Loose entry formulas and the reduction of dixon determinant entries

Master'sMASTER OF SCIENC

Computer Science for Continuous Data:Survey, Vision, Theory, and Practice of a Computer Analysis System

Building on George Boole's work, Logic provides a rigorous foundation for the powerful tools in Computer Science that underlie nowadays ubiquitous processing of discrete data, such as strings or graphs. Concerning continuous data, already Alan Turing had applied "his" machines to formalize and study the processing of real numbers: an aspect of his oeuvre that we transform from theory to practice.The present essay surveys the state of the art and envisions the future of Computer Science for continuous data: natively, beyond brute-force discretization, based on and guided by and extending classical discrete Computer Science, as bridge between Pure and Applied Mathematics

Analysis and Design of Low-Cost Waveguide Filters for Wireless Communications

The area of research of this thesis is built around advanced waveguide filter structures. Waveguide filters and the waveguide technology in general are renowned for high power capacity, low losses and excellent electromagnetic shielding. Waveguide filters are important components in fixed wireless communications as well as in satellite and radar systems. Furthermore, their advantages and utilization become even greater with increase in frequency, which is a trend in modern communication systems because upper frequency bands offer larger channel capacities. However, waveguide filters are relatively bulky and expensive. To comply with more and more demanding miniaturization and cost-cutting requirements, compactness and economical design represent some of the main contemporary focuses of interest. Approaches that are used to achieve this include use of planar inserts to build waveguide discontinuities, additive manufacturing and substrate integration. At the same time, waveguide filters still need to satisfy opposed stringent requirements like small insertion loss, high selectivity and multiband operation. Another difficulty that metal waveguide components face is integration with other circuitry, especially important when solid-state active devices are included. Thus, improvements of interconnections between waveguide and other transmission interfaces are addressed too. The thesis elaborates the following aspects of work: Further analysis and improved explanations regarding advanced waveguide filters with E-plane inserts developed by the Wireless Communications Research Group, using both cross coupled resonators and extracted pole sections (Experiments with higher filter orders, use of tuning screws, degrees of freedom in design, etc. Thorough performance comparison with competing filter technologies) - Proposing novel E-plane filter sections with I-shaped insets - Extension of the E-plane filtering structures with metal fins to new compact dual band filters with high frequency selectivity and miniaturized diplexers. - Introduction of easy-to-build waveguide filters with polymer insert frames and high-performance low-profile cavity filters, taking advantage of enhanced fabrication capabilities when using additive manufacturing - Developing new substrate integrated filters, as well as circuits used to transfer signals between different interfaces Namely, these are substrate integrated waveguide to metal waveguide planar transitions that do not require any modifications of the metal waveguides. Such novel transitions have been designed both for single and orthogonal signal polarizations

The Bernstein basis in set-theoretic geometric modelling

SIGLEAvailable from British Library Document Supply Centre-DSC:DXN037062 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Extremal Metric and Topological Properties of Vertex Transitive and Cayley Graphs

We shall consider problems in two broad areas of mathematics, namely the area of the degree diameter problem and the area of regular maps. In the degree diameter problem we investigate finding graphs as large as possible with a given degree and diameter. Further, we may consider additional properties of such extremal graphs, for example restrictions on the kinds of symmetries that the graph in question exhibits. We provide two pieces of research relating to the degree diameter problem. First, we provide a new derivation of the Hoffman-Singleton graph and show that this derivation may be used with minor modification to derive the Bosák graph. Ultimately we show that no further natural modification of the construction we use can derive any other Moore or mixed-Moore graphs. Second, we answer the previously open question of whether the Gómez graphs, which are known to be vertex-transitive, are in addition also Cayley. In doing this, we also generalise the construction of the Gómez graphs and show that the Gómez graphs are the largest graphs for given degree and diameter following the generalised construction. We also provide two pieces of research relating to regular maps. We aim to address the related questions of for which triples of parameters k, l and m there exist finite regular maps of face length k, vertex order l and Petrie walk length m. We then address the related question of determining for which n there exist regular maps which are self dual and self Petrie dual which have face length, vertex order and Petrie dual walk length n. We address both questions by constructions of regular maps in fractional linear groups, necessarily leading us to study some interesting related number theoretic questions

Q(sqrt(-3))-Integral Points on a Mordell Curve

We use an extension of quadratic Chabauty to number fields,recently developed by the author with Balakrishnan, Besser and M ̈uller,combined with a sieving technique, to determine the integral points overQ(√−3) on the Mordell curve y2 = x3 − 4

Feynman integrals and hyperlogarithms

We study Feynman integrals in the representation with Schwinger parameters and derive recursive integral formulas for massless 3- and 4-point functions. Properties of analytic (including dimensional) regularization are summarized and we prove that in the Euclidean region, each Feynman integral can be written as a linear combination of convergent Feynman integrals. This means that one can choose a basis of convergent master integrals and need not evaluate any divergent Feynman graph directly. Secondly we give a self-contained account of hyperlogarithms and explain in detail the algorithms needed for their application to the evaluation of multivariate integrals. We define a new method to track singularities of such integrals and present a computer program that implements the integration method. As our main result, we prove the existence of infinite families of massless 3- and 4-point graphs (including the ladder box graphs with arbitrary loop number and their minors) whose Feynman integrals can be expressed in terms of multiple polylogarithms, to all orders in the epsilon-expansion. These integrals can be computed effectively with the presented program. We include interesting examples of explicit results for Feynman integrals with up to 6 loops. In particular we present the first exactly computed counterterm in massless phi^4 theory which is not a multiple zeta value, but a linear combination of multiple polylogarithms at primitive sixth roots of unity (and divided by $\sqrt{3}$). To this end we derive a parity result on the reducibility of the real- and imaginary parts of such numbers into products and terms of lower depth.Comment: PhD thesis, 220 pages, many figure

Proceedings of the GIS Research UK 18th Annual Conference GISRUK 2010

This volume holds the papers from the 18th annual GIS Research UK (GISRUK). This year the conference, hosted at University College London (UCL), from Wednesday 14 to Friday 16 April 2010. The conference covered the areas of core geographic information science research as well as applications domains such as crime and health and technological developments in LBS and the geoweb. UCL’s research mission as a global university is based around a series of Grand Challenges that affect us all, and these were accommodated in GISRUK 2010. The overarching theme this year was “Global Challenges”, with specific focus on the following themes: * Crime and Place * Environmental Change * Intelligent Transport * Public Health and Epidemiology * Simulation and Modelling * London as a global city * The geoweb and neo-geography * Open GIS and Volunteered Geographic Information * Human-Computer Interaction and GIS Traditionally, GISRUK has provided a platform for early career researchers as well as those with a significant track record of achievement in the area. As such, the conference provides a welcome blend of innovative thinking and mature reflection. GISRUK is the premier academic GIS conference in the UK and we are keen to maintain its outstanding record of achievement in developing GIS in the UK and beyond

Robot Manipulators

Robot manipulators are developing more in the direction of industrial robots than of human workers. Recently, the applications of robot manipulators are spreading their focus, for example Da Vinci as a medical robot, ASIMO as a humanoid robot and so on. There are many research topics within the field of robot manipulators, e.g. motion planning, cooperation with a human, and fusion with external sensors like vision, haptic and force, etc. Moreover, these include both technical problems in the industry and theoretical problems in the academic fields. This book is a collection of papers presenting the latest research issues from around the world