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Dissertations / Theses on the topic 'PhD in Mathematics'

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Published: 4 June 2021

Last updated: 11 February 2022

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1

Stone, Jason C. "The Formation of Self-Constructed Identity as Advanced Mathematical Thinker Among Some Female PhD Holders in Mathematics and the Relationship to the "Three-Worlds" Cognitive Model of Advanced Mathematical Thinking." Kent State University / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=kent1436975429.

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Norén, Fanny, and Hanne Wallengren. "Possibilities and Challenges for Female PhD Students in Tanzania : A field study covering current conditions for Tanzanian women undertaking their PhD degree at the Department of Mathematics, University of Dar es Salaam." Thesis, Uppsala universitet, Kulturgeografiska institutionen, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-388305.

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At the largest university in Tanzania, University of Dar es Salaam (UDSM), the gender distribution is unequal. At the University’s Department of Mathematics (DoM), the number of women ranges between 20-30 %. As a PhD degree can pose an important bridge into higher academic positions, the purpose of this study is to discern the current prerequisites for women to complete a doctoral degree at UDSM, compared to their male colleagues. The thesis is based on a field study carried out at DoM, in the spring of 2018. As such, both the formal and the perceived conditions could be examined. During the field study, both focus groups and individual interviews were held. By means of Grounded Theory, a mainly inductive method, the empirical framework obtained from the field research has guided the study and recurrent observations from the local context analysis have shaped the results. As the methodological outset for the study also draws on abductive reasoning, it results in that the analysis is concurrently theoretically guided and based on obtained data. The conclusions from the field research show that the conditions for female and male PhD students at UDSM are not equal. There are policies, quotas and other initiatives introduced in an attempt to level the playfield, however, other policies and social norms that create challenges for women in their strive for an academic career are still in motion. Among other things, as women are expected to be the primary caretaker and there are no support systems in place, the decision to start a family affects women’s studies more than men’s.

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3

Hua, Jiale. "Glimm type functional and one dimensional systems of hyperbolic conservation laws /." access abstract and table of contents access full-text, 2009. http://libweb.cityu.edu.hk/cgi-bin/ezdb/thesis.pl?phd-ma-b23749921f.pdf.

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Thesis (Ph.D.)--City University of Hong Kong, 2009.<br>"Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves 88-95)

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Amin, Md Ashraful. "Gabor wavelets for human biometrics = Gaibo xiao bo zai ren ti shi bie zhong de ying yong /." access full-text access abstract and table of contents, 2009. http://libweb.cityu.edu.hk/cgi-bin/ezdb/thesis.pl?phd-ee-b23749489f.pdf.

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Thesis (Ph.D.)--City University of Hong Kong, 2009.<br>"Submitted to the Department of Electronic Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references.

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Zhang, Mei. "Some problems on conservation laws and Vlasov-Poisson-Boltzmann equation /." access full-text access abstract and table of contents, 2009. http://libweb.cityu.edu.hk/cgi-bin/ezdb/thesis.pl?phd-ma-b23749465f.pdf.

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Thesis (Ph.D.)--City University of Hong Kong, 2009.<br>"Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves [90]-94)

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6

Sanders, Edel Marie. "Music learning and mathematics achievement : a real-world study in English primary schools." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/283610.

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Music Learning and Mathematics Achievement: A Real-World Study in English Primary Schools Edel Marie Sanders Abstract This study examines the potential for music education to enhance children's mathematical achievement and understanding. Psychological and neuroscientific research on the relationship between music and mathematics has grown considerably in recent years. Much of this, however, has been laboratory-based, short-term or small-scale research. The present study contributes to the literature by focusing on specific musical and mathematical elements, working principally through the medium of singing and setting the study in five primary schools over a full school year. Nearly 200 children aged seven to eight years, in six school classes, experienced structured weekly music lessons, congruent with English National Curriculum objectives for music but with specific foci. The quasi-experimental design employed two independent variable categories: musical focus (form, pitch relationships or rhythm) and mathematical teaching emphasis (implicit or explicit). In all other respects, lesson content was kept as constant as possible. Pretests and posttests in standardised behavioural measures of musical, spatial and mathematical thinking were administered to all children. Statistical analyses (two-way mixed ANOVAs) of student scores in these tests reveal positive significant gains in most comparisons over normative progress in mathematics for all musical emphases and both pedagogical conditions with slightly greater effects in the mathematically explicit lessons. This investigation addresses concerns that UK and US governments' quests for higher standards in mathematics typically result in impoverished curricula with limited access to the arts. In showing that active musical engagement over time can improve mathematical achievement, as hypothesised, this work adds to a growing body of research suggesting that policy-makers and educationalists should reconsider curriculum balance.

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7

Mariotto, Rachel. "Um estudo sobre o processo que desencadeou o doutoramento de Joaquim Gomes de Sousa (1829-1864) e alguns apontamentos sobre sua tese /." Rio Claro, 2019. http://hdl.handle.net/11449/182123.

