Tesis: "Mathematical Sciences"

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Kaya, Ahmet. "Modern mathematical methods for actuarial sciences". Thesis, University of Leicester, 2017. http://hdl.handle.net/2381/39613.

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In the ruin theory, premium income and outgoing claims play an important role. We introduce several ruin type mathematical models and apply various mathematical methods to find optimal premium price for the insurance companies. Quantum theory is one of the significant novel approaches to compute the finite time non-ruin probability. More exactly, we apply the discrete space Quantum mechanics formalism (see main thesis for formalism) and continuous space Quantum mechanics formalism (see main thesis for formalism) with the appropriately chosen Hamiltonians. Several particular examples are treated via the traditional basis and quantum mechanics formalism with the different eigenvector basis. The numerical results are also obtained using the path calculation method and compared with the stochastic modeling results. In addition, we also construct various models with interest rate. For these models, optimal premium prices are stochastically calculated for independent and dependent claims with different dependence levels by using the Frank copula method.

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2

Wilensky, Uriel Joseph. "Connected mathematics : builiding concrete relationships with mathematical knowledge". Thesis, Massachusetts Institute of Technology, 1993. http://hdl.handle.net/1721.1/29066.

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3

Holdaway, Emma Lynn. "Mathematical Identities of Students with Mathematics Learning Dis/abilities". BYU ScholarsArchive, 2020. https://scholarsarchive.byu.edu/etd/8536.

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The majority of research on the mathematics teaching and learning of students with mathematics learning dis/abilities is not performed in the field of mathematics education, but in the field of special education. Due to this theoretical divide, students with mathematics learning dis/abilities are far more likely to be in classes that emphasize memorization, direct instruction, and the explicit teaching of rules and procedures. Additionally, students with mathematics learning dis/abilities are often seen as "unable" to succeed in school mathematics and are characterized by their academic difficulties and deficits. The negative assumptions, beliefs, and expectations resulting from ableistic practices in the education system color the interactions educators, parents, and other students have with students with mathematics learning dis/abilities. These interactions in turn influence how students with mathematics learning dis/abilities view and position themselves as learners and doers of mathematics. My study builds on the theoretical framework of positioning theory (Harré, 2012) in order to better understand the mathematical identities of students with mathematics learning dis/abilities. The results of my study show how these students use their prepositions and enduring positions to inform the in-the-moment positions they take on in the mathematics classroom.

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4

Brown, Adam. "Infeasibility of solving finite mathematical problems". Thesis, McGill University, 2010. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=86989.

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We prove that the decision problem for finite mathematical state- ments, though recursive, is infeasible in seemingly any realistic model of computation. In particular, we construct of a set of finite mathematical statements which can only be feasibly solved by programs long enough to explicitly encode a decision for each statement. This result was published in Hungarian, in 1973, by Michael Makkai and appears here for the first time in English. In this paper we: 1) elucidate Makkai's proof as an adaptation of Gödel's first incompleteness proof, 2) strengthen his 1973 result and 3) reflect on this result from the perspectives of computational complexity and algorithmic information theory (Kolmogorov complexity).
Nous avons démontré que le problème quand à prendre des décisions concernant des énoncés mathématiques finis, bien que récursif, est infaisable accordé à n'importe quel modèle de calcul. Plus précisément, nous avons établi un ensemble de problèmes mathématiques ne pouvant être résolus que par des programmes assez long qui suggéreraient la décision finale implicitement, au fil des calculs. Ce fait a d'abord été publié en 1973 par un Hongrois du nom de Michael Makkai, et il sera expliqué en anglais pour la toute première fois ici. Dans ce travail, nous 1) éluciderons la démonstration faite par Makkai basé sur l'adaptation de la première démonstration du théorème incomplétude de Gödel, 2) appuierons les résultats trouvés en 1973 par Makkai et 3) tirerons des conclusions sur ses résultats en utilisant la théorie de la complexité et la théorie algorithmique de l'information, aussi appelée complexité de Kolmogorov.

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5

Jakobsson-Åhl, Teresia. "Encouraging Participation in Mathematical Practices : Messages in the Boost for Mathematics". Thesis, Luleå tekniska universitet, Institutionen för konst, kommunikation och lärande, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-67660.

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In this thesis, focused attention is given to the idea of task solvers as active participants in mathematical practices. The theoretical assumptions of the study, reported in this thesis, are inspired by socio-political concerns. The aim of the study is to investigate the underlying view of participation in mathematical practices, as understood in a nationwide teacher professional development programme, the Boost for Mathematics, in Sweden. To be more precise, the study is arranged to problematise ways of encouraging students as active participants. This aim is approached by means of the following research questions: (1) What messages do mathematical tasks in the Boost for Mathematics send about people as participants in mathematical practices? and (2) What is the role of multiple representations in these messages? An empirical study is reported. The data of the study, i.e., three collections of problems, are drawn from the Boost for Mathematics. Data processing is conducted by using a modified version of a pre-existing data processing framework, focusing on mathematical practices as socio-political practices. The empirical study uncovers an implicit view of task solvers in mathematical practices and especially a detachment between students, as potential task solvers, and the social contexts where mathematical ideas and concepts are embedded. This implicit view is challenged from the assumption that it is motivating for a student to conceive him/herself as someone who is ‘qualified’ to take part in mathematical practices.

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6

Courvoisier, Pierre. "Mathematical modelling of composting processes using finite element method". Thesis, McGill University, 2011. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=103735.

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Composting is one element of waste management. It allows waste to be transformed into a valuable product. The processes involved and the final product, however, may vary in terms of quality, efficiency or security. Models have been established to represent some features of the composting process, but never all of them together. We hypothesized that all the key features from the literature could be gathered in one model. This model should be qualitatively faithful, reliable, and easily adapted to any situation. We used COMSOL TM, software that uses proven algorithms and the finite element method to solve partial differential equations in high spatial resolution in up to three dimensions. The behavior of this model was studied through parameter variations and sensitivity analysis. Patterns in temperature, biomass, substrate, oxygen and water concentration curves were consistent with the typical curves found in literature about composting. Initial water concentration and airflow were found to have an important impact on the composting process, while inlet air temperature did not. The resolution of the mathematical problem in a two-dimensional, longitudinal cross-section of the rectangular vessel allowed the observation of spatial patterns. This model can be used as a basis for further studies as new features are easy to implement. It can likewise be adapted to any apparatus, which makes it useful for comparative analysis. The suggested model, however, has yet to be validated against a physical system and this should be the next step.
Le compostage est un composant de la gestion des déchets et permet de les transformer en un produit à valeur ajouté. Les procédés en jeu, ainsi que les produits finis peuvent cependant varier au niveau de la qualité, de l'efficacité, et de la sécurité. Des modèles ont été mis au point pour prendre en compte certaines caractéritiques du compostage, mais jamais de façon exhaustive. Notre hypothèse était que toutes les caractéristiques clés décrites dans la littérature peuvent être réunies en un seul modèle. Ce modèle doit être qualitativement fidèle, fiable, et facilement adaptable à toutes les situations. Nous avons utilisé COMSOL TM, un logiciel qui utilise des algorithmes établis et se base sur la méthode des éléments finis pour résoudre les systèmes d'équations différentielles partielles avec une bonne résolution spatiale en deux ou trois dimensions. La réponse de ce modèle face à des variations paramètriques et à une analyse de sensitivité a été étudiée. Les comportements de la température, de la biomasse, du substrat, de l'oxygène, et de la quantité d'eau ont été cohérents avec ceux trouvés dans la littérature sur le compostage. La concentration initiale en eau, ainsi que l'aération, ont été prouvés avoir un impact important sur le compostage, contrairement à la température de l'air entrant. La résolution du problème mathématique dans une coupe bidimensionnelle longitudinale du container rectangulaire permet l'observation de comportements spatiaux. Ce modèle pourra être utilisé comme un fondement pour de futures études car l'ajout de nouvelles caractéristiques y est aisé. Le modèle peut aussi être facilement adapté à différentes conditions expérimentales, ce qui en fait un bon outil comparatif. Cependant, le modèle suggéré doit d'abord être validé par des données expérimentales.

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7

Boyaval, Sébastien. "Mathematical modelling and numerical simulation in materials science". Phd thesis, Université Paris-Est, 2009. http://tel.archives-ouvertes.fr/tel-00499254.

