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Dissertations / Theses on the topic 'Mathematics, formulae'

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Published: 4 June 2021

Last updated: 30 July 2024

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1

Witt, Ingo. "Green formulae for cone differential operators." Universität Potsdam, 2003. http://opus.kobv.de/ubp/volltexte/2008/2663/.

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Green formulae for elliptic cone differential operators are established. This is achieved by an accurate description of the maximal domain of an elliptic cone differential operator and its formal adjoint; thereby utilizing the concept of a discrete asymptotic type. From this description, the singular coefficients replacing the boundary traces in classical Green formulas are deduced.

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2

Gorokhovsky, Alexander. "Explicit formulae for characteristic classes in Noncommutative Geometry /." The Ohio State University, 1999. http://rave.ohiolink.edu/etdc/view?acc_num=osu1488191124570879.

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3

Small, Anthony James. "A twistorial interpretation of the Weierstrass representation formulae." Thesis, University of Warwick, 1988. http://wrap.warwick.ac.uk/34811/.

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The theory of minimal surfaces represents an important chapter in the study of global analysis and remains a testing ground for our understanding of the non-linear partial differential equations of geometry. Perhaps its greatest charm lies in its mercurial avoidance of isolation. Today we see profound applications to such diverse fields as 3-manifold topology and non-abelian gauge theory, to name two ; see [En] for a recent survey and extensive bibliography. (Very recently there have been exciting new applications of the theory of periodic minimal surfaces in 30 to crystallography, see [T&A&H&H].) Consequently, the principal aim of this thesis, which is to establish the groundwork for the investigation of new interactions between minimal surface theory in V, algebraic geometry and soliton theory, see §4.F, is very much in the traditional spirit of the subject.

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4

Deka, Rabin. "Formulae and multiprocessor algorithms for digital signal microprocessors." Thesis, University of Bradford, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.304030.

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5

Sharp, Richard John. "Asymptotic formulae for closed orbits of hyperbolic flows." Thesis, University of Warwick, 1990. http://wrap.warwick.ac.uk/107982/.

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This thesis consists of three chapters and an appendix each with its own notation and references. Chapter 0 is an introduction which sets out the definitions and results needed in the main part of the thesis. In Chapter 1 we prove an analogue of Mertens' theorem of prime number theory for the closed orbits of an Axiom A flow (restricted to a non-trivial basic set). A similar result is established for the geodesic flow on a non-compact, finite area surface of constant negative curvature. Applying this result to the modular suface yields some asymptotic formulae concerning quadratic forms. In Chapter 2 we give a new proof of an asymptotic formula for the number of closed orbits of a weak-mixing Axiom A flow subject to certain constaints due to S. Lalley. We extend this result to cover the case of finite group extensions and, for transitive Anosov flows, give an application to homology. We also discuss asymptotics for closed orbits in a fixed homology class, extending a result of A. Katsuda and T. Sunada. The appendix, which is included for completeness, is an account of the proof of a technical result of A. Katsuda and T. Sunada which is used extensively in Chapter 2.

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6

Dehkordi, Massoud Hadian. "Asymptotic formulae for some arithmetic functions in number theory." Thesis, Loughborough University, 1998. https://dspace.lboro.ac.uk/2134/12177.

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This thesis gives some asymptotic formulae associated with some non-negative multiplicative functions, and introduce a new method for proof of some classical formulae in number theory using the Laplace transform.

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7

Andersson, Johan. "Summation formulae and zeta functions." Doctoral thesis, Stockholm : Department of Mathematics, Stockholm University, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-1074.

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8

Hostetter, Michael. "Analogical representation in temporal, spatial, and mnemonic reasoning." Thesis, This resource online, 1990. http://scholar.lib.vt.edu/theses/available/etd-03242009-040545/.

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9

Abdulla, Thuraya J. A. M. "Modified extended backward differentiation formulae for differential-algebraic equations with applications to time dependent PDEs." Thesis, Imperial College London, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.369071.

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10

Murr, Rüdiger. "Reciprocal classes of Markov processes : an approach with duality formulae." Phd thesis, Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2012/6209/.

