Dissertations / Theses: 'Parabolic'

1

Hertz, Erik. "Parabolic Synthesis." Licentiate thesis, Department of Electrical and Information Technology Faculty of Engineering, LTH, Lund University, Lund, Sweden, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-22338.

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Many consumer products, such as within the computer areas, computer graphics, digital signal processing, communication systems, robotics, navigation, astrophysics, fluid physics, etc. are searching for high computational performance as a consequence of increasingly more advanced algorithms in these applications. Until recently the down scaling of the hardware technology has been able to fulfill these higher demands from the more advanced algorithms with higher clock rates on the chips. This that the development of hardware technology performance has stagnated has moved the interest more over to implementation of algorithms in hardware. Especially within wireless communication the desire for higher transmission rates has increased the interest for algorithm implementation methodologies. The scope of this thesis is mainly on the developed methodology of parabolic synthesis. The parabolic synthesis methodology is a methodology for implementing approximations of unary functions in hardware. The methodology is described with the criteria's that have to be fulfilled to perform an approximation on a unary function. The hardware architecture of the methodology is described and to this a special hardware that performs the squaring operation. The outcome of the presented research is a novel methodology for implementing approximations of unary functions such as trigonometric functions, logarithmic functions, as well as square root and division functions etc. The architecture of the processing part automatically gives a high degree of parallelism. The methodology is founded on operations that are simple to implement in hardware such as addition, shifts, multiplication, contributes to that the implementation in hardware is simple to perform. The hardware architecture is characterized by a high degree of parallelism that gives a short critical path and fast computation. The structure of the methodology will also assure an area efficient hardware implementation.

2

Heyer, Claudius. "Applications of parabolic Hecke algebras: parabolic induction and Hecke polynomials." Doctoral thesis, Humboldt-Universität zu Berlin, 2019. http://dx.doi.org/10.18452/20137.

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Im ersten Teil wird eine neue Konstruktion der parabolischen Induktion für pro-p Iwahori-Heckemoduln gegeben. Dabei taucht eine neue Klasse von Algebren auf, die in gewisser Weise als Interpolation zwischen der pro-p Iwahori-Heckealgebra einer p-adischen reduktiven Gruppe $G$ und derjenigen einer Leviuntergruppe $M$ von $G$ gedacht werden kann. Für diese Algebren wird ein Induktionsfunktor definiert und eine Transitivitätseigenschaft bewiesen. Dies liefert einen neuen Beweis für die Transitivität der parabolischen Induktion für Moduln über der pro-p Iwahori-Heckealgebra. Ferner wird eine Funktion auf einer parabolischen Untergruppe untersucht, die als Werte nur p-Potenzen annimmt. Es wird gezeigt, dass sie eine Funktion auf der (pro-p) Iwahori-Weylgruppe von $M$ definiert, und dass die so definierte Funktion monoton steigend bzgl. der Bruhat-Ordnung ist und einen Vergleich der Längenfunktionen zwischen der Iwahori-Weylgruppe von $M$ und derjenigen der Iwahori-Weylgruppe von $G$ erlaubt. Im zweiten Teil wird ein allgemeiner Zerlegungssatz für Polynome über der sphärischen (parahorischen) Heckealgebra einer p-adischen reduktiven Gruppe $G$ bewiesen. Diese Zerlegung findet über einer parabolischen Heckealgebra statt, die die Heckealgebra von $G$ enthält. Für den Beweis des Zerlegungssatzes wird vorausgesetzt, dass die gewählte parabolische Untergruppe in einer nichtstumpfen enthalten ist. Des Weiteren werden die nichtstumpfen parabolischen Untergruppen von $G$ klassifiziert.
The first part deals with a new construction of parabolic induction for modules over the pro-p Iwahori-Hecke algebra. This construction exhibits a new class of algebras that can be thought of as an interpolation between the pro-p Iwahori-Hecke algebra of a p-adic reductive group $G$ and the corresponding algebra of a Levi subgroup $M$ of $G$. For these algebras we define a new induction functor and prove a transitivity property. This gives a new proof of the transitivity of parabolic induction for modules over the pro-p Iwahori-Hecke algebra. Further, a function on a parabolic subgroup with p-power values is studied. We show that it induces a function on the (pro-p) Iwahori-Weyl group of $M$, that it is monotonically increasing with respect to the Bruhat order, and that it allows to compare the length function on the Iwahori-Weyl group of $M$ with the one on the Iwahori-Weyl group of $G$. In the second part a general decomposition theorem for polynomials over the spherical (parahoric) Hecke algebra of a p-adic reductive group $G$ is proved. The proof requires that the chosen parabolic subgroup is contained in a non-obtuse one. Moreover, we give a classification of non-obtuse parabolic subgroups of $G$.

3

Gantz, Christian. "On parabolic bundles." Thesis, University of Oxford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.320221.

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4

Boger, D. (Dorin). "Parabolic Springer resolution." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/104605.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2016.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 73-75).
Let G be a reductive group over a field k = k. Let P be a parabolic subgroup. We construct a functor Groupoid ... is a connected space, which induces an action of generalizing a classical result. It is also a part of a study of natural equivalences between ... for P, Q associated parabolic subgroups.
by D. Boger.
Ph. D.

5

Žúrek, Dan. "Nízkoprofilová směrová anténa." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2016. http://www.nusl.cz/ntk/nusl-242122.