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In a first part, we study numerical schemes using the finite-element method to discretize the Oldroyd-B system of equations, modelling a viscoelastic fluid under no flow boundary condition in a 2- or 3- dimensional bounded domain. The goal is to get schemes which are stable in the sense that they dissipate a free-energy, mimicking that way thermodynamical properties of dissipation similar to those actually identified for smooth solutions of the continuous model. This study adds to numerous previous ones about the instabilities observed in the numerical simulations of viscoelastic fluids (in particular those known as High Weissenberg Number Problems). To our knowledge, this is the first study that rigorously considers the numerical stability in the sense of an energy dissipation for Galerkin discretizations. In a second part, we adapt and use ideas of a numerical method initially developped in the works of Y. Maday, A.T. Patera et al., the reduced-basis method, in order to efficiently simulate some multiscale models. The principle is to numerically approximate each element of a parametrized family of complicate objects in a Hilbert space through the closest linear combination within the best linear subspace spanned by a few elementswell chosen inside the same parametrized family. We apply this principle to numerical problems linked : to the numerical homogenization of second-order elliptic equations, with two-scale oscillating diffusion coefficients, then ; to the propagation of uncertainty (computations of the mean and the variance) in an elliptic problem with stochastic coefficients (a bounded stochastic field in a boundary condition of third type), last ; to the Monte-Carlo computation of the expectations of numerous parametrized random variables, in particular functionals of parametrized Itô stochastic processes close to what is encountered in micro-macro models of polymeric fluids, with a control variate to reduce its variance. In each application, the goal of the reduced-basis approach is to speed up the computations without any loss of precision

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8

Reeves, Laurence H. "Mathematical Programming Applications in Agroforestry Planning". DigitalCommons@USU, 1991. https://digitalcommons.usu.edu/etd/6495.

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Agroforestry as a sustainable production system has been recognized as a land use system with the potential to slow encroachment of agriculture onto forested lands in developing countries. However, the acceptance of nontraditional agroforestry systems has been hampered in some areas due to the risk-averse nature of rural agriculturalists. By explicitly recognizing risk in agroforestry planning, a wider acceptance of agroforestry is possible. This thesis consists of a collection of three papers that explore the potential of modern stock portfolio theory to reduce financial risk in agroforestry planning. The first paper presents a theoretical framework that incorporates modern stock portfolio theory through mathematical programming. This framework allows for the explicit recognition of financial risk by using a knowledge of past net revenue trends and fluctuations for various cropping systems, with the assumption that past trend behavior is indicative of future behavior. The paper demonstrates how financial risk can be reduced by selecting cropping systems with stable and/or negatively correlated net revenues, thereby reducing the variance of future net revenues. Agroforestry systems generally entail growing simultaneously some combination of plant and/or animal species. As a result, interactions between crops usually cause crop yields within systems to deviate from what would be observed under monocultural conditions, thus requiring some means of incorporating these interactions into mathematical models. The second paper presents two approaches to modeling such interactions, depending on the nature of the interaction. The continuous system approach is appropriate under conditions where yield interactions are linear between crops and allows for a continuous range of crop mixtures. The discrete system approach should be used where nonlinear interactions occur. Under this second approach, decision variables are defined as fixed crop mixtures with known yields. In the third paper, the techniques presented above were applied to a case study site in Costa Rica. Using MOTAD programming and a discrete system approach, a set of minimum-risk farm plans were derived for a hypothetical farm. For the region studied, results indicate that reductions in risk require substantial reductions in expected net revenue.

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9

Behzadi, Mahsa. "A mathematical model of Phospholipid Biosynthesis". Phd thesis, Ecole Polytechnique X, 2011. http://pastel.archives-ouvertes.fr/pastel-00674401.

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A l'heure de l'acquisition de donn'ees 'a haut d'ebit concernant le m'etabolisme cellulaire et son 'evolution, il est absolument n'ecessaire de disposer de mod'eles permettant d'int'egrer ces donn'ees en un ensemble coh'erent, d'en interpr'eter les variations m'etaboliques r'ev'elatrice, les 'etapes clefs o'u peuvent s'exercer des r'egulations, voire mˆeme d'en r'ev'eler des contradictions apparentes met- tant en cause les bases sur lesquelles le mod'ele lui-mˆeme est construit. C'est ce type de travail que j'ai entrepris 'a propos de donn'ees exp'erimentales obtenues dans le laboratoire biologique sur le m'etabolisme de cellules tu- morales en r'eponse 'a un traitement anti-canc'ereux. Je me suis attach'ee 'a la mod'elisation d'un point particulier de ce m'etabolisme. Il concerne le m'etabolisme des glyc'erophospholipides qui sont de bons marqueurs de la prolif'eration cellulaire. Les phospholipides constituent l'essentiel des mem- branes d'une cellule et l''etude de leur synth'ese (en particulier chez les cellules de mammif'eres) est de ce fait un sujet important. Ici, nous avons pris le parti de mettre en place un mod'ele math'ematique par 'equations diﬀ'erentielles ordinaires, qui est essentiellement bas'e sur des 'equations hyperboliques (Michaelis-Menten), mais aussi sur des cin'etiques type loi d'action de masse et diﬀusion. Le mod'ele, compos'e de 8 'equations diﬀ'erentielles, donc de 8 substrats d'int'erˆet, comporte naturellementdes param'etres inconnus in vivo, et certains d'ependents des conditions cellulaires (diﬀ'erentiations de cellules, pathologies, . . .). Le mod'ele s'epare la structure du r'eseau m'etabolique, l''ecriture de la matrice de stoechiom'etrie, celles des 'equations de vitesse et enﬁn des 'equations diﬀ'erentielles. Le mod'ele choisi est le mod'ele murin (souris/rat), parce qu'il est lui-mˆeme un mod'ele de l'homme. Plusieurs con- ditions sont successivement consid'er'ees pour l'identiﬁcation des param'etres, aﬁn d''etudier les liens entre la synth'ese de phospholipides et le cancer : - le foie sain du rat, - le m'elanome B16 et le carcinome de la lign'ee 3LL chez la souris, respectivement sans traitement, en cours de traitement 'a la Chloro'ethyl-nitrosour'ee et apr'es traitement, - enﬁn le m'elanome B16 chez la souris sous stress de privation de m'ethionine. En r'esum'e, ce tra- vail fourni une interpr'etation nouvelle des donn'ees exprimentales en mon- trant le rˆole essentiel de la PEMT et la nature superstable de l''etat sta- tionnaire de fonctionnement du r'eseau m'etabolique des phospholipides lors de la canc'erog'en'ese et du traitement des cancers. Il montre bien l'avantage de l'utilisation d'un mod'ele math'ematique dans l'interpr'etation de donn'ees m'etaboliques complexes.

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10

Du, Toit Jacques Pierre. "The discrete pulse transform and applications". Thesis, Link to the online version, 2007. http://hdl.handle.net/10019/1052.

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11

Jernigan, Jonathan. "Mathematical Modeling of Convective Heat Transfer in Mammoth Cave". TopSCHOLAR®, 1997. http://digitalcommons.wku.edu/theses/787.

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Around two centuries ago, changes were made to the entrances of Mammoth Cave and its passages. Today the Historic Entrance to Mammoth Cave is enlarged and the passage just beyond the entrance known as Houchins' Narrows has been cleared of rubble and filled with sediments. These enlargements have resulted in an increase in airflow throughout the Historic Section of the cave causing environmental conditions such as air temperature and airflow to fluctuate. These fluctuations have negatively impacted inhabitants and contents of the cave system. To restore natural conditions within the cave, Science and Resource Management personnel at Mammoth Cave National Park have been collecting large data sets on atmospheric conditions inside the cave. The author has access to data from eight sites within the cave. In this thesis, the author provides a brief introduction to the effects of the increase in airflow as well as a short discussion of the data gathered by Science and Resource Management. The author then proposes a natural cause for airflow (i.e., convection) in Mammoth Cave, constructs empirical models with this as the underlying driving force, and uses atmospheric data to verify the validity of the claim of convection as the force driving airflow in Mammoth Cave. Data from the site in Houchins' Narrows is used to predict atmospheric data at other locations in the cave. The author concludes this thesis with time series analysis on data from Houchins' Narrows.

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12

Trichtchenko, Olga. "Electron transport in nano devices: mathematical introduction and preconditioning". Thesis, McGill University, 2009. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=66812.