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Orientador: Sergio Roberto Nobre<br>Resumo: Joaquim Gomes de Sousa (1829-1864) ficou por muito tempo conhecido como o maior matemático brasileiro, tanto por seu modo inabitual de conseguir o grau de bacharel, quanto por sua tese de doutorado, ambos obtidos em 1848. Buscando retomar esse personagem da História da Matemática brasileira, por meio de um estudo documentado, este trabalho tem como foco os processos que desencadearam o doutoramento de Joaquim Gomes de Sousa (1829-1864), todos os processos relacionados a entrega de sua tese e um primeiro estudo da mesma. Para tal, foram realizadas buscas em diversos acervos, com destaque para o Arquivo Nacional, a Biblioteca de Obras Raras do Centro de Tecnologia da UFRJ e a Hemeroteca Nacional da Biblioteca Nacional. A partir das fontes encontradas, procedeu-se dois tipos de análise documental: indiciária e comparativa. Com a primeira, foi possível confirmar e descobrir novos fatos desde a obtenção de seu título de bacharel pela Escola Militar, mesmo sem ter esse personagem frequentado tal instituição, até a entrega de sua tese e colação do grau de doutor. Usando um método comparativo, estudou-se a tese de Gomes de Sousa destacando partes de seu conteúdo em relação ao que foi anteriormente desenvolvido por Laplace e Le Verrier. Para de uma revisão bibliográfica a respeito do, Através dessas análises foi possível compreender sua importância dentro do contexto científico da época, e ainda esclarecer alguns mitos que abordavam a história do personagem. Além disso, esse trabalho ... (Resumo completo, clicar acesso eletrônico abaixo)<br>Doutor

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8

Thompson, Kent M. "The relationship between mathematical leadership skills and the mathematics achievement of elementary students." Laramie, Wyo. : University of Wyoming, 2005. http://proquest.umi.com/pqdweb?did=1095430511&sid=2&Fmt=2&clientId=18949&RQT=309&VName=PQD.

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9

Blechle, Nancy M. "Attitudes toward mathematics and mathematical performance : a comparison of single-sex and mixed-sex mathematics classrooms in a mixed-sex United States public school /." Available to subscribers only, 2007. http://proquest.umi.com/pqdweb?did=1456283761&sid=12&Fmt=2&clientId=1509&RQT=309&VName=PQD.

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10

Liu, Ruochuan. "On the slope filtration of [phi]-modules over the Robba ring." Thesis, Massachusetts Institute of Technology, 2008. http://hdl.handle.net/1721.1/45350.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2008.<br>In title on title page, [phi] appears as lower case Greek letter.<br>Includes bibliographical references (leaves 63-65).<br>Given a p-adic representation of the Galois group of a local field, we show that its Galois cohomology can be computed using the associated étale ([phi], [Gamma])-module over the Robba ring; this is a variant of a result of Herr. We then establish analogues, for not necessarily étale (([phi], [Gamma])-modules over the Robba ring, of the Euler-Poincaré characteristic formula and Tate local duality for p-adic representations. These results are expected to intervene in the duality theory for Selmer groups associated to de Rham representations. We introduce the notion of families of [phi]-modules which arises naturally from both rigid cohomology and p-adic Hodge theory. We then prove the local constancy of generic HN-polygons of families of overconvergent [phi]-modules and the semicontinuity of HN-polygons of families of [phi]-modules over reduced affinoid algebras. These results are prospective for a slope theory of families of (overconvergent) [phi]-modules.<br>by Ruochuan Liu.<br>Ph.D.

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11

Mazzag, Barbara Cathrine. "Mathematical models in biology /." For electronic version search Digital dissertations database. Restricted to UC campuses. Access is free to UC campus dissertations, 2002. http://uclibs.org/PID/11984.

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12

Le, Borgne Jérémy. "Représentations galoisiennes et phi-modules : aspects algorithmiques." Phd thesis, Université Rennes 1, 2012. http://tel.archives-ouvertes.fr/tel-00720023.

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Nous nous intéressons aux aspects algorithmiques de la théorie des représentations modulo p de groupes de Galois p-adiques. À cet eﬀet, l'un des outils introduits par Fontaine est la théorie de ϕ-modules : un ϕ-module sur un corps K de caractéristique p est la donnée d'un espace vectoriel de dimension ﬁnie sur K muni d'un endomorphisme ϕ, semi-linéaire par rapport au morphisme de Frobenius sur K. Les représentations à coeﬃcients dans un corps ﬁni du groupe de Galois absolu de K forment une catégorie équivalente à la catégorie des ϕ-modules dits " étales " sur K. Le but des travaux rassemblés ici est donner des algorithmes pour décrire le plus complètement possible la représentation associée à un ϕ-module donné. Nous étudions en préambule les ϕ-modules sur les corps ﬁnis, ce qui nous permet d'obtenir de nouveaux résultats décrivant les polynômes tordus sur un corps ﬁni, qui sont des ob jets utilisés notamment en théorie des codes correcteurs. Cela nous permet d'améliorer en partie l'algorithme dû à Giesbrecht pour la factorisation de ces polynômes. Nous nous intéressons ensuite à la catégorie des ϕ-modules sur un corps de séries formelles de caractéristique p. Nous donnons une classiﬁcation des ob jets simples de cette catégorie lorsque le corps résiduel est algébrique- ment clos, et décrivons un algorithme eﬃcace pour décomposer un ϕ-module en ϕ-modules " isoclines ". Nous donnons des applications à l'étude algorithmique des représentations de p-torsion de groupes de Galois p-adiques.

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13

Davis, Ann. "So I'm done because I'm confused now measuring metacognition in elementary algebra community college students /." Diss., Restricted to subscribing institutions, 2009. http://proquest.umi.com/pqdweb?did=2026651711&sid=4&Fmt=2&clientId=1564&RQT=309&VName=PQD.

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Barcellos, Anthony. "Mathematical misconceptions of college-age algebra students /." For electronic version search Digital dissertations database. Restricted to UC campuses. Access is free to UC campus dissertations, 2005. http://uclibs.org/PID/11984.

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15

Bahr, Peter Riley. "The rough and rocky road of remediation : racial inequalities in postsecondary remedial mathematics /." For electronic version search Digital dissertations database. Restricted to UC campuses. Access is free to UC campus dissertations, 2004. http://uclibs.org/PID/11984.

