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Jaksic, Vojkan Simon Barry Simon Barry. "Solutions to some problems in mathematical physics /." Diss., Pasadena, Calif. : California Institute of Technology, 1992. http://resolver.caltech.edu/CaltechETD:etd-09122005-162352.
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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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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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Kozlowska, Katarzyna. "Riemann-Hilbert problems and their applications in mathematical physics." Thesis, University of Reading, 2017. http://centaur.reading.ac.uk/73488/.
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The aim of this thesis is to present the reader with the very effective and rigorous Riemann-Hilbert approach of solving asymptotic problems. We consider a transition problem for a Toeplitz determinant; its symbol depends on an additional parameter t. When t > 0, the symbol has one Fisher-Hartwig singularity at an arbitrary point z1 6= 1 on the unit circle (with associated α1, β1 ∈ C strengths) and as t → 0, a new Fisher-Hartwig singularity emerges at the point z0 = 1 (with α0, β0 ∈ C strengths). The asymptotics we present for the determinant are uniform for sufficiently small t. The location of the β-parameters leads to the consideration of two cases, both of which are addressed in this thesis. In the first case, when | Re β0 − Re β1| < 1 we see a transition between two asymptotic regimes, both given by the same result by Ehrhardt, but with different parameters, thus producing different asymptotics. In the second case, when | Re β0 − Re β1| = 1 the symbol has Fisher-Hartwig representations at t = 0, and the asymptotics are given the Tracy-Basor conjecture. These double scaling limits are used to explain transition in the theory of XY spin chains between different regions in the phase diagram across critical lines.
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Tzou, Leo. "Linear and nonlinear analysis and applications to mathematical physics /." Thesis, Connect to this title online; UW restricted, 2007. http://hdl.handle.net/1773/5761.
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Lundberg, Erik. "Problems in Classical Potential Theory with Applications to Mathematical Physics." Scholar Commons, 2011. http://scholarcommons.usf.edu/etd/3220.
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In this thesis we are interested in some problems regarding harmonic functions. The topics are divided into three chapters.
Chapter 2 concerns singularities developed by solutions of the Cauchy problem for a holomorphic elliptic equation, especially Laplace's equation. The principal motivation is to locate the singularities of the Schwarz potential. The results have direct applications to Laplacian growth (or the Hele-Shaw problem).
Chapter 3 concerns the Dirichlet problem when the boundary is an algebraic set and the data is a polynomial or a real-analytic function. We pursue some questions related to the Khavinson-Shapiro conjecture. A main topic of interest is analytic continuability of the solution outside its natural domain.
Chapter 4 concerns certain complex-valued harmonic functions and their zeros. The special cases we consider apply directly in astrophysics to the study of multiple-image gravitational lenses.
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Rodrigues, Sérgio da Silva. "Methods of nonlinear control theory in problems of mathematical physics." Doctoral thesis, Universidade de Aveiro, 2008. http://hdl.handle.net/10773/2931.
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Doutoramento em Matemática<br>Consideramos a equação de Navier-Stokes num domínio bidimensional e estudamos a sua controlabilidade aproximada e a sua controlabilidade nas projecções em subespaços de campos vectoriais de dimensão finita. Consideramos controlos internos que tomam valores num espaço de dimensão finita. Mais concretamente, procuramos um subespaço de campos vectoriais de divergência nula de dimensão finita de tal modo que seja possível controlar aproximadamente a equação, através de controlos que tomam valores no mesmo subespaço. Usando algumas propriedades de continuidade da equação nos dados iniciais, nomeadamente a continuidade da solução quando o controlo varia na chamada métrica relaxada, reduzimos os resultados em controlabilidade à existência de um chamado conjunto saturante. Consideramos ambas as condições de fronteira do tipo Navier e Dirichlet homogéneas. Damos alguns exemplos de domínios e respectivos conjuntos saturantes. No caso especial das condições de fronteira do tipo Lions - um caso particular das condições do tipo Navier - através de uma técnica envolvendo perturbação analítica de métricas, transferimos a chamada controlabilidade nas projecções em espaços coordenados de dimensão finita de uma métrica para (muitas) outras.<br>We consider the Navier-Stokes equation on a two-dimensional domain and study its approximate controllability and its controllability on projections onto finite-dimensional subspaces of vector fields. We consider body controls taking values in a finite-dimensional space. More precisely we look for a finitedimensional subspace of divergence free vector fields that allow us to control approximately the equation using controls taking values in that subspace. Using some continuity properties of the equation on the initial data, namely the continuity of the solution when the control varies in so-called relaxation metric, we reduce the controllability issues to the existence of a so-called saturating set. Both Navier and no-slip boundary conditions are considered. We present some examples of domains and respective saturating sets. For the special case of Lions boundary conditions - a particular case of Navier boundary conditions - trough a technique involving analytic perturbation of metrics, we transfer so-called controllability on observed coordinate space from one metric to (many) other.
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Del, Punta Jessica A. "Mathematical methods in atomic physics." Thesis, Université de Lorraine, 2017. http://www.theses.fr/2017LORR0035/document.
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Les problèmes de diffusion de particules, à deux et à trois corps, ont une importance cruciale en physique atomique, car ils servent à décrire différents processus de collisions. Actuellement, le cas de deux corps peut être résolu avec une précision numérique désirée. Les problèmes de diffusion à trois particules chargées sont connus pour être bien plus difficiles mais une déclaration similaire peut être affirmée. L’objectif de ce travail est de contribuer, d’un point de vue analytique, à la compréhension des processus de diffusion Coulombiens à trois corps. Ceci a non seulement un intérêt fondamental, mais est également utile pour mieux maîtriser les approches numériques en cours d’élaboration au sein de la communauté de collisions atomiques. Pour atteindre cet objectif, nous proposons d’approcher la solution du problème avec des développements en séries sur des ensembles de fonctions appropriées et possédant une expression analytique. Nous avons ainsi développé un nombre d’outils mathématiques faisant intervenir des fonctions Coulombiennes, des équations différentielles de second ordre homogènes et non-homogènes, et des fonctions hypergéométriques à une et à deux variables<br>Two and three-body scattering problems are of crucial relevance in atomic physics as they allow to describe different atomic collision processes. Nowadays, the two-body cases can be solved with any degree of numerical accuracy. Scattering problem involving three charged particles are notoriously difficult but something similar -- though to a lesser extent -- can be stated. The aim of this work is to contribute to the understanding of three-body Coulomb scattering problems from an analytical point of view. This is not only of fundamental interest, it is also useful to better master numerical approaches that are being developed within the collision community. To achieve this aim we propose to approximate scattering solutions with expansions on sets of appropriate functions having closed form. In so doing, we develop a number of related mathematical tools involving Coulomb functions, homogeneous and non-homogeneous second order differential equations, and hypergeometric functions in one and two variables
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Kidd, Julie Elizabeth. "Mathematical problems in liquid crystal theory and elastic plate theory." Thesis, University of Strathclyde, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.248570.
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Chemama, Michael Leopold. "Flames, Splashes and Microdroplets: A Mathematical Approach to Three Fluid Dynamics Problems." Thesis, Harvard University, 2015. http://nrs.harvard.edu/urn-3:HUL.InstRepos:14226101.
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Three different problems in fluid mechanics are presented in this thesis. The first one deals with the mechanism behind the extinction of a flame by an alternating electric field. A simple model for the interaction between the field and the ions produced by the reaction is presented, which agrees quantitatively with the experiments. It also indicates that charges diffusion is responsible for the non-zero time averaged force on the flame. The second problem focuses on the role of viscosity during the splash of liquid droplets. We show that contrary to what was done in previous theoretical studies, the role of viscosity cannot be investigated within the framework of a boundary layer approximation. Rather, the full viscous term must be included in the equations. Finally, we present the theory behind a new microfluidic device (called centipede) which produces microdroplets at a very high rate without relying on any active element to precipitate the detachment of the drops. We clearly show that the drops detach through a Rayleigh-Plateau instability in an otherwise quasi-static flow. We also predict how the throughput and size of the drops are affected by the geometrical parameters of the device.