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This work is concerned with the characterization of certain classes of stochastic processes via duality formulae. In particular we consider reciprocal processes with jumps, a subject up to now neglected in the literature. In the first part we introduce a new formulation of a characterization of processes with independent increments. This characterization is based on a duality formula satisfied by processes with infinitely divisible increments, in particular Lévy processes, which is well known in Malliavin calculus. We obtain two new methods to prove this duality formula, which are not based on the chaos decomposition of the space of square-integrable function- als. One of these methods uses a formula of partial integration that characterizes infinitely divisible random vectors. In this context, our characterization is a generalization of Stein’s lemma for Gaussian random variables and Chen’s lemma for Poisson random variables. The generality of our approach permits us to derive a characterization of infinitely divisible random measures. The second part of this work focuses on the study of the reciprocal classes of Markov processes with and without jumps and their characterization. We start with a resume of already existing results concerning the reciprocal classes of Brownian diffusions as solutions of duality formulae. As a new contribution, we show that the duality formula satisfied by elements of the reciprocal class of a Brownian diffusion has a physical interpretation as a stochastic Newton equation of motion. Thus we are able to connect the results of characterizations via duality formulae with the theory of stochastic mechanics by our interpretation, and to stochastic optimal control theory by the mathematical approach. As an application we are able to prove an invariance property of the reciprocal class of a Brownian diffusion under time reversal. In the context of pure jump processes we derive the following new results. We describe the reciprocal classes of Markov counting processes, also called unit jump processes, and obtain a characterization of the associated reciprocal class via a duality formula. This formula contains as key terms a stochastic derivative, a compensated stochastic integral and an invariant of the reciprocal class. Moreover we present an interpretation of the characterization of a reciprocal class in the context of stochastic optimal control of unit jump processes. As a further application we show that the reciprocal class of a Markov counting process has an invariance property under time reversal. Some of these results are extendable to the setting of pure jump processes, that is, we admit different jump-sizes. In particular, we show that the reciprocal classes of Markov jump processes can be compared using reciprocal invariants. A characterization of the reciprocal class of compound Poisson processes via a duality formula is possible under the assumption that the jump-sizes of the process are incommensurable.
Diese Arbeit befasst sich mit der Charakterisierung von Klassen stochastischer Prozesse durch Dualitätsformeln. Es wird insbesondere der in der Literatur bisher unbehandelte Fall reziproker Klassen stochastischer Prozesse mit Sprungen untersucht. Im ersten Teil stellen wir eine neue Formulierung einer Charakterisierung von Prozessen mit unabhängigen Zuwächsen vor. Diese basiert auf der aus dem Malliavinkalkül bekannten Dualitätsformel für Prozesse mit unendlich oft teilbaren Zuwächsen. Wir präsentieren zusätzlich zwei neue Beweismethoden dieser Dualitätsformel, die nicht auf der Chaoszerlegung des Raumes quadratintegrabler Funktionale beruhen. Eine dieser Methoden basiert auf einer partiellen Integrationsformel fur unendlich oft teilbare Zufallsvektoren. In diesem Rahmen ist unsere Charakterisierung eine Verallgemeinerung des Lemma fur Gaußsche Zufallsvariablen von Stein und des Lemma fur Zufallsvariablen mit Poissonverteilung von Chen. Die Allgemeinheit dieser Methode erlaubt uns durch einen ähnlichen Zugang die Charakterisierung unendlich oft teilbarer Zufallsmaße. Im zweiten Teil der Arbeit konzentrieren wir uns auf die Charakterisierung reziproker Klassen ausgewählter Markovprozesse durch Dualitätsformeln. Wir beginnen mit einer Zusammenfassung bereits existierender Ergebnisse zu den reziproken Klassen Brownscher Bewegungen mit Drift. Es ist uns möglich die Charakterisierung solcher reziproken Klassen durch eine Dualitätsformel physikalisch umzudeuten in eine Newtonsche Gleichung. Damit gelingt uns ein Brückenschlag zwischen derartigen Charakterisierungsergebnissen und der Theorie stochastischer Mechanik durch den Interpretationsansatz, sowie der Theorie stochastischer optimaler Steuerung durch den mathematischen Ansatz. Unter Verwendung der Charakterisierung reziproker Klassen durch Dualitätsformeln beweisen wir weiterhin eine Invarianzeigenschaft der reziproken Klasse Browscher Bewegungen mit Drift unter Zeitumkehrung. Es gelingt uns weiterhin neue Resultate im Rahmen reiner Sprungprozesse zu beweisen. Wir beschreiben reziproke Klassen Markovscher Zählprozesse, d.h. Sprungprozesse mit Sprunghöhe eins, und erhalten eine Charakterisierung der reziproken Klasse vermöge einer Dualitätsformel. Diese beinhaltet als Schlüsselterme eine stochastische Ableitung nach den Sprungzeiten, ein kompensiertes stochastisches Integral und eine Invariante der reziproken Klasse. Wir präsentieren außerdem eine Interpretation der Charakterisierung einer reziproken Klasse im Rahmen der stochastischen Steuerungstheorie. Als weitere Anwendung beweisen wir eine Invarianzeigenschaft der reziproken Klasse Markovscher Zählprozesse unter Zeitumkehrung. Einige dieser Ergebnisse werden fur reine Sprungprozesse mit unterschiedlichen Sprunghöhen verallgemeinert. Insbesondere zeigen wir, dass die reziproken Klassen Markovscher Sprungprozesse vermöge reziproker Invarianten unterschieden werden können. Eine Charakterisierung der reziproken Klasse zusammengesetzter Poissonprozesse durch eine Dualitätsformel gelingt unter der Annahme inkommensurabler Sprunghöhen.