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Zhang, Xingyou. "Dynamics and numerics of generalised Euler equations : a thesis submitted to Massey University in partial fulfillment of the requirements for the degree of Ph.D in Mathematics." Massey University, 2008. http://hdl.handle.net/10179/980.

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This thesis is concerned with the well-posedness, dynamical properties and numerical treatment of the generalised Euler equations on the Bott-Virasoro group with respect to the general Hk metric , k 2. The term “generalised Euler equations” is used to describe geodesic equations on Lie groups, which unifies many differential equations and has found many applications in such as hydrodynamics, medical imaging in the computational anatomy, and many other fields. The generalised Euler equations on the Bott-Virasoro group for k = 0, 1 are well-known and intensively studied— the Korteweg-de Vries equation for k = 0 and the Camassa-Holm equation for k = 1. Unlike these, the equations for k 2, which we call the modified Camassa-Holm (mCH) equation, is not known to be integrable. This distinction motivates the study of the mCH equation. In this thesis, we derive the mCH equation and establish the short time existence of solutions, the well-posedness of the mCH equation, long time existence, the existence of the weak solutions, both on the circle S and R, and three conservation laws, show some quite interesting properties, for example, they do not lead to the blowup in finite time, unlike the Camassa-Holm equation. We then consider two numerical methods for the modified Camassa-Holm equation: the particle method and the box scheme. We prove the convergence result of the particle method. The numerical simulations indicate another interesting phenomenon: although mCH does not admit blowup in finite time, it admits solutions that blow up (which means their maximum value becomes infinity) at infinite time, which we call weak blowup. We study this novel phenomenon using the method of matched asymptotic expansion. A whole family of self-consistent blowup profiles is obtained. We propose a mechanism by which the actual profile is selected that is consistent with the simulations, but the mechanism is only partly supported by the analysis. We study the four particle systems for the mCH equation finding numerical evidence both for the non-integrability of the mCH equations and for the existence of the fourth integral. We also study the higher dimensional case and obtain the short time existence and well-posedness for the generalised Euler equation in the two dimension case.

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Sokhansanj, Bahrad Ali. "Mathematical models of human DNA base excision repair /." For electronic version search Digital dissertations database. Restricted to UC campuses. Access is free to UC campus dissertations, 2002. http://uclibs.org/PID/11984.

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Guerrero, Shannon Marie. "Case studies of reform in mathematics education through the development of technology-using teacher leaders /." For electronic version search Digital dissertations database. Restricted to UC campuses. Access is free to UC campus dissertations, 2005. http://uclibs.org/PID/11984.

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Tamaresis, John S. "Mathematical modeling of arterial endothelial cell responsiveness to flow /." For electronic version search Digital dissertations database. Restricted to UC campuses. Access is free to UC campus dissertations, 2004. http://uclibs.org/PID/11984.

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Hameister, Heike. "Mathematical models for DNA replication machinery." Thesis, University of Aberdeen, 2012. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=186178.

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DNA replication and associated processes take place in all living organisms with the same constitutions. The knowledge of the duplication process, chromatin building and repair mechanisms has increased explosively over the last years, but the complex interplay of different proteins and their mechanisms are not conceived properly. During DNA replication, the DNA has to be unpacked, duplicated and finally repacked into chromatin. These steps require different proteins, e.g. new histone proteins on demand to secure an error-free and undelayed DNA replication. This thesis includes different mathematical models for DNA replication, repair and chromatin formation, which are based on experimental results. Three models of chromatin formation provide a simplified description of histone gene expression and protein synthesis during G1/S/G2 phase and include the contribution of different regulatory elements. Furthermore, all models present two different mechanisms of regulation to test possible scenarios of newly synthesised histones and free DNA binding sites. The basic model presents a single histone gene, which codes for a single histone protein. The stem-loop binding protein (SLBP) acts as a master regulator, which is only present during S phase. Different analyses of early S-phase, over- and underexpressed replication and the down-regulation of SLBP proof the model under extreme conditions. This basic model serves as a template for further scenarios with several genes and different histone families. For this, a second model is realised to simulate imbalances in the histone mRNA synthesis and translation. Additionally, a third model tests a gene knock-out and mRNA silencing. The initial histone model is able to qualitatively reproduce experimental observations and shows basic regulatory principles. The adaptation with several genes and different histone families presents qualitatively different system responses for the discussed regulatory mechanisms and illustrates the ability to compensate the effect of mRNA silencing.

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Delgado, San Martin Juan A. "Mathematical models for preclinical heterogeneous cancers." Thesis, University of Aberdeen, 2016. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=230139.