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In this thesis we outline the mathematical principles behind density functional theory, and describe the iterative Kohn-Sham formulation for computation of electronic density calculations in nano devices. The model for computation of the density of electrons in such device is a non-linear eigenvalue problem that is solved iteratively using the resolvent formalism. There are several bottlenecks to this approach and we propose methods to resolve them. This iterative method involves a matrix inversion. This matrix inversion is called upon when calculating the Green's function for a particular system, the two-probe device. A method to speed up this calculation is to use a preconditioning technique to accelerate the convergence of the iterative metho d. Tests the existing algorithm for a one-dimensional system are presented. The results indicate that these preconditioning methods reduce the condition number of the matrices.
Dans cette thèse, nous présentons les principes mathématiques à la base de la théorie de la fonctionnelle de la densité, et nous décrivons la formule Kohn-Sham itérative pour le calcul des densités d'électron dans les composants nano-électroniques. Le modèle de densité électronique est un problème de valeurpropre non-linéaire que l'on résout de manière itérative. Il y a plusieurs complications liées à cette technique et nous proposons des méthodes pour y remédier. On formule le système à l'aide du calcul de l'opérateur hamiltonien dans une base particulière. Cette inversion de matrice est nécessaire lors du calcul de la fonction de Green pour le système en question: l'appareil à deux sondes. Aﬁn d'accélérer ce calcul, nous utilisons une technique de préconditionnement basée sur la nature itérative du problème. Nous présentons les résultats de nos essais avec différents préconditionneurs. Ceux-ci indiquent que ces méthodes réduisent le nombre de conditionnement de notre matrice. Ce préconditionnement est donc appliqué à des algorithmes d'inversion itératives classiques tels que la méthode de Gauss-Seidel et la méthode du résidu minimal généralisée. En effet, nous observons une réduction du nombre d'itérations nécessaires pour le calcul de la matrice inverse.

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13

Wilford, Christopher Richard. "Mathematical studies of the terrestrial ionosphere : helium ion behaviour". Thesis, University of Sheffield, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.251221.

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14

Dunn, Sara-Jane Nicole. "Towards a computational model of the colonic crypt with a realistic, deformable geometry". Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:c3c9440a-52ac-4a3d-8e1c-5dc276b8eb6c.

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Colorectal cancer (CRC) is one of the most prevalent and deadly forms of cancer. Its high mortality rate is associated with difficulties in early detection, which is crucial to survival. The onset of CRC is marked by macroscopic changes in intestinal tissue, originating from a deviation in the healthy cell dynamics of glands known as the crypts of Lieberkuhn. It is believed that accumulated genetic alterations confer on mutated cells the ability to persist in the crypts, which can lead to the formation of a benign tumour through localised proliferation. Stress on the crypt walls can lead to buckling, or crypt fission, and the further spread of mutant cells. Elucidating the initial perturbations in crypt dynamics is not possible experimentally, but such investigations could be made using a predictive, computational model. This thesis proposes a new discrete crypt model, which focuses on the interaction between cell- and tissue-level behaviour, while incorporating key subcellular components. The model contains a novel description of the role of the surrounding tissue and musculature, which allows the shape of the crypt to evolve and deform. A two-dimensional (2D) cross-sectional geometry is considered. Simulation results reveal how the shape of the crypt base may contribute mechanically to the asymmetric division events typically associated with the stem cells in this region. The model predicts that epithelial cell migration may arise due to feedback between cell loss at the crypt collar and density-dependent cell division, an hypothesis which can be investigated in a wet lab. Further, in silico experiments illustrate how this framework can be used to investigate the spread of mutations, and conclude that a reduction in cell migration is key to confer persistence on mutant cell populations. A three-dimensional (3D) model is proposed to remove the spatial restrictions imposed on cell migration in 2D, and preliminary simulation results agree with the hypotheses generated in 2D. Computational limitations that currently restrict extension to a realistic 3D geometry are discussed. These models enable investigation of the role that mechanical forces play in regulating tissue homeostasis, and make a significant contribution to the theoretical study of the onset of crypt deformation under pre-cancerous conditions.

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15

Xiros, Nikolaos I. "Mathematical Formulation of Fusion Energy Magnetohydrodynamics". ScholarWorks@UNO, 2017. https://scholarworks.uno.edu/td/2438.

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Chapter 1 presents the basic principles of Controlled Thermonuclear Fusion, and the approaches to achieve nuclear fusion on Earth. Furthermore, the basic components of the Tokamak, the reactor which will house the fusion reaction, are analyzed. Finally, the chapter ends with a discussion on how the present thesis is related to the Controlled Thermonuclear Fusion. Chapter 2 introduces briefly the basic concepts of the Electromagnetic and Magnetohydrodynamic theories as well as MHD turbulence. Chapter 3 presents a first glance in OpenFOAM CFD library. Chapter 4 introduces the Orszag-Tang vortex flow, which is a benchmark test case for MHD numerical models. Also, the results obtained by the model developed in this thesis are presented and discussed. Chapter 5 describes an analytical solution method for the MHD natural convection in an internally heated horizontal shallow cavity. Also, a finite volume numerical model is presented for solving the aforementioned problem and properly validated. The results of the numerical model are compared with the analytical solutions for a range of Rayleigh and Hartmann numbers. Finally, conclusions based on this work are drawn and recommendations for future work are made.

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16

Yame, Joseph. "Contribution to the mathematical theory of sampled-data control systems". Doctoral thesis, Universite Libre de Bruxelles, 2001. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/211597.

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17

Ivarsson, Niklas. "Electronic Scoring System : An Electronic & Mathematical Approach". Thesis, Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-43314.

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This dissertation describes a project to create an electronic shooting system made of simple and inexpensive components, namely a Raspberry Pi computer and sound detectors. The initial goals are to create a system that can be used with an acceptable precision. Secondly a performance analysis will be carried out to determine the precision that can be obtained using these components. The project was developed into three modules: back-end, Cloud and front-end. The back-end is used to gather the information of a projectile on the target, calculate the coordinates and send it to the Cloud. The Cloud acts as the interface between the back-end with the front-end. Lastly the front-end is the Viewer Client that presents the score and positon at which the projectile hit the target. After developing all the components and applications there was a functional system, but not a reliable system. This combination of Raspberry Pi and sound detectors were not good enough to obtain the precision required for the system to work as an electronic scoring system.

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18

Matthews, Amanda. "A Mathematical Model for Anti-Malarial Drug Resistance". VCU Scholars Compass, 2009. http://scholarscompass.vcu.edu/etd/1721.

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Despite the array of medical advances of our modern day society, infectious diseases still plague millions of people worldwide. Malaria, in particular, causes substantial suffering and death throughout both developed and developing countries. Aside from the socioeconomic challenges presented by the disease's prevalence in impoverished nations, one of the major difficulties scientists have encountered while attempting to eradicate the disease is the parasite's ability to become resistant to new drugs and methods of treatment. In an effort to better understand the dynamics of malaria, we analyze a mathematical model that accounts for both the treatment aspect as well as the drug resistance that accompanies it. Simulations demonstrating the effects of treatment rates and the level of resistance are studied and discussed in hopes of shedding additional light on the characteristics of this devastating epidemic.

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19

Brizic, Biloglav Marija. "Preschool teachers´ views on preschool mathematical environment". Thesis, Malmö högskola, Fakulteten för lärande och samhälle (LS), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:mau:diva-31962.

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Föreliggande studie handlar om förskolans uppdrag att skapa goda förutsättningar för barns matematiska förståelse. Studiens syfte är att beskriva hur sex pedagoger arbetar för att skapa en matematisk lärandemiljö för barn i ålder 3-5 år. För att uppnå studiens syfte ställs två frågeställningar som är: Hur ordnar sex pedagoger förskolans miljö och material för att stimulera barns matematiska förståelse? samt Vilka matematiska aktiviteter beskriver pedagogerna som ett led i att stimulera barns matematiska förståelse?Studien grundas i ett Sociokulturellt perspektiv med fokus på miljö, språk och samlärande. I urvalet ingår sex pedagoger med varierande utbildning och arbetserfarenhet men har det gemensamt att arbeta inom samma storstadskommun. Empirin samlades in med kvalitativ intervjumetod.Studiens viktigaste resultat visar att de intervjuade pedagogerna arbetar målmedvetet med att skapa och omskapa miljö och material allt efter barnens intressen och behov. De redskap som pedagogerna använder i sin verksamhet och i syfte att utveckla barns matematiska förståelse är redskap som barnen på ett lekfullt sätt kan sortera, para ihop, bygga och konstruera med, räkna antal, samt arbeta med rumsuppfattning. Alla pedagogerna arbetar med matematik som kan kopplas till de sex matematiska aktiviteterna: räkna, lokalisera, mäta, konstruera, lokalisera och förklara. Studien visar också att pedagogerna skapar matematiska aktiviteter i samråd med barnen och, för barnen, i meningsfulla sammanhang. Enligt de sex pedagogerna behövs det skapas en lugn miljö med tydlig struktur som utmanar barnen i deras matematiska lärande.De slutsatser som kan dras av resultaten är att pedagogerna i de aktuella förskolorna är väl förberedda för att uppfylla förskolans uppdrag att skapa goda förutsättningar för barns matematiska förståelse.