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11

Chau, Teresa C. "IFE, an interactive formula editor." FIU Digital Commons, 1988. http://digitalcommons.fiu.edu/etd/2117.

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IFE, the Interactive Formula Editor is an experimental system designed, developed and implemented to propose a different approach to handle mathematical formulae. Its main characteristics are: (1) Interactive creation and edition of a mathematical formula, (2) Tex-form output for a printed version of a formula, and (3) Ability to generate a new set of characters by means of a character editor. Mathematical symbols are provided and adjusted by the system, automatically. The system also, guides the user during the formula description because it knows the syntax of the graphical representation. The system seems to be complete and perform well. The listing of the program is included, as are suggestions for further development.

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12

Giraud, François. "Analyse des modèles particulaires de Feynman-Kac et application à la résolution de problèmes inverses en électromagnétisme." Phd thesis, Université Sciences et Technologies - Bordeaux I, 2013. http://tel.archives-ouvertes.fr/tel-00834920.

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Dans une première partie théorique, nous nous penchons sur une analyse rigoureuse des performances de l'algorithme Sequential Monte Carlo (SMC) conduisant à des résultats de type bornes L^p et inégalités de concentration. Nous abordons notamment le cas particulier des SMC associés à des schémas de température, et analysons sur ce sujet un processus à schéma adaptatif.Dans une seconde partie appliquée, nous illustrons son utilisation par la résolution de problèmes inverses concrets en électromagnétisme. Le plus important d'entre eux consiste à estimer les propriétés radioélectriques de matériaux recouvrant un objet de géométrie connue, et cela à partir de mesures de champs rétrodiffusés. Nous montrons comment l'algorithme SMC, couplé à des calculs analytiques, permet une inversion bayésienne, et fournit des estimées robustes enrichies d'estimations des incertitudes.

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13

Mwangota, Lutufyo. "Cubature on Wiener Space for the Heath--Jarrow--Morton framework." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-42804.

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This thesis established the cubature method developed by Gyurkó & Lyons (2010) and Lyons & Victor (2004) for the Heath–Jarrow–Morton (HJM) model. The HJM model was first proposed by Heath, Jarrow, and Morton (1992) to model the evolution of interest rates through the dynamics of the forward rate curve. These dynamics are described by an infinite-dimensional stochastic equation with the whole forward rate curve as a state variable. To construct the cubature method, we first discretize the infinite dimensional HJM equation and thereafter apply stochastic Taylor expansion to obtain cubature formulae. We further used their results to construct cubature formulae to degree 3, 5, 7 and 9 in 1-dimensional space. We give, a considerable step by step calculation regarding construction of cubature formulae on Wiener space.

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14

Freiman, Viktor, and Danis Michaud. "One mathematical formula in the science textbook: looking into innovative potential of interdisciplinary mathematics teaching." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-79834.

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Our paper presents some preliminary observation from a collaborative exploratory study linking mathematics, science and reading within a technology enhanced problem-based learning scenario conducted at one French Canadian Elementary and Middle School. Presented in a form of dialogue between teacher and researcher, our findings give some meaningful insight in how an innovative mathematics teaching can be developed and implemented using a real-world problem solving. Instead of a traditional presentation of material about lighting up homes, participating mathematics, science and French teachers were working collaboratively with the ICT integration mentor and two university professors helping students investigate a problem from various perspectives using a variety of cognitive and metacognitive strategies, discussing and sharing the finding with peers and presenting them to a larger audience using media tools. Our preliminary results may prompt further investigation of how innovation in teaching and learning can help students become better critical thinkers and scientifically empowered citizens.

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15

Silva, Ana M. L. G. Canas da. "Multiplicity formulas for orbifolds." Thesis, Massachusetts Institute of Technology, 1996. http://hdl.handle.net/1721.1/38409.

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16

Almomen, Randa. "Context classification for improved semantic understanding of mathematical formulae." Thesis, University of Birmingham, 2018. http://etheses.bham.ac.uk//id/eprint/8611/.