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Cancer is a deadly, complex disease with 14 million new cases diagnosed every year and the endeavour to develop a cure is a global multidisciplinary effort. The complexity of cancer and the resulting vast volume of data derived from its research necessitates a robust and cutting-edge system of mathematical and statistical modelling. This thesis proposes novel mathematical models of quantification and modelling applied to heterogeneous preclinical cancers, focusing on the translation of animal studies into patients with particular emphasis on tumour stroma. The first section of this thesis (quantification) will present different techniques of extracting and quantifying data from bioanalytical assays. The overall aim will be to present and discuss potential methods of obtaining data regarding tumour volume, stromal morphology, stromal heterogeneity, and oxygen distribution. Firstly, a 3D scanning technique will be discusses. This technique aims to assess tumour volume in mice more precisely than the current favoured method (callipers) and record any cutaneous symptoms as well, with the potential to revolutionise tumour growth analysis. Secondly, a series of image processing methods will be presented which, when applied to tumour histopathology, demonstrate that tumour stromal morphology and its microenvironment play a key role in tumour physiology. Lastly, it will be demonstrated through the integration of in-vitro data from various sources that oxygen and nutrient distribution in tumours is very irregular, creating metabolic niches with distinct physiologies within a single tumour. Tumour volume, oxygen, and stroma are the three aspects central to the successful modelling of tumour drug responses over time. The second section of this thesis (modelling) will feature a mathematical oxygen-driven model - utilising 38 cell lines and 5 patient-derived animal models - that aims to demonstrate the relationship between homogeneous oxygen distribution and preclinical tumour growth. Finally, all concepts discussed will be merged into a computational tumour-stroma model. This cellular automaton (stochastic) model will demonstrate that tumour stroma plays a key role in tumour growth and has both positive (at a molecular level) and negative (at both a molecular and tissue level) effects on cancers. This thesis contains a useful set of algorithms to help visualise, quantify, and understand tissue phenomena in cancer physiology, as well as providing a series of platforms to predict tumour outcome in the preclinical setting with clinical relevance.

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Göckler, Tanja [Verfasser], and V. [Akademischer Betreuer] Grimm. "Rational Krylov subspace methods for phi-functions in exponential integrators / Tanja Göckler. Betreuer: V. Grimm." Karlsruhe : KIT-Bibliothek, 2014. http://d-nb.info/1060425408/34.

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Kley, Marius [Verfasser], and Peter [Akademischer Betreuer] Schneider. "Etale (Phi, Gamma)-modules with values in linear algebraic groups / Marius Kley ; Betreuer: Peter Schneider." Münster : Universitäts- und Landesbibliothek Münster, 2019. http://d-nb.info/1202075320/34.

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Hofbauer, Pamela S. Mooney Edward S. "Characterizing high school students' understanding of the purpose of graphical representations." Normal, Ill. : Illinois State University, 2007. http://proquest.umi.com/pqdweb?index=0&did=1414114601&SrchMode=1&sid=6&Fmt=2&VInst=PROD&VType=PQD&RQT=309&VName=PQD&TS=1207664408&clientId=43838.

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Thesis (Ph. D.)--Illinois State University, 2007.<br>Title from title page screen, viewed on April 8, 2008. Dissertation Committee: Edward S. Mooney (chair), Cynthia W. Langrall, Sherry L. Meier, Norma C. Presmeg. Includes bibliographical references (leaves 112-121) and abstract. Also available in print.

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Tavares, Ribeiro Floric. "(phi, Gamma)-modules et loi explicite de réciprocité." Phd thesis, Université de Franche-Comté, 2008. http://tel.archives-ouvertes.fr/tel-00379771.

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Le cadre de cette thèse est celui de la théorie des représentations p-adiques, et plus particulièrement la théorie de Fontaine. Je m'intéresse au cas d'une extension métabélienne d'un corps local et construit un (phi, Gamma)-module adapté à cette extension, puis je fournis des généralisations de certains outils usuels associés à ce (phi, Gamma)-module tel qu'un complexe calculant la cohomologie de la représentation. J'établis encore les formules explicites du dictionnaire entre le monde des représentations et celui des (phi, Gamma)-modules, pour le complexe de Herr, le cup-produit ou l'application de Kummer.<br /><br />La seconde partie de ce travail est dévolue à la preuve de la loi de réciprocité de Brückner-Vostokov pour un groupe formel. Je combine pour cela des méthodes relevant des (phi, Gamma)-modules à l'aide des résultats de la première partie et des techniques spécifiques introduites par Abrashkin à travers une interprétation cohomologique de ses travaux. J'obtiens ainsi une preuve de la loi de réciprocité libre de toute hypothèse non naturelle sur l'appartenance de racines de l'unité au corps de base.

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Knapp, Andrea K. Barrett Jeffrey Edward. "Prompting mathematics teacher development through dynamic discourse." Normal, Ill. : Illinois State University, 2007. http://proquest.umi.com/pqdweb?index=0&did=1417799381&SrchMode=1&sid=8&Fmt=2&VInst=PROD&VType=PQD&RQT=309&VName=PQD&TS=1207665349&clientId=43838.

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Thesis (Ph. D.)--Illinois State University, 2007.<br>Title from title page screen, viewed on April 8, 2008. Dissertation Committee: Jeffrey Barrett (chair), Nerida Ellerton, Sharon Soucy McCrone, Cynthia Moore, Michael Plantholt, Agida Manizade. Includes bibliographical references (leaves 200-215) and abstract. Also available in print.

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Johnson, Leah R. "Mathematical modeling of cholera : from bacterial life histories to human epidemics /." Diss., Digital Dissertations Database. Restricted to UC campuses, 2006. http://uclibs.org/PID/11984.

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Preisser, Evan Landrieu. "What forces structure food web interactions? : theoretical, experimental, and mathematical approaches /." For electronic version search Digital dissertations database. Restricted to UC campuses. Access is free to UC campus dissertations, 2004. http://uclibs.org/PID/11984.

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Shaikh, Zain U. "Some mathematical structures arising in string theory." Thesis, University of Aberdeen, 2010. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=158375.

