Dissertations / Theses: 'Mathematics in physics'

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Murphy, Michael A. "Measuring the Effects of Mathematics Instruction in a Physics Classroom with Mathematics and Physics Diagnostics." Fogler Library, University of Maine, 2005. http://www.library.umaine.edu/theses/pdf/MurphyMA2005.pdf.

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Borrelli, Arianna. "Angular Momentum between Physics and Mathematics." Wissenschaftlicher Verlag Harri Deutsch, 2011. https://slub.qucosa.de/id/qucosa%3A16267.

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Kural, Mehmet Hamdi. "Student Perceptions On Their Physics And Mathematics Teachers." Master's thesis, METU, 2006. http://etd.lib.metu.edu.tr/upload/12608017/index.pdf.

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The purpose of this study was to investigate the high school students&rsquo
perceptions on effectiveness of their physics and mathematics teachers. For this purpose a 71-item questionnaire, with a reliability coefficient of 0.97, was developed and applied to 1237 9th grade students in Ankara. 30 Physics teachers and 33 Mathematics teachers were evaluated by student ratings in 13 regular high schools and 6 Anatolian lycees. As a result, 17 % of physics teachers and 27% of mathematics teachers found to be considered effective by their students. In addition to this, it is found that specific effective teacher characteristics about teaching ability and interpersonal relationships are possessed in low amounts by most of the physics and mathematics teachers.

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Kim, Jae Ill S. M. Massachusetts Institute of Technology. "Graph polynomials and statistical physics." Thesis, Massachusetts Institute of Technology, 2007. http://hdl.handle.net/1721.1/39000.

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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2007.
Includes bibliographical references (p. 53-54).
We present several graph polynomials, of which the most important one is the Tutte polynomial. These various polynomials have important applications in combinatorics and statistical physics. We generalize the Tutte polynomial and establish its correlations to the other graph polynomials. Finally, our result about the decomposition of planar graphs and its application to the ice-type model is presented.
by Jae Ill Kim.
S.M.

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Wallace, Michelle L. Ellerton Nerida F. "Characterization of high school mathematics and physics language genres." Normal, Ill. : Illinois State University, 2004. http://wwwlib.umi.com/cr/ilstu/fullcit?p3127139.

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Thesis (Ph. D.)--Illinois State University, 2004.
Title from title page screen, viewed Jan. 21, 2005. Dissertation Committee: Nerida F. Ellerton (chair), Sherry L. Meier, Sharon Soucy McCrone, Tami S. Martin. Includes bibliographical references (leaves 153-163) and abstract. Also available in print.

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Minton, Gregory T. (Gregory Thomas). "Computer-assisted proofs in geometry and physics." Thesis, Massachusetts Institute of Technology, 2013. http://hdl.handle.net/1721.1/84405.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Department of Mathematics, 2013.
Cataloged from PDF version of thesis.
Includes bibliographical references.
In this dissertation we apply computer-assisted proof techniques to two problems, one in discrete geometry and one in celestial mechanics. Our main tool is an effective inverse function theorem which shows that, in favorable conditions, the existence of an approximate solution to a system of equations implies the existence of an exact solution nearby. This allows us to leverage approximate computational techniques for finding solutions into rigorous computational techniques for proving the existence of solutions. Our first application is to tight codes in compact spaces, i.e., optimal codes whose optimality follows from linear programming bounds. In particular, we show the existence of many hitherto unknown tight regular simplices in quaternionic projective spaces and in the octonionic projective plane. We also consider regular simplices in real Grassmannians. The second application is to gravitational choreographies, i.e., periodic trajectories of point particles under Newtonian gravity such that all of the particles follow the same curve. Many numerical examples of choreographies, but few existence proofs, were previously known. We present a method for computer-assisted proof of existence and demonstrate its effectiveness by applying it to a wide-ranging set of choreographies.
by Gregory T. Minton.
Ph.D.

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Pollock, Evan B. "Student Understanding of P-V Diagrams and the Associated Mathematics." Fogler Library, University of Maine, 2008. http://www.library.umaine.edu/theses/pdf/PollockEB2008.pdf.

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Morris, Kathryn 1970. "Geometrical physics : mathematics in the natural philosophy of Thomas Hobbes." Thesis, McGill University, 2001. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=37789.

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My thesis examines Thomas Hobbes's attempt to develop a mathematical account of nature. I argue that Hobbes's conception of how we should think quantitatively about the world was deeply indebted to the ideas of his ancient and medieval predecessors. These ideas were often amenable to Hobbes's vision of a demonstrative, geometrically-based science. However, he was forced to adapt the ancient and medieval models to the demands of his own thoroughgoing materialism. This hybrid resulted in a distinctive, if only partially successful, approach to the problems of the new mechanical philosophy.

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Cornell, Brennan. "An introduction to classical gauge theory in mathematics and physics." Thesis, University of Ottawa (Canada), 2008. http://hdl.handle.net/10393/27583.

