Dissertations / Theses on the topic 'Analytic'
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Hassell, Andrew. "Analytic surgery and analytic torsion." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/32611.
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Abobakr, Mona R. H. "Quantum circuit analysis using analytic functions." Thesis, University of Bradford, 2019. http://hdl.handle.net/10454/18330.
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In this thesis, classical computation is first introduced. Finite quantum systems are considered with D-dimensional Hilbert space, and position x and
momentum p taking values in Z(D) (the integers modulo D). An analytic rep resentation of finite quantum systems that use Theta function is presented and
considered. The first novel part of this thesis is contribution to study reversible
classical CNOT gates and their binary inputs and outputs with reversible cir cuits. Furthermore, a reversible classical Toffoli gates are considered, as well as
implementation of a Boolean expression with classical CNOT and Toffoli gates.
Reversible circuits with classical CNOT and Toffoli gates are also considered.
The second novel part of this thesis the study of quantum computation in
terms of CNOT and Toffoli gates. Analytic representations and their zeros
are considered, while zeros of the inputs and outputs for quantum CNOT and
Toffoli gates are studied. Also, approximate computation of their zeros on the
output are calculated. Finally, some quantum circuits are discussed.
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Lewis, Kenneth Anthony. "Analytic Structures." Thesis, University of Southampton, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.485516.
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This thesis presents the development of an innovative method for describing the behaviour of steel members under load. It uses a direct solution to a set of six differential equations key to the state of a cross-section of a member. Because the method focuses upon cross-sectional response to· loading, it incorporates member deflection and is ideal for use in numerical equation solvers which are becoming more prevalent as personal computing power continues to rise. The six equations are described, a novel method for ascertaining their solutions is introduced and the whole system is set to . work. Simulated structures include a f~ily of pinned struts of varying slenderness, and single-span steel portal frames. The method may be used at varying levels of detail, having the flexibility to make use of a selection of stress-strain relationships, and families of struts are tested under a number of these conditions. The results of these simulations are compared and the result best comparable to design code crushing strength is that which carries the most data: a full elastic-plastic-strain-hardening stress strain curve used in simulations which consider the impact of bending moments and thrusts through each cross-section, without neglecting the internal stresses of hotrolled steel sections. The portal frame computer models are an evolution of the strut simulations, providing a rigorous analysis of a sample frame as well as comparisons with existing design methods. Results from both series of structural model are discussed before future developments of the method and its application to enhanced simulations.
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Collautt, C. F. "Analytic rigour." Thesis, University of Essex, 2009. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.495807.
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Ahmad, Khan Mumtaz, and M. Najmi. "Discrete analytic continuation of a (p, q)- analytic function." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/95729.
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Ens, Barrett. "Spatial Analytic Interfaces." ACM, 2014. http://hdl.handle.net/1993/31595.
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We propose the concept of spatial analytic interfaces (SAIs) as a tool for performing in-situ, everyday analytic tasks. Mobile computing is now ubiquitous and provides access to information at nearly any time or place. However, current mobile interfaces do not easily enable the type of sophisticated analytic tasks that are now well-supported by desktop computers. Conversely, desktop computers, with large available screen space to view multiple data visualizations, are not always available at the ideal time and place for a particular task. Spatial user interfaces, leveraging state-of-the-art miniature and wearable technologies, can potentially provide intuitive computer interfaces to deal with the complexity needed to support everyday analytic tasks. These interfaces can be implemented with versatile form factors that provide mobility for doing such taskwork in-situ, that is, at the ideal time and place.
We explore the design of spatial analytic interfaces for in-situ analytic tasks, that leverage the benefits of an upcoming generation of light-weight, see-through, head-worn displays. We propose how such a platform can meet the five primary design requirements for personal visual analytics: mobility, integration, interpretation, multiple views and interactivity. We begin with a design framework for spatial analytic interfaces based on a survey of existing designs of spatial user interfaces. We then explore how to best meet these requirements through a series of design concepts, user studies and prototype implementations. Our result is a holistic exploration of the spatial analytic concept on a head-worn display platform.October 2016
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Xu, Su Huai. "Random analytic signals." Thesis, University of Macau, 2009. http://umaclib3.umac.mo/record=b1944056.
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Peatfield, Nicholas John. "Analytic Zariski structures." Thesis, University of Oxford, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.398234.
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Simandiras, Emmanuel D. "Analytic energy derivatives." Thesis, University of Cambridge, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.257217.
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Porta, Mauro. "Derived analytic geometry." Sorbonne Paris Cité, 2016. http://www.theses.fr/2016USPCC118.