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This thesis is concerned with mathematical interpretations of some recent develop- ments in string theory. All theories are considered before quantisation. The rst half of the thesis investigates a large class of Lagrangians, L, that arise in the physics literature. Noether's famous theorem says that under certain conditions there is a bijective correspondence between the symmetries of L and the \conserved currents" or integrals of motion. The space of integrals of motion form a sheaf and has a bilinear bracket operation. We show that there is a canonical sheaf d1;0 J1( ) that contains a representation of the higher Dorfman bracket. This is the rst step to de ne a Courant algebroid structure on this sheaf. We discuss the existence of this structure proving that, for a re ned de nition, we have the necessary components. The pure spinor formalism of string theory involves the addition of the algebra of pure spinors to the data of the superstring. This algebra is a Koszul algebra and, for physicists, Koszul duality is string/gauge duality. Motivated by this, we investigate the intimate relationship between a commutative Koszul algebra A and its graded Lie superalgebra Koszul dual to A, U(g) = A!. Classically, this means we obtain the algebra of syzygies AS from the cohomology of a Lie subalgebra of g. We prove H (g 2;C) ' AS again and extend it to the notion of k-syzygies, which we de ne as H (g k;C). In particular, we show that H B er(A) ' H (g 3;C), where H Ber(A) is the Berkovits cohomology of A.

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Riedel, Andreas [Verfasser], and Otmar [Akademischer Betreuer] Venjakob. "On Perrin-Riou's exponential map and reciprocity laws for (phi,Gamma)-modules / Andreas Riedel ; Betreuer: Otmar Venjakob." Heidelberg : Universitätsbibliothek Heidelberg, 2013. http://d-nb.info/1177248247/34.

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Lovelace, Stephen D. "Teacher beliefs about conceptual understanding in mathematics." Laramie, Wyo. : University of Wyoming, 2005. http://proquest.umi.com/pqdweb?did=990277791&sid=1&Fmt=2&clientId=18949&RQT=309&VName=PQD.

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Radmaneshfar, Elahe. "Mathematical modelling of the cell cycle stress response." Thesis, University of Aberdeen, 2012. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=192232.

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Karschau, Jens. "Mathematical modelling of chromosome replication and replicative stress." Thesis, University of Aberdeen, 2013. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=202763.

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Previous theoretical work on DNA replication neglected how the starting points (origins) take their place and how replication time is a ected when origins fail to activate. It is however crucial that origin loci are chosen so that too large gaps between them are avoided; otherwise the time until completion of chromosome replication becomes much longer than is allowed by the cell cycle. We investigate what the optimal origin location should be depending on the likelihood of origins failing. We show analytically and numerically that there exist regimes for origins, either to be positioned together in groups spaced far away from the next, or as equally scattered single origins depending on the uncertainty when activation occurs. The model reproduces origin distributions of frog embryos which are thought to be random, and shows contrarily that grouping must occur in order to swiftly complete replication; known as the random completion problem. The model also holds when considering a circular DNA topology for archaeal genomes, as well as if applied to the whole replication pro ling data of yeast. We study how an optimal origin distribution can arise and propose a mechanism to solve the random completion problem. We show that regular spacing emerges as an inherent property of the car parking model. We introduce a spatial requirement for origins to bind to DNA; origins occupy space on the DNA and can only bind stably if there is su cient space for them. Such a model leads to a well ordered origin distribution with minimal gaps as required for on time DNA replication in frog embryos. The optimal origin distribution emerges directly from our model because origins have a higher chance to bind to large empty regions instead of small once, therefore destroying large inter origin gaps. We also introduce a model to account for the interaction of replication forks with each other which leads to their assembly into replication factories. We show using Boltzmann statistics that their assembly is stochastic. A rst model only considers two pairs of forks which we then extend to describe properties of measured experimental distributions such as fork numbers per factory during on a whole yeast genome approach. Our in silico distribution of forks per factory matches in vivo data well; which suggests that active forks encounter each other randomly for an association into replication factories.

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Ha, Phi [Verfasser], Volker [Akademischer Betreuer] Mehrmann, Peter [Akademischer Betreuer] Kunkel, and Caren [Akademischer Betreuer] Tischendorf. "Analysis and numerical solutions of delay differential-algebraic equations / Phi Ha. Gutachter: Peter Kunkel ; Caren Tischendorf. Betreuer: Volker Mehrmann." Berlin : Technische Universität Berlin, 2015. http://d-nb.info/1069159697/34.

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35

Ye, Shuyang [Verfasser], Elmar [Gutachter] Große-Klönne, Laurent [Gutachter] Berger, and Adriano [Gutachter] Marmora. "On G-(phi,nabla)-modules over the Robba ring / Shuyang Ye ; Gutachter: Elmar Große-Klönne, Laurent Berger, Adriano Marmora." Berlin : Humboldt-Universität zu Berlin, 2019. http://d-nb.info/1192753151/34.

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36

Martin, Helen. "Learning mathematics for teaching : an exploratory study of e-formative assessment within initial teacher education." Thesis, University of Aberdeen, 2014. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=210704.

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This study explores learning mathematics for teaching through a particular enactment of e-formative assessment, a series of six online study sessions. The data involved 173 student teachers registered on the Bachelor of Education (BEd) degree programme within a School of Education of a Scottish University. It is located within a relatively uncharted area of formative assessment where our attention is refocused from the assessor to the learner's perspective. The aim to develop mathematical understanding and a greater sense of autonomy meant looking for those ‘cracks where the light gets in' rather than ‘gaps to be bridged': a more divergent approach to formative assessment which required a delicate orchestration of social, pedagogical and technological systems. A mixed methods multistrand parallel design was used to take a stereoscopic view of learner interactions with the online study sessions. The concepts and methods within this thesis are not necessarily new, however the way they have been brought together is innovative. These have been used not only to support student teachers in developing their own mathematical understanding but also to let them experience different ways of working with children. A conceptual framework developed for practising teachers and activity types designed for a mathematics classroom have been adapted for student teachers in a mathematics education classroom. Findings indicate that the capacity to change habits and to understand the reasoning of others is more important than formal mathematics qualifications. An informed design and use of e-formative assessment can support student teachers in developing their mathematical reasoning where it is embedded within their experiences of learning mathematics for teaching involving both specialised mathematical knowledge and mathematical pedagogical content knowledge. As such, this study hopefully adds to and provides another perspective on e-formative assessment and mathematics education, in particular, learning mathematics for teaching.