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We describe some aspects of classical gauge theory from the perspective of connections on vector bundles. We begin by examining classical electromagnetism, and use it to motivate the development of gauge theory on vector bundles. If G is a Lie group, we review some of the theory of vector G-bundles, their associated principal G-bundles, and the related theory of connections. We then discuss the idea of gauge transformations on principal and vector G-bundles, and view electromagnetism as an example of an abelian gauge theory. We briefly review the action principle in order to describe non-abelian gauge theories such as the Yang-Mills equation. Finally, we present the main results from an article by John Baez entitled "Higher Yang-Mills Theory" where he attempts to abstract Yang-Mills theory using some concepts from category theory.

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Szudzik, Matthew P. "Some Applications of Recursive Functionals to the Foundations of Mathematics and Physics." Research Showcase @ CMU, 2010. http://repository.cmu.edu/dissertations/26.

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We consider two applications of recursive functionals. The first application concerns Gödel’s theory T , which provides a rudimentary foundation for the formalization of mathematics. T can be understood as a theory of the simply-typed lambda calculus that is extended to include the constant 0N, the successor function S, and the operator RT for primitive recursion on objects of type T . It is known that the functions from non-negative integers to non-negative integers that can be defined in this theory are exactly the <ε0-recursive functions of non-negative integers. But it is not well-known which functionals of arbitrary type can be defined in T . We show that when the domain and codomain are restricted to pure closed normal forms, the functionals of arbitrary type that are definable in T are exactly those functionals that can be encoded as <ε0-recursive functions of non-negative integers. This result has many interesting consequences, including a new characterization of T . The second application is concerned with the question: “When can a model of a physical system be regarded as computable?” We provide the definition of a computable physical model to answer this question. The connection between our definition and Kreisel’s notion of a mechanistic theory is discussed, and several examples of computable physical models are given, including models which feature discrete motion, a model which features non-discrete continuous motion, and nondeterministic models such as radioactive decay. We show how computable physical models on effective topological spaces can be formulated with recursive functionals in the theory of type-two effectivity (TTE). Various common operations on computable physical models are described, such as the operation of coarse-graining and the formation of statistical ensembles. The definition of a computable physical model also allows for a precise formalization of the computable universe hypothesis— the claim that all the laws of physics are computable.

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Cobb, Anthea Phyllis Doreen. "GCE 'A' Level physics and mathematics examinations 1970-2001 : have standards fallen?" Thesis, University of Portsmouth, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.271372.

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Bing, Thomas Joseph. "An epistemic framing analysis of upper level physics students' use of mathematics." College Park, Md.: University of Maryland, 2008. http://hdl.handle.net/1903/8528.

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Thesis (Ph. D.) -- University of Maryland, College Park, 2008.
Thesis research directed by: Dept. of Physics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

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Rippy, Scott Randall. "Applications of hyperbolic geometry in physics." CSUSB ScholarWorks, 1996. https://scholarworks.lib.csusb.edu/etd-project/1099.

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Adams, Alyssa M. "Exploring the Properties of Mira-Type Stars with Spectropolarimetry." Digital Commons @ East Tennessee State University, 2013. https://dc.etsu.edu/honors/118.

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Mira-type stars are luminous red giants that have pulsation periods that last anywhere between 100 and 700 days. The irregular behavior of their periods and atmospheric properties flag them as excellent candidates for astrophysical studies of non-spherical stars. This paper focuses on the linear polarization of light emitted from three Mira- type stars: Mira itself, R Leo, and V CVn. Polarimetric data from the University of Wisconsin’s Half-Wave Spectropolarimeter (HPOL) database, as well as other archives of polarimetric data, provide us with insight into the atmospheric and geometrical prop- erties of these three stars. We were able to study the net polarizations and position angles alongside light curves provided by AAVSO. The observed variable polarization is a clear signature of evolving aspherical geometries for these stars. However, we found a major surprise concerning the polarimetric characteristics in V CVn, which suggest that V CVn is unlike a traditional Mira-type variable star. We end with an exploration of new possibilities regarding the atmospheric properties of V CVn.

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Middlemas, Erin. "Soliton Solutions of the Nonlinear Schrödinger Equation." Digital Commons @ East Tennessee State University, 2013. https://dc.etsu.edu/honors/66.

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The nonlinear Schrödinger equation is a classical field equation that describes weakly nonlinear wave-packets in one-dimensional physical systems. It is in a class of nonlinear partial differential equations that pertain to several physical and biological systems. In this project we apply a pseudo-spectral solution-estimation method to a modified version of the nonlinear Schrödinger equation as a means of searching for solutions that are solitons, where a soliton is a self-reinforcing solitary wave that maintains its shape over time. The pseudo-spectral method estimates solutions by utilizing the Fourier transform to evaluate the spatial derivative within the nonlinear Schrödinger equation. An ode solver is then applied to the resulting ordinary differential equation. We use this method to determine whether cardiac action potential states, which are perturbed solutions to the Fitzhugh-Nagumo nonlinear partial differential equation, create soliton-like solutions. After finding soliton-like solutions, we then use symmetry group properties of the nonlinear Schrödinger equation to explore these solutions. We also use a Lie algebra related to the symmetries to look for more solutions to our modified nonlinear Schrödinger equation.

