Connectedness of the Isospectral Manifold for One-Dimensional Half-Line Schr\"odinger Operators

Let V_0 be a real-valued function on [0,\infty) and V\in L^1([0,R]) for all R>0 so that H(V_0)= -\f{d^2}{dx^2}+V_0 in L^2([0,\infty)) with u(0)=0 boundary conditions has discrete spectrum bounded from below. Let \calM (V_0) be the set of V so that H(V) and H(V_0) have the same spectrum. We prove that \calM(V_0) is connected.Comment: LaTeX, 5 page

A new approach to inverse spectral theory, II. General real potentials and the connection to the spectral measure

We continue the study of the A-amplitude associated to a half-line Schrodinger operator, -d^2/dx^2+ q in L^2 ((0,b)), b <= infinity. A is related to the Weyl-Titchmarsh m-function via m(-\kappa^2) =-\kappa - \int_0^a A(\alpha) e^{-2\alpha\kappa} d\alpha +O(e^{-(2a -\epsilon)\kappa}) for all \epsilon > 0. We discuss five issues here. First, we extend the theory to general q in L^1 ((0,a)) for all a, including q's which are limit circle at infinity. Second, we prove the following relation between the A-amplitude and the spectral measure \rho: A(\alpha) = -2\int_{-\infty}^\infty \lambda^{-\frac12} \sin (2\alpha \sqrt{\lambda})\, d\rho(\lambda) (since the integral is divergent, this formula has to be properly interpreted). Third, we provide a Laplace transform representation for m without error term in the case b<\infty. Fourth, we discuss m-functions associated to other boundary conditions than the Dirichlet boundary conditions associated to the principal Weyl-Titchmarsh m-function. Finally, we discuss some examples where one can compute A exactly.Comment: 41 pages, published versio

On the Koplienko spectral shift function, I. Basics

We study the Koplienko Spectral Shift Function (KoSSF), which is distinct from the one of Krein (KrSSF). KoSSF is defined for pairs $A,B$ with (A-B)\in\calI_2, the Hilbert-Schmidt operators, while KrSSF is defined for pairs $A,B$ with (A-B)\in\calI_1, the trace class operators. We review various aspects of the construction of both KoSSF and KrSSF. Among our new results are: (i) that any positive Riemann integrable function of compact support occurs as a KoSSF; (ii) that there exist $A,B$ with (A-B)\in\calI_2 so $\det_2((A-z)(B-z)^{-1})$ does not have nontangential boundary values; (iii) an alternative definition of KoSSF in the unitary case; and (iv) a new proof of the invariance of the a.c. spectrum under \calI_1-perturbations that uses the KrSSF.Comment: Submitted to the Marchenko and Pastur birthday issue of Journal of Mathematical Physics, Analysis and Geometr

p-Dimethylaminobenzaldehyde: preliminary investigations into a novel reagent for the detection of latent fingermarks on paper surfaces

A new method for the detection of latent fingermarks on paper surfaces using p-dimethylaminobenzaldehyde (DMAB) is described. The method is based upon the reaction of DMAB with the amino acids present in the latent fingermark to give a yellow-brown impression that is photoluminescent when illuminated with a high intensity filtered light source at 490 nm and viewed through orange goggles (OG550). A wet contact method proved effective on non-fragile porous substrates such as white photocopy paper and various other substrates, while a dry contact (solventless) method afforded development on thermal paper. Luminescence spectrophotometry of developed L-alanine, glycine and L-serine spots on paper was used to confirm that DMAB was reacting with amino acids in the latent fingermark

Ein Assistenzsystem zur kontextsensitiven Unterstützung des anforderungsbasierten Wissensmanagements

Das Anforderungs- und Wissensmanagement wird in kleinen und mittelständischen Unternehmen häufig in seiner Wichtigkeit unterschätzt. Vor allem das systematische Dokumentieren und Verwalten von Anforderungen, kann über Erfolg oder Misserfolg eines Projektes entscheiden. Werden Anforderungen nicht vollständig dokumentiert oder nicht an die relevanten Personen kommuniziert, kann es zu Abweichungen gegenüber dem ursprünglichen Kundenwunsch kommen, was im schlimmsten Fall zum Scheitern des Projekts führen kann. Stand heute werden überwiegend Office-basierte Softwarelösungen für die Dokumentation und Verwaltung von Informationen, Anforderungen und Aufgaben verwendet. Diese führen jedoch aufgrund ihres filebasierten Ansatzes zu häufigen Redundanzen oder unterschiedlichen Versionsständen, was zu Fehlern führt. Spezialisierte Softwarelösungen für das Verwalten von Anforderungen hingegen sind meist für Experten entwickelt worden und erfordern daher Schulungen und/oder neue Prozesse. Das schreckt viele Unternehmer davor ab derartige Lösungen in ihr Unternehmen zu integrieren. Die vorliegende Arbeit nimmt sich daher zum Ziel, ein Assistenzsystem zur kontextsensitiven Unterstützung eines anforderungs-basierten Wissensmanagements zu entwickeln, welches vor allem kleine und mittelständische Unternehmen befähigen soll, vollständige und standardisierte Anforderungs- und Wissensdokumentationen ohne aufwändige Schulungen oder Prozesse zu erstellen und zu verwalten. Die entwickelten Konzepte werden anhand einer prototypischen Implementierung evaluiert und die generelle Machbarkeit bewiesen

Benchmarking Big Data Technologies for Energy Procurement Efficiency

The electrical power industry is undergoing radical change due to the push for renewable energy that makes energy supply less predictable. Smart meters along with analytics software can grant insights into customer-specific consumption and thereby enable a better match between the demand and supply side for an electric utility. However, the vast amount of allocatable smart metering data and complexity of analytics pose challenges to database system. We address the implementation of an analytics ap-proach to optimize customer portfolios, eventually preventing excess energy procurement. Using real-world and simulated data, we test the suitability of big data approaches as well as traditional relational database technology. Furthermore, we present solutions based on big data platforms and demonstrate their cost effectiveness and performance. Our findings suggest economic feasibility of big data solutions for large utilities. Small and medium-sized utilities are advised to invest in more cost-effective solutions such as cluster-based systems