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Dans cette thèse on extend ultérieurement les fondations de la géométrie analytique complexe proposées par J. Lurie dans DAG IX. En plus, on montre que ses idées peuvent être utilisées pour développer une théorie des espaces analytiques non-archimédiens dérivés. Les motivations arrivent de la théorie de Hodge nonabelienne et de la symétrie miroir. Les résultats principaux contiennent les généralisations du théorème de Grauert et des théorèmes GAGA pour les champs analytiques dérivés (et donc en particulier pour les orbifolds complexes et les analogues analytiques des champs d'Artin). On étudie en détail la théorie de la déformation analytique, et on développe le complexe cotangent analytique et ses propriétés de base. Finalement, on obtient une version analytique du théorème de représentabilité de Lurie. Pendant toute la thèse, on utilise le langage des infini catégorieIn this thesis we extend further the foundations of derived C-analytic geometry proposed by J. Lurie in DAG IX. Moreover, we show that his ideas can be used to develop a theory of derived non-archimdean spaces. Motivations are coming from nonabelian Hodge theory and from mirror symmetry. Among the main results there are generalizations of Grauert theorem and GAGA theorems for derived analytic stacks (including C-analytic orbifolds and analytic analogues of Artin stacks). We extensively study analytic deformation theory, including the analytic cotangent complex and its basic properties. Finally, we obtain an analytic version of Lurie's representability theorem. We use the language of infinity categories throughout the whole thesis
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Figueirinhas, Diogo. "On the Properties of Gevreyand Ultra-analytic Spaces." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-55596.
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We look at the algebraic properties of Gevrey, analytic and ultraanalytic function spaces, namely their closure under composition, division and inversion. We show that both Gevrey and ultra-analytic spaces, G s with 1 ≤ s < ∞ and 0 < s < 1 respectively, form algebras. Closure under composition, division and inversion is shown to hold for the Gevrey case. For the ultra-analytic case we show it is not closed under composition. We also show that if a function is in G s , with 0 < s < 1 on a compact set, then it is in G s everywhere.
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Singh, Rajinder J. "A Meta-Analytic Review of Functional Analytic Psychotherapy Single-Subject Research." Bowling Green State University / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1453574647.
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Cai, Yue. "Nondestructive multi-element analysis of colorants for forensic applications and artwork authentication." HKBU Institutional Repository, 2013. https://repository.hkbu.edu.hk/etd_ra/1528.
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Seasholtz, Mary Beth. "Parsimonious construction of multivariate calibration models in chemometrics /." Thesis, Connect to this title online; UW restricted, 1992. http://hdl.handle.net/1773/8705.
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Tabar, Matthew J. "Analysis of decisions made using the analytic hierarchy process." Thesis, Monterey, California: Naval Postgraduate School, 2013. http://hdl.handle.net/10945/37727.
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Approved for public release; distribution is unlimitedThis thesis analyzes the use of the Analytic Hierarchy Process (AHP) as a decision-making tool. The analysis shows what information can be gained about a military decision-maker who uses the AHP, and how this information can be utilized, permitting U.S. and allied forces to execute efficient and effective military operations. A case study of the AHP decision-making process demonstrates techniques that can be used to garner information about the decision-maker and potentially influence their future decisions.
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Venkataraman, Siddharth. "Analytic, Simulation and Experimental Analysis of Fluid-Pipe Systems." Thesis, KTH, MWL Marcus Wallenberg Laboratoriet, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-249996.
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Inviscid fluid inside thin pipe system is first analytically solved for eigenfrequencies and eigenmodes using Modal Interaction Model method with fluid-structure interaction condition at boundary. Shear-diaphragm boundary condition is used for comparing and validating Analytic results with Simulation using COMSOL Multiphysics. Effect of viscosity is also compared using Newtonian fluid model. Experiment is performed using simple pipe geometry and fluid to measure transfer accelerance which is post-processed to extract cirumferential modes up to order 4; this is used to compare and validate Experiemental results with Simulation. Good correlation is obtained between Analytic, Experiment and Simulation results with n=0 breathing modes requiring modification of governing equations to incorporate compressibility effects due to changing pipe cross-section area.En analytisk lösning för egenfrekvenser och egenmoder för en icke-viskös fluid inuti ett tunt rörsystem är först framtagen med användning av en modbaserad modell för interaktion mellan fluid och struktur som randvillkor. Idealiserad randvillkor används för att jämföra och validera analytiska resultat med simulationer i COMSOL Multiphysics. Effekten av viskositet jämförs också med hjälp av en Newtonsk fluidmodell. Experiment genomförs med simpel rörgeometri samt fluid för att mäta acceleransen som är analyserad för till att få ut mo-der i omkretsled upp till fjärde ordningen; detta i sin tur används för att jämföra och validera de experimentella resultaten med simulering-ar. Det erhålls bra korrelation mellan de analytiska-, simulerade- samt experimentella resultaten. Undantaget för n=0 grundmoder då krävs modifikation av differentialekvationerna till att inkorporera kompressibilitetseffekter
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Johnson, Robert David. "Parallel analytic tableaux systems." Thesis, Queen Mary, University of London, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.362777.
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Guo, Charng Rang. "On analytic number theory." Thesis, University of Oxford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.357394.
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Gartside, Paul Michael. "Monotonicity in analytic topology." Thesis, University of Oxford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.334965.