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Einav, Amit. "Two problems in mathematical physics: Villani's conjecture and trace inequality for the fractional Laplacian." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/42788.
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The presented work deals with two distinct problems in the field of Mathematical Physics.
The first part is dedicated to an 'almost' solution of Villani's conjecture, a known
conjecture related to a Statistical Mechanics model invented by Kac in 1956, giving a rigorous explanation of some simple cases of the Boltzmann equation. In 2003 Villani conjectured that the time it will take the system of particles in Kac's model to equilibrate is proportional to the number of particles in the system. Our main result in this part is a proof, up to an epsilon, of that conjecture, showing that for all practical purposes we can consider it to be true.
The second part of the presentation is based on a joint work with Prof. Michael Loss and is dedicated to a newly developed trace inequality for the fractional Laplacian, connecting between the fractional Laplacian of a function and its restriction to intersection of hyperplanes. The newly found inequality is sharp and the functions that attain equality in it are completely classified.
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Cooke, Teman H. "Algebraic structure of central force problems." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/28028.
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Nonnenmacher, Andreas [Verfasser], and Martin [Akademischer Betreuer] Grothaus. "Operator semigroups and infinite dimensional analysis applied to problems from mathematical physics / Andreas Nonnenmacher ; Betreuer: Martin Grothaus." Kaiserslautern : Technische Universität Kaiserslautern, 2020. http://d-nb.info/1220691356/34.
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Movahedi-Lankarani, Hamid. "Canonical equations of motion and estimation of parameters in the analysis of impact problems." Diss., The University of Arizona, 1988. http://hdl.handle.net/10150/184490.
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The transient dynamic analysis of constrained mechanical systems may require the solution of a mixed set of algebraic and differential equations of motion. The usual formulation of these equations is expressed in terms of the accelerations of the system components. A canonical form of the equations of motion in terms of the system velocities and the time derivative of the system momenta may be used instead. This is a natural form of the equations in which all the state variables are explicitly expressed, and have the same physical importance. The numerical solution obtained from the canonical equations shows more accuracy and stability, specifically for systems with large and fluctuating forces. For the mechanical systems that undergo an impact, the usual numerical solution of the equations of motion is not valid. Two different methods of analysis of impact problems are presented. In one method, the variations of the impulsive force during the contact period are directly added to the vector of forces in the canonical equations of motion. In the second method, based on the assumption of instantaneous nature of impact, a set of momentum balance-impulse equations is derived by explicitly integrating the canonical equations. These equations are solved at the time of impact for the jump in the system momenta right after impact. Necessary parameters are evaluated for the performance of the two methods of analysis. These parameters include the maximum relative indentation, the maximum contact force, and the coefficient of restitution. The parameters are determined for the collision between two bodies in a system with any general geometric or material properties. The influence of friction modeling in the magnitude and the direction of the total force at the contact surfaces is discussed. The dynamics of a vehicle collision is studied in order to illustrate the efficiency of obtaining a solution to the canonical equations, the simplicity of solving the momentum balance-impulse equations.
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Boonserm, Petarpa. "Rigorous bounds on transmission, reflection, and Bogoliubov coefficients : a thesis submitted to the Victoria University of Wellington in fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics /." ResearchArchive@Victoria e-Thesis, 2009. http://hdl.handle.net/10063/942.
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Nnanyereugo, Iwuanyanwu Paul. "An analysis of pre-service teachers' ability to use a dialogical argumentation instructional model to solve mathematical problems in physics." University of the Western Cape, 2017. http://hdl.handle.net/11394/6252.
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Philosophiae Doctor - PhD (Education)<br>This study chronicles a teacher training education programme. The findings emerged from
the observation of argumentation skills employed by students in a physical science
education classroom for pre-service high school teachers. Their task was to use the nature
of arguments to solve mathematical problems of mechanics in a physics classroom. Forty
first-year students were examined on how they used a dialogical argumentation
instructional model (DAIM) based on Toulmin's (1958/2003) Argument Pattern (TAP),
Downing's (2007) Analytical Model (DAM) and Ogunniyi's (2007a & b) Contiguity
Argumentation Theory (CAT) to solve mathematical problems in physics. Thus efforts to
judge the pre-service teachers' capability to solve mathematical problems in physics with
respect to mechanics were compounded by the demand for the inclusion of a self-efficacy
framework. According to Bandura (2006) self-efficacy is the judgment of capability. Selfefficacy
plays a key role in human functioning in that it affects not only people's behaviour
but other issues such as goals and aspirations, outcome expectations, affective proclivities
and perception of impediments and opportunities in the social environment (Bandura, 1995,
1997 & 2006).
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Boller, Stefan. "Spectral Theory of Modular Operators for von Neumann Algebras and Related Inverse Problems." Doctoral thesis, Universitätsbibliothek Leipzig, 2004. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-37397.
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In dieser Arbeit werden die Modularobjekte zu zyklischen und separierenden Vektoren für von-Neumann-Algebren untersucht. Besondere Beachtung erfahren dabei die Modularoperatoren und deren Spektraleigenschaften. Diese Eigenschaften werden genutzt, um Klassifikationen für Lösungen einiger inverser Probleme der Modulartheorie anzugeben. Im ersten Teil der Arbeit wird zunächst der Zusammenhang zwischen dem zyklischen und separierenden Vektor und seinen Modularobjekten mit Hilfe (verallgemeinerter) Spurvektoren für halbendliche und Typ $III_{\lambda}$ Algebren ($0<\lambda<1$) näher untersucht. Diese Untersuchungen erlauben es, das Spektrum der Modularoperatoren für Typ $I$ Algebren anzugeben. Dazu werden die Begriffe {\em zentraler Eigenwert} und zentrale Vielfachheit eingeführt. Weiterhin ergibt sich, dass die Modularoperatoren durch ihre Spektraleigenschaften eindeutig charakterisiert sind. Modularoperatoren für Typ $I_{n}$ Algebren sind genau die $n$-zerlegbaren Operatoren, die multiplikatives, zentrales Spektrum vom Typ $I_{n}$ besitzen. ähnliche Ergebnisse werden auch für Typ $II$ und $III_{\lambda}$ Algebren gewonnen unter der Vorausetzung, dass die zugehörigen Vektoren diagonalisierbar sind. Im zweiten Teil der Arbeit werden diese Ergebnisse exemplarisch auf ein inverses Problem der Modulartheorie angewendet. Dabei stellt sich heraus, dass die Begriffe zentraler Eigenwert und zentrale Vielfachheit Invarianten des inversen Problems sind und eine vollständige Klassifizierung seiner Lösungen unter obigen Voraussetzungen erlauben. Außerdem wird eine Klasse von Modularoperatoren untersucht, für die das inversese Problem nur ein oder zwei Lösungsklassen besitzt<br>In this work modular objects of cyclic and separating vectors for von~Neumann~algebras are considered. In particular, the modular operators and their spectral properties are investigated. These properties are used to classify the solutions of some inverse problems in modular theory. In the first part of the work the correspondence between cyclic and separating vectors and their modular objects are considered for semifinite and type $III_{\lambda}$ algebras ($0<\lambda<1$) in more detail, where (generalized) trace vectors are used. These considerations allow to compute the spectrum of modular operators for type $I$ algebras. To this end, the notions of central eigenvalue and central multiplicity are introduced. Furthermore, it is stated that modular operators are uniquely determined by their spectral properties. Modular operators for type $I_{n}$ algebras are exactly the $n$-decomposable operators, which possess {\em multiplicative central spectrum of type $I_{n}$}. Similar results are derived for type $II$ and $III_{\lambda}$ algebras under the assumption that the corresponding vectors are diagonalizable. In the second part of this work these results are applied to an inverse problem of modular theory. It comes out, that the central eigenvalues and central multiplicities are invariants of this inverse problem and that they give a complete classification of its solutions. Moreover, a class of modular operators is investigated, whose inverse problem possesses only one or two classes of solutions
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Visco, Comandini Filippo. "Some inverse scattering problems on star-shaped graphs: application to fault detection on electrical transmission line networks." Phd thesis, Université de Versailles-Saint Quentin en Yvelines, 2011. http://tel.archives-ouvertes.fr/tel-00748216.