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20

Roose, T. "Mathematical model of plant nutrient uptake". Thesis, University of Oxford, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.365790.

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This thesis deals with the mathematical modelling of nutrient uptake by plant roots. It starts with the Nye-Tinker-Barber model for nutrient uptake by a single bare cylindrical root. The model is treated using matched asymptotic expansion and an analytic formula for the rate of nutrient uptake is derived for the first time. The basic model is then extended to include root hairs and mycorrhizae, which have been found experimentally to be very important for the uptake of immobile nutrients. Again, analytic expressions for nutrient uptake are derived. The simplicity and clarity of the analytical formulae for the solution of the single root models allows the extension of these models to more realistic branched roots. These models clearly show that the `volume averaging of branching structure' technique commonly used to extend the Nye-Tinker-Barber with experiments can lead to large errors. The same models also indicate that in the absence of large-scale water movement, due to rainfall, fertiliser fails to penetrate into the soil. This motivates us to build a model for water movement and uptake by branched root structures. This model considers the simultaneous flow of water in the soil, uptake by the roots, and flow within the root branching network to the stems of the plant. The water uptake model shows that the water saturation can develop pseudo-steady-state wet and dry zones in the rooting region of the soil. The dry zone is shown to stop the movement of nutrient from the top of the soil to the groundwater. Finally we present a model for the simultaneous movement and uptake of both nutrients and water. This is discussed as a new tool for interpreting available experimental results and designing future experiments. The parallels between evolution and mathematical optimisation are also discussed.

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21

Zhang, Yaojun. "Mathematical bases for gear inspection by 3D coordinate measuring machine". Doctoral thesis, Universite Libre de Bruxelles, 1995. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/212619.

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22

Redelinghuys, Gideon. "Symbolic string execution". Thesis, Stellenbosch : Stellenbosch University, 2012. http://hdl.handle.net/10019.1/20335.

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Thesis (MSc)--Stellenbosch University, 2012.
ENGLISH ABSTRACT: Symbolic execution is a well-established technique for automated test generation and for nding errors in complex code. Most of the focus has however been on programs that manipulate integers, booleans, and even, references in object-oriented programs. Recently researchers have started looking at programs that do lots of string processing, motivated, in part, by the popularity of the web and the risk that errors in web servers may lead to security violations. Attempts to extend symbolic execution to the domain of strings are mainly divided into one of two camps: automata-based approaches and approaches based on bitvector analysis. Here we investigate these two approaches in a uni ed setting, namely the symbolic execution framework of Java PathFinder. We describe the implementations of both approaches and then do an evaluation to show under what circumstances each approach performs well (or not so well). We also illustrate the usefulness of the symbolic execution of strings by nding errors in real-world examples.
AFRIKAANSE OPSOMMING: Simboliese uitvoering is 'n bekende tegniek vir automatiese genereering van toetse en om foute te vind in ingewikkelde bronkode. Die fokus sover was grotendeels op programme wat gebruik maak van heelgetalle, boolse waardes en selfs verwysings in objek geörienteerde programme. Navorsers het onlangs begin kyk na programme wat baie gebruik maak van string prosessering, deelteliks gemotiveerd deur die populariteit van die web en die gepaardgaande risiko's daarvan. Vorige implementasies van simboliese string uitvoering word binne twee kampe verdeel: die automata gebaseerde benadering en bitvektoor gebaseerde benadering. Binne hierdie tesis word die twee benaderings onder een dak gebring, naamliks Java PathFinder. Die implentasie van beide benaderings word bespreek en ge-evalueer om die omstandighede uit te wys waarbinne elk beter sou vaar. Die nut van simboliese string uitvoering word geïllustreer deur dit toe te pas in foutiewe regte wêreld voorbeelde.

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23

Alonso, Chavez Vasthi. "Mathematical studies of conservation and extinction in inhomogeneous environments". Thesis, University of Southampton, 2011. https://eprints.soton.ac.uk/341661/.

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A fragmented ecosystem contains communities of organisms that live in fragmented habitats. Understanding the way biological processes such as reproduction and dispersal over the fragmented habitats take place constitutes a major challenge in spatial ecology. In this thesis we discuss a number of mathematical models of density-dependent populations in inhomogeneous environments presenting growth, decay and diffusion amongst woodland patches of variable potential for reproductive success. These models include one- and two-dimensional analyses of single population systems in fragmented environments. We investigate and compute effective properties for single patch systems in one dimension, linking ecological features with landscape structure and size. A mathematical analysis of potential impacts on spread rates due to the behaviour of individuals in the population is then developed. For the analysis of the population dispersal between areas of plentiful resources and areas of scarce resources, we introduce a novel development that models individuals hazard sensitivity when outside plentiful regions. This sensitivity is modelled by introducing a term called endrotaxis that generates a dispersal gradient, resulting in realistically low migration between regions of plentiful resources. Numerical methods and semi-analytic results yield maximum patch separations for one and two dimensional systems and show that the velocity of spread depends on inter-patch distances and patch geometries. By introducing Allee effects (i.e., inverse density-dependent responses to the difficulty of finding mates at low density) over the population growth function, we find that dispersal is slowed down when combined with hazard sensitivity. In the final Chapter we sumarise the results of the previous chapters, concluding that the work performed in this thesis complements and enriches the current mathematical models of movement behaviour.

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24

Stipp, Eugene Heinz. "Bounds for Ramsey numbers in multipartite graphs". Thesis, Stellenbosch : Stellenbosch University, 2000. http://hdl.handle.net/10019.1/51640.

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Thesis (MSc.)--University of Stellenbosch, 2000.
ENGLISH ABSTRACT: The notion of a classical graph theoretic Ramsey number is generalized by assuming that both the original graph whose edges are arbitrarily bicoloured and the monochromatic subgraphs to be forced are complete, balanced, multipartite graphs, instead of complete graphs as in the standard definition. Some small multipartite Ramsey numbers are found, while upper- and lower bounds are established for others. Analytic arguments as well as computer searches are used.
AFRIKAANSE OPSOMMING: Die klassieke grafiek-teoretiese definisie van ’n Ramsey getal word veralgemeen deur te aanvaar dat beide die oorspronklike grafiek, waarvan die lyne willekeurig met twee kleure gekleur word en die gesogte subgrafieke almal volledige, gebalanseerde, veelledige grafieke is, anders as in die standaard definisie. Klein veelledige Ramsey getalle word gevind, terwyl bo- en ondergrense vir ander daargestel word. Analitiese argumente en rekenaarsoektogte word gebruik.

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25

Gahamanyi, Marcel. "Mathematics at work : a study of mathematical organisations in Rwandan workplaces and educational settings". Doctoral thesis, Linköpings universitet, Avdelningen för studier av vuxenutbildning, folkbildning och högre utbildning (VUFo), 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-60260.