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Volec, Jan. "Analytic methods in combinatorics." Thesis, University of Warwick, 2014. http://wrap.warwick.ac.uk/71063/.
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In the thesis, we apply the methods from the recently emerged theory of limits of discrete structures to problems in extremal combinatorics. The main tool we use is the framework of ag algebras developed by Razborov. We determine the minimum threshold d that guarantees a 3-uniform hypergraph to contain four vertices which span at least three edges, if every linear-size subhypergraph of the hypergraph has density more than d. We prove that the threshold value d is equal to 1=4. The extremal configuration corresponds to the set of cyclically oriented triangles in a random orientation of a complete graph. This answers a question raised by Erdos. We also use the ag algebra framework to answer two questions from the extremal theory of permutations. We show that the minimum density of monotone subsequences of length �ve in any permutation is asymptotically equal to 1=256, and that the minimum density of monotone subsequences of length six is asymptotically equal to 1=3125. Furthermore, we characterize the set of (su�ciently large) extremal con�gurations for these two problems. Both the values and the characterizations of extremal con�gurations were conjectured by Myers. Flag algebras are also closely related to the theory of dense graph limits, where the main objects of study are convergent sequences of graphs. Such a sequence can be assigned an analytic object called a graphon. In this thesis, we focus on finitely forcible graphons. Those are graphons determined by �nitely many subgraph densities. We construct a �nitely forcible graphon such that the topological space of its typical vertices is not compact. In our construction, the space even fails to be locally compact. This disproves a conjecture of Lovasz and Szegedy.
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Lesák, Petr. "Metoda Analytic Network Process." Master's thesis, Vysoká škola ekonomická v Praze, 2010. http://www.nusl.cz/ntk/nusl-72098.
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The thesis is concerned with Multi-Criteria Decision Making, in particular the Analytic Network Process method. The introductory part is dedicated to compile all the theory necessary to understand the method and utilized throughout the paper. The Analytic Hierarchy Process method is described and later generalized in the form of the ANP. Part of the paper is a description of available software products that are able to solve the ANP models. The main focus is on the application of the method, the usability and efficiency of possible use in macroeconomics is tested. In the third chapter a macroeconomic forecasting model is developed in cooperation with experts. The results of this model are compared with the best available up-to-date forecasts by local and international institutions.
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Rollens, Michael William. "Theory of analytic journalism." Phd thesis, Canberra, ACT : The Australian National University, 2014. http://hdl.handle.net/1885/151613.
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Shimokawa, Kenichi. "A Patient-Focused Psychotherapy Quality Assurance System: Meta-Analytic and Multilevel Analytic Review." BYU ScholarsArchive, 2010. https://scholarsarchive.byu.edu/etd/2544.
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Outcome research has documented worsening among a minority of the patient population (5 to 10%). In this study a psychotherapy quality assurance system intended to enhance outcomes in patients at risk of treatment failure was reviewed through the use of meta-analytic, mega-analytic, and multilevel analytic techniques. A pooled dataset from six major studies conducted at a large university counseling center and a hospital outpatient setting (N = 6151, mean age = 23.3 years, female = 63.2%, Caucasian = 85%) were re-analyzed to examine the effects of progress feedback on patient outcome. In this quality assurance system, the Outcome Questionnaire-45 was routinely administered to patients to monitor their therapeutic progress and was utilized as part of an early alert system to identify patients at risk of treatment failure. Patient progress feedback based on this alert system was provided to clinicians to help them intervene before treatment failure occurred. Intent-to-treat and efficacy analyses of the effects of feedback interventions were conducted to obtain the estimates of effects expected from implementation of this quality assurance system as a policy as well as in clinical trials. Three forms of feedback interventions—integral elements of this quality assurance system—were effective in enhancing treatment outcome, especially for signal alarm patients. Two of the three feedback interventions were also effective in preventing treatment failure (Clinical Support Tools and the provision of patient progress feedback to therapists). The Clinical Support Tool intervention was effective not only in terms of the amount of outcome enhancing effect, but also in the rate of patient recovery. The current state of evidence appears to support the efficacy and effectiveness of feedback interventions in enhancing treatment outcome.
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Mampa, Richard Mokome. "X-ray and NMR spectropscopic studies of selected heterocyclic compounds of phosphorus and nitrogen /." Pretoria : [s.n.], 2000. http://upetd.up.ac.za/thesis/available/etd-02092006-155713/.
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Vazquez, Rita Esther Zapata. "Bayesian cost-effectiveness analysis based on a decision analytic model." Thesis, University of Sheffield, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.522516.
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Zhao, Kaiyu. "A Model-driven Visual Analytic Framework for Local Pattern Analysis." Digital WPI, 2016. https://digitalcommons.wpi.edu/etd-dissertations/446.