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The correct semantic interpretation of mathematical formulae in electronic mathematical documents is an important prerequisite for advanced tasks such as search, accessibility or computational processing. Especially in advanced maths, the meaning of characters and symbols is highly domain dependent, and only limited information can be gained from considering individual formulae and their structures. Although many approaches have been proposed for semantic interpretation of mathematical formulae, most of them rely on the limited semantics from maths representation languages whereas very few use maths context as a source of information. This thesis presents a novel approach for principal extraction of semantic information of mathematical formulae from their context in documents. We utilised different supervised machine learning (SML) techniques (i.e. Linear-Chain Conditional Random Fields (CRF), Maximum Entropy (MaxEnt) and Maximum Entropy Markov Models (MEMM) combined with Rprop- and Rprop+ optimisation algorithms) to detect definitions of simple and compound mathematical expressions, thereby deriving their meaning. The learning algorithms demand annotated corpus which its development considered as one of this thesis contributions. The corpus has been developed utilising a novel approach to extract desired maths expressions and sub-formulae and manually annotated by two independent annotators employing a standard measure for inter-annotation agreement. The thesis further developed a new approach to feature representation depending on the definitions' templates that extracted from maths documents to defeat the restraint of conventional window-based features. All contributions were evaluated by various techniques including employing the common metrics recall, precision, and harmonic F-measure.

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17

Hendricks, Deborah J. "The use of propositional structures and subgoals in solving multi-step college statistical word and formula problems." Morgantown, W. Va. : [West Virginia University Libraries], 1999. http://etd.wvu.edu/templates/showETD.cfm?recnum=531.

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Thesis (Ed. D.)--West Virginia University, 1999.
Title from document title page. Document formatted into pages; contains viii, 142 p. : ill. Vita. Includes abstract. Includes bibliographical references (p. 100-108).

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18

Duerinckx, Mitia. "Topics in the mathematics of disordered media." Doctoral thesis, Universite Libre de Bruxelles, 2017. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/262390.

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Cette thèse est consacrée à l’étude mathématique des effets de désordre dans divers systèmes physiques. On commence par trois problèmes d’homogénéisation stochastique en lien avec des questions statiques de physique classique. Premièrement, en vue de la déduction rigoureuse de l’élasticité non-linéaire à partir de la physique statistique de réseaux de chaînes de polymères, on établit l’existence de propriétés effectives pour des matériaux hyperélastiques hétérogènes aléatoires sous des hypothèses générales de croissance. Deuxièmement, dans un cadre linéarisé simplifié, on étudie les formules de Clausius-Mossotti pour les propriétés effectives d’alliages binaires dilués: on donne la première preuve générale et rigoureuse de ces formules, ainsi qu’une extension aux ordres supérieurs. Troisièmement, encore pour des systèmes linéarisés, on propose d’étudier les déviations par rapport aux propriétés effectives et on établit la première théorie générale des fluctuations en homogénéisation stochastique. Dans la seconde partie de cette thèse, on se focalise sur la compétition entre désordre et interactions, et on étudie plus particulièrement la dynamique des vortex de Ginzburg-Landau dans des supraconducteurs 2D de type II en présence d’impuretés. Bien que la compréhension mathématique des propriétés vitreuses complexes de ces systèmes semble hors de portée, on établit rigoureusement la limite de champ moyen pour la dynamique d’un grand nombre de vortex, et on étudie l’homogénéisation de ces équations limites et leurs propriétés.
Doctorat en Sciences
info:eu-repo/semantics/nonPublished

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19

Duduchava, Roland. "The Green formula and layer potentials." Universität Potsdam, 1999. http://opus.kobv.de/ubp/volltexte/2008/2560/.

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The Green formula is proved for boundary value problems (BVPs), when "basic" operator is arbitrary partial differential operator with variable matrix coefficients and "boundary" operators are quasi-normal with vector-coeficients. If the system possesses the fundamental solution, representation formula for a solution is derived and boundedness properties of participating layer potentials from function spaces on the boundary (Besov, Zygmund spaces) into appropriate weighted function spaces on the inner and the outer domains are established. Some related problems are discussed in conclusion: traces of functions from weighted spaces, traces of potential-type functions, Plemelji formulae,Calderón projections, restricted smoothness of the underlying surface and coefficients. The results have essential applications in investigations of BVPs by the potential method, in apriori estimates and in asymptotics of solutions.

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20

Reyes, Noli N. "An asymptotic formula in best approximation /." The Ohio State University, 1992. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487760357819651.

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21

Tsai, Cheng-Chiang. "A Formula for Some Shalika Germs." Thesis, Harvard University, 2015. http://nrs.harvard.edu/urn-3:HUL.InstRepos:17467210.