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37

McDonald, Kevin. "Modelling multi-layered network and security architectures using mathematical logic." Thesis, University of Aberdeen, 2014. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=214154.

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Complex systems, be they natural or synthetic, are ubiquitous. In particular, complex networks of devices and services underpin most of society's operations. By their very nature, such systems are di cult to conceptualize and reason about e ectively. One seemingly natural notion, which helps to manage complexity and which is commonly found in discussions of complex systems, is that of layering: the system is considered to consist of a collection of interconnected layers that have distinct, identi able roles in the overall operations of the system. Noting that graphs are a key formalism in the description of complex systems, this thesis establishes a notion of a layered graph. A logical characterization of this notion of layering using a non-associative, non-commutative substructural, sepa- rating logic is provided. In addition, soundness and completeness results for a class of algebraic models that includes layered graphs are provided, which give a math- ematically substantial semantics to this very weak logic. Examples in information processing and security are used to show the applicability of the logic. The examples given use an informal notion of action. The thesis also presents a discussion of a number of possible languages that could be used to provide a dynamic extension of the logic. The key components of each language are identi ed and the semantics that would be required in the case of a full, theoretical, development are presented. Examples, mainly in access control, are used to illustrate situations where each extension could be applied. The logic is then used to describe a uniform logical framework for reasoning compositionally about access control policy models. The approach takes account of the underlying system architecture, and so provides a way to identify and reason about how vulnerabilities may arise (and be removed) as a result of the architecture of the system. The logic is then used to describe a uniform logical framework for reasoning compositionally about access control policy models. The approach takes account of the underlying system architecture, and so provides a way to identify and reason about how vulnerabilities may arise (and be removed) as a result of the architecture of the system. Using frame rules, it is also considered how local properties of access control policies are maintained as the system architecture evolves.

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38

Koc, Nazire Pinar. "A survey of computerized course models in mathematics classes /." Available to subscribers only, 2007. http://proquest.umi.com/pqdweb?did=1453226651&sid=13&Fmt=2&clientId=1509&RQT=309&VName=PQD.

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39

Vienney, Mathieu. "Construction de (phi,gamma)-modules en caractéristique p." Phd thesis, Ecole normale supérieure de lyon - ENS LYON, 2012. http://tel.archives-ouvertes.fr/tel-00763785.

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Cette thèse est constituée de deux parties indépendantes, étudiant deux aspects de la théorie des (φ,Γ)-modules en caractéristique p. La première partie porte sur l'étude de la réduction modulo p des représentations cristallines irréductibles de dimension deux. Nous donnons, pour des poids k ≤ p², un calcul explicite de la réduction de V(k,a) pour a dans un disque fermé centré en zéro, généralisant ainsi des résultats déjà connus pour k ≤ 2p. En particulier, nous calculons le plus grand rayon possible pour ce disque, et montrons que dans certains cas, la réduction qui est constante à l'intérieur du disque change sur son bord. Dans la seconde partie, nous nous intéressons aux représentations d'un sous-groupe de Borel de GL[indice]2(Q[indice]p) sur un corps de caractéristique p, et en particulier à celles qui sont lisses, irréductibles et admettent un caractère central. Une méthode pour construire de telles représentations à partir de (φ,Γ)-modules irréductibles a été décrite par Colmez dans sa construction de la correspondance de Langlands p-adique. Après avoir donné un cadre un peu plus général dans lequel la construction de Colmez fonctionne encore, nous classifions les représentations irréductibles du Borel, prouvant que la construction précédente permet d'obtenir toutes les représentations de dimension infinie. Lorsque le corps des coefficients est fini, ou algébriquement clos, nous disposons d'une interprétation galoisienne des (φ,Γ)-modules irréductibles, et la classification précédente permet alors d'obtenir une correspondance entre ces représentations du Borel et des représentations galoisiennes modulaires.

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40

Armah, Prince Hamidu. "Teaching mathematical problem solving in Ghana : teacher beliefs, intentions and behaviour." Thesis, University of Aberdeen, 2015. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=228052.

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Recent curriculum reform agendas appear to exert pressure on teachers to incorporate Mathematical Problem Solving (MPS) meaningfully into their lessons, with the view to engaging pupils with real life problems, guessing, discovering, and making sense of mathematics. However, a comprehensive review of both government and academic literature indicate that understanding teachers' reform implementation decisions is largely unexplored, particularly within the Ghanaian context. The purpose of this mixed-methods sequential explanatory study was to identify factors contributing to teacher intentions to teach MPS by obtaining quantitative results from a survey of 375 primary teachers and then following up with six purposefully selected teachers to explore those results in more depth through interviews. Based on the Theory of Planned Behaviour (TPB), the quantitative phase of the study explored how certain different but interrelated belief variables such as attitudes towards the behaviour (AB), perceived norms (PN) and perceived behavioural control (PBC) lead to an explanation of teacher intentions to teach MPS, and an understanding of the contributions of relevant socio-demographic factors in defining these intentions in this context. In the follow up, qualitative phase, semi-structured interviews with six teachers were conducted to explore in depth the results from the statistical analyses. Results indicated that several beliefs about teaching MPS significantly contributed to AB, PN and PBC. Two factors, AB and PBC were found to have significant influences and accounted for 80% of the variance in the teachers' intent to teach MPS. Differences appeared to exist between private and public school teachers' for both intent and the three constructs (AB, PN, and PBC), whilst familiarity with the curriculum had an effect on teachers intentions only. In the qualitative phase, the study addressed some factors found to potentially influence teachers' intentions including MPS conceptions, past experience in mathematics, availability of resources, adequate classroom spaces and professional development opportunities. The quantitative and qualitative findings from the two phases of the study are discussed with reference to prior research. The results provide an understanding of the relevant social-cognitive processes which may influence a teacher's reform decisions, and in particular suggest strong implications for developing the capacity of schools to support teachers' intentions to implement curriculum reform policies.