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The ultimate goal of any visual analytic task is to make sense of the data and gain insights. Unfortunately, the process of discovering useful information is becoming more challenging nowadays due to the growing data scale. Particularly, the human cognitive capabilities remain constant whereas the scale and complexity of data are not. Meanwhile, visual analytics largely relies on human analytic in the loop which imposes challenge to traditional human-driven workflow. It is almost impossible to show every aspect of details to the user while diving into local region of the data to explain phenomenons hidden in the data. For example, while exploring the data subsets, it is always important to determine which partitions of data contain more important information. Also, determining the subset of features is vital before further doing other analysis. Furthermore, modeling on these subsets of data locally can yield great finding but also introduces bias. In this work, a model driven visual analytic framework is proposed to help identify interesting local patterns from the above three aspects. This dissertation work aims to tackle these subproblems in the following three topics: model-driven data exploration, model-driven feature analysis and local model diagnosis. First, the model-driven data exploration focus on the problem of modeling subset of data to identify the co-movement of time-series data within certain subset time partitions, which is an important application in a number of domains such as medical science, finance, business and engineering. Second, the model-driven feature analysis is to discover the important subset of interesting features while analyzing local feature similarities. Within the financial risk dataset collected by domain expert, we discover that the feature correlation among different data partitions (i.e., small and large companies) are very different. Third, local model diagnosis provides a tool to identify interesting local regression models at local regions of the data space which makes it possible for the analysts to model the whole data space with a set of local models while knowing the strength and weakness of them. The three tools provide an integrated solution for identifying interesting patterns within local subsets of data.
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Han, Jin Hee. "Isolation of phenylalanine hydroxylases and enzymatic studies with 3- and 4- pyridylalanine." Diss., Georgia Institute of Technology, 1988. http://hdl.handle.net/1853/27313.
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Kostov, I. K., I. Krichever, M. Mineev--Weinstein, P. B. Wiegmann, A. Zabrodin, and Andreas Cap@esi ac at. "$\tau$-Function for Analytic Curves." ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi888.ps.
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Farah, Ilijas. "Analytic ideals and their quotients." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ27642.pdf.
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Jones, Megan. "Immunisation : a discourse analytic study /." Title page, abstract and contents only, 1998. http://web4.library.adelaide.edu.au/theses/09PM/09pmj78.pdf.
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Kobayashi, Rika. "Analytic gradients for correlated methods." Thesis, University of Cambridge, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.239154.
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Bayliffe, David Michael. "Analytic modelling for sovereign debt." Thesis, Imperial College London, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.248464.
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Dyke, Steven Douglas. "Topics in analytic number theory." Thesis, University of Oxford, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.334817.
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Alberts, Ian Lee. "Analytic derivatives using correlated wavefunctions." Thesis, University of Cambridge, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.276837.
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SILVA, SÉRGIO FERREIRA. "ANALYTIC GEOMETRY: PATHWAYS TO LEARNING." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2015. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=25720@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCOORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
A presente pesquisa tem como tema o processo de ensino e aprendizagem de geometria analítica, assunto no qual os alunos do ensino médio têm apresentado dificuldades. Por isto se faz necessário que o professor utilize um maior número de ferramentas pedagógicas, explorando os caminhos algébrico e geométrico para resolução de problemas. O objetivo deste estudo é propor caminhos para o ensino da geometria analítica tendo como base três eixos norteadores: A história das geometrias, a proposição de problemas matemáticos que podem ser resolvidos tanto pela geometria plana como pela geometria analítica e o uso da ferramenta tecnológica através do software Geogebra. Utilizamos neste trabalho materiais didáticos disponibilizados em escolas públicas estaduais do Estado do Rio de Janeiro, material voltado para a formação do professor de matemática e livros sobre a história da matemática.
The topic of this research is the process of teaching and learning analytical geometry, aThe topic of this research is the process of teaching and learning analytical geometry, a theme in which the students from high school have great difficulties. It is necessary that the teacher use a greater number of educational tools, exploring the algebraic and geometric aspects for problem solving. The aim of this study is to propose new methods for teaching analytical geometry based on three guiding principles: The history of geometry, the proposition of mathematical problems that can be solved either by analytical geometry or by plane geometry and the use of a technological tool, the software Geogebra. In this work, we use teaching materials available in public schools of the state of Rio de Janeiro, material focused in the training of mathematical teachers and books of history of mathematics.
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Charbonneau, Benoit 1976. "Analytic aspects of periodic instantons." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/26746.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Includes bibliographical references (p. 131-134) and index.
The main result is a computation of the Nahm transform of a SU(2)-instanton over R x T³, called spatially-periodic instanton. It is a singular monopole over T³, a solution to the Bogomolny equation, whose rank is computed and behavior at the singular points is understood under certain conditions. A full description of the Riemannian ADHMN construction of instantons on R⁴ is given, preceding a description of the heuristic behind the theory of instantons on quotients of R⁴. The Fredholm theory of twisted Dirac operators on cylindrical manifolds is derived, the spectra of spin Dirac operators on spheres and on product manifolds are computed. A brief discussion on the decay of spatially-periodic and doubly-periodic instantons is included.
by Benoit Charbonneau.