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Dominquez, Alberto Luis. "Meson-meson scattering in 2+1 dimensional lattice quantum electrodynamics." FIU Digital Commons, 1994. http://digitalcommons.fiu.edu/etd/3634.

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For three-dimensional compact lattice quantum electrodynamics, the meson-meson energy spectrum is obtained from a truncated time-correlation matrix of field operators. The energy levels indicate a slightly attractive residual interaction between the mesons. From the finite-volume spectrum, the scattering phase shifts can be calculated for the various irreducible representations of the lattice symmetry group. The s-wave phase shifts indicate short-range repulsion, while the d-wave data indicate intermediate-range attraction. This work serves as a model for describing the strong nuclear force from basic principles.

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Faxas, Miguel A. Jr. "Experiments in the dissociative recombination of xenon and krypton." FIU Digital Commons, 2005. http://digitalcommons.fiu.edu/etd/3288.

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Experiments were conducted using the Time of Flight (TOF) method to identify the final product states of the dissociative recombination reaction of krypton and xenon. In the dissociative recombination (DR) reaction the molecular ion breaks up into product atoms whose velocities can be measured. These velocities can then be used to identify the final product states. The DR of krypton had been studied by Shiu and Biondi using spectrometric techniques. They observed the 5p states. Hardy et al. using TOF techniques had observed the 5s states. Mitchell et al. studied the DR of xenon. They observed the 6p and 5d states of xenon. In this laboratory using the TOF method I have recently identified the 5s, 6p and the 4d final states of the DR of krypton. Then I was able to identify the 5d, 7s, 6d, and 6p' final product states of vi the DR of xenon. The study of the DR of these heavy inert gases can shed light on the theory of the DR of heavy polyatomic gases, which is not well developed.

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Khammang, Alex. "Investigating Mechanical Properties of Metallic Nanowires using Molecular Dynamics." VCU Scholars Compass, 2014. http://scholarscompass.vcu.edu/etd/3409.

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Metallic nanowires have useful applications in scanning tunneling microscopes and atomic force microscopes due to their unique sensitivity to force and electricity. These unique properties arise because of the large surface area to volume ratio. One of these properties is that introducing twinning planes the mechanical properties of metallic nanowires can be altered. The effects of twinning planes on metallic nanowires were studied using molecular dynamics simulations. Silver, copper, and nickel nanowires with and without twinning planes were simulated with engineering strain until the first yielding stress was obtained. The radial simulations showed that as the radius of twinned nanowires increased, the strength gained by introducing the twinning planes increased. The temperature simulations showed that nanowires with twinning planes were stronger than their un-twinned counterparts as temperature increased. The purpose of this investigation was to better understand the effect twinning planes had on metallic nanowires, so that future technological advances would benefit from the results.

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Ferguson, Josephus. "Local Charging Behavior on GaN Surfaces." VCU Scholars Compass, 2010. http://scholarscompass.vcu.edu/etd/82.

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Gallium nitride is an important III-V semiconductor which is used in many optoelectronic and high-frequency devices. The nature of the GaN surface and its electrical characteristics can impact the performance of such devices. In this study, several GaN surfaces are locally charged using an atomic force microscope, and then subsequently studied by measuring the surface potential with scanning Kelvin probe microscopy (SKPM). The charging and discharging behavior of the surface appears to be strongly influenced by surface preparation and the presence of a surface oxide layer. If a substantial oxide layer exists, then both positive and negative charging is possible on n-type and p-type samples. Surface treatments and photoemission spectroscopy (XPS) data confirm the presence and influence of the oxide layer on surface charging behavior. In the case of forward-bias charging, a small change in surface contact potential (0.1 – 0.3 eV) is observed that is primarily due to a small voltage drop across the surface oxide. Reverse-bias charging produces a substantially larger change in surface potential (~1 – 3 eV) that must be explained by a large increase in surface band bending. Temperature-dependent SKPM measurements also indicate that the decay behavior of deposited surface charge in dark involves a thermionic mechanism.

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MUTISYA, STEPHEN. "SYNTHESIS OF NANOCOMPOSITES BY LASER ABLATION." VCU Scholars Compass, 2011. http://scholarscompass.vcu.edu/etd/231.

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Immunoglobulin E (IgE)-conjugated gold nanoparticles were produced via in situ conjugation of gold nanoparticles with immunoglobulin E by laser ablation of Au in a liquid solution. The colloidal stability and the size distribution of the resulting bio-nanoconjugates were examined with UV-Visible spectroscopy (UV-Vis), dynamic light scattering (DLS), and transmission electron microscopy (TEM). These techniques showed that the Au nanoparticles in aqueous solutions were highly monodispersed spherical particles with a very narrow size distribution. The particles net diameter using TEM, was found to be D5 =3.8±0.9nm and D10 =4.7±1.3nm while the hydrodynamic diameter obtained with DLS was found to be h5 D =171±12nm , h10 D =164±18nm for 5min and 10min laser ablation time respectively. Enzyme-Linked immunosorbent Assay (ELISA) and flow cytometry measurements of the conjugates confirmed that the gold-bound protein remained biologically active, thus paving the way for the application of these nanoparticles in immuno-diagnostics, particularly in tumor-targeted drug delivery.