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41

Rzymski, Tomasz. "The PHD finger protein 5 is a part of the spliceosome and acts as a DNA-binding protein." Doctoral thesis, 2004. http://hdl.handle.net/11858/00-1735-0000-0006-ABA9-F.

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42

"Descartes' eternal truths and mathematical essences." Tulane University, 1999.

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One of the most interesting aspects of Descartes' philosophy is the notion that mathematical truths are, in some sense, contingent. In what has become known as the doctrine of the eternal truths, Descartes writes that mathematical truths are grounded in divinely created essences, and that, like all divine creations, these essences were freely chosen. Thus, Descartes concludes, God could have made two times four unequal to eight. My project is to understand what Descartes' metaphysics and epistemology must be like in order to accommodate this contingency I begin by arguing for the coherence of the claim that God contingently chose to make mathematical truths necessary. Mathematical essences are contingent creations, but they nonetheless ground the immutable truths of mathematics. Alvin Plantinga and Harry Frankfurt have both argued that admitting to such contingency makes all truth suspect; I argue instead that mathematical truths are logically distinct from both the laws of motion and from logical truths. While these truths are also eternal, I argue that the laws of motion stem directly from God's nature (and not from his will, as mathematical truths do), and logical truths have no metaphysical grounding at all As creations, mathematical essences must have some kind of being, but they do not neatly fit into any existing category of Cartesian ontology. By rejecting interpretations such as Jonathan Bennett's and Walter Edelberg's, I argue that they are not reducible to either of the two created substances that Descartes recognizes. I therefore conclude that the essences of mathematics have the same kind of being that the essence of material things would have if there were no material things. The essences of mathematics must be ontologically on a par with the essences of created substances, and they must also be particulars---e.g., the essence of triangularity must be distinct from the essence of circularity The ontological independence of particular mathematical essences from the essences of created substances does complicate the usual picture of Cartesian ontology, but ultimately it is the only way to accommodate all of Descartes' texts and retain the notion that mathematical truths are contingent<br>acase@tulane.edu

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43

"Case studies of Experimental Mathematics: p-adic valuations of recurrences." Tulane University, 2008.

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This work presents some instances of Experimental Mathematics in Number Theory. The arithmetical properties of an arctangent sum is explored, in particular, its connections to different mathematical objects are shown. One of this connections is the link between the sum and a sequence of type tn=Pnt n-1, 0.0.1 where P(x) is a polynomial with integer coefficients. These type of sequences arise in different types of problems like the integration of rational functions and the evaluation of infinite sums The asymptotic behavior of the p-adic valuation for sequences of type (0.0.1) is described. In particular, the connection between the zeros of the polynomials P(x) in the finite field Z/pZ and the growth of the p-adic valuation is presented Finally, in the last chapter a relation between Dirichlet Series and the evaluation of a class of logarithmic integrals is studied<br>acase@tulane.edu

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44

Desjarlais, Melissa A. "Gender differences on the American Mathematics Competition AMC 8 contest." 2009. http://proquest.umi.com/pqdweb?did=1694328921&sid=7&Fmt=2&clientId=14215&RQT=309&VName=PQD.

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Thesis (Ph.D.)--University of Nebraska-Lincoln, 2009.<br>Title from title screen (site viewed June 26, 2009). PDF text: ix, 105 p. ; 894 Kb. UMI publication number: AAT 3350443. Includes bibliographical references. Also available in microfilm and microfiche formats.

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45

"Mathematical contributions to Thomas-Fermi theory (quantum-mechanics)." Tulane University, 1986.

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Mathematically rigorous versions of Thomas-Fermi Theory and its generalizations were developed in the 1970's and 1980's by Lieb, Simon, Benilan, Brezis, Gallouet, Morel and others. At issue is the electron density for an N electron quantum mechanical system in its ground state. The energy minimization problem is reduced to the solution of the Euler-Lagrange equation, which is reduced to the solution of a nonlinear elliptic equation in L('1) The theory which will be presented includes extensions of the existing theory to d ((GREATERTHEQ)3) dimensions and the introduction of weight functions into the kinetic energy term. Existence, nonexistence, and uniqueness results will be presented, as well as qualitative properties of the solutions<br>acase@tulane.edu

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46

"rho-rational extensions of modules." Tulane University, 1991.

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For any given radical $\rho$, the $\rho$-rational extensions of modules is a stronger version of rational extensions of modules, and its properties are studied. However, when $\rho$ is the identity functor both these concepts coincide. In most of the work of this thesis, the ring of the module structure is not assumed to be commutative. Just as every module has a rational completion, it is shown that for any given radical $\rho$, every module has a $\rho$-rational completion, which is unique upto isomorphism in its $\rho$-divisible hull. For any ring R with identity, the $\rho$-rational completion $\overline{R} \sp\rho$ of R is a ring. The $\rho$-rational completion of a module in terms of filters are studied, and the behavior of $\rho$-rationally complete modules under the formation of direct products and direct sums is obtained. Finally, we establish the invariance of the $\rho$-rational completeness of a module under a change of rings<br>acase@tulane.edu

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47

"A Mathematical Foundation For Locality." Tulane University, 2014.