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In this thesis, having in mind applications to the fault-detection/diagnosis of electrical networks, we consider some inverse scattering problems for the Zakharov-Shabat equations and time-independent Schrödinger operators over star-shaped graphs. The first chapter is devoted to describe reflectometry methods applied to electrical networks as an inverse scattering problems on the star-shaped network. Reflectometry methods are presented and modeled by the telegrapher's equations. Reflectometry experiments can be written as inverse scattering problems for Schrödinger operator in the lossless case and for Zakharov-Shabat system for the lossy transmission network. In chapter 2 we introduce some elements of the inverse scattering theory for 1 d Schrödinger equations and the Zakharov-Shabat system. We recall the basic results for these two systems and we present the state of art of scattering theory on network. The third chapter deals with some inverse scattering for the Schrödinger operators. We prove the identifiability of the geometry of the star-shaped graph: the number of the edges and their lengths. Next, we study the potential identification problem by inverse scattering. In the last chapter we focus on the inverse scattering problems for lossy transmission star-shaped network. We prove the identifiability of some geometric informations by inverse scattering and we present a result toward the identification of the heterogeneities, showing the identifiability of the loss line factor.
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Athanassenas, Maria. "Kapillarflächen mit freien Rändern." Bonn : [s.n.], 1991. http://catalog.hathitrust.org/api/volumes/oclc/26530983.html.
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Ting, Lycretia Englang. "Sturm-Liouville theory." CSUSB ScholarWorks, 1996. https://scholarworks.lib.csusb.edu/etd-project/1206.
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Cattoën, Céline. "Applied mathematics of space-time & space+time : problems in general relativity and cosmology : a thesis submitted to the Victoria University of Wellington in fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics /." ResearchArchive@Victoria e-thesis, 2009. http://hdl.handle.net/10063/972.
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Lentz, Simon. "Exact eigenstates of the Inozemtsev spin chain." Thesis, KTH, Fysik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-297571.
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This thesis deals with the following question: are there more eigenfunctions, other than the already known eigenfunctions, of the spin chain with elliptic interactions known as the Inozemtsev spin chain? The Inozemtsev spin chain interpolates between two quantum integrable spin chains, theHeisenberg spin chain and the Haldane-Shastry spin chain. Therefore it is interesting to explore eigenfunctions of the Inozemtsev spin chain in greater detail. Moreover, there exists connections between spin chains and their corresponding spinless continuum model, namely theCalogero-Sutherland models; a derivation of the connection between the Haldane-Shastry spin chain and the trigonometric interacting Calogero-Sutherland model is presented in this thesis. These connections state that the eigenfunctions of the Calogero-Sutherland model are also eigenfunctionsof the corresponding spin chain. An established connection between the Inozemtsev spin chain and the elliptic interacting Calogero-Sutherland model yields exact eigenfunctions with simple poles at coinciding arguments of the Inozemtsev spin chain. However, there are eigenfunctions of theelliptic Calogero-Sutherland model with second order zeros instead of simple poles at coinciding arguments. It is therefore interesting to see if a connection exists that relates the eigenfunctions of the elliptic Calogero-Sutherland model with second order zeros to eigenfunctionsof the Inozemtsev spin chain also with second order zeros. The main goal of this thesis is to explore eigenfunctions of the Inozemtsev spin chain with second order zeros for two magnons. This thesis uses analytical methods for finding these eigenfunctions and numerical methods have beenresorted to in the end. The numerical results indicate that the functions explored in this thesis fail to parametrise the eigenfunctions of the Inozemtsev spin chain, except for a few special cases.<br>Den här avhandlingen behandlar följande frågeställning: finns det fler egenfunktioner än de redan kända till spinnkedjan med elliptisk växelverkan känd som Inozemtsevs spinnkedja? Inozemtsevs spinnkedja interpolerar mellan Heisenbergs spinnkedja och Haldane-Shastrys spinnkedja som båda ärkvant-integrerbara. Därför är det intressant att vidare utforska egenfunktionerna hos Inozemtsevs spinnkedja. Det finns kopplingar mellan spinnkedjor och spinnfria en-dimensionella kontinuumsystem, nämligen Calogero-Sutherlands system; en sådan koppling mellan Haldane-Shastrysspinnkedja och Calogero-Sutherlands modell med trigonometrisk växelverkan härleds i denna avhandling. Dessa kopplingar konstaterar att egenfunktionerna för Calogero-Sutherland systemet är egenfunktioner för spinnkedjan också. En koppling existerar mellan Calogero-Sutherland modellen med elliptisk växelverkan och Inozemtsevs spinnkedja vilket ger exakta egenfunktioner hos Inozemtsevs modell med enkla poler vid sammanfallande argument. Däremot existerar det egenfunktioner till Calogero-Sutherland modellen med elliptisk växelverkan med andra ordningens nollor vid sammanfallande argument istället för enkla poler. Det är därför intressant att undersöka om det existerar en koppling mellan dessa två system med egenfunktioner med andra ordningens nollor; det här skulle då ge exakta egenfunktioner till Inozemtsevs spinnkedja med andra ordningens nollor. Detta är huvudsyftet med avhandlingen. Egenfunktioner med andra ordningens nollor för två magnoner undersöks. Avhandlingen använder sig av analytisk metod och har prövats med numeriska metoder. De numeriska resultaten indikerar att de undersökta funktionerna i denna avhandling misslyckas med att parametrisera egenfunktionerna till Inozemtsevs spinnkedja förutom vissa specifika fall.
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Farlow, Brian. "Square Peg Thinking, Round Hole Problems: An Investigation of Student Thinking About and Mathematical Preparation for Vector Concepts in Cartesian and Non-Cartesian Coordinates Used in Upper-Division Physics." Diss., North Dakota State University, 2019. https://hdl.handle.net/10365/31479.
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Rigaud, Gaël. "Study of generalized Radon transforms and applications in Compton scattering tomography." Phd thesis, Université de Cergy Pontoise, 2013. http://tel.archives-ouvertes.fr/tel-00945739.