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Sanders, Jacob N. "Compressed Sensing for Chemistry." Thesis, Harvard University, 2016. http://nrs.harvard.edu/urn-3:HUL.InstRepos:33493432.

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Many chemical applications, from spectroscopy to quantum chemistry, involve measuring or computing a large amount of data, and then compressing this data to retain the most chemically-relevant information. In contrast, compressed sensing is an emergent technique that makes it possible to measure or compute an amount of data that is roughly proportional to its information content. In particular, compressed sensing enables the recovery of a sparse quantity of information from significantly undersampled data by solving an l1-optimization problem. This thesis represents the application of compressed sensing to problems in chemistry. The first half of this thesis is about spectroscopy. Compressed sensing is used to accelerate the computation of vibrational and electronic spectra from real-time time-dependent density functional theory simulations. Using compressed sensing as a drop-in replacement for the discrete Fourier transform, well-resolved frequency spectra are obtained at one-fifth the typical simulation time and computational cost. The technique is generalized to multiple dimensions and applied to two-dimensional absorption spectroscopy using experimental data collected on atomic rubidium vapor. Finally, a related technique known as super-resolution is applied to open quantum systems to obtain realistic models of a protein environment, in the form of atomistic spectral densities, at lower computational cost. The second half of this thesis deals with matrices in quantum chemistry. It presents a new use of compressed sensing for more efficient matrix recovery whenever the calculation of individual matrix elements is the computational bottleneck. The technique is applied to the computation of the second-derivative Hessian matrices in electronic structure calculations to obtain the vibrational modes and frequencies of molecules. When applied to anthracene, this technique results in a threefold speed-up, with greater speed-ups possible for larger molecules. The implementation of the method in the Q-Chem commercial software package is described. Moreover, the method provides a general framework for bootstrapping cheap low-accuracy calculations in order to reduce the required number of expensive high-accuracy calculations.
Chemical Physics

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de, la Puente Alejandro M. "Kaon photoproduction of the proton: contribution of higher angular momentum and energy resonances to the cross-section and polarization asymmetries through an effective Lagrangian model." FIU Digital Commons, 2008. http://digitalcommons.fiu.edu/etd/3014.

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The differential cross-section and polarization observables in the process γ + p --> K++ Λ are studied within an isobaric approach that includes resonances with total angular momentum J ≤ 5/2 over a center of mass energy range from W = 1.6 GeV to W=2.6 GeV. The model is used to fit recent experimental data as a function of the coupling products at the photon and strong vertices for the well established low energy resonances, as well as the total decay width for the high energy less well-established resonances. The model employed in this study is based on an effective hadronic lagrangian using a tree-level approximation. The model uses Feynman diagrammatic techniques to extract the interaction vertices at a first order level in perturbation theory. To extract the coupling strength products involved in the reaction, a X2- minimization technique is used to fit experimental data. The results suggests that both differential cross-section and double polarization observables need to be fit simultaneously to obtain an accurate description of the data. In addition, it was found that while resonances with angular momentum J= 5/2 do not couple strongly to the KΛ channel, higher energy states with J = 3/2 do couple strongly to the KΛ channel and are highly relevant for an accurate description of the data at energies beyond 1.9 GeV.

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Fagan, Dorothy Violet. "Reading competence and Advanced level physics." Thesis, University College London (University of London), 1996. http://discovery.ucl.ac.uk/10021630/.

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Language, for various reasons, tends to be a neglected area in the school physics curriculum. Discussion of "literacy" in the context of science teaching is limited, and many teachers are unclear about the issues involved. However, so-called "active reading" exercises have had an impact on the science curriculum up to GCSE level as part of a broader campaign for enhancing reading for learning. This has helped to highlight reading in science but without necessarily clarifying the issues or attempting to integrate results with what might be called "standard measures of progress". This study uses reading exercises constructed around topics in the Advanced level physics course, to investigate reading among physics students. Evidence of student progress and achievement such as homework marks and the A level grade, are related to students' responses on the exercises, to obtain an objective assessment of the value of language-related activities. Reasons for the choice of texts and methodologies are two-fold: From the point of view of the physics teacher, to allow an investigation into the range of skills and abilities which students demonstrate on language-based material. For the students involved, to make participating in the exercises useful and relevant to their studies. Analyses are directed at looking at the text, task and responses individually from a linguistic as well as a pedagogic perspective, and more particularly at the relationships between the areas. Connections between reading competence and achievement in physics are shown and suggestions are made on how teachers could encourage reading, monitor the reading competence of students and identify students with problems. Implications for future research into language in physics are also discussed.

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Hu, Dehui. "Understanding introductory students’ application of integrals in physics from multiple perspectives." Diss., Kansas State University, 2013. http://hdl.handle.net/2097/16190.