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This work is motivated by two non-intuitive predictions of Quantum Mechanics: non-locality and contextuality. Non-locality is a phenomenon whereby interactions between spatially separated objects appear to be occurring faster than the speed of light. Contextuality is a phenomenon whereby the outcome of a measurement cannot be interpreted as the revelation of an intrinsic fixed property of the system being measured, but instead necessarily depends on the configuration of the measurement apparatus. Quantum Mechanics predicts non-local behavior in certain types of experiments collectively known as Bell tests. However, ruling out all possible alternative local theories is a subtle and demanding task. In this work, we lay out a mathematically-rigorous framework for analyzing Bell experiments. Using this framework, we derive the famous Clauser-Horne-Shimony-Holt (CHSH) inequality, an important constraint that is obeyed by all local theories and violated by Quantum Mechanics. We further demonstrate how to analyze the data of a CHSH experiment without assuming that successive experimental trials are independent and/or identically distributed. We also derive the Clauser-Horne (CH74) inequality, an inequality that is more well-suited for realistic Bell experiments using photons. We demonstrate a robust method for statistically analyzing the data of a CH74 experiment, and show how to calculate exact p-values for this analysis, improving on the previously-best-known (loose) upper bounds obtained from Hoeffding-style inequalities. The work concludes with an exploration of contextuality. The Kochen-Specker theorem -- a result demonstrating the contextual nature of Quantum Mechanics -- is applied to resolve a conjecture in Domain Theory regarding the spectral order on quantum states.<br>acase@tulane.edu

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48

Agarwal, Sanghmitra. "The nature of pre-service secondary mathematics teachers' knowledge of mathematics for teaching of functions." 2006. http://proquest.umi.com/pqdweb?did=1192179591&sid=5&Fmt=2&clientId=39334&RQT=309&VName=PQD.

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Thesis (Ph.D.)--State University of New York at Buffalo, 2006.<br>Title from PDF title page (viewed on Feb. 21, 2007) Available through UMI ProQuest Digital Dissertations. Thesis adviser: Schroeder, Thomas L. Includes bibliographical references.

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49

"Mathematical modeling of spiral wave reentry and defibrillation shocks in ventricular myocardium." Tulane University, 1998.

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The mechanisms of cardiac defibrillation, the most effective clinical procedure for termination of lethal cardiac arrhythmias, are not well understood. Shocks establish an electric field in the heart, which, in turn, induces changes in the transmembrane potential leading to defibrillation. The complexity of cardiac structure makes it difficult to explain, based on experiments alone, how exactly the electric field affects transmembrane potential. In an attempt to provide additional insight into the issue, in this computational study we explore the effects of strong electric shocks on myocardium in fibrillation Cardiac tissue is represented by the two-dimensional anisotropic bidomain model with active membrane kinetics and various fiber geometries. A single reentrant circuit of excitation serves as a simple model of the arrhythmic behavior. Bidomain model allows us to study currents introduced by the shock into the extracellular space of the myocardium We illustrate various mechanisms by which cardiac tissue structure, as well as the electrode shape, assists the changes in transmembrane potential throughout the myocardium that result in defibrillation. We observe the shock-induced regions of the reverse polarity of transmembrane potential, so-called virtual electrodes, that form at a distance from the physical electrodes. These regions affect the electrical state of the tissue globally by perturbing reentrant wavefronts and generating new excitations Our results support the hypothesis that virtual electrodes play an important role in defibrillation. The variety of simulation results described here offers a new level of understanding of the virtual electrode concept and provides a theoretical ground for future experimental studies<br>acase@tulane.edu

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50

"An algorithm for the efficient integration of rational functions and some classical theorems in analysis." Tulane University, 1997.

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The primary focus of this work is the closed-form evaluation of integrals of the form$$\int\sbsp{0}{\infty}{P(x\sp2)\over Q(x\sp2)} dx,$$where P and Q are polynomials in x Most of our results are expressed in terms of the polynomial $$\eqalign{\Phi(a\sb1,\cdots,a\sb{p},q;x)&=x\sp{q}+a\sb{p}x \sp{q-1}+a\sb{p-1}x\sp{q-2}\cr&{+}\cdots{+}a\sb1x\sp{q/2}{+}a\sb2x\sp{q/2{-}1}{+}\cdots{+}1,\cr}$$and the integrals$$M\sb{q}(a\sb1,\cdots,a\sb{p};m)=\int\sbsp{0}{\infty} \left\lbrack{x\sp{q/2}\over \Phi(a\sb1,\cdots,a\sb{p},q;x)} \right\rbrack\sp{m}\ dx$$and$$ N\sb{j,q}(a\sb1,\cdots,a\sb{p};m)=\int\sbsp{0}{\infty} \left\lbrack{x\sp{2j}\over \Phi(a\sb1,\cdots,a\sb{p},q;x)}\right\rbrack\sp{m+1}\ dx,$$where $q=4p$ or $4p+2$ according to the residue of q modulo 4 A number of other types of results follow from our integral evaluations. These include some series, among the most notable being$$\eqalign{\sqrt{a+\sqrt{1+c}}\ =\ &\sqrt{a+1}+\cr &+{1\over \pi\sqrt{2}}\sum\sbsp{k=0}{\infty}{(-1)\sp{k-1}\over k}N\sb{0,4}(a;k-1).\cr}$$ The special case with $a=1$ has been studied extensively by Lagrange, Ramanujan and others<br>acase@tulane.edu

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