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In this article, for nilpotent orbits in (the Lie algebras of) ramified quasi-split unitary groups with two Jordan blocks, we give the values of their Shalika germs at certain equi-valued elements with half-integral depth previously studied by Hales. These elements are parametrized by hyperelliptic curves defined over the residue field, and the values we obtain can be expressed in terms of Frobenius eigenvalues on the l-adic H^1 of the curves, generalizing previous result of Hales on stable subregular Shalika germs. Using the Shalika germ formulas, we obtain some new results on stability and endoscopic transfer of nilpotent orbital integrals.
Mathematics

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22

Böhm, Ulrike, Gesche Pospiech, Hermann Körndle, and Susanne Narciss. "Physicists use mathematics to describe physical principles an mathematicians use physical phenomena to illustrate mathematical formula - Do they really mean the same?" Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-82341.

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23

Ganter, Nora 1976. "Orbifold genera, product formulas and power operations." Thesis, Massachusetts Institute of Technology, 2004. http://hdl.handle.net/1721.1/30147.

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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2004.
Includes bibliographical references (p. 53-56).
There is a formula by the string theorists Dijkgraaf, Moore, Verlinde and Verlinde, expressing the orbifold elliptic genus of the symmetric powers of an almost complex manifold M in terms of the elliptic genus of M itself. We show that from the point of view of elliptic cohomology an analogous p-typical statement follows as an easy corollary from the fact that the map of spectra corresponding to the genus preserves power operations. We define higher chromatic versions of the notion of orbifold genus, involving h-tuples rather than pairs of commuting elements. Using homotopy theoretic methods we are able to prove an integrality result and show that our definition is independent of the representation of the orbifold. Our setup is so simple, that it allows us to prove DMVV-type product formulas for these higher chromatic orbifold genera in the same way that the product formula for the topological Todd genus is proved. More precisely, we show that any genus induced by an H[omega]-map into one of the Morava-Lubin-Tate cohomology theories Eh has such a product formula and that the formula depends only on h and not on the genus. Since the complex H[omega]-genera into Eh have been classified in [And95], a large family of genera to which our results apply is completely understood. Loosely speaking, our result says that some Borcherds lifts have a well-known homotopy theoretic refinement, namely total symmetric powers in elliptic cohomology.
by Nora Ganter.
Ph.D.

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24

Kytmanov, Alexander, Simona Myslivets, and Nikolai Tarkhanov. "Holomorphic Lefschetz formula for manifolds with boundary." Universität Potsdam, 2002. http://opus.kobv.de/ubp/volltexte/2008/2635/.

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The classical Lefschetz fixed point formula expresses the number of fixed points of a continuous map f : M -> M in terms of the transformation induced by f on the cohomology of M. In 1966 Atiyah and Bott extended this formula to elliptic complexes over a compact closed manifold. In particular, they presented a holomorphic Lefschtz formula for compact complex manifolds without boundary, a result, in the framework of algebraic geometry due to Eichler (1957) for holomorphic curves. On compact complex manifolds with boundary the Dolbeault complex is not elliptic, hence the Atiyah-Bott theory is no longer applicable. To get rid of the difficulties related to the boundary behaviour of the Dolbeault cohomology, Donelli and Fefferman (1986) derived a fixed point formula for the Bergman metric. The purpose of this paper is to present a holomorphic Lefschtz formula on a compact complex manifold with boundary

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25

Williams, Ellison Anne. "A Formula for N-Row Macdonald Polynomials." NCSU, 2004. http://www.lib.ncsu.edu/theses/available/etd-01272004-104704/.

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26

Pedroza, Andrés. "Equivariant formality and localization formulas /." Thesis, Connect to Dissertations & Theses @ Tufts University, 2004.

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Thesis (Ph.D.)--Tufts University, 2004.
Adviser: Loring W. Tu. Submitted to the Dept. of Mathematics. Includes bibliographical references (leaves 43-45). Access restricted to members of the Tufts University community. Also available via the World Wide Web;

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27

Tarkhanov, Nikolai. "A fixed point formula in one complex variable." Universität Potsdam, 2003. http://opus.kobv.de/ubp/volltexte/2008/2649/.

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We show a Lefschetz fixed point formula for holomorphic functions in a bounded domain D with smooth boundary in the complex plane. To introduce the Lefschetz number for a holomorphic map of D, we make use of the Bergman kernal of this domain. The Lefschetz number is proved to be the sum of usual contributions of fixed points of the map in D and contributions of boundary fixed points, these latter being different for attracting and repulsing fixed points.