Ph.D.
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Brohan, Anthony. "Analytic bias in coocurrence restrictions." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/93026.
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Thesis: S.M., Massachusetts Institute of Technology, Department of Linguistics and Philosophy, 2014.Cataloged from PDF version of thesis.
Includes bibliographical references (pages 57-59).
The representation, content and learning of phonotactic constraints has spurred a lot of recent research phonology. This work concerns the constraints involved in the representation of place-based coocurrence restrictions. A single OCP-[PLACE] constraint is argued to compete in in constraint learning with other place-based and feature-based coocurrence constraints. The key prediction of this constraint participating in learning is generalization of a coocurrence restriction on to a novel place. This prediction, along with others, are tested in a series of artificial language learning experiments. A modification of the existing Hayes and Wilson (2008) phonotactic learner is presented (HWgain). This modified model is more robust in inducing gradient constraints, induces more general constraints and significantly improves on regression fit with English well-formedness ratings
by Anthony Brohan.
S.M.
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Barnett, Anthony. "Developing a creative analytic paradigm." Thesis, University of Worcester, 2013. http://eprints.worc.ac.uk/3089/.
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The thesis is essentially an explication of a research paradigm, referred to as the Creative Analytic Paradigm (CAP), which is a basic category of social research encompassed by a superordinate category, referred to as generative social research. The thesis presents a contrasting concept of social research to that of paradigms located within quantitative, qualitative or mixed methods research. The approach to writing the thesis has endeavoured to reflect the character of the research process by incorporating extracts from a memo dataset and by dispersing elements from the substantive content within the encompassing context of paradigm development. The thesis contributes to the burgeoning discourse related to the development of reflective practice and future of qualitative research, including prospects for post qualitative research. The substantive content of the thesis comprises five satellite topics illustrating the genealogy of the CAP with a particular focus on the Generative Divergent Analysis (GDA) model. The general area of interest, referred to as the primary sensitizing concept within the terminology of the CAP, is the early-years physical learning environment. The thesis presents a process model of research which supports a being-in-relation to evocative objects related to the physical learning environment. The contemplative dispositional nature of the paradigm valorises acquaintanceship and ongoing relationship as part of a personal aesthetic. The potential for professional practitioners utilising this approach to research in the context of an ongoing professional conversation is in the focus on fluency and flexibility of reflective thinking, the generation of unbounded ideas and differentiation of the perceptual and conceptual field. The thesis concludes by exploring the potential for developing approaches to research within an alternative generative social research category in contrast to quantitative, qualitative or mixed methods approaches.
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Kassa, Debassey Fesehaye. "Analytic models of TCP performance." Thesis, Stellenbosch : University of Stellenbosch, 2011. http://hdl.handle.net/10019.1/16608.
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Thesis (MSc)--University of Stellenbosch, 2005.ENGLISH ABSTRACT: The majority of tra c on the Internet uses the Transmission Control Protocol (TCP) as a transport layer protocol for the end-to-end control of information transfer. Measurement, simulation and analytical models are the techniques and tools that can be used to understand and investigate the Internet and its performance. Measurements can only be used to explore existing network scenario or otherwise become costly and in exible with the growth and complexity of the Internet. Simulation models do not scale with the growth of network capacities and the number of users. Computationally e cient analytical models are therefore important tools for investigating, designing, dimensioning and planning IP (Internet Protocol) networks. Existing analytical models of TCP performance are either too simple to capture the internal dynamics of TCP or are too complex to be used to analyze realistic network topologies with several bottleneck links. The literature shows that the xed point algorithm (FPA) is a very useful way of solving analytical models of Internet performance. This thesis presents fast and accurate analytical models of TCP performance with the FPA used to solve them. Apart from what is observed in experimental literature, no comprehensive proof of the convergence and uniqueness of the FPA is given. In this thesis we show how the FPA of analytical models of reliable Internet protocols such as TCP converges to a unique xed point. The thesis speci es the conditions necessary in order to use the FPA for solving analytical models of reliable Internet protocols. We also develop a general implementation algorithm of the FPA of analytical models of TCP performance for realistic and arbitrary network topologies involving heterogenous TCP connections crossing many bottleneck links. The models presented in this thesis give Internet performance metrics, assuming that only basic network parameters such as the network topology, the number of TCP connections, link capacity, distance between network nodes and router bu er sizes are known. To obtain the performance metrics, TCP and network sub{models are used. A closed network of :=G=1 queues is used to develop each TCP sub-model where each queue represents a state of a TCP connection. An M=M=1=K queue is used for each network sub{model which represents the output interface of an IP router with a bu er capacity of K ��������1 packets. The two sub-models are iteratively solved. We also give closed form expressions for important TCP performance values and distributions. We show how the geometric, bounded geometric and truncated geometric distributions can be used to model reliable protocols such as TCP. We give models of the congestion window cwnd size distribution by conditioning on the slow start threshold ssthresh distribution and vice-versa. We also present models of the probabilities of TCP timeout and triple duplicate ACK receptions. Numerical results based on comparisons against ns2 simulations show that our models are more accurate, simpler and computationally more e cient than another well known TCP model. Our models can therefore be used to rapidly analyze network topologies with several bottlenecks and obtain detailed performance metrics.