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Since the advent of the first ionizing radiation imaging devices initiated by Godfrey Newbold Hounsfield and Allan MacLeod Cormack, Nobel Prizes in 1979, the requirement for new non-invasive imaging techniques has grown. These techniques rely upon the properties of penetration in the matter of X and gamma radiation for detecting a hidden structure without destroying the illuminated environment. They are used in many fields ranging from medical imaging to non-destructive testing through. However, the techniques used so far suffer severe degradation in the quality of measurement and reconstructed images. Usually approximated by a noise, these degradations require to be compensated or corrected by collimating devices and often expensive filtering. These degradation is mainly due to scattering phenomena which may constitute up to 80% of the emitted radiation in biological tissue. In the 80's a new concept has emerged to circumvent this difficulty : the Compton scattering tomography (CST).This new approach proposes to measure the scattered radiation considering energy ranges ( 140-511 keV) where the Compton effect is the phenomenon of leading broadcast. The use of such imaging devices requires a deep understanding of the interactions between radiation and matter to propose a modeling, consistent with the measured data, which is essential to image reconstruction. In conventional imaging systems (which measure the primary radiation) the Radon transformdefined on the straight lines emerged as the natural modeling. But in Compton scattering tomography, the measured information is related to the scattering energy and thus the scattering angle. Thus the circular geometry induced by scattering phenomenon makes the classical Radon transform inadequate.In this context, it becomes necessary to provide such Radon transforms on broader geometric manifolds.The study of the Radon transform on new manifolds of curves becomes necessary to provide theoretical needs for new imaging techniques. Cormack, himself, was the first to extend the properties of the conventional Radon transform of a family of curves of the plane. Thereafter several studies have been done in order to study the Radon transform defined on different varieties of circles, spheres, broken lines ... . In 1994 S.J. Norton proposed the first modality in Compton scattering tomography modeled by a Radon transform on circular arcs, the CART1 here. In 2010, Nguyen and Truong established the inversion formula of a Radon transform on circular arcs, CART2, to model the image formation in a new modality in Compton scattering tomography. The geometry involved in the integration support of new modalities in Compton scattering tomography lead them to demonstrate the invertibility of the Radon transform defined on a family of Cormack-type curves, called C_alpha. They illustrated the inversion procedure in the case of a new transform, the CART3, modeling a new modeling of Compton scattering tomography. Based on the work of Cormack and Truong and Nguyen, we propose to establish several properties of the Radon transform on the family C_alpha especially on C1. We have thus demonstrated two inversion formulae that reconstruct the original image via its circular harmonic decomposition and itscorresponding transform. These formulae are similar to those established by Truong and Nguyen. We finally established the well-known filtered back projection and singular value decomposition in the case alpha = 1. All results established in this study provide practical problems of image reconstruction associated with these new transforms. In particular we were able to establish new inversion methods for transforms CART1,2,3 as well as numerical approaches necessary for the implementation of these transforms. All these results enable to solve problems of image formation and reconstruction related to three Compton scattering tomography modalities.In addition we propose to improve models and algorithms es
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Noel, Jonathan A. "Extremal combinatorics, graph limits and computational complexity." Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:8743ff27-b5e9-403a-a52a-3d6299792c7b.
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This thesis is primarily focused on problems in extremal combinatorics, although we will also consider some questions of analytic and algorithmic nature. The d-dimensional hypercube is the graph with vertex set {0,1}<sup>d</sup> where two vertices are adjacent if they differ in exactly one coordinate. In Chapter 2 we obtain an upper bound on the 'saturation number' of Q<sub>m</sub> in Q<sub>d</sub>. Specifically, we show that for m ≥ 2 fixed and d large there exists a subgraph G of Q<sub>d</sub> of bounded average degree such that G does not contain a copy of Q<sub>m</sub> but, for every G' such that G ⊊ G' ⊆ Q<sub>d</sub>, the graph G' contains a copy of Q<sub>m</sub>. This result answers a question of Johnson and Pinto and is best possible up to a factor of O(m). In Chapter 3, we show that there exists ε > 0 such that for all k and for n sufficiently large there is a collection of at most 2<sup>(1-ε)k</sup> subsets of [n] which does not contain a chain of length k+1 under inclusion and is maximal subject to this property. This disproves a conjecture of Gerbner, Keszegh, Lemons, Palmer, Pálvölgyi and Patkós. We also prove that there exists a constant c ∈ (0,1) such that the smallest such collection is of cardinality 2<sup>(1+o(1))<sup>ck</sup> </sup> for all k. In Chapter 4, we obtain an exact expression for the 'weak saturation number' of Q<sub>m</sub> in Q<sub>d</sub>. That is, we determine the minimum number of edges in a spanning subgraph G of Q<sub>d</sub> such that the edges of E(Q<sub>d</sub>)\E(G) can be added to G, one edge at a time, such that each new edge completes a copy of Q<sub>m</sub>. This answers another question of Johnson and Pinto. We also obtain a more general result for the weak saturation of 'axis aligned' copies of a multidimensional grid in a larger grid. In the r-neighbour bootstrap process, one begins with a set A<sub>0</sub> of 'infected' vertices in a graph G and, at each step, a 'healthy' vertex becomes infected if it has at least r infected neighbours. If every vertex of G is eventually infected, then we say that A<sub>0</sub> percolates. In Chapter 5, we apply ideas from weak saturation to prove that, for fixed r ≥ 2, every percolating set in Q<sub>d</sub> has cardinality at least (1+o(1))(d choose r-1)/r. This confirms a conjecture of Balogh and Bollobás and is asymptotically best possible. In addition, we determine the minimum cardinality exactly in the case r=3 (the minimum cardinality in the case r=2 was already known). In Chapter 6, we provide a framework for proving lower bounds on the number of comparable pairs in a subset S of a partially ordered set (poset) of prescribed size. We apply this framework to obtain an explicit bound of this type for the poset 𝒱(q,n) consisting of all subspaces of 𝔽<sub>q</sub><sup>n</sup>ordered by inclusion which is best possible when S is not too large. In Chapter 7, we apply the result from Chapter 6 along with the recently developed 'container method,' to obtain an upper bound on the number of antichains in 𝒱(q,n) and a bound on the size of the largest antichain in a p-random subset of 𝒱(q,n) which holds with high probability for p in a certain range. In Chapter 8, we construct a 'finitely forcible graphon' W for which there exists a sequence (ε<sub>i</sub>)<sup>∞</sup><sub>i=1</sub> tending to zero such that, for all i ≥ 1, every weak ε<sub>i</sub>-regular partition of W has at least exp(ε<sub>i</sub><sup>-2</sup>/2<sup>5log∗ε<sub>i</sub><sup>-2</sup></sup>) parts. This result shows that the structure of a finitely forcible graphon can be much more complex than was anticipated in a paper of Lovász and Szegedy. For positive integers p,q with p/q ❘≥ 2, a circular (p,q)-colouring of a graph G is a mapping V(G) → ℤ<sub>p</sub> such that any two adjacent vertices are mapped to elements of ℤ<sub>p</sub> at distance at least q from one another. The reconfiguration problem for circular colourings asks, given two (p,q)-colourings f and g of G, is it possible to transform f into g by recolouring one vertex at a time so that every intermediate mapping is a p,q-colouring? In Chapter 9, we show that this question can be answered in polynomial time for 2 ≤ p/q < 4 and is PSPACE-complete for p/q ≥ 4.
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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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Corn, John Russell. "Optimization Problems in Hilbert Space with POSS Complexes." Digital Commons @ East Tennessee State University, 2011. https://dc.etsu.edu/etd/1381.
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Beginning with a survey of functional variation methods in classical physics, we derive the Hartree-Fock theory from canonical quantization. Following a development of density functional theory, many-body perturbation theory, and other techniques of computational condensed matter physics, we perform a systematic study of metal-polyhydride impurities in T8 and T12 polyhedral oligomeric silsesquioxane (POSS) cage molecules. Second-quantized methods motivate the derivations throughout.
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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<br>Department of Physics<br>N. Sanjay Rebello<br>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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Santacesaria, Matteo. "Unicité, reconstruction, stabilité pour des problèmes inverses bidimensionnels." Phd thesis, Ecole Polytechnique X, 2012. http://pastel.archives-ouvertes.fr/pastel-00759992.
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Dans cette thèse nous étudions quelques problèmes inverses de valeurs au bord en dimension deux. Les problèmes considérés sont le problème de Calderon et le problème de Gel'fand-Calderon dans le cas scalaire et multi-canal, c'est-à-dire matriciel : cela peut etre vu notamment comme une approximation non-surdéterminée du cas tridimensionnel. Nous montrons d'abord quelques résultats pour le problème de Calderon anisotrope : nous présentons une nouvelle formulation du résultat d'unicité sur le plan ainsi que le premier résultat d'unicité globale pour le cas des surfaces à bord. Après, nous démontrons une nouvelle estimation de stabilité globale pour le problème de Gel'fand-Calderon dans le cas scalaire et multi-canal. Des techniques similaires donnent aussi une procédure de reconstruction globale pour le meme problème. Nous proposons ensuite un algorithme d'approximation rapidement convergent pour le problème de Gel'fand-Calderon multi-canal : cet algorithme est principalement motivé par des résultats de la théorie de diffusion inverse multi-dimensionnelle. Comme derniers résultats nous présentons des nouvelles estimations de stabilité globale pour les deux problèmes mentionnés plus haut qui dépendent explicitement de la régularité et de l'énergie.