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Doctor of Philosophy
Department of Physics
N. Sanjay Rebello
Calculus is used across many physics topics from introductory to upper-division level college courses. The concepts of differentiation and integration are important tools for solving real world problems. Using calculus or any mathematical tool in physics is much more complex than the straightforward application of the equations and algorithms that students often encounter in math classes. Research in physics education has reported students’ lack of ability to transfer their calculus knowledge to physics problem solving. In the past, studies often focused on what students fail to do with less focus on their underlying cognition. However, when solving physics problems requiring the use of integration, their reasoning about mathematics and physics concepts has not yet been carefully and systematically studied. Hence the main purpose of this qualitative study is to investigate student thinking in-depth and provide deeper insights into student reasoning in physics problem solving from multiple perspectives. I propose a conceptual framework by integrating aspects of several theoretical constructs from the literature to help us understand our observations of student work as they solve physics problems that require the use of integration. I combined elements of three important theoretical constructs: mathematical resources or symbolic forms, which are the small pieces of knowledge elements associated with students’ use of mathematical ideas; conceptual metaphors, which describe the systematic mapping of knowledge across multiple conceptual domains – typically from concrete source domain to abstract target domain; and conceptual blending, which describes the construction of new learning by integrating knowledge in different mental spaces. I collected data from group teaching/learning interviews as students solved physics problems requiring setting up integrals. Participants were recruited from a second-semester calculus-based physics course. I conducted qualitative analysis of the videotaped student conversations and their written work. The main contributions of this research include (1) providing evidence for the existence of symbolic forms in students’ reasoning about differentials and integrals, (2) identifying conceptual metaphors involved in student reasoning about differentials and integrals, (3) categorizing the different ways in which students integrate their mathematics and physics knowledge in the context of solving physics integration problems, (4)exploring the use of hypothetical debate problems in shifting students’ framing of physics problem solving requiring mathematics.

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Woo, Jung Min. "Two mathematical problems in disordered systems." Diss., The University of Arizona, 2000. http://hdl.handle.net/10150/289124.

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Two mathematical problems in disordered systems are studied: geodesics in first-passage percolation and conductivity of random resistor networks. In first-passage percolation, we consider a translation-invariant ergodic family {t(b): b bond of Z²} of nonnegative random variables, where t(b) represent bond passage times. Geodesics are paths in Z², infinite in both directions, each of whose finite segments is time-minimizing. We prove part of the conjecture that geodesics do not exist in any fixed half-plane and that they have to intersect all straight lines with rational slopes. In random resistor networks, we consider an independent and identically distributed family {C(b): b bond of a hierarchical lattice H} of nonnegative random variables, where C(b) represent bond conductivities. A hierarchical lattice H is a sequence {H(n): n = 0, 1, 2} of lattices generated in an iterative manner. We prove a central limit theorem for a sequence x(n) of effective conductivities, each of which is defined on lattices H(n), when a system is in a percolating regime. At a critical point, it is expected to have non-Gaussian behavior.

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Nam, Jayoung. "Mathematical studies on the human eye." [Bloomington, Ind.] : Indiana University, 2007. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:3274988.

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Thesis (Ph.D.)--Indiana University, Dept. of Mathematics, 2007.
Source: Dissertation Abstracts International, Volume: 68-07, Section: B, page: 4528. Adviser: Jacob Rubinstein. Title from dissertation home page (viewed Apr. 22, 2008).

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Chan, Terence. "Stochastic differential equations and related problems inspired by physics." Thesis, University of Cambridge, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.335063.

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李群慶 and Qunqing Li. "Vortex physics of unconventional superconductors: Ginzburg-Lindau theory." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31242017.

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Sadaghiani, Homeyra R. "Conceptual and mathematical barriers to students learning quantum mechanics." Connect to resource, 2005. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1123878116.

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Thesis (Ph. D.)--Ohio State University, 2005.
Title from first page of PDF file. Document formatted into pages; contains xvii, 321 p.; also includes graphics (some col.). Includes bibliographical references. Available online via OhioLINK's ETD Center

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Brown, Natalie. "Matrix continued fraction approach to the relativistic quantum mechanical spin-zero Feshbach-Villars equations." Thesis, California State University, Long Beach, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=1597738.

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In this thesis we solve the Feshbach-Villars equations for spin-zero particles through use of matrix continued fractions. The Feshbach-Villars equations are derived from the Klein-Gordon equation and admit, for the Coulomb potential on an appropriate basis, a Hamiltonian form that has infinite symmetric band-matrix structure. The corresponding representation of the Green's operator of such a matrix can be given as a matrix continued fraction. Furthermore, we propose a finite dimensional representation for the potential operator such that it retains some information about the whole Hilbert space. Combining these two techniques, we are able to solve relativistic quantum mechanical problems of a spin-zero particle in a Coulomb-like potential with a high level of accuracy.

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Bouya, Ismaël. "Instabilités en magnétohydrodynamique." Phd thesis, Université Paris-Diderot - Paris VII, 2013. http://tel.archives-ouvertes.fr/tel-00867318.