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This diploma thesis deals with a study of low-profile directional antennas, followed by design and optimization of parabolic reflector antenna in centimeter and millimeter band. The first part of this work is focused on the analysis of several kinds of directional antennas, mainly on parabolic reflector and on SIW technology, which will be used for final antenna realization. The next part of this project is about the particular concept of the substrate integrated parabolic antenna for 60 GHz ISM band, its simulation and optimization in the CST Microwave Studio software. The final part of this thesis is devoted to the results achieved.

6

Taher, Chadi. "Calculating the parabolic chern character of a locally abelain parabolic bundle : the chern invariants for parabolic bundles at multiple points." Nice, 2011. http://www.theses.fr/2011NICE4013.

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In this thesis we calculate the parabolic Chern character of a bundle with locally abelian parabolic structure on a smooth strict normal crossings divisor, using the definition in terms of Deligne-Mumford stacks. We obtain explicit formulas for ch_1, ch_2 and ch_3, and verify that these correspond to the formulas given by Borne for ch_1 and Mochizuki for ch_2. The second part of the thesis we take D subset in X is a curve with multiple points in a surface, a parabolic bundle defined on (X, D) away from the singularities can be extended in several ways to a parabolic bundle on a resolution of singularities. We investigate the possible parabolic Chern classes for these extensions.

7

Deolmi, Giulia. "Computational Parabolic Inverse Problems." Doctoral thesis, Università degli studi di Padova, 2012. http://hdl.handle.net/11577/3423351.

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This thesis presents a general approach to solve numerically parabolic Inverse Problems, whose underlying mathematical model is discretized using the Finite Element method. The proposed solution is based upon an adaptive parametrization and it is applied specically to a geometric conduction inverse problem of corrosion estimation and to a boundary convection inverse problem of pollution rate estimation.
In questa tesi viene presentato un approccio numerico volto alla risoluzione di problemi inversi parabolici, basato sull'utilizzo di una parametrizzazione adattativa. L'algoritmo risolutivo viene descritto per due specici problemi: mentre il primo consiste nella stima della corrosione di una faccia incognita del dominio, il secondo ha come scopo la quanticazione di inquinante immesso in un fiume.

8

Bauwe, Anne, and Wilfried Grecksch. "A parabolic stochastic differential inclusion." Universitätsbibliothek Chemnitz, 2005. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200501221.

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Stochastic differential inclusions can be considered as a generalisation of stochastic differential equations. In particular a multivalued mapping describes the set of equations, in which a solution has to be found. This paper presents an existence result for a special parabolic stochastic inclusion. The proof is based on the method of upper and lower solutions. In the deterministic case this method was effectively introduced by S. Carl.

9

Baysal, Arzu. "Inverse Problems For Parabolic Equations." Master's thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/12605623/index.pdf.

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In this thesis, we study inverse problems of restoration of the unknown function in a boundary condition, where on the boundary of the domain there is a convective heat exchange with the environment. Besides the temperature of the domain, we seek either the temperature of the environment in Problem I and II, or the coefficient of external boundary heat emission in Problem III and IV. An additional information is given, which is the overdetermination condition, either on the boundary of the domain (in Problem III and IV) or on a time interval (in Problem I and II). If solution of inverse problem exists, then the temperature can be defined everywhere on the domain at all instants. The thesis consists of six chapters. In the first chapter, there is the introduction where the definition and applications of inverse problems are given and definition of the four inverse problems, that we will analyze in this thesis, are stated. In the second chapter, some definitions and theorems which we will use to obtain some conclusions about the corresponding direct problem of our four inverse problems are stated, and the conclusions about direct problem are obtained. In the third, fourth, fifth and sixth chapters we have the analysis of inverse problems I, II, III and IV, respectively.

10

Eberhardt, Jens Niklas [Verfasser], and Wolfgang [Akademischer Betreuer] Soergel. "Graded and geometric parabolic induction." Freiburg : Universität, 2017. http://d-nb.info/113557216X/34.

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Alphonse, Amal. "Parabolic PDEs on evolving spaces." Thesis, University of Warwick, 2016. http://wrap.warwick.ac.uk/77658/.

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This thesis is concerned with the well-posedness of solutions to certain linear and nonlinear parabolic PDEs on evolving spaces. We first present an abstract framework for the formulation and well-posedness of linear parabolic PDEs on abstract evolving Hilbert spaces. We introduce new function spaces and a notion of a weak time derivative called the weak material derivative for this purpose. We apply this general theory to moving hypersurfaces and Sobolev spaces and study four different linear problems including a coupled bulk-surface system and a dynamical boundary problem. Then we formulate a Stefan problem itself on an evolving surface and consider weak solutions given integrable data through the enthalpy approach, using a generalisation to the Banach space setting of the function spaces introduced in the abstract framework. We finish by studying a nonlocal problem: a porous medium equation with a fractional diffusion posed on an evolving surface and we prove well-posedness for bounded initial data.

12

Sa, Ngiamsunthorn Parinya. "Domain perturbation for parabolic equations." Thesis, The University of Sydney, 2011. http://hdl.handle.net/2123/7775.