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To make mathematics more significant for the beneficiaries, the problem studied in this thesis is to investigate how to connect mathematical daily practices with educational contexts. The overarching aim is to investigate how to contextualise school mathematics within Rwandan cultural mathematics practices. The content of the thesis reports on the characteristics of mathematical organisations in three workplace settings (taxi driving, house construction and restaurant management) which in turn serve as source for the design of contextualised mathematical activities for student teachers in a teacher education programme. Three levels of mathematical practices are described: (1) mathematical practices that are performed by workers within their respective workplaces, (2) mathematical practices that are performed by student teachers while solving and posing contextualised mathematical tasks for secondary school students, (3) mathematical practices that are carried out by secondary school students. Data gathered from individual and group interviews, transcripts of group discussions and students’ written reports of mathematical work were analysed from the perspective of both activity theory and anthropological theory of didactics. Findings from workplace settings revealed that mathematical organisations performed by workers are characterised by techniques which are functional to the problem at hand, the cultural constraints and the educational background of the workers. As long as they are pragmatic towards the goals of the activity no further justification of the techniques used is needed, resulting in a mathematical organisation with undeveloped know-why (logos). On the contrary, at university and secondary school settings, students justified the used techniques throughout the related taught content of the subject mathematics. Also from each category of mathematical practice, it is shown that while connecting workplaces and educational settings the didactic transposition process was much influenced by the institutional conditions and constraints.
För att göra matematiken betydelsefull för avnämarna är problemområdet som studeras i denna avhandling hur den matematik som finns i samhället kan överbryggas till en undervisningskontext. Syftet med avhandlingen är att undersöka hur man kan kontextualisera skolmatematik i kulturella praktiker i Rwanda. I avhandlingen belyses först matematisk organisation på tre arbetsplatser – i en taxiverksamhet, hos en byggmästare och hos en restaurangägare. Matematik i dessa verksamheter utgör underlag för att konstruera uppgifter för lärarstudenter inom ämnet matematik som först löser uppgifterna och sedan i sin tur konstruerar uppgifter för elever motsvarande årskurs nio i grundskolan. Uppgifterna konstrueras med utgångspunkt i den information studenterna fått om de tre verksamheterna. Datainsamlingen skedde med hjälp av individuella intervjuer, gruppintervjuer och bandinspelade gruppdiskussioner samt studenters och elevers nedtecknade lösningar på respektive uppgifter. Data analyserades med hjälp av aktivitetsteori och antropologisk didaktisk teori. Resultaten från arbetsplatserna visade att matematisk organisation kännetecknades av tekniker som är funktionella för de problem som behövde lösas, de kulturella villkor som förelåg och deltagarnas utbildningsbakgrund. Så länge som teknikerna ledde till önskade mål för verksamheten fanns inga behov att utveckla tekniken som kännetecknades av en matematisk organisation med outvecklad logos. I kontrast till denna strategi sågs studenter och elever i respektive miljöer redovisa de tekniker som användes och motivera dem i enlighet med vad som krävs inom matematikämnet. Den matematiska transpositionsprocessen som utfördes av deltagarna i de olika miljöerna influerades i hög grad av rådande institutionella villkor och begränsningar.

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26

Racheal, Cooper. "Analysis of Mathematical Models of the Human Lung". VCU Scholars Compass, 2013. http://scholarscompass.vcu.edu/etd/3289.

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The processes of lung ventilation and perfusion, diffusion, and gas transport make up the system of breathing and tissue oxygenation. Here, we present several mathematical formulations of the essential processes that contribute to breathing. These models aid in our understanding and analysis of this complex system and can be used to form treatments for patients on ventilators. With the right analysis and treatment options, patients can be helped and money can be saved. We conclude with the formulation of a mathematical model for the exchange of gasses in the body based on basic reaction kinetics.

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27

Paul-Michael, Salomonsky. "A Mathematical System for Human Implantable Wound Model Studies". VCU Scholars Compass, 2013. http://scholarscompass.vcu.edu/etd/3187.

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Dermal wound healing involves a myriad of highly regulated and sophisticated mechanisms, which are coordinated and carried out via several specialized cell types. The dominant players involved in this process include platelets, neutrophils, macrophages and fibroblasts. These cells play a vital role in the repair of the wound by orchestrating tasks such as forming a fibrin clot to stanch blood flow, removing foreign organisms and cellular debris, depositing new collagen matrix and establishing the contractile forces which eventually bridge the void caused by the initial infraction.\\[5pt] \indent Our current understanding of these mechanisms has been primarily based upon animal models. Unfortunately, these models lack insight into pathologic conditions, which plague human beings, such as keloid scar or chronic ulcer formation. Consequently, investigators have proposed a number of {\it in vivo} techniques to study wound repair in humans in order to overcome this barrier. One approach, which has been devised to increase our level of understanding of these chronic conditions, involves the cutaneous placement of a small cylindrical structure within the appendage of a human test subject.\\[5pt] \indent Researches have designed a variety of these implantable structures to examine different aspects of wound healing in both healthy subjects and individuals that experience some trauma related condition. In each case, several implants are surgically positioned at multiple locations under sterile conditions. These structures are later removed at distinct time intervals at which point they are histologically analyzed and biochemically assayed to deduce the presence of biological markers involved in the repair process. Implantable structures used in this way are often referred to as Human Implantable Models or Systems.\\[5pt] \indent Clinical studies with implantable models open up tremendous opportunities in fields such as biomathematics because they provide an experimentally controlled setting that aids in the development and validation of mathematical models. Furthermore, experiments carried out with implants greatly simplify the mathematics required to describe the repair process because they minimize the modeling of complex features associated with healing such as wound geometry and the evolution of contractile forces.\\[5pt] \indent In this work, we present a notional mathematical model, which accounts for two fundamental processes involved in the repair of an acute dermal wound. These processes include the inflammatory response and fibroplasia. Our system describes each of these events through the time evolution of four primary species or variables. These include the density of initial damage, inflammatory cells, fibroblasts and deposition of new collagen matrix. Since it is difficult to populate the equations of our model with coefficients that have been empirically derived, we fit these constants by carrying out a large number of simulations until there is reasonable agreement between the time response of the variables of our system and those reported by the literature for normal healing. Once a suitable choice of parameters has been made, we then compare simulation results with data obtained from clinical investigations. While more data is desired, we have a promising first step toward describing the primary events of wound repair within the confines of an implantable system.

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28

Kneller, James Ralph William. "Mechanisms of atrial fibrillation and antiarrhythmic drug therapy evaluated by mathematical modeling". Thesis, McGill University, 2002. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=82903.

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Atrial fibrillation (AF) is the most common sustained arrhythmia encountered in clinical practice. The objectives of this study were to determine the mechanisms and significance of ionic transients in mathematical action potential models, determine the relative contributions of tachycardia-related myocyte remodeling processes to the pathologic features of the remodeled action potential, and to investigate mechanisms of AF maintenance and antiarrhythmic drugs in atrial tissue.
We began by formulating expressions for myocyte Cl- transport processes which allowed us to evaluate model stability and the influence of model equation singularity, and to characterize pacing-induced ionic transients. We found that tissue and model transients are comparable, indicating that any distortion arising from dynamic equation instabilities is not likely to be significant.
We then measured Ca2+-transients in isolated atrial myocytes in control and following tachycardia-induced remodeling and formulated the first atrial action potential model with realistic Ca2+-handling properties. Our results demonstrate that both remodeling of sarcolemmal ionic currents and subcellular Ca2+-handling processes contribute significantly to action potential shortening and loss of rate adaptation as occurs in chronic AF.
Next we developed a two-dimensional model of canine atrial tissue and the first model of AF with realistic ionic and propagation properties. The model provides the first theoretical confirmation of the recent experimentally-determined conception of the mechanisms of AF maintenance, indicating that discrete "driver regions" underlie AF, and that wavelets generated by emanating wavefronts give rise to fibrillation but play a relatively passive role in maintaining AF.
Finally we used our model of AF to determine the mechanisms of AF termination by sodium channel blocking agents (class I antiarrhythmic drugs). In agreement with recent experimental findings, our results demonstrate how sodium channel inhibition first slows and organizes AF, and how the effects of decreased excitability cause AF termination in a way that is independent of wavelength changes, previously thought to be necessary for antiarrhythmic efficacy. (Abstract shortened by UMI.)

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29

Foley, Catherine. "Mathematical modeling for designing new treatment strategies with Granulocyte-Colony Stimulating Factor". Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=21947.