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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<br>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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Lindqvist, Simon, and Martin Stenholm. "Verkligheten i matematikbokens textuppgifter Reality in problems in mathematics textbooks." Thesis, Malmö högskola, Lärarutbildningen (LUT), 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:mau:diva-27797.
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Detta arbete handlar om förekomsten av verklighetsbaserade matematikuppgifter i matematikläroböcker. För att få underlag till undersökningen har vi granskat fyra svenska läroböcker i matematik, samtliga avsedda för årskurs sju. Undersökningen är fokuserad på textuppgifter, som vi valt att granska genom textanalys. I samtliga läroböcker fann vi att textuppgifterna var underrepresenterade. Av textuppgifterna var det en stor andel som baserades på verkliga händelser. Dock var det vanligt att uppgifternas händelser inte kunde kopplas till elevens egen vardagskontext.
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Srinivasan, Subhashini. "Modeling the Homeschool timetabling problem using Integer programming." VCU Scholars Compass, 2011. http://scholarscompass.vcu.edu/etd/2555.
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Home schooling has steadily been increasing in the past decade. According to a survey in 2007, about 2.5 million children were being home schooled in the US. Typically, parents provide education at the convenience of their home and in some cases an instructor is appointed for the same. The Home School Timetabling problem (HSTP) deals with assigning subjects, timeslots and rooms to every student. In doing so, there are certain hard and specialty constraints that are to be satisfied. Integer programming (IP) has been used in solving the HSTP as it has the advantage of being able to provide information about the relative significance of each constraint with respect to the objective. A prototype in the form of a GUI has been built such that the parent can enter each student’s name, his/her subjects, duration, days and time for each subject, availability times of the parent etc. This data is then fed into the IP model so that it can generate a feasible timetable satisfying all of the constraints. When a solution is found it is formatted to provide the weekly timetable for each student, individually, as well as a complete timetable for all students each day.
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Stoltz, Gabriel. "Simulation moléculaire : Problèmes dynamiques et hors d'équilibre." Habilitation à diriger des recherches, Université Paris-Est, 2012. http://tel.archives-ouvertes.fr/tel-00709965.
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L'objectif de la simulation moléculaire est de comprendre et prédire les propriétés macroscopiques des matériaux à partir de leur description à l'échelle microscopique. Ce mémoire présente quelques contributions à ce sujet, pour des modèles de la physique statistique et de la physique quantique. Mes travaux en physique statistique numérique peuvent être classés en deux catégories : le calcul de propriétés d'équilibre, l'accent étant porté sur le calcul de différences d'énergie libre (chapitre 2), et l'étude de dynamiques hors d'équilibre en régime permanent pour le calcul de propriétés de transport (chapitre 3). Dans les deux cas, les méthodes numériques reposent sur des dynamiques hors d'équilibre ou nonlinéaires, la distinction entre ces classes de méthodes provenant du fait que l'état invariant du système est soit un état d'équilibre (éventuellement, à une correction près) ou un état hors d'équilibre. Le chapitre 4 présente quelques résultats pour des dynamiques quantiques : fictives, comme pour la transition adiabatique d'états dégénérés ; ou authentiques, comme pour l'évolution en temps des défauts locaux dans les cristaux.
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Aiello, Gordon J. "An application of the theory of moments to Euclidean relativistic quantum mechanical scattering." Diss., University of Iowa, 2017. https://ir.uiowa.edu/etd/5902.
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One recipe for mathematically formulating a relativistic quantum mechanical scattering theory utilizes a two-Hilbert space approach, denoted by $\mathcal{H}$ and $\mathcal{H}_{0}$, upon each of which a unitary representation of the Poincaré Lie group is given. Physically speaking, $\mathcal{H}$ models a complicated interacting system of particles one wishes to understand, and $\mathcal{H}_{0}$ an associated simpler (i.e., free/noninteracting) structure one uses to construct 'asymptotic boundary conditions" on so-called scattering states in $\mathcal{H}$. Simply put, $\mathcal{H}_{0}$ is an attempted idealization of $\mathcal{H}$ one hopes to realize in the large time limits $t\rightarrow\pm\infty$.
The above considerations lead to the study of the existence of strong limits of operators of the form $e^{iHt}Je^{-iH_{0}t}$, where $H$ and $H_{0}$ are self-adjoint generators of the time translation subgroup of the unitary representations of the Poincaré group on $\mathcal{H}$ and $\mathcal{H}_{0}$, and $J$ is a contrived mapping from $\mathcal{H}_{0}$ into $\mathcal{H}$ that provides the internal structure of the scattering asymptotes.
The existence of said limits in the context of Euclidean quantum theories (satisfying precepts known as the Osterwalder-Schrader axioms) depends on the choice of $J$ and leads to a marvelous connection between this formalism and a beautiful area of classical mathematical analysis known as the Stieltjes moment problem, which concerns the relationship between numerical sequences $\{\mu_{n}\}_{n=0}^{\infty}$ and the existence/uniqueness of measures $\alpha(x)$ on the half-line satisfying
\begin{equation*}
\mu_{n}=\int_{0}^{\infty}x^{n}d\alpha(x).
\end{equation*}
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Romain, Vasseur. "Indecomposabilité dans les théories des champs et applications aux systèmes désordonnés et aux problèmes géométriques." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2013. http://tel.archives-ouvertes.fr/tel-00876155.
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Les théories des champs conformes logarithmiques (LCFTs) sont cruciales pour décrire le comportement critique de systèmes physiques variés: les transitions de phase dans les systèmes électroniques désordonnés sans interaction (comme par exemple la transition entre plateaux dans l'effet Hall quantique entier), les points critiques désordonnés dans les systèmes statistiques classiques (comme le modèle d'Ising avec liens aléatoires), ou encore les modèles géométriques critiques (comme la percolation ou les marches aléatoires auto-évitantes). Les LCFTs décrivent des théories non unitaires, qui ne seraient probablement pas pertinentes dans le contexte de la physique des particules, mais qui apparaissent naturellement en matière condensée et en physique statistique. Sans cette condition d'unitarité, toute la puissance algébrique qui a fait le succès des théories conformes est fortement compromise à cause de ''l'indécomposabilité'' de la théorie des représentations sous-jacente. Ceci a pour conséquence de modifier les fonctions de corrélation algébriques par des corrections logarithmiques, et réduit sévèrement l'espoir d'une classification générale. Le but de cette thèse est d'analyser ces théories logarithmiques en étudiant leur régularisation sur réseau, l'idée principale étant que la plupart des difficultés algébriques causées par l'indécomposabilité sont déjà présentes dans des systèmes de taille finie. Notre approche consiste à considérer des modèles statistiques critiques avec matrice de transfert non diagonalisable (ou des chaînes de spins critiques avec Hamiltonien non diagonalisable) et d'analyser leur limite thermodynamique à l'aide de différentes méthodes numériques, algébriques et analytiques. On explique en particulier comment mesurer numériquement les paramètres universels qui caractérisent les représentations indécomposables qui apparaissent à la limite continue. L'analyse détaillée d'une vaste classe de modèles sur réseau nous permet également de conjecturer une classification de toutes les LCFTs chirales pertinentes physiquement, pour lesquelles la seule symétrie est donnée par l'algèbre de Virasoro. Cette approche est aussi partiellement étendue aux théories non chirales, avec une attention particulière portée au problème bien connu de la formulation d'une théorie des champs cohérente qui décrirait la percolation en deux dimensions. On montre que les modèles sur réseaux périodiques ou avec bords peuvent être reliés algébriquement seulement dans le cas des modèles minimaux, impliquant des conséquences intéressantes pour les théories des champs sous-jacentes. Un certain nombre d'applications aux systèmes désordonnés et aux modèles géométriques sont également abordées, avec en particulier une discussion détaillée des observables avec comportement logarithmique au point critique dans le modèle de Potts en dimension arbitraire.