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We study the effect of domain perturbation on the behaviour of parabolic equations. The first aspect considered in this thesis is the behaviour of solutions under changes of the domain. We show how solutions of linear and semilinear parabolic equations behave as a sequence of domains $\Omega_n$ converges to an open set $\Omega$ in a certain sense. In particular, we are interested in singular domain perturbations so that a change of variables is not possible on these domains. For autonomous linear equations, it is known that convergence of solutions under domain perturbation is closely related to the corresponding elliptic equations via a standard semigroup theory. We show that there is also a relation between domain perturbation for non-autonomous linear parabolic equations and domain perturbation for elliptic equations. The key result for this is the equivalence of Mosco convergences between various closed and convex subsets of Banach spaces. An important consequence is that the same conditions for a sequence of domains imply convergence of solutions under domain perturbation for both parabolic and elliptic equations. By applying variational methods, we obtain the convergence of solutions of initial value problems under Dirichlet or Neumann boundary conditions. A similar technique can be applied to obtain the convergence of weak solutions of parabolic variational inequalities when the underlying convex set is perturbed. Using the linear theory, we then study domain perturbation for initial boundary value problems of semilinear type. We are also interested in the behaviour of bounded entire solutions of parabolic equations defined on the whole real line. We establish a convergence result for bounded entire solutions of linear parabolic equations under $L^2$ and $L^p$-norms. For the $L^p$-theory, we also prove H\"{o}lder regularity of bounded entire solutions with respect to time. In addition, the persistence of some classes of bounded entire solutions is given for semilinear equations using the Leray-Schauder degree theory. The second aspect is to study the dynamics of parabolic equations under domain perturbation. In this part, we consider parabolic equation as a dynamical system in an $L^2$ space and study the stability of invariant manifolds near a stationary solution. In particular, we prove the continuity (upper and lower semicontinuity) of both, the local stable invariant manifolds and the local unstable invariant manifolds under domain perturbation.

13

Floridia, Giuseppe. "Approximate multiplicative controllability for degenerate parabolic problems and regularity properties of elliptic and parabolic systems." Doctoral thesis, Università di Catania, 2012. http://hdl.handle.net/10761/1051.

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This thesis consists of two parts, both related to the theory of parabolic equations and systems. The first part is devoted to control theory which studies the possibility of influencing the evolution of a given system by an external action called control. Here we address approximate controllability problems via multiplicative controls, motivated by our interest in some differential models for the study of climatology. In the second part of the thesis we address regularity issues on the local differentiability and H\"older regularity for weak solutions of nonlinear systems in divergence form. In order to improve readability, the two parts have been organized as completely independent chapters, with two separate introductions and bibliographies. All the new results of this thesis have been presented at conferences and workshops, and most of them appeared or are to appear as research articles in international journals. Related directions for future research are also outlined in body of the work.

14

Lobkova, Tatiana. "Homogenization Results for Parabolic and Hyperbolic-Parabolic Problems and Further Results on Homogenization in Perforated Domains." Licentiate thesis, Mittuniversitetet, Avdelningen för kvalitetsteknik, maskinteknik och matematik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:miun:diva-30683.

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This thesis is based on four papers. The main focus is on homogenization of selected parabolic problems with time oscillations, and hyperbolic-parabolic problems without time oscillations. The approaches are prepared by means of certain methods, such as two-scale convergence, multiscale convergence and evolution multiscale convergence. We also discuss further results on homogenization of evolution problems in perforated domains.

Vid tidpunkten för försvar av avhandlingen var följande delarbeten opublicerade: delarbete 1 inskickat, delarbete 2 accepterat, delarbete 4 inskickat.

At the time of the defence the following papers were unpublished: paper 1 submitted, paper 2 accepted, paper 4 submitted.

15

Yolcu, Türkay. "Parabolic systems and an underlying Lagrangian." Diss., Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29760.

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In this thesis, we extend De Giorgi's interpolation method to a class of parabolic equations which are not gradient flows but possess an entropy functional and an underlying Lagrangian. The new fact in the study is that not only the Lagrangian may depend on spatial variables, but also it does not induce a metric. Assuming the initial condition is a density function, not necessarily smooth, but solely of bounded first moments and finite "entropy", we use a variational scheme to discretize the equation in time and construct approximate solutions. Moreover, De Giorgi's interpolation method is revealed to be a powerful tool for proving convergence of our algorithm. Finally, we analyze uniqueness and stability of our solution in L¹.

16

Rael, Michael Brian. "Results on the Parabolic Anderson Model." Thesis, University of California, Irvine, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=3562176.

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In this dissertation we present various results pertaining to the Parabolic Anderson Model. First we show that the Lyapunov exponent, λ(κ), of the Parabolic Anderson Model in continuous space with Stratonovich differential is O(κ^1/3) near 0. We prove the required upper bound, the lower bound having been proven in (Cranston & Mountford 2006).

Second, we prove the existence of stationary measures for the Parabolic Anderson Model in continuous space with Ito differential. Furthermore, we prove that these measures are associated and determined by the average mass of the initial configuration.

Finally we present progress towards computing the Lyapunov exponent of the Quasi-Stationary Parabolic Anderson Model. We prove a smaller upper bound on λ(κ), improving on the work in (Boldrighini, Molchanov, & Pellegrinotti 2007), but our bound is not sharp. Computing λ(κ) in this model remains an open problem.

17

Yung, Tamara. "Traffic Modelling Using Parabolic Differential Equations." Thesis, Linköpings universitet, Kommunikations- och transportsystem, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-102745.