AFRIKAANSE OPSOMMING: Die meerderheid van die verkeer op die Internet gebruik die Transmission Control Protocol (TCP) as `n vervoer laag protokol vir die einde-tot-einde kontrole van inligting oordrag. Meting, simulasie en analitiese modelle is die tegnieke en gereedskap wat gebruik kan word om die Internet te ondersoek en verstaan. Meting kan slegs gebruik word om bestaande netwerke scenarios te verken. Meting is duur en onbuigsaam met die groei en samegesteldheid van die Internet. Simulasie modelle skaal nie met die groei van netwerk kapasiteit en gebruikers nie. Analitiese modelle wat berekening e ektief is is dus nodige gereedskap vir die ondersoek, ontwerp, afmeting en beplanning van IP (Internet Protocol) netwerke. Bestaande analitiese TCP modelle is of te eenvoudig om die interne dinamiek van die TCP saam te vat of hulle is te ingewikkeld om realistiese netwerk topologie met heelwat bottelnek skakels te analiseer. Literatuur toon dat die xed point algorithm (FPA) baie handig is vir die oplos van analitiese modelle van Internet verrigting. In hierdie tesis word vinnige en akkurate analitiese modelle van TCP verrigting opgelos deur FPA weergegee. Buiten wat deur eksperimentele literatuur aangedui word is daar geen omvattende bewyse van die konvergensie en uniekheid van die FPA nie. In hierdie tesis word aangedui hoe die FPA van analitiese modelle van betroubare Internet protokolle soos die TCP konvergeer na `n unieke vaste punt. Hierdie tesis spesi seer die voorwaardes benodig om die FPA te gebruik vir die oplos van analitiese modelle van realistiese Internet protokolle. `n Algemene uitvoer algoritme van die FPA van analitiese modelle van TCP vir realistiese en arbitr^ere netwerk topogra e insluitende heterogene TCP konneksies oor baie bottelnek skakels is ontwikkel. Die model in hierdie tesis gee Internet verrigting metodes met die aanname dat slegs basiese netwerk parameters soos netwerk topologie, die aantal TCP konneksies, die konneksie kapasiteit, afstand tussen netwerk nodusse en die roete bu er grotes bekend is. Om die verrigting metodes te verkry, word TCP en netwerk sub-modelle gebruik. `n Geslote netwerk van :=G=1 rye is gebruik om elke TCP sub-model, waar elke ry 'n toestand van `n TCP konneksie voorstel, te ontwikkel. `n M=M=1=K ry is gebruik vir elke netwerk sub-model wat die uitset koppelvlak van `n IP roetemaker met `n bu er kapasiteit van K ������� 1 pakkies voorstel. Die twee submodelle word iteratief opgelos. Geslote vorm uitdrukkings vir belangrike TCP verrigting waardes en verspreidings word gegee. Daar word getoon hoe geometriese, begrensde geometriese en geknotte geometriese verspreidings gebruik kan word om betroubare protokolle soos die TCP te modelleer. Modelle van die kongestie venster cwnd grootte verspreiding word gegee deur die kondisionering van die stadige aanvang drempel ssthresh verspreiding en andersom. Modelle van die voorspelling van TCP tyduit en trippel duplikaat ACK resepsie word weergegee. Numeriese resultate gebaseer op vergelykings met ns2 simulasies wys dat ons modelle meer akkuraat, eenvoudiger en berekeningsgewys meer e ektief is as ander wel bekende TCP modelle. Ons modelle kan dus gebruik word vir vinnig analise van netwerk topologie met verskeie bottelnekke en om gedetailleerde verrigting metodes te bekom.
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Maynard, James. "Topics in analytic number theory." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:3bf4346a-3efe-422a-b9b7-543acd529269.