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28

Culler, Lucas Howard. "The blowup formula for higher rank Donaldson invariants." Thesis, Massachusetts Institute of Technology, 2014. http://hdl.handle.net/1721.1/90181.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2014.
16
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 73-74).
In this thesis, I study the relationship between the higher rank Donaldson invariants of a smooth 4-manifold X and the invariants of its blowup X#CP2 . This relationship can be expressed in terms of a formal power series in several variables, called the blowup function. I compute the restriction of the blowup function to one of its variables, by solving a special system of ordinary differential equations. I also compute the SU(3) blowup function completely, and show that it is a theta function on a family of genus 2 hyperelliptic Jacobians. Finally, I give a formal argument to explain the appearance of Abelian varieties and theta functions in four dimensional topological field theories.
by Lucas Howard Culler.
Ph. D.

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29

Nelte, Karen. "Formulas of first-order logic in distributive normal form." Master's thesis, University of Cape Town, 1997. http://hdl.handle.net/11427/9648.

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Bibliography: leaves 140-143.
It was shown by Jaakko Hintikka that every formula of ﬁrst-order logic can be written as a disjunction of formulas called constituents. Such a disjunction is called a distributive normal form of the formula. It is a generalization of the disjunctive normal form for propositional logic. However, there are some signiﬁcant differences between these two normal forms, caused chieﬂy by the impossibility of deﬁning the constituents in such a way that they are all consistent. Distributive normal forms and some of their properties are studied. For example, the size of distributive normal forms is examined, and although we can't determine exactly how many constituents (of each form) are consistent, it is shown that the vast majority are inconsistent. Hintikka's deﬁnition of trivial inconsistency is studied, and a new deﬁnition of trivial inconsistency is given in terms of a necessary condition for the consistency of a constituent which is stronger than the condition which Hintikka used in his deﬁnition of trivial inconsistency. An error in Hintikka's attempted proof of the completeness theorem of the theory of distributive normal forms is pointed out, and a similar completeness theorem is proved using the new deﬁnition of trivial inconsistency.

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30

Tabony, Sawyer. "Adelic Fourier-Whittaker coefficients and the Casselman-Shalika formula." Thesis, Massachusetts Institute of Technology, 2009. http://hdl.handle.net/1721.1/54665.

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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2009.
Cataloged from PDF version of thesis.
Includes bibliographical references (p. 29).
In their paper Metaplectic Forms, D. A. Kazhdan and S. J. Patterson developed a generalization of automorphic forms that are defined on metaplectic groups. These groups are non-trivial covering groups of usual algebraic groups, and the forms defined on them are representations that respect the covering. As in the case for automorphic forms, these representations fall into a principle series, indexed by characters on a torus of the metaplectic group, and there is an associated an L-function. In the final section of their paper, an equivalence is shown in the rank one case between this -function and an Dirichlet series defined using Gauss sums, in order to demonstrate the arithmetic content. In this paper we reexamine this connection in the particular case that was discussed in Metaplectic Forms. By looking through the scope of twisted multiplicativity, a property of L-series, the computation is simplified and more easily generalized.
by Sawyer Tabony.
S.M.

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31

Reiner-Roth, Griffin. "Rodrigues Formula for Jacobi Polynomials on the Unit Circle." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1365772575.

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Hlavacek, Jan. "Asymptotic formula for the norms of exp(inh(t)) /." The Ohio State University, 1998. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487950153601176.

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Monheim, Frank [Verfasser], and Anton [Akademischer Betreuer] Deitmar. "Non-unitary Trace Formulae / Frank Monheim ; Betreuer: Anton Deitmar." Tübingen : Universitätsbibliothek Tübingen, 2015. http://d-nb.info/1163396885/34.

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Toyozumi, Kenichi, Takahiro Suzuki, Kensaku Mori, and Yasuhito Suenaga. "A system for real-time recognition of handwritten mathematical formulas." IEEE, 2001. http://hdl.handle.net/2237/6867.

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35

Rozenblum, G. "On some analytical index formulas related to operator-valued symbols." Universität Potsdam, 2000. http://opus.kobv.de/ubp/volltexte/2008/2581/.

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For several classes of pseudodifferential operators with operator-valued symbol analytic index formulas are found. The common feature is that uasual index formulas are not valid for these operators. Applications are given to pseudodifferential operators on singular manifolds.

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36

Malek, Fadi. "Formules de type Runge-Kutta-Nystrom." Thesis, University of Ottawa (Canada), 1992. http://hdl.handle.net/10393/7564.

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Explicit Runge-Kutta-Nystrom pairs, which solve directly second order initial value problems of the form $y\sp{\prime\prime}$ = $f(x,y)$ with the first derivative $y\sp\prime$ absent, are considered. Pairs consisting of formulae of order $p-1$ and p, respectively, can be designed to control the local error in y, in $y\sp\prime$ or in y and $y\sp\prime$. They may also advance the numerical approximations using the lower order formulae or the higher order formulae. These two sets of choices lead to five types of pairs. We establish the minimum number of stages required to form the five types of pairs for p = 2, ...,6, by producing an existing pair and disproving the existence of a similar pair with fewer stages. Notions of Nystrom methods and Nystrom trees are recalled along with the order conditions for these methods.