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The need of a working infrastructure in a city also requires an understanding of how the traffic flows. It is known that increasing number of drivers prolong the travel time and has an environmental effect in larger cities. It also makes it more difficult for commuters and delivery firms to estimate their travel time. To estimate the traffic flow the traffic department can arrange cameras along popular roads and redirect the traffic, but this is a costly method and difficult to implement. Another approach is to apply theories from physics wave theory and mathematics to model the traffic flow; in this way it is less costly and possible to predict the traffic flow as well. This report studies the application of wave theory and expresses the traffic flow as a modified linear differential equation. First is an analytical solution derived to find a feasible solution. Then a numerical approach is done with Taylor expansions and Crank-Nicolson’s method. All is performed in Matlab and compared against measured values of speed and flow retrieved from Swedish traffic department over a 24 hours traffic day. The analysis is performed on a highway stretch outside Stockholm with no entries, exits or curves. By dividing the interval of the highway into shorter equal distances the modified linear traffic model is expressed in a system of equations. The comparison between actual values and calculated values of the traffic density is done with a nominal average difference. The results reveal that the numbers of intervals don’t improve the average difference. As for the small constant that is applied to make the linear model stable is higher than initially considered.

18

Hofmanová, Martina. "Degenerate parabolic stochastic partial differential equations." Phd thesis, École normale supérieure de Cachan - ENS Cachan, 2013. http://tel.archives-ouvertes.fr/tel-00916580.

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In this thesis, we address several problems arising in the study of nondegenerate and degenerate parabolic SPDEs, stochastic hyperbolic conservation laws and SDEs with continues coefficients. In the first part, we are interested in degenerate parabolic SPDEs, adapt the notion of kinetic formulation and kinetic solution and establish existence, uniqueness as well as continuous dependence on initial data. As a preliminary result we obtain regularity of solutions in the nondegenerate case under the hypothesis that all the coefficients are sufficiently smooth and have bounded derivatives. In the second part, we consider hyperbolic conservation laws with stochastic forcing and study their approximations in the sense of Bhatnagar-Gross-Krook. In particular, we describe the conservation laws as a hydrodynamic limit of the stochastic BGK model as the microscopic scale vanishes. In the last part, we provide a new and fairly elementary proof of Skorkhod's classical theorem on existence of weak solutions to SDEs with continuous coefficients satisfying a suitable Lyapunov condition.

19

Dekkers, Sophia Antonia Janna. "Degenerate parabolic equations on Riemannanian manifolds." Thesis, Imperial College London, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.405755.

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20

Blanke, Sarah [Verfasser]. "Quasilinear Elliptic-Parabolic Systems / Sarah Blanke." Berlin : epubli, 2017. http://d-nb.info/1124291873/34.

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21

Parvin, S. "Diffusion-convection problems in parabolic equations." Thesis, University of Manchester, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.382761.

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Ribeiro, Saraiva L. M. "Removable singularities and quasilinear parabolic equations." Thesis, University of Sussex, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.356520.

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23

Elbirki, Asma. "On parabolic equations with gradient terms." Thesis, University of Sussex, 2016. http://sro.sussex.ac.uk/id/eprint/66012/.

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This thesis is concerned with the study of the important effect of the gradient term in parabolic problems. More precisely, we study the global existence or nonexistence of solutions, and their asymptotic behaviour in finite or infinite time. Particularly when the power of the gradient term can increase to the power function of the solution. This thesis consists of five parts. (i) Steady-State Solutions, (ii) The Blow-up Behaviour of the Positive Solutions, (iii) Parabolic Liouville-Type Theorems and the Universal Estimates, (iv) The Global Existence of the Positive Solutions, (v) Viscous Hamilton-Jacobi Equations (VHJ). Under certain conditions on the exponents of both the function of the solution and the gradient term, the nonexistence of positive stationary solution of parabolic problems with gradient terms are proved in (i). In (ii), we extend some known blow-up results of parabolic problems with perturbation terms, which is not too strong, to problems with stronger perturbation terms. In (iii), the nonexistence of nonnegative, nontrivial bounded solutions for all negative and positive times on the whole space are showed for parabolic problems with a strong perturbation term. Moreover, we study the connections between parabolic Liouville-type theorems and local and global properties of nonnegative classical solutions to parabolic problems with gradient terms. Namely, we use a general method for derivation of universal, pointwise a priori estimates of solutions from Liouville type theorems, which unifies the results of a priori bounds, decay estimates and initial and final blow up rates. Global existence and stability, and unbounded global solutions are shown in (iv) when the perturbation term is stronger. In (v) we show that the speed of divergence of gradient blow up (GBU) of solutions of Dirichlet problem for VHJ, especially the upper GBU rate estimate in n space dimensions is the same as in one space dimension.

24

Noppakaew, Passawan. "Parabolic projection and generalized Cox configurations." Thesis, University of Bath, 2014. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.642047.

