We classify plethories over fields of characteristic zero, thus answering a question of Borger-Wieland and Bergman-Hausknecht. All plethories over characteristic zero fields are linear, in the sense that they are free plethories on a bialgebra. For the proof we need some facts from the theory of ring schemes where we extend previously known results. We also classify plethories with trivial Verschiebung over a perfect field of non-zero characteristic and indicate future work. / <p>QC 20151117</p>

A new implicit and compact optimization-based method is presented for high order derivative calculation for finite-volume numerical method on unstructured meshes. Highorder approaches to gradient calculation are often based on variants of the Least-Squares (L-S) method, an explicit method that requires a stencil large enough to accommodate the necessary variable information to calculate the derivatives. The new scheme proposed here is applicable for an arbitrary order of accuracy (demonstrated here up to 3rd order), and uses just the first level of face neighbors to compute all derivatives, thus reducing stencil size and avoiding stiffness in the calculation matrix. Preliminary results for a static variable field example and solution of a simple scalar transport (advection) equation show that the proposed method is able to deliver numerical accuracy equivalent to (or better than) the nominal order of accuracy for both 2nd and 3rd order schemes in the presence of a smoothly distributed variable field (i.e., in the absence of discontinuities). This new Optimization-based Gradient REconstruction (herein denoted OGRE) scheme produces, for the simple scalar transport test case, lower error and demands less computational time (for a given level of required precision) for a 3rd order scheme when compared to an equivalent L-S approach on a two-dimensional framework. For three-dimensional simulations, where the L-S scheme fails to obtain convergence without the help of limiters, the new scheme obtains stable convergence and also produces lower error solution when compared to a third order MUSCL scheme. Furthermore, spectral analysis of results from the advection equation shows that the new scheme is better able to accurately resolve high wave number modes, which demonstrates its potential to better solve problems presenting a wide spectrum of wavelengths, for example unsteady turbulent flow simulations.

In this bachelor’s thesis an introduction to the fundamentals of algebraic geometry is given. Some concepts in algebraic geometry are introduced such as Spec of a ring and Proj of a graded ring and several results related to these are either proven or stated. Special focus is directed towards defining the so called ”Hilbert scheme” which is the main topic in a lot of modern algebraic geometry research.

High-speed transmission over contemporary communication networks has drawn many research efforts. Traffic scheduling schemes which play a critical role in managing network transmission have been pervasively studied and widely implemented in various practical communication networks. In a sophisticated communication system, a variety of applications co-exist and require differentiated Quality-of-Service (QoS). Innovative scheduling schemes and hybrid scheduling disciplines which integrate multiple traditional scheduling mechanisms have emerged for QoS differentiation. This study aims to develop novel analytical models for commonly interested scheduling schemes in communication systems under more realistic network traffic and use the models to investigate the issues of design and development of traffic scheduling schemes. In the open literature, it is commonly recognized that network traffic exhibits self-similar nature, which has serious impact on the performance of communication networks and protocols. To have a deep study of self-similar traffic, the real-world traffic datasets are measured and evaluated in this study. The results reveal that selfsimilar traffic is a ubiquitous phenomenon in high-speed communication networks and highlight the importance of the developed analytical models under self-similar traffic. The original analytical models are then developed for the centralized scheduling schemes including the Deficit Round Robin, the hybrid PQGPS which integrates the traditional Priority Queueing (PQ) and Generalized Processor Sharing (GPS) schemes, and the Automatic Repeat reQuest (ARQ) forward error control discipline in the presence of self-similar traffic. Most recently, research on the innovative Cognitive Radio (CR) techniques in wireless networks is popular. However, most of the existing analytical models still employ the traditional Poisson traffic to examine the performance of CR involved systems. In addition, few studies have been reported for estimating the residual service left by primary users. Instead, extensive existing studies use an ON/OFF source to model the residual service regardless of the primary traffic. In this thesis, a PQ theory is adopted to investigate and model the possible service left by selfsimilar primary traffic and derive the queue length distribution of individual secondary users under the distributed spectrum random access protocol.

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Yes / In a novel development on previous computational fluid dynamics studies, the work reported here used an Eulerian two-fluid model with the shear stress transport k–ω turbulence closure model and bubble interaction models to simulate aeration tank performance at full scale and to identify process performance issues resulting from design parameters and operating conditions. The current operating scenario was found to produce a fully developed spiral flow. Reduction of the airflow rates to the average and minimum design values led to a deterioration of the mixing conditions and formation of extended unaerated fluid regions. The influence of bubble-induced mixing on the reactor performance was further assessed via simulations of the residence time distribution of the fluid. Internal flow recirculation ensured long contact times between the phases; however, hindered axial mixing and the presence of dead zones were also identified. Finally, two optimization schemes based on modified design and operating scenarios were evaluated. The adjustment of the airflow distribution between the control zones led to improved mixing and a 20% improvement to the mass transfer coefficient. Upgrading the diffuser grid was found to be an expensive and ineffective solution, leading to worsening of the mixing conditions and yielding the lowest mass transfer coefficient compared with the other optimization schemes studied. / College of Engineering and Physical Sciences, University of Birmingham, UK

The present work aims at an efficient, portable, and robust design of a data-distributed massively parallel DIRECT, the deterministic global optimization algorithm widely used in multidisciplinary engineering design, biological science, and physical science applications. The original algorithm is modified to adapt to different problem scales and optimization (exploration vs.\ exploitation) goals. Enhanced with a memory reduction technique, dynamic data structures are used to organize local data, handle unpredictable memory requirements, reduce the memory usage, and share the data across multiple processors. The parallel scheme employs a multilevel functional and data parallelism to boost concurrency and mitigate the data dependency, thus improving the load balancing and scalability. In addition, checkpointing features are integrated to provide fault tolerance and hot restarts. Important algorithm modifications and design considerations are discussed regarding data structures, parallel schemes, error handling, and portability. Using several benchmark functions and real-world applications, the present work is evaluated in terms of optimization effectiveness, data structure efficiency, memory usage, parallel performance, and checkpointing overhead. Modeling and analysis techniques are used to investigate the design effectiveness and performance sensitivity under various problem structures, parallel schemes, and system settings. Theoretical and experimental results are compared for two parallel clusters with different system scale and network connectivity. An analytical bounding model is constructed to measure the load balancing performance under different schemes. Additionally, linear regression models are used to characterize two major overhead sources---interprocessor communication and processor idleness, and also applied to the isoefficiency functions in scalability analysis. For a variety of high-dimensional problems and large scale systems, the data-distributed massively parallel design has achieved reasonable performance. The results of the performance study provide guidance for efficient problem and scheme configuration. More importantly, the generalized design considerations and analysis techniques are beneficial for transforming many global search algorithms to become effective large scale parallel optimization tools. / Ph. D.