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MACEDO, CLAUDIA. "STUDENT EVASION IN MATHEMATICS, CHEMISTRY AND PHYSICS COURSES AT THE FEDERAL UNIVERSITY FLUMINENSE: A SILENT PROBLEM." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2012. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=20730@1.
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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO<br>A presente dissertação tem como objetivo conhecer os fatores que
ocasionam a evasão escolar no ensino superior, com enfoque específico sobre os
Cursos de Licenciaturas em Matemática, Química e Física da Universidade
Federal Fluminense no ano de 2009. A UFF caracteriza evasão estudantil em
09(nove) categorias. Este estudo propõe pesquisar a categoria evasão por
abandono de curso. Para contextualizar a pesquisa foi realizado um resgate da
história do Ensino Superior no Brasil e da Assistência Estudantil no Ensino
Superior, foram realizadas ainda algumas reflexões a respeito do papel social da
universidade e sobre as questões que permeiam o problema da evasão escolar no
ensino superior. No desenvolvimento do trabalho utilizaram-se dados
quantitativos e qualitativos. A coleta de dados foi realizada através de entrevistas
semi-estruturadas baseada em um roteiro previamente definido com 12 (doze) exestudantes,
distribuídos do seguinte modo: 06 (seis) Matemática, 03 (três)
Química e 03 (três) Física. Nas últimas décadas houve um aumento significativo
de vagas para o ensino superior o que possibilitou maior acesso aos estudantes às
universidades públicas e privadas, no entanto, houve também um aumento do
número de estudantes que não conseguiu por diversos motivos concluir os seus
cursos. Com base nesta situação, esta pesquisa buscou identificar quais os fatores
determinantes que levaram os estudantes entrevistados a abandonarem os seus
cursos. Em nosso trabalho também foi elaborado o perfil do estudante evadido
considerando suas características socioeconômicas e educacionais atuais. Ainda
neste trabalho foi identificado o grau de participação dos estudantes evadidos nos
programas de bolsas acadêmicas ou da assistência estudantil visando à
permanência dos mesmos na universidade.<br>This thesis aims to identify the factors that cause school evasion in higher
education, focused specifically on Mathematics, Physics and Chemistry
undergraduate courses of the Universidade Federal Fluminense in 2009. The
university characterises student evasion in 09 (nine) categories. This study
proposes to investigate the school evasion by courses abandonment. To
contextualize this research was recovered the understanding about the history of
higher education in Brazil and Student Assistance in Higher Education,
furthermore some reflections were done about the social role of the university and
the issues that cross the school evasion problems in higher education. To develop
this work were used quantitative and qualitative data. The data capture was
performed through semi-structured interviews based on a predetermined route
with 12(twelve) ex-students, distributed as follows: 06 (six) Mathematics, 03
(three) and Chemistry 03 (three) physics. In the last recent decades there has been
a significant increase of vacancies for higher education which allowed more
access to students at public and private universities, however, there was also an
increase of students who for various reasons, could not complete their courses.
Based on this situation, this study sought to identify the factors that stimulated the
students interviewed to leave their courses and was designed this student profile
considering its current socioeconomic and educational situation. Also, this work
identified the participation degree of the students that left their courses in
programs of scholarships or student assistance in order to promote their
permanency in the university.
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Boukari, Yosra. "Méthodes innovantes en contrôle non destructif des structures: applications à la détection de fissures." Phd thesis, Ecole Polytechnique X, 2012. http://pastel.archives-ouvertes.fr/pastel-00702479.
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L'application des problèmes inverses de diffraction à la détection de fissures via l'utilisation d'ondes acoustiques, électromagnétiques ou élastiques s'élargit dans de nombreux domaines. Des exemples d'application incluent le contrôle non destructif, la prospection géophysique... Cette thèse a pour objectif d'identifier des fissures en utilisant des méthodes d'échantillonnage bien connues. Dans ce travail, nous utilisons la Linear Sampling Method et la méthode de Factorisation pour reconstruire la géométrie de fissures à partir de plusieurs données statiques de champs lointains dans le cas de conditions d'impédance sur les deux bords de la fissure se trouvant dans un domaine homogène. Par ailleurs, une application de la méthode de la Reciprocity Gap Linear Sampling Method est proposée pour la reconstruction de la géométrie de fissures dans un domaine hétérogène avec les mêmes conditions au bord. Dans le but d'élargir l'application de cette dernière méthode, une méthode de complétion de données pour le problème de Cauchy associé à l'équation de Helmholtz a été proposée. La performance des méthodes proposées est montrée à travers de tests numériques pour différentes formes de fissures et pour différentes valeurs de l'impédance.
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Dewhurst, David Rushing. "Some results on a class of functional optimization problems." ScholarWorks @ UVM, 2018. https://scholarworks.uvm.edu/graddis/884.
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We first describe a general class of optimization problems that describe many natu- ral, economic, and statistical phenomena. After noting the existence of a conserved quantity in a transformed coordinate system, we outline several instances of these problems in statistical physics, facility allocation, and machine learning. A dynamic description and statement of a partial inverse problem follow. When attempting to optimize the state of a system governed by the generalized equipartitioning princi- ple, it is vital to understand the nature of the governing probability distribution. We show that optimiziation for the incorrect probability distribution can have catas- trophic results, e.g., infinite expected cost, and describe a method for continuous Bayesian update of the posterior predictive distribution when it is stationary. We also introduce and prove convergence properties of a time-dependent nonparametric kernel density estimate (KDE) for use in predicting distributions over paths. Finally, we extend the theory to the case of networks, in which an event probability density is defined over nodes and edges and a system resource is to be partitioning among the nodes and edges as well. We close by giving an example of the theory’s application by considering a model of risk propagation on a power grid.
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Qin, Yu. "Computations and Algorithms in Physical and Biological Problems." Thesis, Harvard University, 2014. http://dissertations.umi.com/gsas.harvard:11478.
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This dissertation presents the applications of state-of-the-art computation techniques and data analysis algorithms in three physical and biological problems: assembling DNA pieces, optimizing self-assembly yield, and identifying correlations from large multivariate datasets. In the first topic, in-depth analysis of using Sequencing by Hybridization (SBH) to reconstruct target DNA sequences shows that a modified reconstruction algorithm can overcome the theoretical boundary without the need for different types of biochemical assays and is robust to error. In the second topic, consistent with theoretical predictions, simulations using Graphics Processing Unit (GPU) demonstrate how controlling the short-ranged interactions between particles and controlling the concentrations optimize the self-assembly yield of a desired structure, and nonequilibrium behavior when optimizing concentrations is also unveiled by leveraging the computation capacity of GPUs. In the last topic, a methodology to incorporate existing categorization information into the search process to efficiently reconstruct the optimal true correlation matrix for multivariate datasets is introduced. Simulations on both synthetic and real financial datasets show that the algorithm is able to detect signals below the Random Matrix Theory (RMT) threshold. These three problems are representatives of using massive computation techniques and data analysis algorithms to tackle optimization problems, and outperform theoretical boundary when incorporating prior information into the computation.<br>Engineering and Applied Sciences
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Vodhanel, Michael Thomas. "Problems in GPS Accuracy." Scholarship @ Claremont, 2011. http://scholarship.claremont.edu/cgu_etd/22.