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Building on the work of Longuet-Higgins in 1972 and Calderbank and Macpherson in 2009, we study the combinatorics of symmetric configurations of hyperplanes and points in projective space, called generalized Cox configurations. To do so, we use the formalism of morphisms between incidence systems. We notice that the combinatorics of Cox configurations are closely related to incidence systems associated to certain Coxeter groups. Furthermore, the incidence geometry of projective space P (V ), where V is a vector space, can be viewed as an incidence system of maximal parabolic subalgebras in a semisimple Lie algebra g, in the special case g = pgl (V ) the projective general linear Lie algebra of V . Using Lie theory, the Coxeter incidence system for the Coxeter group, whose Coxeter diagram is the underlying diagram of the Dynkin diagram of the g, can be embedded into the parabolic incidence system for g. This embedding gives a symmetric geometric configuration which we call a standard parabolic configuration of g. In order to construct a generalized Cox configuration, we project a standard parabolic configuration of type Dn into the parabolic incidence system of projective space using a process called parabolic projection, which maps a parabolic subalgebra of the Lie algebra to a parabolic subalgebra of a lower dimensional Lie algebra. As a consequence of this construction, we obtain Cox configurations and their analogues in higher dimensional projective spaces. We conjecture that the generalized Cox configurations we construct using parabolic projection are nondegenerate and, furthermore, any non-degenerate Cox configuration is obtained in this way. This conjecture yields a formula for the dimension of the space of non-degenerate generalized Cox configurations of a fixed type, which enables us to develop a recursive construction for them. This construction is closely related to Longuet-Higgins’ recursive construction of (generalized) Clifford configurations but our examples are more general and involve the extra parameters.

25

Pang, Huadong. "Parabolic equations without a minimum principle." Thesis, Massachusetts Institute of Technology, 2007. http://hdl.handle.net/1721.1/38958.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2007.
Includes bibliographical references (p. 63-64).
In this thesis, we consider several parabolic equations for which the minimum principle fails. We first consider a two-point boundary value problem for a one dimensional diffusion equation. We show the uniqueness and existence of the solution for initial data, which may not be continuous at two boundary points. We also examine the circumstances when these solutions admit a probabilistic interpretation. Some partial results are given for analogous problems in more than one dimension.
by Huadong Pang.
Ph.D.

26

Byrne, Jesse William. "Multifractal Analysis of Parabolic Rational Maps." Thesis, University of North Texas, 1998. https://digital.library.unt.edu/ark:/67531/metadc278398/.

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The investigation of the multifractal spectrum of the equilibrium measure for a parabolic rational map with a Lipschitz continuous potential, φ, which satisfies sup φ < P(φ) x∈J(T) is conducted. More specifically, the multifractal spectrum or spectrum of singularities, f(α) is studied.

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Yolcu, Türkay. "Parabolic systems and an underlying Lagrangian." Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29760.

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Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2010.
Committee Chair: Gangbo, Wilfrid; Committee Member: Chow, Shui-Nee; Committee Member: Harrell, Evans; Committee Member: Swiech, Andrzej; Committee Member: Yezzi, Anthony Joseph. Part of the SMARTech Electronic Thesis and Dissertation Collection.

28

Crooks, Elaine Craig Mackay. "Travelling-wave solutions for parabolic systems." Thesis, University of Bath, 1996. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.319218.

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Haglund, El Gaidi Sebastian. "Partially Parabolic Wind Turbine Flow Modelling." Thesis, KTH, Mekanik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-226309.

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Climate change is an evermore urging existential treat to the human enterprise. Mean temperature and greenhouse gas emissions have in-creased exponentially since the industrial revolution. But solutions are also mushrooming with exponential pace. Renewable energy technologies, such as wind and solar power, are deployed like never before and their costs have decreased signiﬁcantly. In order to allow for further transformation of the energy system these technologies must be reﬁned and optimised. In wind energy one important ﬁeld with high potential of reﬁnement is aerodynamics. The aerodynamics of wind turbines constitutes one challenging research frontier in aerodynamics today. In this study, a novel approach for calculating wind turbine ﬂow is developed. The approach is based on the partially parabolic Navier-Stokes equations, which can be solved computationally with higher eﬃciency as compared to the fully elliptic version. The modelling of wind turbine thrust is done using actuator-disk theory and the torque is modelled by application of the Joukowsky rotor. A validation of the developed model and force implementation is conducted using four diﬀerent validation cases. In order to provide value for industrial wind energy projects, the model must be extended to account for turbulence (and terrain in case of onshore projects). Possible candidates for turbulence modelling are parabolic k-ε and explicit Reynolds stress turbulence models. The terrain could possibly be incorporated consistently with the used projection method by altering the ﬁnite diﬀerence grid layout.

30

Fontana, Eleonora. "Maximum Principle for Elliptic and Parabolic Equations." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/12061/.

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Nel primo capitolo si riporta il principio del massimo per operatori ellittici. Sarà considerato, in un primo momento, l'operatore di Laplace e, successivamente, gli operatori ellittici del secondo ordine, per i quali si dimostrerà anche il principio del massimo di Hopf. Nel secondo capitolo si affronta il principio del massimo per operatori parabolici e lo si utilizza per dimostrare l'unicità delle soluzioni di problemi ai valori al contorno.

31

Brooks, Michael John. "Performance of a parabolic trough solar collector." Thesis, Link to the online version, 2005. http://hdl.handle.net/10019/984.

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Zacher, Rico. "Quasilinear parabolic problems with nonlinear boundary conditions." [S.l. : s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=969321899.

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Liu, Weian, Yin Yang, and Gang Lu. "Viscosity solutions of fully nonlinear parabolic systems." Universität Potsdam, 2002. http://opus.kobv.de/ubp/volltexte/2008/2621/.

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In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in [2] and [3].