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Nacinovich, Mauro, Bert-Wolfgang Schulze, and Nikolai N. Tarkhanov. "On carleman formulas for the dolbeault cohomology." Universität Potsdam, 1998. http://opus.kobv.de/ubp/volltexte/2008/2522/.

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We discuss the Cauchy problem for the Dolbeault cohomology in a domain of C n with data on a part of the boundary. In this setting we introduce the concept of a Carleman function which proves useful in the study of uniqueness. Apart from an abstract framework we show explicit Carleman formulas for the Dolbeault cohomology.

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Fedchenko, Dmitry, and Nikolai Tarkhanov. "An index formula for Toeplitz operators." Universität Potsdam, 2014. http://opus.kobv.de/ubp/volltexte/2014/7249/.

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We prove a Fedosov index formula for the index of Toeplitz operators connected with the Hardy space of solutions to an elliptic system of first order partial differential equations in a bounded domain of Euclidean space with infinitely differentiable boundary.

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39

Yang, Yixin. "Generalisations and applications of the Clark-Ocone formula." Thesis, University of Warwick, 2011. http://wrap.warwick.ac.uk/55664/.

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Ouyang, Ling. "A symbol layout classification for mathematical formula using layout context /." Online version of thesis, 2009. http://hdl.handle.net/1850/10880.

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Fedosov, Boris, Bert-Wolfgang Schulze, and Nikolai Tarkhanov. "A general index formula on tropic manifolds with conical points." Universität Potsdam, 1999. http://opus.kobv.de/ubp/volltexte/2008/2550/.

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Toyozumi, Kenichi, Naoya Yamada, Takayuki Kitasaka, Kensaku Mori, Yasuhito Suenaga, Kenji Mase, and Tomoichi Takahashi. "A study of symbol segmentation method for handwritten mathematical formula recognition using mathematical structure information." IEEE, 2004. http://hdl.handle.net/2237/6870.

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Murr, Rüdiger. "Characterization of Lévy Processes by a duality formula and related results." Universität Potsdam, 2011. http://opus.kobv.de/ubp/volltexte/2011/4353/.

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Processes with independent increments are characterized via a duality formula, including Malliavin derivative and difference operators. This result is based on a characterization of infinitely divisible random vectors by a functional equation. A construction of the difference operator by a variational method is introduced and compared to approaches used by other authors for L´evy processes involving the chaos decomposition. Finally we extend our method to characterize infinitely divisible random measures.

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Karlsson, Olle. "The Black-Scholes Equation and Formula." Thesis, Uppsala universitet, Analys och tillämpad matematik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-200441.

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Lindloh, René [Verfasser]. "Cubature formulas on wavelet spaces / Rene Lindloh." Kiel : Universitätsbibliothek Kiel, 2010. http://d-nb.info/1019952318/34.

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Xie, Heng. "Grothendieck-Witt groups of quadrics and sums-of-squares formulas." Thesis, University of Warwick, 2015. http://wrap.warwick.ac.uk/76708/.

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This thesis studies Grothendieck-Witt spectra of quadric hypersurfaces. In particular, we compute Witt groups of quadrics. Besides, by calculating Grothendieck-Witt groups of a deleted quadric over an algebraically closed field of characteristic different from 2, we improve Dugger and Isaksen’s condition (some powers of 2 dividing some binomial coefficients) on an old problem Hurwitz concerning the existence of sums-of-squares formulas.

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Aleksandrovič, Alesia. "Formulių redukcija multiplikatyvioje aritmetikoje." Master's thesis, Lithuanian Academic Libraries Network (LABT), 2007. http://vddb.library.lt/obj/LT-eLABa-0001:E.02~2007~D_20070816_170521-57292.