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Improving and predicting the accuracy of positioning estimates derived from the global positioning system (GPS) continues to be a problem of great interest. Dependable and accurate positioning is especially important for navigation applications such as the landing of commercial aircraft. This subject gives rise to many interesting and challenging mathematical problems. This dissertation investigates two such problems. The first problem involves the study of the relationship between positioning accuracy and satellite geometry configurations relative to a user's position. In this work, accuracy is measured by so-called dilution of precision (DOP) terms. The DOP terms arise from the linear regression model used to estimate user position from GPS observables, and are directly related to user position errors. An analysis of the statistical properties explaining the behavior of the DOP terms is presented. The most accurate satellite geometries and worst configurations are given for some cases. The second problem involves finding methods for detecting and repairing cycle-slips in range delay data between a satellite and a receiver. The distance between a satellite and a receiver can be estimated by measuring the difference in the carrier frequency phase shift experienced between the satellite and receiver oscillators. Cycle-slips are discontinuities in the integer number of complete cycles in these data, and are caused by interruptions or degradations in the signal such as low signal to noise ratio, software failures, or physical obstruction of the signals. These slips propagate to errors in user positioning. Cycle-slip detection and repair are crucial to maintaining accurate positioning. Linear regression models and sequential hypothesis testing are used to model, detect, and repair cycle-slips. The effectiveness of these methods is studied using data obtained from ground-station receivers.
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Bernard, Benjamin. "On the Quantization Problem in Curved Space." Wright State University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=wright1344829165.
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Depetri, Gabriela Iunes. "Coreografias no problema de N corpos." Universidade de São Paulo, 2011. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-29092011-162402/.
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O objetivo deste trabalho é a obtenção numérica de soluções periódicas para o problema geral de N corpos sujeitos apenas à atração gravitacional mútua. Em particular, procuramos soluções chamadas de coreografias, que apresentam em comum a propriedade de que todos os corpos se movem sobre a mesma curva. O interesse neste tipo de solução aumentou muito recentemente devido aos avanços na Física das ondas gravitacionais. Com a possível detecção de ondas gravitacionais prevista para um futuro próximo, todas as configurações periódicas do problema de N corpos passam a ser consideradas como possíveis fontes de radiação gravitacional. Identificar os padrões de radiação associados a estas órbitas é uma das tarefas prementes atualmente na área. Tendo isso em vista, iremos calcular também as ondas gravitacionais emitidas por um sistema em que os corpos que o constituem seguem uma órbita coreográfica. Começamos este trabalho com um capítulo que descreve historicamente a busca pela solução geral do problema de N corpos, inicialmente motivada pelo interesse na análise da estabilidade do Sistema Solar. Em seguida, no Capítulo 2, apresentamos as principais definições e teoremas que serão utilizados ao longo do texto. O leitor pode escolher entre seguir este capítulo no início de sua leitura, ou então utilizá-lo para consulta quando necessário. No Capítulo 3, identificamos os graus de liberdade do sistema formado pelos N corpos e determinamos quais grandezas físicas nele se conservam, através do Teorema de Noether. Com isso estabelecemos a não integrabilidade deste sistema, no sentido de Liouville, para N > 2. Escrevemos também a solução geral do problema de dois corpos, conhecido como problema de Kepler, e mostramos duas soluções particulares para o problema de três corpos com massas iguais, conhecidas como soluções de Euler (1765) e Lagrange (1772). Na solução de Euler, os três corpos estão dispostos sobre uma mesma reta que gira com velocidade angular constante ao redor do seu centro de massa, e na de Lagrange, estão dispostos sobre os vértices de um triângulo equilátero que gira com velocidade angular constante ao redor do seu centro de massa. Com o intuito de descrever as soluções periódicas conhecidas para o Problema de N Corpos, no Capítulo 4 estudaremos as órbitas homográficas, que apresentam a característica de que a configuração do sistema em qualquer instante pode ser obtida através de uma rotação composta com uma dilatação/contração da configuração inicial. Essas soluções generalizam as soluções de Euler e Lagrange citadas anteriormente. No Capítulo 5, analisaremos as órbitas coreográficas. Esta classe de soluções foi descoberta por Cris Moore em 1993, que encontrou numericamente uma solução coreográfica para o problema de três corpos em que eles seguem uma mesma curva em forma de oito. A existência e a estabilidade desta solução foram estudadas de maneira rigorosa por Richard Montgomery e Alain Chenciner. Neste trabalho, damos um esboço de como construir a solução em forma de oito no caso em que as massas são idênticas. Simularemos esta e outras órbitas coreográficas, além de algumas outras órbitas periódicas descritas anteriormente, através do método de integração de Runge-Kutta de quarta ordem. Finalmente, no Capítulo 6 calculamos as ondas gravitacionais emitidas pelas órbitas homográficas e coreográficas simuladas anteriormente. Finalizaremos com uma breve discussão comparando os padrões de ondas gravitacionais obtidos para as diferentes órbitas e analisando a possibilidade de determinar a fonte de emissão a partir da medida de um sinal de uma onda gravitacional.<br>The purpose of this work is the numerical computing of the periodic solutions to the N-body problem, that is, the general problem of determinig the motion of N bodies exclusively subject to gravitational forces between them. In particular, we search for solutions that were named choreographies, which have in common the property that all bodies move along the same curve. The interest in this kind of solution has recently increased due to technological advances in Gravitational Wave (GW) Physics. As the detection of Gws is foreseen for the near future, all periodic configurations of the N-body problem may be considered as possible sources of gravitational radiation. Identifying the patterns of radiation associated to these orbits is nowadays one of the pressing tasks in this field. Having this fact in mind, we calculate the GWs emitted by a system in which all bodies describe a choreographic orbit. In Chapter 1, we briefly describe the history of the search for the general solution to the N-body Problem, initially motivated by the interest in the stability analysis of the Solar System. Next, in Chapter 2, we present the main definitions and theorems to which we refer during this text. The reader may opt between following this chapter as he begins to read this thesis and consulting it only if necessary or when he is referred to. In Chapter 3, we identify the degrees of freedom of the system consisting of N bodies and determine the physical quantities it conserves, through Noethers theorem. Doing that, we establish the non-integrability of our dynamical system, in the sense of Liouville integrability, if N > 2. We also give the general solution to the 2-body problem, known as Keplers Problem, and present two particular solutions to the 3-body Problem, known as Eulers solution (1765) and Lagranges solution (1772). In Eulers solution, all three bodies are in the same line, which revolves around its center of mass, and in Lagranges solux tion they are at the vertices of an equilateral triangle, which also revolves around its center of mass. In order to describe all known periodic solutions to the N-body Problem, in Chapter 4 we study homographic orbits, that is, orbits in which the configuration at any instant can be obtained by a rotation and a dilation/contraction of the initial configuration. These solutions generalize the solutions by Euler and Lagrange mentioned above. In Chapter 5, we analyze choreographic orbits. This class of solutions was discovered by Cris Moore in 1993, who computed numerically a choreographic solution in which the bodies move along the same curve in the shape of an eight. The existence and stability of this orbit were rigorously studied by Richard Montgomery and Alain Chenciner. Here, we sketch the construction of the figure eight solution in the particular case where all masses are identical. We simulate this and other choreographic solutions, as well as some other periodic solutions described before, through the use of a fourth order Runge- Kutta method of numerical integration. Finally, in Chapter 6 we calculate the Gws emitted by the homographic and choreographic orbits simulated before. We end this work with a brief discussion comparing the GW patterns obtained to different orbits and analyzing the possibility of determining the mission source from a measurement of a GW signal.
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Nguyen, Fonzie T. "THE HAHN-BANACH THEOREM AND SOLUTION OF RELATED PROBLEMS." CSUSB ScholarWorks, 2014. https://scholarworks.lib.csusb.edu/etd/115.
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Srinivasan, Sudharshana. "Spatial Scheduling Algorithms for Production Planning Problems." VCU Scholars Compass, 2014. http://scholarscompass.vcu.edu/etd/3406.