34

Takayama, Yuuya. "Nahm’s equations, quiver varieties and parabolic sheaves." 京都大学 (Kyoto University), 2016. http://hdl.handle.net/2433/204570.

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Keras, Sigitas. "Numerical methods for parabolic partial differential equations." Thesis, University of Cambridge, 1997. https://www.repository.cam.ac.uk/handle/1810/251611.

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36

Tsang, Siu Chung. "Preconditioners for linear parabolic optimal control problems." HKBU Institutional Repository, 2017. https://repository.hkbu.edu.hk/etd_oa/464.

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In this thesis, we consider the computational methods for linear parabolic optimal control problems. We wish to minimize the cost functional while fulfilling the parabolic partial differential equations (PDE) constraint. This type of problems arises in many fields of science and engineering. Since solving such parabolic PDE optimal control problems often lead to a demanding computational cost and time, an effective algorithm is desired. In this research, we focus on the distributed control problems. Three types of cost functional are considered: Target States problems, Tracking problems, and All-time problems. Our major contribution in this research is that we developed a preconditioner for each kind of problems, so our iterative method is accelerated. In chapter 1, we gave a brief introduction to our problems with a literature review. In chapter 2, we demonstrated how to derive the first-order optimality conditions from the parabolic optimal control problems. Afterwards, we showed how to use the shooting method along with the flexible generalized minimal residual to find the solution. In chapter 3, we offered three preconditioners to enhance our shooting method for the problems with symmetric differential operator. Next, in chapter 4, we proposed another three preconditioners to speed up our scheme for the problems with non-symmetric differential operator. Lastly, we have the conclusion and the future development in chapter 5.

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Schwarzacher, Sebastian. "Regularity for degenerate elliptic and parabolic systems." Diss., Ludwig-Maximilians-Universität München, 2013. http://nbn-resolving.de/urn:nbn:de:bvb:19-162092.

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In this work local behavior for solutions to the inhomogeneous p-Laplace in divergence form and its parabolic version are studied. It is parabolic and non-linear generalization of the Calderon-Zygmund theory for the Laplace operator. I.e. the borderline case BMO is studied. The two main results are local BMO and Hoelder estimates for the inhomogenious p-Laplace and the parabolic p-Laplace system. An adaption of some estimates to fluid mechanics, namely on the p-Stokes equation are also proven. The p-Stokes system is a very important physical model for so-called non Newtonian fluids (e.g. blood). For this system BMO and Hoelder estimates are proven in the stationary 2-dimensional case.

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Dyer, Luke Oliver. "Parabolic boundary value problems with rough coefficients." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/33276.

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This thesis is motivated by some of the recent results of the solvability of elliptic PDE in Lipschitz domains and the relationships between the solvability of different boundary value problems. The parabolic setting has received less attention, in part due to the time irreversibility of the equation and difficulties in defining the appropriate analogous time-varying domain. Here we study the solvability of boundary value problems for second order linear parabolic PDE in time-varying domains, prove two main results and clarify the literature on time-varying domains. The first result shows a relationship between the regularity and Dirichlet boundary value problems for parabolic equations of the form Lu = div(A∇u)−ut = 0 in Lip(1, 1/2) time-varying cylinders, where the coefficient matrix A = [aij(X, t)] is uniformly elliptic and bounded. We show that if the Regularity problem (R)p for the equation Lu = 0 is solvable for some 1 < p < then the Dirichlet problem (D*) 1 p, for the adjoint equation L*v = 0 is also solvable, where p' = p/(p − 1). This result is analogous to the one established in the elliptic case. In the second result we prove the solvability of the parabolic Lp Dirichlet boundary value problem for 1 < p ≤ ∞ for a PDE of the form ut = div(A∇u)+B ·∇u on time-varying domains where the coefficients A = [aij(X, t)] and B = [bi(X, t)] satisfy a small Carleson condition. This result brings the state of affairs in the parabolic setting up to the current elliptic standard. Furthermore, we establish that if the coefficients of the operator A and B satisfy a vanishing Carleson condition, and the time-varying domain is of VMO-type then the parabolic Lp Dirichlet boundary value problem is solvable for all 1 < p ≤ ∞. This is related to elliptic results where the normal of the boundary of the domain is in VMO or near VMO implies the invertibility of certain boundary operators in Lp for all 1 < p < ∞. This then (using the method of layer potentials) implies solvability of the Lp boundary value problem in the same range for certain elliptic PDE. We do not use the method of layer potentials, since the coefficients we consider are too rough to use this technique but remarkably we recover Lp solvability in the full range of p's as the elliptic case. Moreover, to achieve this result we give new equivalent and localisable definitions of the appropriate time-varying domains.

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Ravotti, Davide. "Mixing via shearing in some parabolic flows." Thesis, University of Bristol, 2018. http://hdl.handle.net/1983/3223f101-f30e-4877-b4e5-07be52945a9d.