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Mathematical modeling can help providing better understanding of the nature and characteristics of regulatory processes in hematology. We first review different mathematical approaches used for modeling so-called dynamical hematological diseases, which are characterized by oscillations in one or more blood cell lines. Then, we present two delay differential equation (DDE) models of the hematopoietic system designed for the study of the effects of Granulocyte-Colony Stimulating Factor (G-CSF) administration. G-CSF is used clinically for treating subjects presenting low numbers of white blood cells, a condition referred to as neutropenia that can result from different causes. However, even though G-CSF is widely used in clinical practice, it is not clear whether the standard G-CSF administration schedule is optimal. The aim of this work is to study alternative treatment regimens that would optimize the use of G-CSF using a mathematical modeling approach. The first model we propose is a comprehensive model that considers G-CSF administration for cyclical neutropenia, a dynamical disorder characterized by oscillations in the circulating neutrophil count. The second model focuses on the effects of two recombinant forms of G-CSF (filgrastim and pegfilgrastim) for the treatment of chemotherapy-induced neutropenia. For each model, we use a combination of mathematical analysis and numerical simulations to study alternative G-CSF treatment regimens that would be efficient while reducing the amount of drug. We found that the dynamical properties of the model could be exploited for designing better G-CSF treatment strategies.
La modélisation mathématique est un outil qui permet d'obtenir une meilleure compréhension des différents processus de régulation en hématologie. Dans un premier temps, nous révisons différentes approches qui sont utilisées pour modéliser les maladies hématologiques dites dynamiques. Celles-ci sont caractérisées par la présence d'oscillations dans le niveau d'un ou de plusieurs types de cellules sanguines. Ensuite, nous présentons deux nouveaux modèles d'équations différentielles à délais (EED) du système hématopoïétique, qui sont dédiés à l'étude des effets de l'administration du granulocyte-colony stimulating factor (G-CSF). Le G-CSF est utilisé en pratique pour traiter les patients dont le niveau de globules blancs est faible, une condition appelée neutropénie, qui peut survenir dans plusieurs contextes. Cependant, même si le G-CSF est largement utilisé dans le milieu médical, il n'est pas clair que le protocole d'administration standard soit optimal. L'objectif de cette thèse est d'étudier des protocoles de traitement alternatifs qui optimiseraient l'utilisation du G-CSF en utilisant une approche de modélisation mathématique. Le premier modèle que nous proposons est un modèle qui inclut tous les types de cellules sanguines et qui considère l'administration du G-CSF dans le cas de la neutropénie cyclique, une maladie caractérisée par la présence d'oscillations dans le nombre de globules blancs, de plaquettes et de globules rouges. Dans le second modèle, nous nous intéressons aux effets de deux formes de G-CSF (filgrastim et pegfilgrastim) qui sont utilisés pour traiter la neutropénie qui survient fréquemment suite à la chimiothérapie. Pour chacun des modèles, nous utilisons une combinaison d'analyse mathématique et de simulations numériques pour étudier des traitements alternatifs de G-CSF qui seraient efficaces tout en réduisant la quantité de médicament utilisée. Nos résultats suggèrent que les pr

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30

Cui, Zheng. "A Generalized Adaptive Mathematical Morphological Filter for LIDAR Data". FIU Digital Commons, 2013. http://digitalcommons.fiu.edu/etd/995.

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Airborne Light Detection and Ranging (LIDAR) technology has become the primary method to derive high-resolution Digital Terrain Models (DTMs), which are essential for studying Earth’s surface processes, such as flooding and landslides. The critical step in generating a DTM is to separate ground and non-ground measurements in a voluminous point LIDAR dataset, using a filter, because the DTM is created by interpolating ground points. As one of widely used filtering methods, the progressive morphological (PM) filter has the advantages of classifying the LIDAR data at the point level, a linear computational complexity, and preserving the geometric shapes of terrain features. The filter works well in an urban setting with a gentle slope and a mixture of vegetation and buildings. However, the PM filter often removes ground measurements incorrectly at the topographic high area, along with large sizes of non-ground objects, because it uses a constant threshold slope, resulting in “cut-off” errors. A novel cluster analysis method was developed in this study and incorporated into the PM filter to prevent the removal of the ground measurements at topographic highs. Furthermore, to obtain the optimal filtering results for an area with undulating terrain, a trend analysis method was developed to adaptively estimate the slope-related thresholds of the PM filter based on changes of topographic slopes and the characteristics of non-terrain objects. The comparison of the PM and generalized adaptive PM (GAPM) filters for selected study areas indicates that the GAPM filter preserves the most “cut-off” points removed incorrectly by the PM filter. The application of the GAPM filter to seven ISPRS benchmark datasets shows that the GAPM filter reduces the filtering error by 20% on average, compared with the method used by the popular commercial software TerraScan. The combination of the cluster method, adaptive trend analysis, and the PM filter allows users without much experience in processing LIDAR data to effectively and efficiently identify ground measurements for the complex terrains in a large LIDAR data set. The GAPM filter is highly automatic and requires little human input. Therefore, it can significantly reduce the effort of manually processing voluminous LIDAR measurements.

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31

Silal, Sheetal Prakash. "A mathematical modelling approach for the elimination of malaria in Mpumalanga, South Africa". Doctoral thesis, University of Cape Town, 2014. http://hdl.handle.net/11427/13010.

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Mpumalanga in South Africa is committed to eliminating malaria by 2018 and efforts are increasing beyond that necessary for malaria control. The eastern border of Mpumalanga is most affected by malaria with imported cases in Mpumalanga overtaking local cases in recent years. Mathematical modelling may be used to study the incidence and spread of disease with an important benefit being the ability to enact exogenous change on the system to predict impact without committing any real resources. Three models are developed to simulate malaria transmission: (1) a deterministic non-linear ordinary differential equation model, (2) a stochastic non-linear metapopulation differential equation model and (3) a stochastic hybrid metapopulation differential equation, individual-based model. These models are fitted to weekly case data from Mpumalanga from 2002 to 2008, and validated with data from 2009 to 2012. Interventions such as scaling-up vector control, mass drug administration, focal screen and treat campaign at the Mpumalanga-Maputo border-control point and source reduction are applied to the model to assess their potential impact on transmission and whether they may be used alone or in combination to achieve malaria elimination. The models predicted that scaling up vector control results in substantial decreases in local infections, though with little impact on imported infections. Mass drug administration is a high impacting but short-lived intervention with transmission reverting to pre-intervention levels within three years. Focal screen and treat campaigns are predicted to result in substantial decreases in local infections, though success of the campaign is dependent on the ability to detect low parasitemic infections. Large decreases in local infections are also predicted to be achieved through foreign source reduction. The impact of imported infections is such that malaria elimination is only predicted if all imported infections are treated before entry into Mpumalanga, or are themselves eliminated at their source. Thus a regionally-focused strategy may stand a better chance at achieving elimination in Mpumalanga and South Africa compared to a nationally-focused one. In this manner, mathematical models may form an integral part of the research, planning and evaluation of the research, planning and evaluation of elimination-focused strategies so that malaria elimination is possible in the foreseeable future.

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32

Wagenaar, Elmien. "A mathematical approach to financial allocation strategies". Thesis, Stellenbosch : Stellenbosch University, 2002. http://hdl.handle.net/10019.1/52648.

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33

Iwuanyanwu, Paul Nnanyereugo. "Pre-service science teachers’ conceptual and procedural difficulties in solving mathematical problems in physical science". Thesis, University of the Western Cape, 2014. http://hdl.handle.net/11394/4002.

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>Magister Scientiae - MSc
Students frequently leave first-year physical science classes with a dual set of physical laws in mind- the equations to be applied to qualitative problems and the entrenched set of concepts, many erroneous, to be applied to qualitative, descriptive, or explanatory problems. It is in this sense that the emphasis of this study is on ‘change’ rather than acquisition. Thus, a blend of theoretical framework was considered according to the aim of the study. Of immediate relevance in this regard within the “constructivist paradigm” are: Posner, Strike, Hewson and Gertzog’s (1982) conceptual change theory and the revised Bloom’s Taxonomy. Moreover, the very shift or restructuring of existing knowledge, concepts or schemata is what distinguishes conceptual change from other types of learning, and provides students with a more fruitful conceptual framework to solve problems, explain phenomena, and function in the world (Biemans & Simons, 1999; Davis, 2011). A quasi-experimental design was adopted to explore pre-service teachers’ conceptual and procedural difficulties in solving mathematical problems in physical science. Sixteen second and third year pre-service teachers in one of the historically black universities in the Western Cape, South Africa, participated in the study. Two inseparable concepts of basic mechanics, work-energy concepts were taught and used for data collection. Data were collected using questionnaires, Physical Science Achievement Test (PSAT), Multiple Reflective Questions (MRQ) and an interview. An explicit problem solving strategy (IDEAL strategy versus maths-in-science instructional model) was taught in the intervention sessions for duration of three weeks to the experimental group (E-group). IDEAL strategy placed emphasis on drill and practice heuristics that helped the pre-service teachers’ (E-group) understanding of problem-solving. Reinforcing heuristics of this IDEAL strategy include breaking a complex problem into sub-problems. Defining and representing problem (e.g. devising a plan-using Free-Body-Diagram) was part of the exploring possible strategies of the IDEAL. More details on IDEAL strategy are discussed in Chapter 3. The same work-energy concepts were taught to the control group (C-group) using lecture-demonstration method. A technique (i.e. revised taxonomy table for knowledge and cognitive process dimension) was used to categorize and analyse the level of difficulties for each item tested (e.g. D1 = minor difficulty, D2 = major difficulty, and D3 = atypical difficulty

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34

Andersson, Erik y Soha Abdelmalek. "Dyscalculia/Dyslexia - A Dichotomy?" Thesis, Malmö universitet, Fakulteten för lärande och samhälle (LS), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:mau:diva-27452.