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In this thesis we prove several different results about the number of primes represented by linear functions. The Brun-Titchmarsh theorem shows that the number of primes which are less than x and congruent to a modulo q is less than (C+o(1))x/(phi(q)log{x}) for some value C depending on log{x}/log{q}. Different authors have provided different estimates for C in different ranges for log{x}/log{q}, all of which give C>2 when log{x}/log{q} is bounded. We show in Chapter 2 that one can take C=2 provided that log{x}/log{q}> 8 and q is sufficiently large. Moreover, we also produce a lower bound of size x/(q^{1/2}phi(q)) when log{x}/log{q}>8 and is bounded. Both of these bounds are essentially best-possible without any improvement on the Siegel zero problem. Let k>1 and Pi(n) be the product of k linear functions of the form a_in+b_i for some integers a_i, b_i. Suppose that Pi(n) has no fixed prime divisors. Weighted sieves have shown that for infinitely many integers n, the number of prime factors of Pi(n) is at most r_k, for some integer r_k depending only on k. In Chapter 3 and Chapter 4 we introduce two new weighted sieves to improve the possible values of r_k when k>2. In Chapter 5 we demonstrate a limitation of the current weighted sieves which prevents us proving a bound better than r_k=(1+o(1))klog{k} for large k. Zhang has shown that there are infinitely many intervals of bounded length containing two primes, but the problem of bounded length intervals containing three primes appears out of reach. In Chapter 6 we show that there are infinitely many intervals of bounded length containing two primes and a number with at most 31 prime factors. Moreover, if numbers with up to 4 prime factors have `level of distribution' 0.99, there are infinitely many integers n such that the interval [n,n+90] contains 2 primes and an almost-prime with at most 4 prime factors.
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Irving, Alastair James. "Topics in analytic number theory." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:40f5511c-af6b-4215-b1ab-97f203e8936b.
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In this thesis we prove several results in analytic number theory. 1. We show that there exist 3-digit palindromic primes in base b for a set of b having density 1 and that if b is sufficiently large then there is a $3$-digit palindrome in base b having precisely two prime factors. 2. We prove various estimates for averages of sums of Kloosterman fractions over primes. The first of these improves previous results of Fouvry-Shparlinski and Baker. 3. By using the q-analogue of van der Corput's method to estimate short Kloosterman sums we study the divisor function in an arithmetic progression to modulus q. We show that the expected asymptotic formula holds for a larger range of q than was previously known, provided that q has a certain factorisation. 4. Let ‖x‖ denote the distance from x to the nearest integer. We show that for any irrational α and any ϴ< 8/23 there are infinitely many n which are the product of two primes for which ‖nalpha‖ ≤ n -ϴ. 5. By establishing an improved level of distribution we study almost-primes of the form f(p,n) where f is an irreducible binary form over Z. 6. We show that for an irreducible cubic f ? Z[x] and a full norm form $mathbf N$ for a number field $K/Q$, satisfying certain hypotheses, the variety $$f(t)=mathbf N(x_1,ldots,x_k) e 0$$ satisfies the Hasse principle. Our proof uses sieve methods.
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Eissa, Hend Abdelgader. "Analytic representation of quantum systems." Thesis, University of Bradford, 2016. http://hdl.handle.net/10454/14562.
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Finite quantum systems with d-dimension Hilbert space, where position x and momentum p take values in Zd(the integers modulo d) are studied. An analytic representation of finite quantum systems, using Theta function is considered. The analytic function has exactly d zeros. The d paths of these zeros on the torus describe the time evolution of the systems. The calculation of these paths of zeros, is studied. The concepts of path multiplicity, and path winding number, are introduced. Special cases where two paths join together, are also considered. A periodic system which has the displacement operator to real power t, as time evolution is also studied. The Bargmann analytic representation for infinite dimension systems, with variables in R, is also studied. Mittag-Leffler function are used as examples of Bargmann function with arbitrary order of growth. The zeros of polynomial approximations of the Mittag-Leffler function are studied.
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Letendre, Patrick. "Topics in analytic number theory." Doctoral thesis, Université Laval, 2018. http://hdl.handle.net/20.500.11794/31443.
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Le présent document est un compte-rendu de quatre présentations que j'ai faites au congrès de Théorie des Nombres Québec-Maine entre 2013 et 2016. Au fil des ans, j'ai effectué quelques améliorations et corrections aux documents originaux. Le contenu, l'esprit et l'organisation sont restés essentiellement inchangés. Les quatre sujets sont fondamentalement distincts tout en étant dans un même cercle d'idées. Le premier chapitre traite d'un certain nombre de sujets en relation avec le comportement moyen de certaines fonctions multiplicatives, dans un ensemble bien précis, qui partagent plusieurs propriétés avec la fonction indicatrice des nombres libres de puissance k-ième. En particulier, on y établit plusieurs estimations de la variance dans des intervalles courts et dans des progressions arithmétiques. Le deuxième chapitre étudie un problème du crible combinatoire. Il y est question d'établir une majoration analogue à la célèbre inégalité de Brun-Titchmarsh, mais pour les nombres libres de puissance k-ième. Après quelques remarques élémentaires, on établit une nouvelle inégalité en supposant une conjecture forte en lien avec la densité maximale d'une suite de nombres ayant un diviseur de la forme pk 1pk 2 où p1 et p2 sont des nombres premiers qui satisfont certaines conditions. La méthode fournit aussi une majoration effective pour le nombre de nombres libres de puissance k-ième dans un intervalle [x + 1, x + h] lorsque h est petit par rapport à x. Le troisième chapitre, écrit en collaboration avec Jean-Marie De Koninck, établit des inégalités particulières pour la fonction τ(n) qui compte le nombre de diviseurs de n. L'objectif est d'obtenir une majoration de τ(n) qui ne dépend pas des facteurs premiers de n, mais seulement du nombre de facteurs premiers distincts de n et de son ordre de grandeur, i.e. de log n. L'inégalité principale (Théorèmes 3.4 et 3.5) a nécessité un bon volume de calcul sur ordinateur, et donc beaucoup de programmation avec Maple. Finalement, le Chapitre 4 est le début d'une étude du nombre de points entiers près d'une courbe dans l'espace R3. Le problème peut aussi être vu comme celui du nombre de points entiers près de deux courbes dans le plan Euclidien simultanément. L'objectif principal est d'utiliser l'information des deux courbes de façon nontriviale, soit de faire mieux que les meilleurs résultats connus pour une seule courbe. Étant donné la complexité du problème déjà en deux dimensions et du nombre de méthodes disponibles, il nous a semblé impossible de faire un traitement complet de la question. On s'est donc concentré sur une méthode qui utilise des approximations linéaires. Cette dernière peut sans doute être substantiellement améliorée.Résumé en anglais
Théorie analytique des nombres
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Muller, Kimberly (Kimberly Orisja). "Polish Spaces and Analytic Sets." Thesis, University of North Texas, 1997. https://digital.library.unt.edu/ark:/67531/metadc277605/.