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La magnétohydrodynamique, ou effet dynamo, consiste en la génération d'énergie électrique à partir d'énergie mécanique. Plus précisément, on étudie l'évolution d'un champ magnétique généré par un fluide conducteur. Ce phénomène se retrouve dans les planètes, les étoiles, ou même les galaxies, où le champ magnétique provient du mouvement interne. Dans cette thèse, nous nous intéressons plus précisément aux instabilités en magnétohydrodynamique : partant d'un fluide conducteur sans champs magnétique, est-ce qu'une perturbation légère de l'écoulement et du champ magnétique (par exemple, un résidu de champs magnétique arrivant d'un autre système) peut engendrer une amplification de ce champ magnétique, créant ainsi une dynamo ? La deuxième interrogation consiste en le temps nécessaire pour obtenir une telle amplification du champ magnétique. Cette thèse consiste donc en l'étude de ces deux questions, et donne deux résultats d'ordre théorique et deux résultats d'ordre numérique.

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Hohberger, Horst. "Semiclassical asymptotics for the scattering amplitude in the presence of focal points at infinity." Phd thesis, Universität Potsdam, 2006. http://opus.kobv.de/ubp/volltexte/2007/1157/.

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Olofsson, Rikard. "Problems in Number Theory related to Mathematical Physics." Doctoral thesis, Stockholm : Engineering sciences, Kungliga Tekniska högskolan, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-9514.

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Johnson, Fen Rui. "A study of finite and linear elasticity." CSUSB ScholarWorks, 1996. https://scholarworks.lib.csusb.edu/etd-project/1096.

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Williams, Brett W. "Higher-order modes in free electron lasers." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 2005. http://library.nps.navy.mil/uhtbin/hyperion/05Sep%5FWilliams.pdf.

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Jakobsen, Per Kristen. "Stability and instability in two laser models." Diss., The University of Arizona, 1990. http://hdl.handle.net/10150/185255.

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In the first part we study linear stability of travelling wave solutions of a system of equations derived from the Maxwell-Bloch system by adiabatically eliminating the polarization. For the reduced system we find exact conditions for stability and instability. We also find that the adiabatic elimination procedure produces a very badly behaved system in the presence of diffraction. The full Maxwell-Bloch system or the system we get by removing both the polarization and the inversion adiabatically does not have these problems. In the second part we study the stability of index guided laser arrays using an ODE model derived by a coupled mode approach. Stationary solutions to the model equations are found under free running and injection locking conditions and their stability are investigated numerically and analytically for large arrays.

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Ludwig, Mark Allen. "Numerical solutions of lattice quantum fields with a hierarchy of Schroedinger-like equations." Diss., The University of Arizona, 1990. http://hdl.handle.net/10150/185265.

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Systems of quantized fields can be described by an infinite hierarchy of coupled equations. Such a hierarchy is derived from first principles for a simple interacting field theory to illustrate this type of a representation. The perturbation series for the S matrix is derived from the hierarchy equations in order to show its equivalence to the usual expansion in Feynman amplitudes. An inquiry is then conducted to determine whether this type of representation is useful for solving problems. Truncations of the hierarchy which predict simple bound states are examined in the weak coupling limit, and equations describing a hydrogen-like atom are obtained. Next, the numerical approximation of a truncated hierarchy is studied, and a scattering/particle creation process is modeled in one dimension with a resulting accuracy of 1 to 2 percent. Finally, the mathematical questions of convergence which arise in connection with quantized fields are discussed within the context of the hierarchy equations.

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Martinez, II Roberto. "Singularities, Supersymmetry and Combinatorial Reciprocity." Thesis, Harvard University, 2013. http://dissertations.umi.com/gsas.harvard:10093.

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This work illustrates a method to investigate certain smooth, codimension-two, real submanifolds of spheres of arbitrary odd dimension (with complements that fiber over the circle) using a novel supersymmetric quantum invariant. Algebraic (fibered) links, including Brieskorn-Pham homology spheres with exotic differentiable structure, are examples of said manifolds with a relative diffeomorphism-type that is determined by the corresponding (multivariate) Alexander polynomial.
Engineering and Applied Sciences

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39

Ling, Eric. "The Big Bang Singularity." Thesis, University of California, Santa Barbara, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=1600215.

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The big bang theory is a model of the universe which makes the striking prediction that the universe began a finite amount of time in the past at the so called "Big Bang singularity." We explore the physical and mathematical justification of this surprising result. After laying down the framework of the universe as a spacetime manifold, we combine physical observations with global symmetrical assumptions to deduce the FRW cosmological models which predict a big bang singularity. Next we prove a couple theorems due to Stephen Hawking which show that the big bang singularity exists even if one removes the global symmetrical assumptions. Lastly, we investigate the conditions one needs to impose on a spacetime if one wishes to avoid a singularity. The ideas and concepts used here to study spacetimes are similar to those used to study Riemannian manifolds, therefore we compare and contrast the two geometries throughout.

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Caballero, David. "Discrete Variable Representation Of The Angular Variables In Quantum Three-Body Scattering." Scholarship @ Claremont, 2011. http://scholarship.claremont.edu/cgu_etd/11.

