Computer Programming to Advance Gravitational Lensing

The purpose of this research was to create a computer code that would numerically test a Poisson equation relating the mass distribution of a lens galaxy cluster to weak gravitational shear. Einstein’s theory of general relativity predicts that space-time is bent by massive objects, and in weak gravitational lensing, galaxy clusters act as lenses. The observable result is that galaxies far behind the gravitational lens will appear slightly more elliptical than they actually are. The ellipticity of the background galaxies is quantifiable and is directly related to the weak gravitational shear, and the shear is used to determine the mass distribution of the lensing cluster. Within the gravitational lensing community, there are two other well-known methods of determining the mass distribution of a lensing galaxy cluster from the weak gravitational shear. This new method is unique in that it uses a Poisson equation, potentially simplifying the approach to the numerical integrations required. Part of the overall goal of this project was to clarify the effectiveness of this Poisson equation method in relation to the existing methods, with the hope that the Poisson method is more accurate. The Poisson equation method described here refers to the method of numerical relaxation to determine the mass distribution of a lensing galaxy cluster by using the Poisson equation. Over 2000 lines of original C++ code were written for this project, and the code simulates a typical lensing galaxy cluster mass distribution, calculates the weak gravitational shear from the simulated cluster, adds realistic random noise to the shear data, then finally applies a second order Taylor series expansion of the Poisson equation to the noisy shear data and checks how closely the computed mass distribution matches the original simulated galaxy cluster’s distribution. This project has provided the tools needed to perform more rigorous testing of the Poisson equation

Chemistry of (Z)-2H-Heptafluorobut-2-ENE

The research described within this thesis may be divided into four areas:1) The synthesis of (8) was investigated, and was shown to produce some novel by-products, including highly fluorinated dienes and even a triene. Perhaps most remarkable, was the presence of potassium pentakis(trifluoromethyl)cyclopentadienide in the reaction residue, since this constitutes a one step synthesis of this system from non- fluorinated precursors. The isolation of this salt proved challenging, but a variety of these salts have been isolated via the formation of 5H-pentakis(trifluoromethyl)cyclopentadiene, which is reported to be the strongest non- conjugated organic acid.2) The elimination of HF from (8) to give hexafluorobut-2-yne was explored, and several successful routes have been found. Equally interesting was the variety of products formed with bases. The 'non-nucleophilic' base DBU, was even shown to behave as a difunctional nucleophile with (8), resulting in a novel tricyclic pyrrole product, and the product structure was confirmed by a single X-ray crystallographic study.3) The use of (8) as a synthon for hexafluorobut-2-yne in Diels Alder reactions was investigated. This resulted in the discovery of a novel one pot route to a variety of bis(trifluoromethylated) furans.4) The reactions of (8) with a variety of nucleophiles was explored. The products obtained were identical to those that have been formed, or would be expected to be formed, from the reaction of the same nucleophile with hexafluorobutyne

Elementary methods for incidence problems in finite fields

We use elementary methods to prove an incidence theorem for points and spheres in $\mathbb{F}_q^n$. As an application, we show that any point set of $P\subset \mathbb{F}_q^2$ with $|P|\geq 5q$ determines a positive proportion of all circles. The latter result is an analogue of Beck's Theorem for circles which is optimal up to multiplicative constants.Comment: 9 pages. In this new version, Theorem 3 has been significantly improved, whilst the proof has been simplified. Also, Ben Lund has been added as an autho

Executive summary of workshop to consider secular trends and possible pooling of data in relation to the revision of the NCHS growth charts

Alex F. Roche.Title from title screen (viewed on Oct. 19, 2010)."November 1995."Mode of access: Internet from the NCHS web site. Address as of 3/6/07: http://www.cdc.gov/nchs/data/misc/poolwork.pdfIncludes bibliographical references (p. 18-21)

Executive summary of the Growth Chart Workshop

Alex F. Roche.Title from title screen (viewed on Oct. 19, 2010)."Sponsored by the Division of Health Examination Statistics, National Center for Health Statistics, College Park, MD, December 13-14, 1992.""Prepared under Professional Services contract (Order #0009330376; Project #NM193.2; EIN2370560985)."Mode of access: Internet from the NCHS web site. Address as of 10/19/2010: http://www.cdc.gov/nchs/data/misc/growork.pdf; current access available via PURL.Includes bibliographical references

Pudendusneuralgie: Anatomisch-chirurgische Aspekte

Zusammenfassung: Anatomie:: Das Perineum wird hauptsächlich von den Nervi pudendi versorgt. Der Nervus pudendus, ein tiefliegender Dammnerv, durchläuft mehrere Zonen, in denen Kompressionen auftreten können: zwischen dem Ligamentum supraspinatum und dem Ligamentum sacrococcygeum, zwischen dem Ligamentum sacrotuberale und dem Ligamentum sacrospinale, im Alcock-Kanal sowie im Bereich des Musculus obturatorius internus. Eine derartige Kompression kann zu einem Schmerzsyndrom im Dammbereich führen. Symptome:: Klinisch äußert sich die Kompression des Nervus pudendus durch neurologische Symptome einer Nervenkompression. Derartige Kompressionen können zu schwer diagnostizierbaren Schmerzzuständen führen. Brennende Schmerzen im Dammbereich, die eindeutig dem Versorgungsgebiet des Nervus pudendus zugeordnet werden können, im Sitzen verstärkt und einseitig auftreten, müssen an eine Kompression des Nervus pudendus denken lassen. Diagnose:: Die Diagnose stützt sich auf Anamnese und Klinik. Elektrophysiologische und bildgebende Untersuchungen dienen dem Ausschluss anderer Pathologien. Die diagnostische Infiltration des Canalis pudendalis kann in 30-40% der Fälle therapeutisch sein. Ein chirurgischer Eingriff zur Dekompression ist in 65-70% der Fälle erfolgreich. Da die Besserung oft nicht sofort eintritt, müssen die Patienten über diese Tatsache präoperativ informiert werden. Eine multidisziplinäre Betreuung ist unerlässlic