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Parabolic flows are slowly chaotic flows for which nearby trajectories diverge polynomially in time. Examples of smooth parabolic flows are unipotent flows on semisimple Lie groups and nilflows on nilmanifolds, which are both well-understood. Beyond the homogeneous set-up, however, very little is known for generic smooth parabolic flows and a general theory about their ergodic properties is missing. In this thesis, we study three classes of smooth, non-homogeneous parabolic flows and we show how a common geometric shearing mechanism can be exploited to prove mixing. We first establish a quantitative mixing result in the setting of locally Hamiltonian flows on compact surfaces. More precisely, given a compact surface with a smooth area form, we consider an open and dense set of locally Hamiltonian flows which admit at least one saddle loop homologous to zero and we prove that the restriction to any minimal component of typical such flows is mixing. We provide an estimate of the speed of the decay of correlations for a class of smooth observables. We then focus on perturbations of homogeneous flows. We study time-changes of quasi-abelian filiform nilflows, which are nilflows on a class of higher dimensional nilmanifolds. We prove that, within a dense set of time-changes of any uniquely ergodic quasi-abelian filiform nilflow, mixing occurs for any time-change which is not cohomologous to a constant, and we exhibit a dense set of explicit mixing examples. Finally, we construct a new class of perturbations of unipotent flows in compact quotients of SL(3,R) which are not time-changes and we prove that, if they preserve a measure equivalent to Haar, then they are ergodic and, in fact, mixing.

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Abdul, Kadhim Rasheed Maan. "On blow-up solutions of parabolic problems." Thesis, University of Sussex, 2012. http://sro.sussex.ac.uk/id/eprint/42740/.

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This thesis is concerned with the study of the Blow-up phenomena for parabolic problems, which can be defined in a basic way as the inability to continue the solutions up to or after a finite time, the so called blow-up time. Namely, we consider the blow-up location in space and its rate estimates, for special cases of the following types of problems: (i) Dirichlet problems for semilinear equations, (ii) Neumann problems for heat equations, (iii) Neumann problems for semilinear equations, (iv) Dirichlet (Cauchy) problems for semilinear equations with gradient terms. For problems of type (i), (ii), we extend some known blow-up results of parabolic problems with power and exponential type nonlinearities to problems with nonlinear terms, which grow faster than these types of functions for large values of solutions. Moreover, under certain conditions, some blow-up results of the single semilinear heat equation are extended to the coupled systems of two semilinear heat equations. For problems of type (iii), we study how the reaction terms and the nonlinear boundary terms affect the blow-up properties of the blow-up solutions of these problems. The noninuence of the gradient terms on the blow-up bounds is showed for problems of type (iv).

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Sabawi, Mohammad Abd Moheemmeed. "Discontinuous Galerkin timestepping for nonlinear parabolic problems." Thesis, University of Leicester, 2018. http://hdl.handle.net/2381/41216.

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We study space–time finite element methods for semilinear parabolic problems in (1 + d)–dimensions for d = 2, 3. The discretisation in time is based on the discontinuous Galerkin timestepping method with implicit treatment of the linear terms and either implicit or explicit multistep discretisation of the zeroth order nonlinear reaction terms. Conforming finite element methods are used for the space discretisation. For this implicit-explicit IMEX–dG family of methods, we derive a posteriori and a priori energy-type error bounds and we perform extended numerical experiments. We derive a novel hp–version a posteriori error bounds in the L∞(L2) and L2(H1) norms assuming an only locally Lipschitz growth condition for the nonlinear reactions and no monotonicity of the nonlinear terms. The analysis builds upon the recent work in [60], for the respective linear problem, which is in turn based on combining the elliptic and dG reconstructions in [83, 84] and continuation argument. The a posteriori error bounds appear to be of optimal order and efficient in a series of numerical experiments. Secondly, we prove a novel hp–version a priori error bounds for the fully–discrete IMEX–dG timestepping schemes in the same setting in L∞(L2) and L2(H1) norms. These error bounds are explicit with respect to both the temporal and spatial meshsizes kn and h, respectively, and, where possible, with respect to the possibly varying temporal polynomial degree r. The a priori error estimates are derived using the elliptic projection technique with an inf-sup argument in time. Standard tools such as Grönwall inequality and discrete stability estimates for fully discrete semilinear parabolic problems with merely locally-Lipschitz continuous nonlinear reaction terms are used. The a priori analysis extends the applicability of the results from [52] to this setting with low regularity. The results are tested by an extensive set of numerical experiments.

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Sande, Olow. "Boundary Estimates for Solutions to Parabolic Equations." Doctoral thesis, Uppsala universitet, Matematiska institutionen, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-281451.

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This thesis concerns the boundary behavior of solutions to parabolic equations. It consists of a comprehensive summary and four scientific papers. The equations concerned are different generalizations of the heat equation. Paper I concerns the solutions to non-linear parabolic equations with linear growth. For non-negative solutions that vanish continuously on the lateral boundary of an NTA cylinder the following main results are established: a backward Harnack inequality, the doubling property for the Riesz measure associated with such solutions, and the Hölder continuityof the quotient of two such solutions up to the boundary. Paper 2 concerns the solutions to linear degenerate parabolic equations, where the degeneracy is controlled by a Muckenhoupt weight of class 1+2/n. For non-negative solutions that vanish continuously on the lateral boundary of an NTA cylinder the following main results are established: a backward Harnack inequality, the doubling property for the parabolic measure, and the Hölder continuity of the quotient of two such solutions up to the boundary. Paper 3 concerns a fractional heat equation. The first main result is that a solution to the fractional heat equation in Euclidean space of dimension n can be extended as a solution to a certain linear degenerate parabolic equation in the upper half space of dimension n+1. The second main result is the Hölder continuity of quotients of two non-negative solutions that vanish continuously on the latteral boundary of a Lipschitz domain. Paper 4 concerns the solutions to uniformly parabolic linear equations with complex coefficients. The first main result is that under certain assumptions on the opperator the bounds for the single layer potentials associated to the opperator are bounded. The second main result is that these bounds always hold if the opperator is realvalued and symmetric.

