to the study of $L^2$-loads.     

Asymptotic Behaviour of Coupled Systems in Discrete and Continuous Time

This paper investigates the asymptotic behaviour of solutions to certain infinite systems of coupled recurrence relations. In particular, we obtain a characterisation of those initial values which lead to a convergent solution, and for initial values satisfying a slightly stronger condition we obtain an optimal estimate on the rate of convergence. By establishing a connection with a related problem in continuous time, we are able to use this optimal estimate to improve the rate of convergence in the continuous setting obtained by the authors in a previous paper. We illustrate the power of the general approach by using it to study several concrete examples, both in continuous and in discrete time.     

Inverse Scattering Problem for a Two Dimensional Random Potential

We study an inverse problem for the two-dimensional random Schrödinger equation (Δ + q + k ²)u = 0. The potential q(x) is assumed to be a Gaussian random function whose covariance operator is a classical pseudodifferential operator. We show that the backscattered field, obtained from a single realization of the random potential q, determines uniquely the principal symbol of the covariance operator of q. The analysis is carried out by combining harmonic and microlocal analysis with stochastic methods.     

Correlation of aluminum doping and lithiation temperature with electrochemical performance of LiNi1-xAlxO2 cathode material

Journal of Solid State Electrochemistry - This article presents a process for producing LiNi1-xAlxO2 (0 <  ×  < 0.05) cathode material with...     

Vibrational spectroscopy of articular cartilage

Articular cartilage is a connective tissue that is located at the ends of long bones. Type II collagen, proteoglycans, water, and chondrocytes are the main constituents of articular cartilage. Osteoarthritis, the most common joint disease in the world, causes degenerative changes in articular cartilage tissue. Fourier transform infrared, Raman, and near infrared spectroscopic techniques offer versatile tools to assess biochemical composition and quality of articular cartilage. These vibrational spectroscopic techniques can be used to broaden our understanding about the compositional changes during osteoarthritis, and they also hold promise in disease diagnostics. In this article, the current literature of articular cartilage spectroscopic studies is reviewed.     

An n-dimensional Borg–Levinson theorem for singular potentials

We prove in this paper that the boundary spectral data, i.e. the Dirichlet eigenvalues and normal derivatives of the eigenfunctions at the boundary uniquely determines a potential in L^p on bounded domains. This result generalizes the result of Nachman, Sylvester and Uhlmann to unbounded potentials. This result can be viewed as a generalization of the classical one-dimensional Borg–Levinson theorem.     

Robustness of strong stability of semigroups

In this paper we study the preservation of strong stability of strongly continuous semigroups on Hilbert spaces. In particular, we study a situation where the generator of the semigroup has a finite number of spectral points on the imaginary axis and the norm of its resolvent operator is polynomially bounded near these points. We characterize classes of perturbations preserving the strong stability of the semigroup. In addition, we improve recent results on preservation of polynomial stability of a semigroup under perturbations of its generator. Theoretic results are illustrated with an example where we consider the preservation of the strong stability of a multiplication semigroup.     

Preprocessing Strategies for Sparse Infrared Spectroscopy: A Case Study on Cartilage Diagnostics

The aim of the study was to optimize preprocessing of sparse infrared spectral data. The sparse data were obtained by reducing broadband Fourier transform infrared attenuated total reflectance spectra of bovine and human cartilage, as well as of simulated spectral data, comprising several thousand spectral variables into datasets comprising only seven spectral variables. Different preprocessing approaches were compared, including simple baseline correction and normalization procedures, and model-based preprocessing, such as multiplicative signal correction (MSC). The optimal preprocessing was selected based on the quality of classification models established by partial least squares discriminant analysis for discriminating healthy and damaged cartilage samples. The best results for the sparse data were obtained by preprocessing using a baseline offset correction at 1800 cm⁻¹, followed by peak normalization at 850 cm⁻¹ and preprocessing by MSC.