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There are many numerical methods to study the quantum mechanical three-body scattering system using the Schrodinger equation. Traditionally, a partial-wave decomposition of the total wave function is carried out first, allowing the scattering system to be solved one partial wave at a time. This is convenient when the interaction is central, causing the total angular momentum to be conserved during the collision process. This is not possible in the presence of a non-central interaction such as a laser field, where the total angular momentum is not conserved during the collision process. The Discrete Variable Representation is a new method for solving the quantum-mechanical three-body scattering problem to obtain the total cross section. The implementation of this new method for the two-body problem has been successfully applied to real systems. The extension to the three-body problem is the next logical step. For this thesis bipolar spherical harmonics are used in the implementation of the three-body Discrete Variable Representation. This Discrete Variable Representation is capable of working with any combination of interactions, including non-central interactions. The total cross section computation for a three-particle elastic-scattering numerical example is used to illustrate the potential of this Discrete Variable Representation method. The three-particle system consists of a positron scattering against a ground state hydrogen atom (an electron bound to a proton).

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Van, Tilburg Ken. "Identifying boosted objects with N-subjettiness and linear k-means clustering." Thesis, Massachusetts Institute of Technology, 2011. http://hdl.handle.net/1721.1/65536.

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Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics; and, (S.B.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2011.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 57-59).
In this thesis, I explore aspects of a new jet shape - N-subjettiness - designed to identify boosted hadronically-decaying objects (with a particular focus on tagging top quarks) at particle accelerators such as the Large Hadron Collider. Combined with an invariant mass cut on jets, N-subjettiness is a powerful discriminating variable for tagging boosted objects such as top quarks and rejecting the fake background of QCD jets with large invariant mass. In a crossover analysis, the N-subjettiness method is found to outperform the common top tagging methods of the BOOST2010 conference, with top tagging efficiencies of 50% and 20% against mistag rates of 4.0% and 0.19%, respectively. The N-subjettiness values are calculated using a new infrared- and collinear-safe minimization procedure which I call the linear k-means clustering algorithm. As a true jet shape with highly effective tagging performances, N-subjettiness has many advantages on the experimental as well as on the theoretical side.
by Ken Van Tilburg.
S.B.

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Nelson, Justin Matthew 1981. "Total-to-peak ratios of high purity germanium gamma ray detector." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/32746.

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Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics; and, (S.B.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.
MIT Institute Archives copy: leaves 2-22 bound in reverse order.
Includes bibliographical references (leaf 22).
This study is concerned with the percentage of [gamma]-rays of a certain energy having their energy correctly measured by a high purity Germanium [gamma]-ray detector. The ratio between the total counts and the counts within the energy peak (total-to-peak ratio) is determined for seven energies ranging from 89 keV to 1275 keV. A Monte Carlo based on the physical parameters of the detector was used to extrapolate between these points and after an energy independent scaling factor fit the data with a reduced [chi]² slightly below 1. The same experiment was repeated with a lead brick and then a β detector near the Ge detector and these objects were found to not have an effect on the total-to-peak ratios within the precision of the experiment.
by Justin Matthew Nelson.
S.B.

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Mukherji, Shankar 1982. "The dynamics of enzymatic switch cascades." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/32747.

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Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics; and, (S.B.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.
Includes bibliographical references (leaf 67).
We examine the dynamics of the mitogen-activated protein kinase (MAPK) multi-step enzymatic switching cascade, a highly conserved architecture utilised in cellular signal transduction. In treating the equations of motion, we replace the usual deterministic differential equation formalism with stochastic equations to accurately model the 'effective collisions' picture of the biochemical reactions that constitute the network. Furthermore we measure the fidelity of the signaling process through the mutual information content between the output of a given switch and the original environmental input to the system. We find that the enzymatic switches act as low-pass filters, with each switch in the cascade able to average over high frequency stochastic fluctuations in the network and throughput cleaner signals to downstream switches. We find optimal regions of mutual information transfer with respect to reaction velocity and species number parameters, and observe the dynamical memory-gain and memory-loss as well as decay in mutual information in quadruple-linked switch systems.
by Shankar Mukherji.
S.B.

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Fakhouri, Onsi Joe 1983. "Constraining the QSO luminosity function using gravitational lensing statistics." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/32733.

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Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Physics; and, (S.B.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.
Includes bibliographical references (leaves 85-87).
In this thesis we use gravitational lensing statistics to constrain the QSO luminosity function at a variety of redshifts. We present a theoretical discussion of gravitational lensing statistics and illustrate how high resolution QSO imagery can be used to constrain the QSO luminosity function. We then discuss the selection and observation of the 1073 QSO exposures in our sample. The sample covers a redshift range of 0.7by Onsi Joe Fakhouri.
S.B.

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Fluder, Martin Felix. "Aspects of the class S superconformal index, and gauge/gravity duality in five/six dimensions." Thesis, University of Oxford, 2015. http://ora.ox.ac.uk/objects/uuid:3362dc52-f87c-4d58-bf82-eeb9a46f8fb3.