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In this article, we analyse similarities and differences in and between two very topical issues in today's learning disabilities, namely dyscalculia and dyslexia. More precisely, we introduce the nature of mathematics as science, which - of course - is the essence of the matter. From this, we will try to prove that dyscalculia is not a concept by itself, but merely yet another one of the sad guises of dyslexia. This will completely answer the question given by the title of the thesis.

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35

Mabaso, Automan Sibusiso. "Some exponential diophantine equations". Thesis, Stellenbosch : Stellenbosch University, 2013. http://hdl.handle.net/10019.1/85587.

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Thesis (MSc)--Stellenbosch University, 2013.
ENGLISH ABSTRACT: The aim of this thesis is to study some methods used in solving exponential Diophan- tine equations. There is no generic method or algorithm that can be used in solving all Diophantine equations. The main focus for our study will be solving the exponential Dio- phantine equations using the modular approach and the linear forms in two logarithms approach.
AFRIKAANSE OPSOMMING: Die doel van hierdie tesis is om sommige metodes te bestudeer om sekere Diophantiese vergelykings op te los. Daar is geen metode wat alle Diophantiese vergelykings kan oplos nie. Die fokus van os studie is hoofsaaklik om eksponensiele Diophantiese vergelykings op te los met die modul^ere metode en met die metode van line^ere vorms in twee logaritmes.

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36

Hart, John Walker. "SIMPLE TWO-SIDED RATIONAL VECTOR SPACES OF RANK TWO". The University of Montana, 2010. http://etd.lib.umt.edu/theses/available/etd-03102010-094108/.

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The purpose of this thesis is to find sufficient conditions under which a non-commutative version of the polynomial ring in two variables exists. The non-commutative rings we construct are non-commutative symmetric algebras over a two-sided vector space. After reviewing the definition of a two-sided vector space and giving some examples, we briefly recall the theory of simple two-sided vector spaces. We then assume k is a field of characteristic zero and t is transcendental over k and we find sufficient conditions under which a simple k-central two-sided vector space V over k(t) has left and right dimension two. Given such a V, and letting ^*V and V^* denote the left and right duals we find conditions under which (V^i*,V^(i+1)*,V^(i+2)* ) has a simultaneous for all i, i an integer. This condition implies the non-commutative symmetric algebra over V can be constructed. We conclude by exhibiting a five-dimensional family of simple k-central two-sided vector spaces over k(t) of left and right dimension two who non-commutative symmetric algebras exist.

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37

Goldes, John. "REGULARIZATION PARAMETER SELECTION METHODS FOR ILL POSED POISSON IMAGING PROBLEMS". The University of Montana, 2010. http://etd.lib.umt.edu/theses/available/etd-07072010-124233/.

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A common problem in imaging science is to estimate some underlying true image given noisy measurements of image intensity. When image intensity is measured by the counting of incident photons emitted by the object of interest, the data-noise is accurately modeled by a Poisson distribution, which motivates the use of Poisson maximum likelihood estimation. When the underlying model equation is ill-posed, regularization must be employed. I will present a computational framework for solving such problems, including statistically motivated methods for choosing the regularization parameter. Numerical examples will be included.

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38

Gray, Katharine Lynn. "Comparison of Trend Detection Methods". The University of Montana, 2007. http://etd.lib.umt.edu/theses/available/etd-09262007-104625/.

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Trend estimation is important in many fields, though arguably the most important applications appear in ecology. Trend is difficult to quantify; in fact, the term itself is not well-defined. Often, trend is quantified by estimating the slope coefficient in a regression model where the response variable is an index of population size, and time is the explanatory variable. Linear trend is often unrealistic for biological populations; in fact, many critical environmental changes occur abruptly as a result of very rapid changes in human activities. My PhD research has involved formulating methods with greater flexibility than those currently in use. Penalized spline regression provides a flexible technique for fitting a smooth curve. This method has proven useful in many areas including environmental monitoring; however, inference is more difficult than with ordinary linear regression because so many parameters are estimated. My research has focused on developing methods of trend detection and comparing these methods to other methods currently in use. Attention is given to comparing estimated Type I error rates and power across several trend detection methods. This was accomplished through an extensive simulation study. Monte Carlo simulations and randomization tests were employed to construct an empirical sampling distribution for the test statistic under the null hypothesis of no trend. These methods are superior over smoothing methods over other smoothing methods of trend detection with respect to achieving the designated Type I error rate. The likelihood ratio test using a mixed effects model had the most power for detecting linear trend while a test involving the first derivative was the most powerful for detecting nonlinear trend for small sample sizes.

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39

Elias, Joran. "Randomness In Tree Ensemble Methods". The University of Montana, 2009. http://etd.lib.umt.edu/theses/available/etd-10092009-110301/.

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Tree ensembles have proven to be a popular and powerful tool for predictive modeling tasks. The theory behind several of these methods (e.g. boosting) has received considerable attention. However, other tree ensemble techniques (e.g. bagging, random forests) have attracted limited theoretical treatment. Specifically, it has remained somewhat unclear as to why the simple act of randomizing the tree growing algorithm should lead to such dramatic improvements in performance. It has been suggested that a specific type of tree ensemble acts by forming a locally adaptive distance metric [Lin and Jeon, 2006]. We generalize this claim to include all tree ensembles methods and argue that this insight can help to explain the exceptional performance of tree ensemble methods. Finally, we illustrate the use of tree ensemble methods for an ecological niche modeling example involving the presence of malaria vectors in Africa.

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40

Laobeul, N'Djekornom Dara. "REGULARIZATION METHODS FOR ILL-POSED POISSON IMAGING". The University of Montana, 2009. http://etd.lib.umt.edu/theses/available/etd-12092008-133704/.

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The noise contained in images collected by a charge coupled device (CCD) camera is predominantly of Poisson type. This motivates the use of the negative logarithm of the Poisson likelihood in place of the ubiquitous least squares t-to-data. However, if the underlying mathematical model is assumed to have the form z = Au, where A is a linear, compact operator, the problem of minimizing the negative log-Poisson likelihood function is ill-posed, and hence some form of regularization is required. In this work, it involves solving a variational problem of the form u def = arg min u0 `(Au; z) + J(u); where ` is the negative-log of a Poisson likelihood functional, and J is a regularization functional. The main result of this thesis is a theoretical analysis of this variational problem for four dierent regularization functionals. In addition, this work presents an ecient computational method for its solution, and the demonstration of the eectiveness of this approach in practice by applying the algorithm to simulated astronomical imaging data corrupted by the CCD camera noise model mentioned above.

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41

Munganga, Justin Manango Wazute. "Existence and stability of solutions to the equations of fibre suspension flows". Doctoral thesis, University of Cape Town, 1999. http://hdl.handle.net/11427/9728.

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Includes bibliographical references.
A popular approach to formulating the initial-boundary value problem for fibre suspension flows is that in which fibre orientation is accounted for in an averaged sense, through the introduction of a second-order orientation tensor A. This variable, together with the velocity and pressure, then constitutes the set of unknown variables for the problem. The governing equations are balance of linear momentum, the incompressibility condition, an evolution equation for A, and a constitutive equation for the stress. The evolution equation contains a fourth-order orientation tensor A, and it is necessary to approximate A as a function of A, through a closure relation. The purpose of this these is to examine the well-posedness of the equations governing fibre fibre suspension ﬂows, for various closure relations. It has previously been shown by GP Galdi and BD Reddy that, for the linear closure, the problem is wellposed provided that the particle number, a material constant, is less than a critical value. The work by Galdi and Reddy made of a model in which rotary diffusivity is a function of the ﬂow. This thesis re-examines these issues in two different ways. First, the second law of thermodynamics is used to establish the constraints that the constitutive equations have to satisfy in order to be compatible with this law. This investigation is carried out for a variety of closure rules. The second contribution of the thesis concerns the existence and uniqueness of solutions to the governing equations, for the linear and quadratic closures; for a model in which the rotary diffusivity is treated as a constant, local and global existence of solutions are established, for sufficiently small data, and in the case of the linear closure, for admissible values of the particle number. The existence theory uses a Schauder fixed point approach.