43

Nocker, Andreas. "Optimization of hydraulic drives for parabolic troughs." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2016. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-200579.

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HAWE Hydraulic SE, Munich, engineers and manufactures hydraulic drives (CSP-drives) for parabolic trough plants consisting of a compact power pack, directional and control valves, over-center valves, two cylinders and the fittings/hoses for connecting these components. Optional, but this is depending on the system and the control philosophy, also a hydralic accumulator. An optimized hydraulic drive for a parabolic trough field makes the power plant operator profit from savings at components, higher system efficiency, lower operational energy supply needs, less time spent on commissioning and first start-up, lower maintenance effort and increased life span of the drive and finally also savings on peripheral and safety devices. Many of shown proposals are even combining two or more of above mentioned advantages.

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Lacombe, Octavio Lima Mendes. "O espaço em camadas de parabolic people." [s.n.], 1998. http://repositorio.unicamp.br/jspui/handle/REPOSIP/284294.

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Orientador: Fernão Pessoa Ramos
Dissertação (mestrado) - Universidade Estadual de Campinas. Instituto de Artes
Made available in DSpace on 2018-07-23T21:30:44Z (GMT). No. of bitstreams: 1 Lacombe_OctavioLimaMendes_M.pdf: 9053988 bytes, checksum: bbed69b70751ddc837206adf2a800f02 (MD5) Previous issue date: 1998
Resumo: Esta dissertação de mestrado trata de questões relativas ao vídeo e a videoarte, levantadas a partir da obra da autora carioca Sandra Kogut. Aborda a constituição da imagem vídeo e seu espaço e a condição da videoarte. Analisa a trajetória da obra de Sandra Kogut e centra-se no estudo de um de seus trabalhos: Parabolic People. A partir deste, propõe relações com o cubismo e com a metrópole: sua imagem, seu espaço e sua poética
Abstract: This disserationdeals with issues related to the video and videoart, raised from the works of Sandra Kogut. It dwells on the constitution of video image and its space and the videoart condition. Analise Sandra kogut¿s trajectory and centers on the study of one of her works: Parabolic People. From this work, proposes relations with the cubism and with the metropolis: its image, its space and its poetic
Mestrado
Mestre em Multimeios

45

Sockell, Michael Elliot. "Similarity solutions of stochastic nonlinear parabolic equations." Diss., Virginia Polytechnic Institute and State University, 1987. http://hdl.handle.net/10919/49898.

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A novel statistical technique introduced by Besieris is used to study solutions of the nonlinear stochastic complex parabolic equation in the presence of two profiles. Specifically, the randomly modulated linear potential and the randomly perturbed quadratic focusing medium. In the former, a class of solutions is shown to admit an exact statistical description in terms of the moments of the wave function. In the latter, all even-order moments are computed exactly, whereas the odd-order moments are solved asymptotically. Lastly, it is shown that this statistical technique is isomorphic to mappings of nonconstant coefficient partial differential equations to constant coefficient equations. A generalization of this mapping and its inherent restrictions are discussed.
Ph. D.
incomplete_metadata

46

Petitta, Francesco. "Nonlinear parabolic equations with general measure data." Doctoral thesis, La Sapienza, 2006. http://hdl.handle.net/11573/917105.

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Žák, Ondřej. "Konstrukční návrh nesymetrické parabolické pružiny." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2018. http://www.nusl.cz/ntk/nusl-377480.

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This thesis is focused on design of parabolic spring for a truck. Characteristics of the spring are designed with respect to loads during heavy braking. Thesis contains a brief summary of current truck suspension, the spring design and suggestion for testing methodology for longitudinal load.

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Procházka, Petr. "Planární parabolická reflektorová anténa." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2015. http://www.nusl.cz/ntk/nusl-221223.

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This master's thesis deals with a design of a planar parabolic reflector antenna. The thesis is divided into several parts. The first section is dedicated to the theory of the parabolic antenna design and a basic introduction of the SIW technology which is used for the realization of an antenna prototype. The second chapter deals with the design of individual parts of the antenna (i. e. a primary and secondary reflector and an antenna feeder excited by a waveguide) for particular assignment. The third part is focused on modeling the designed antenna using ANSYS HFSS. Other parts of the thesis include a conversion of the proposed antenna to the SIW technology and a design of a transition between the antenna and a feeding waveguide WR15. The last part of the thesis deals with measuring of the reflection coefficient and the radiation pattern of the fabricated antenna prototype.

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Heyer, Claudius [Verfasser], Elmar [Gutachter] Große-Klönne, Peter [Gutachter] Schneider, and Fabian [Gutachter] Januszewski. "Applications of parabolic Hecke algebras: parabolic induction and Hecke polynomials / Claudius Heyer ; Gutachter: Elmar Große-Klönne, Peter Schneider, Fabian Januszewski." Berlin : Humboldt-Universität zu Berlin, 2019. http://d-nb.info/1190641402/34.

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Williams, J. F. "Scaling and singularities in higher-order nonlinear differential equations." Thesis, University of Bath, 2003. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.275878.

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Dissertations / Theses on the topic 'Parabolic'

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