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Spatial resource allocation is an important consideration in shipbuilding and large-scale manufacturing industries. Spatial scheduling problems (SSP) involve the non-overlapping arrangement of jobs within a limited physical workspace such that some scheduling objective is optimized. Since jobs are heavy and occupy large areas, they cannot be moved once set up, requiring that the same contiguous units of space be assigned throughout the duration of their processing time. This adds an additional level of complexity to the general scheduling problem, due to which solving large instances of the problem becomes computationally intractable. The aim of this study is to gain a deeper understanding of the relationship between the spatial and temporal components of the problem. We exploit these acquired insights on problem characteristics to aid in devising solution procedures that perform well in practice. Much of the literature on SSP focuses on the objective of minimizing the makespan of the schedule. We concentrate our efforts towards the minimum sum of completion times objective and state several interesting results encountered in the pursuit of developing fast and reliable solution methods for this problem. Specifically, we develop mixed-integer programming models that identify groups of jobs (batches) that can be scheduled simultaneously. We identify scenarios where batching is useful and ones where batching jobs provides a solution with a worse objective function value. We present computational analysis on large instances and prove an approximation factor on the performance of this method, under certain conditions. We also provide greedy and list-scheduling heuristics for the problem and compare their objectives with the optimal solution. Based on the instances we tested for both batching and list-scheduling approaches, our assessment is that scheduling jobs similar in processing times within the same space yields good solutions. If processing times are sufficiently different, then grouping jobs together, although seemingly makes a more effective use of the space, does not necessarily result in a lower sum of completion times.
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Patel, Mayur K. "On the false-diffusion problem in the numerical modelling of convection-diffusion processes." Thesis, University of Greenwich, 1986. http://gala.gre.ac.uk/8697/.
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This thesis is concerned with the classification and evaluation of various numerical schemes that are available for computing solutions for fluid-flow problems, and secondly, with the development of an improved numerical discretisation scheme of the finite-volume type for solving steady-state differential equations for recirculating flows with and without sources. In an effort to evaluate the performance of the various numerical schemes available, some standard test cases were used. The relative merits of the schemes were assessed by means of one-dimensional laminar flows and two-dimensional laminar and turbulent flows, with and without sources. Furthermore, Taylor series expansion analysis was also utilised to examine the limitations that were present. The outcome of this first part of the work was a set of conclusions, concerning the accuracy of the numerous schemes tests, vis-a-vis their stability, ease of implementation, and computational costs. It is hoped that these conclusions can be used by `computational fluid-dynamics' practitioners in deciding on an optimum choice of scheme for their particular problem. From the understanding gained during the first part of the study, and in an effort to combine the attributes of a successful discretisation scheme, eg positive coefficients. conservation and the elimination of 'false-diffusion', a new flow-oriented finite-volume numerical scheme was devised and applied to several test cases in order to evaluate its performance. The novel approach in formulating the new CUPID* scheme (for Corner UPw^nDing) underlines the idea of focussing attention at the control-volume corners rather than at the control-volume cell-faces. In two-dimensions, this leads to an eight neighbour influence for the central grid point value, depending on the flow-directions at the corners of the control-volume. In the formulation of the new scheme, false-diffusion is considered from a pragmatic perspective, with emphasis on physics rather than on strict mathematical considerations such as the order of discretisation, etc. The accuracy of the UPSTREAM scheme (for JJPwind in STREAMIines) indicates that although it is formally only first-order accurate, it considerably reduces 'false-diffusion'. Scalar transport calculations (without sources) show that the UPSTREAM scheme predicts bounded solutions which are more accurate than the upwind-difference scheme and the unbounded skew-upstream-difference scheme. Furthermore, for laminar and turbulent flow calculations, improved results are obtained when compared with the performances of the other schemes. The advantage of the UPSTREAM-difference scheme is that all the influence coefficients are always positive and thus the coefficient matrices are suitable for iterative solution procedures. Finally, the stability and convergence characteristics are similar to those of the upwind-difference scheme, eg converged solutions are guaranteed. What cannot be guaranteed, however, is the conservatism of the scheme and it is recommended that future work should be directed towards improving that disadvantage.
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Taitano, William Tsubasa-Tsutsui. "Moment-Based Accelerators for Kinetic Problems with Application to Inertial Confinement Fusion." Thesis, The University of New Mexico, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=3630377.
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<p> In inertial confinement fusion (ICF), the kinetic ion and charge separation field effects may play a significant role in the difference between the measured neutron yield in experiments and the predicted yield from fluid codes. Two distinct of approaches exists in modeling plasma physics phenomena: fluid and kinetic approaches. While the fluid approach is computationally less expensive, robust closures are difficult to obtain for a wide separation in temperature and density. While the kinetic approach is a closed system, it resolves the full 6D phase space and classic explicit numerical schemes restrict both the spatial and time-step size to a point where the method becomes intractable. Classic implicit system require the storage and inversion of a very large linear system which also becomes intractable. This dissertation will develop a new implicit method based on an emerging moment-based accelerator which allows one to step over stiff kinetic time-scales. The new method converges the solution per time-step stably and efficiently compared to a standard Picard iteration. This new algorithm will be used to investigate mixing in Omega ICF fuel-pusher interface at early time of the implosion process, fully kinetically. </p>
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Anderson, Connor Stanley. "Facing the Hard Problems in FGVC." BYU ScholarsArchive, 2020. https://scholarsarchive.byu.edu/etd/8596.
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In fine-grained visual categorization (FGVC), there is a near-singular focus in pursuit of attaining state-of-the-art (SOTA) accuracy. This work carefully analyzes the performance of recent SOTA methods, quantitatively, but more importantly, qualitatively. We show that these models universally struggle with certain "hard" images, while also making complementary mistakes. We underscore the importance of such analysis, and demonstrate that combining complementary models can improve accuracy on the popular CUB-200 dataset by over 5%. In addition to detailed analysis and characterization of the errors made by these SOTA methods, we provide a clear set of recommended directions for future FGVC researchers.
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Chi, Xuguang. "A non-variational approach to the quantum three-body coulomb problem /." View abstract or full-text, 2004. http://library.ust.hk/cgi/db/thesis.pl?PHYS%202004%20CHI.
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Quayesam, Dennis. "The Food Truck Problem, Supply Chains and Extensions of the Newsvendor Problem." Digital Commons @ East Tennessee State University, 2021. https://dc.etsu.edu/etd/3905.
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Inventory control is important to ensuring sufficient quantities of items are available tomeet demands of customers. The Newsvendor problem is a model used in Operations Research to determine optimal inventory levels for fulfilling future demands. Our study extends the newsvendor problem to a food truck problem. We used simulation to show that the food truck does not reduce to a newsvendor problem if demand depends on exogenous factors such temperature, time etc. We formulate the food truck problem as a multi-product multi-period linear program and found the dual for a single item. We use Discrete Event Simulation to solve the stochastic version of the dual and found the optimal order to maximize the food vendors profit.
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Dreiding, Rebecca. "Allocating Homeland Security Screening Resources Using Knapsack Problem Models." VCU Scholars Compass, 2010. http://scholarscompass.vcu.edu/etd/2289.
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Since the events of September 11, 2001, the federal government is focused on homeland security and the fight against terrorism. This thesis addresses the idea of terrorist groups smuggling nuclear weapons through the borders of the United States. Security screening decisions are analyzed within maritime and aviation domains using discrete optimization models, specifically knapsack problems. The focus of the maritime chapters involves a risk-based approach for prescreening intelligence classifications for primary and secondary screening decisions given limited budget and resources. Results reveal that screening decisions are dependent on prescreening classification and the efficacy of the screening technologies. The screening decisions in the aviation security chapter highlight different performance measures to quantify the effectiveness of covering flights with the intent of covering targets. Results reveal that given scarce resources, such as screening devices capacities and budget, flights and targets can be covered with minimal expense to the system.