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42

Addai, Solomon. "Financial forecasting using machine learning". Thesis, University of Cape Town, 2016. http://hdl.handle.net/11427/26215.

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43

Abdelfattah, Derhham. "General Relativity and penrose process". Master's thesis, University of Cape Town, 2016. http://hdl.handle.net/11427/28961.

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44

Ahmed, Samah. "Perturbation field theory methods for calculating expectation values". Thesis, University of Cape Town, 2016. http://hdl.handle.net/11427/26214.

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45

Carati, Daniele. "Large-eddy simulation for turbulent flows :from mathematical foundations to practical applications". Doctoral thesis, Universite Libre de Bruxelles, 2001. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/211625.

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46

Van, de Merwe Chelsey Lynn. "Student Use of Mathematical Content Knowledge During Proof Production". BYU ScholarsArchive, 2020. https://scholarsarchive.byu.edu/etd/8474.

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Proof is an important component of advanced mathematical activity. Nevertheless, undergraduates struggle to write valid proofs. Research identifies many of the struggles students experience with the logical nature and structure of proofs. Little research examines the role mathematical content knowledge plays in proof production. This study begins to fill this gap in the research by analyzing what role mathematical content knowledge plays in the success of a proof and how undergraduates use mathematical content knowledge during proofs. Four undergraduates participated in a series of task-based interviews wherein they completed several proofs. The interviews were analyzed to determine how the students used mathematical content knowledge and how mathematical content knowledge affected a proof’s validity. The results show that using mathematical content knowledge during a proof is nontrivial for students. Several of the proofs attempted by the students were unsuccessful due to issues with mathematical content knowledge. The data also show that students use mathematical content knowledge in a variety of ways. Some student use of mathematical content is productive and efficient, while other student practices are less efficient in formal proofs.

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47

Ackerman, M. C. (Marthinus Casper). "Kernel support for embedded reactive systems". Thesis, Stellenbosch : Stellenbosch University, 1993. http://hdl.handle.net/10019.1/58022.

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Thesis (MSc)--Stellenbosch University , 1993.
ENGLISH ABSTRACT: Reactive systems are event driven state machines which usually do not terminate, but remain in perpetual interaction with their environment. Such systems usually interact 'With devices which introduce a high degree of concurrency and some real time constraints to the system. Because of the concurrent nature of reactive systems they are commonly implemented as communicating concurrent processes on one or more processors. Jeffay introduces a design paradigm which requires consumer processes to consume messages faster than they are produced by producer processes. If this is guaranteed, the real time constraints of such .. system are always met, and the correctness of the process interaction is guaranteed in terms of the message passing semantics. I developed the ESE kernel, which supports Jeffay systems by providing lightweight processes which communicate over asynchronous channels. Processes are scheduled non-preemptively according to the earliest deadline first policy when they have messages pending on their input channels. The Jeffay design method and the ESE kernel have been found to be highly suitable to implement embedded reactive systems. The general requirements of embedded reactive systems, and kernel support required by such systems, are discussed.
AFRIKAANSE OPSOMMING: Reaktiewe stelsels is toeatandsoutomate wat aangedryf word deur gebeure in hul omgewins. So 'n stelsel termineer gewoonlik nie, maar bly in 'n voortdurende wisselwerking met toestelle in sy omgewing. Toestelle in die omgewing van 'n reaktiewe stelsel veroorsaak in die algemeen 'n hoë mate van gelyklopendheid in die stelsel, en plaas gewoonlik sekere intydse beperkings op die stelsel. Gelyklopende stelsels word gewoonlik as stelsel. van kommunikerende prosesse geïmplementeer op een of meer prosessors. Jeffay beskryf 'n ontwerpsmetodologie waarvolgens die ontvanger van boodskappe hulle vinniger moet verwerk as wat die sender hulle kan stuur. Indien hierdie gedrag tussen alle pare kommunikerende prosesse gewaarborg kan word, sal die stelsel altyd sy intydse beperkings gehoorsaam, en word die korrektheid van interaksies tussen prosesse deur die semantiek van die boodskapwisseling gewaarborg. Die "ESE" bedryfstelselkern wat ek ontwikkel het, ondersteun stelsels wat ontwerp en geïmplementeer word volgens Jeffay se metode. Prosesse kommunikeer oor asinkrone kanale, en die ontvanger van die boodskap met die vroegste keertyd word altyd eerste geskeduleer. Jeffay se ontwerpsmetode en die "ESE" kern blyk in die praktyk baie geskik te wees vir reaktiewe stelsels wat as substelsels van groter stelsels uitvoer. Die vereistes van reaktiewe substelsels, en die kemondersteuning wat daarvoor nodig is, word bespreek.

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48

Kappelin, Frida y Jimmie Rudvall. "Fraud Detection within Mobile Money : A mathematical statistics approach". Thesis, Blekinge Tekniska Högskola, Institutionen för datalogi och datorsystemteknik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-10898.

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Context: Today it is easy to do banking transaction digitally, both on a computer or by using a mobile phone. As the banking-services increases and gets implemented to multi-platforms it makes it easier for a fraudster to commit financial fraud. This thesis will focus on investigating log-files from a Mobile Money system that makes it possible to do banking transactions with a mobile phone. Objectives: The objectives in this thesis is to evaluate if it is possible to combine two statistical methods, Benford's law together with statistical quantiles, to find a statistical way to find fraudsters within a Mobile Money system. Methods: Rules was extracted from a case study with focus on a Mobile Money system and limits was calculated by using quantiles. A fraud detector was implemented that use these rules together with limits and Benford's law in order to detect fraud.The fraud detector used the methods both independently and combined.The performance was then evaluated. Results: The results show that it is possible to use the Benford's law and statistical quantiles within the studied Mobile Money system. It is also shown that there is only a very small difference when the two methods are combined or not both in detection rate and accuracy precision. Conclusions: We conclude that by combining the chosen methods it is possible to get a medium-high true positive rates and very low false positive rates. The most effective method to find fraudsters is by only using quantiles. However, combining Benford's law with quantiles gives the second best result.

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49

Osei, Ofosuhene. "Level Crossing Times in Mathematical Finance". Digital Commons @ East Tennessee State University, 2013. https://dc.etsu.edu/etd/1126.

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Level crossing times and their applications in finance are of importance, given certain threshold levels that represent the "desirable" or "sell" values of a stock. In this thesis, we make use of Wald's lemmas and various deep results from renewal theory, in the context of finance, in modelling the growth of a portfolio of stocks. Several models are employed .

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50

Youssefpour, Hamed. "Mathematical Modeling of Cancer Stem Cells and Therapeutic Intervention Methods". Thesis, University of California, Irvine, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=3557204.

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We develop a multispecies continuum model to simulate the spatiotemporal dynamics of cell lineages in solid tumors is discussed. The model accounts for protein signaling factors produced by cells in lineages, and nutrients supplied by the microenvironment. We find that the combination therapy involving differentiation promoters and radiotherapy is very effective in eradicating such a tumor. We investigate the effect of production of various feedback factors by healthy tissue on tumor morphologies. Our simulation results show that the larger production rate of the negative feedback factor by healthy tissue surrounding the tumor, in general lead to smaller, more compact and more circular tumor shapes. However, the increase in the concentration of these feedback factors may have non-monotone effect on the tumor morphologies. We investigate the effect of initial shape on therapy effectiveness. The results from the simulations show that the initial tumor geometry might play an important role in tumor prognostic and the effectiveness of a specific treatment. We observe that the therapy is more effective on tumors that still respond to the signals received from the healthy tissue in comparison with the ones that do not respond to signaling factors (in this case differentiation signals) by stromal tissue or healthy tissue surrounding the tumor. It is shown that the tumors with larger shape factors and smaller areas (more elongated and thinner) respond better to treatment, and the combination therapy is more successful on tumors with such characteristics. We applied mathematical modeling of radiotherapy using experimental data provided from our collaborative work with radiational oncology department of University of California, Los Angeles. Our investigations show that in order to match the experimental results with the simulations, the dedifferentiation rate of non-stem cells should be increased as a function of radiation dose. It is also observed that the population of induced stem cells followed such exponential relationship with respect to therapy dose. The results from simulations and the analysis of the equations suggest that in order for the simulation results to match with the experimental data, the original stem cells and the induced stem cells may undergo direct differentiation.

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Tesis sobre el tema "Mathematical Sciences"

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