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In the first part of this thesis, we discuss some aspects of the four-dimensional N = 2 superconformal index of theories of class S. We first consider a generalized index on S¹ × S³/Z_r, and prove S-duality in a particular fugacity slice. We then go on to study the (round) superconformal index in the presence of surface defects. We develop a systematic prescription to compute surface defects labeled by arbitrary irreducible representations of the gauge group and subject those defects to various tests in several different limits. Each of these limits is interesting in its own right, and we go on to explore them in some depth. In the second part of this thesis, we construct the gravity duals of large N supersymmetric gauge theories defined on squashed five-spheres with SU(3) × U(1) symmetry. The gravity duals are constructed in Euclidean Romans F(4) gauged supergravity in six- dimensions, and uplift to massive type IIA supergravity. We compute the partition function and Wilson loop in the large N limit of the gauge theory and compare them to their corresponding supergravity dual quantities. As expected from AdS/CFT, both sides agree perfectly. Based on these results, we conjecture a general formula for the partition function and Wilson loop on any five-sphere background, which for fixed gauge theory depends only on a certain supersymmetric Killing vector. We then go on to construct rigid supersymmetric gauge theories on more general Riemannian five-manifolds. We follow a holographic approach, realizing the manifold as the conformal boundary of the six-dimensional bulk supergravity solution. This leads to a systematic classification of five-dimensional supersymmetric backgrounds with gravity duals.

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Bernstein, Lisa Joan. "Quantum theories of self-localization." Diss., The University of Arizona, 1991. http://hdl.handle.net/10150/298722.

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In the classical dynamics of coupled oscillator systems, nonlinearity leads to the existence of stable solutions in which energy remains localized for all time. Here the quantum-mechanical counterpart of classical self-localization is investigated in the context of two model systems. For these quantum models, the terms corresponding to classical nonlinearities modify a subset of the stationary quantum states to be particularly suited to the creation of nonstationary wavepackets that localize energy for long times. The first model considered here is the Quantized Discrete Self-Trapping model (QDST), a system of anharmonic oscillators with linear dispersive coupling used to model local modes of vibration in polyatomic molecules. A simple formula is derived for a particular symmetry class of QDST systems which gives an analytic connection between quantum self-localization and classical local modes. This formula is also shown to be useful in the interpretation of the vibrational spectra of some molecules. The second model studied is the Frohlich/Einstein Dimer (FED), a two-site system of anharmonically coupled oscillators based on the Frohlich Hamiltonian and motivated by the theory of Davydov solitons in biological protein. The Born-Oppenheimer perturbation method is used to obtain approximate stationary state wavefunctions with error estimates for the FED at the first excited level. A second approach is used to reduce the first excited level FED eigenvalue problem to a system of ordinary differential equations. A simple theory of low-energy self-localization in the FED is discussed. The quantum theories of self-localization in the intrinsic QDST model and the extrinsic FED model are compared.

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Van, Deventer Joel. "Comparing Student Performance on Isomorphic Math and Physics Vector Representations." Fogler Library, University of Maine, 2008. http://www.library.umaine.edu/theses/pdf/VanDeventerJ2008.pdf.

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Le, Tuan Minh. "Infinite Volume Limit for Correlation functions in the Dipole Gas." Thesis, State University of New York at Buffalo, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=3565781.

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We consider a classical lattice dipole gas with low activity in dimension d ≥ 3. We study long distance properties by a renormalization group analysis. We prove that various correlation functions have a infinite volume limit. We also get estimates on the decay of correlation functions.

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Cornwell, David J. "Amplified quantum transforms." Thesis, University of Maryland, Baltimore County, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=3624347.

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In this thesis we investigate two new Amplified Quantum Transforms. In particular we create and analyze the Amplified Quantum Fourier Transform (Amplified-QFT) and the Amplified-Haar Wavelet Transform. The Amplified-QFT algorithm is used to solve the Local Period Problem. We calculate the probabilities of success and compare this algorithm with the QFT and QHS algorithms. We also examine the Amplified-QFT algorithm for solving the Local Period Problem with Error Stream. We use the Amplified-Haar Wavelet Transform for solving the Local Constant or Balanced Signal Decision Problem which is a generalization of the Deutsch-Jozsa problem.

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Cottrell, Seth S. "Some Applications of Quantum Walks to a General Class of Searches and the Computation of Boolean Functions." Thesis, New York University, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=3665129.

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In previous papers about searches on star graphs several patterns have been made apparent; the speed up only occurs when graphs are ''tuned'' so that their time step operators have degenerate eigenvalues, and only certain initial states are effective. More than that, the searches are never faster than order square root of N time. In this thesis the problem is defined rigorously, the causes for all of these patterns are identified, sufficient and necessary conditions for quadratic-speed searches for any connected subgraph are demonstrated, the tolerance of these conditions is investigated, and it is shown that (unfortunately) we can do no better than order square root of N time. Along the way, a useful formalism is established that may be useful in future work involving highly symmetric graphs.

The tools and techniques so derived are then used to demonstrate that tree graphs can be used for the computation of Boolean functions. The philosophy of Farhi's work on the continuous-time NAND tree is applied to a discrete-time walk with any (AND, OR, NAND, or NOR) gate at each vertex. Tentative results show that the vast majority of possible Boolean functions on N bits can be calculated in order square root of N time.

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Dissertations / Theses on the topic 'Mathematics in physics'

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