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A Polish space is a separable topological space that can be metrized by means
of a complete metric. A subset A of a Polish space X is analytic if there is a Polish
space Z and a continuous function f : Z —> X such that f(Z)= A. After proving that
each uncountable Polish space contains a non-Borel analytic subset we conclude that there exists a universally measurable non-Borel set.
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Kelly, Annela Rämmer. "Weakly analytic vector-valued measures /." free to MU campus, to others for purchase, 1996. http://wwwlib.umi.com/cr/mo/fullcit?p9821334.
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Kapçak, Sinan Ufuktepe Ünal. "Analytic Functions on Time Scales/." [s.l.]: [s.n.], 2007. http://library.iyte.edu.tr/tezler/master/matematik/T000643.pdf.
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Powell, Kevin James. "Topics in Analytic Number Theory." BYU ScholarsArchive, 2009. https://scholarsarchive.byu.edu/etd/2084.
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The thesis is in two parts. The first part is the paper “The Distribution of k-free integers” that my advisor, Dr. Roger Baker, and I submitted in February 2009. The reader will note that I have inserted additional commentary and explanations which appear in smaller text. Dr. Baker and I improved the asymptotic formula for the number of k-free integers less than x by taking advantage of exponential sum techniques developed since the 1980's. Both of us made substantial contributions to the paper. I discovered the exponent in the error term for the cases k=3,4, and worked the case k=3 completely. Dr. Baker corrected my work for k=4 and proved the result for k=5. He then generalized our work into the paper as it now stands. We also discussed and both contributed to parts of section 3 on bounds for exponential sums. The second part represents my own work guided by my advisor. I study the zeros of derivatives of Dirichlet L-functions. The first theorem gives an analog for a result of Speiser on the zeros of ζ'(s). He proved that RH is equivalent to the hypothesis that ζ'(s) has no zeros with real part strictly between 0 and ½. The last two theorems discuss zero-free regions to the left and right for L^{(k)}(s,χ).
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Eissa, Hend A. "Analytic representation of quantum systems." Thesis, University of Bradford, 2016. http://hdl.handle.net/10454/14562.
Full textAbstract:
Finite quantum systems with d-dimension Hilbert space, where position x and
momentum p take values in Zd(the integers modulo d) are studied. An analytic
representation of finite quantum systems, using Theta function is considered.
The analytic function has exactly d zeros. The d paths of these zeros on the
torus describe the time evolution of the systems. The calculation of these
paths of zeros, is studied. The concepts of path multiplicity, and path winding
number, are introduced. Special cases where two paths join together, are also
considered. A periodic system which has the displacement operator to real
power t, as time evolution is also studied.
The Bargmann analytic representation for infinite dimension systems, with
variables in R, is also studied. Mittag-Leffler function are used as examples of
Bargmann function with arbitrary order of growth. The zeros of polynomial
approximations of the Mittag-Leffler function are studied.Libyan Cultural Affairs
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Johansson, Tomas. "Analytic Solutions to Algebraic Equations." Thesis, Linköpings universitet, Matematiska institutionen, 1998. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-127700.
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This report studies polynomial equations and how one solves them using only the coefficients of the polynomial. It examines why it is impossible to solve equations of degree greater than four using only radicals and how instead one can solve them using elliptic functions. Although the quintic equation is the main area of our investigation, we also present parts of the history of algebraic equations, Galois theory, and elliptic functions.
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Ovenden, Simon P. B. "Preparation of a natural product extract library for investigation against disease states specific to defence health a mini long range research project /." Fishermans Bend Victoria : Defence Science and Technology Organisation, 2009. http://hdl.handle.net/1947/9861.
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