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Magistriniame darbe ,,Formulių redukcija multiplikatyvioje aritmetikoje” nagrinėjamas sekvencinis multiplikatyvios aritmetikos variantas su lygybe. Šis skaičiavimas yra bazė, kuriant skaičiavimus,naudojamus automatizuojant įrodymus įvairiuose aritmetikos fragmentuose. Darbo tikslas- susipažinti su įrodymo teorija bei jos taikymu sekvenciniame multiplikatyviosios aritmetikos variante.Darbas padalintas į 3 skyrius : pargindinės sąvokos, pagalbinės lemos ir formulių redukcija. Pradžioje pateikiamas trumpas įvadas į Peano aritmetiką.Apibrėžiamas sekvencinis skaičiavimas K, turintis neloginių simbolių signatūrą {0,',P, *,=}.Savarankišką darbo dalį sudaro antrasis bei trečiasis skyriai.Bet kuriai bekvantorinei skaičiavimo K formulei A(x) randama tam tikros formos jai ekvivalenti normalioji disjunkcinė forma.Taip pat nagrinėjama sutvarkytųjų formulių redukcija.
In this postgraduate work “Reduction of formulas in the multiplicative arithmetic” the sequential variant with equality of multiplicative arithmetic is being analyzed. This calculus is a base when creating calculations which are used in different fragments of arithmetic. The aim of this work is to get acquainted with a proving theory and its application in sequential variant of multiplicative arithmetic. The work is divided into 3 sections: main conceptions, auxiliary lemmas and formula’s reduction. The short introduction into Pean’s arithmetic is given in the beginning. The sequential calculus K, which has non-logical symbol’s signature {0,`,P,.,=} is being described. Sections 2 and 3 are self-sufficient parts of this work. For any formula A(x) of calculation K the equivalent normal disjunctive form is found. Also the reduction of ordered formulas is analyzed.

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Suzuki, Takahiro, Shiro Aoshima, Kensaku Mori, and Yasuhito Suenaga. "A new system for the real-time recognition of handwritten mathematical formulas." IEEE, 2000. http://hdl.handle.net/2237/6868.

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Holden, Nina Ph D. Massachusetts Institute of Technology. "Cardy embedding of random planar maps and a KPZ formula for mated trees." Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/117865.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 247-259).
The Schramm-Loewner evolution (SLE) is a random fractal curve which describes the scaling limit of interfaces in a wide range of statistical physics models. Liouville quantum gravity (LQG) is a random fractal surface which arises as the scaling limit of discrete surfaces known as random planar maps (RPM). First, we study Hausdorff dimensions for SLE curves. We prove a KPZ-type formula which relates the Hausdorff dimension of an arbitrary subset of an SLE curve to the Hausdorff dimension of a time set for a two-dimensional correlated Brownian motion. Using our formula, we obtain new and simple proofs for a number of SLE Hausdorff dimensions, and we prove an explicit formula which says how much the Hausdorff dimension of a deterministic set increases upon being conformally mapped to an SLE curve. This is joint work with Gwynne and Miller. Then we introduce a mating-of-trees construction of SLE in Euclidean geometry in collaboration with Sun. This is the Euclidean counterpart to the mating-of-trees construction of SLE in an LQG environment by Duplantier, Miller, and Sheffield, which plays an essential role throughout the thesis. Finally, we prove scaling limit results for uniformly sampled RPM known as triangulations. In a joint work with Bernardi and Sun we show that a number of observables associated with critical site percolation on the triangulation converge jointly in law to the associated observables of SLE6 on an independent [square root of] 8/3-LQG surface. In a joint work with Sun we use this and other results to prove convergence of the triangulation under a discrete conformal embedding which we call the Cardy embedding. The conformally embedded triangulation induces an area measure and a metric on the complex plane, and we show that this measure and metric converge jointly in the scaling limit to an instance of the [square root of] 8/3-LQG disk (equivalently, to an instance of the conformally embedded Brownian disk).
by Nina Holden.
Ph. D.

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50

Cartier, Sébastien. "Surfaces des espaces homogènes de dimension 3." Phd thesis, Université Paris-Est, 2011. http://tel.archives-ouvertes.fr/tel-00672332.

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Ce mémoire porte sur l'étude des surfaces minimales et de courbure moyenne constante dans les espaces homogènes de dimension 3. Nous établissons les formules de Sym-Bobenko pour les surfaces de courbure moyenne constante 1/2 de H^2xR et minimales du groupe de Heisenberg, et donnons des exemples de construction de telles immersions par la méthode DPW. Nous montrons également que des propriétés de symétrie passent aux correspondances de type surfaces sœurs et cousines, ce qui entraîne l'existence de graphes entiers de courbure moyenne constante 1/2 à bout vertical dans H^2xR qui ne sont pas de révolution. Nous reprenons ensuite l'étude des bouts verticaux d'immersions de courbure moyenne constante 1/2 dans H^2xR. Nous munissons une famille de graphes entiers d'une structure de variété lisse et en déduisons un analogue pour H^2xR d'un théorème de A. E. Treibergs pour l'espace de Minkowski. Nous nous intéressons également aux déformations des anneaux de révolution. Une conséquence directe est l'existence d'anneaux immergés qui ne sont pas de révolution. Nous construisons notamment des anneaux dont les bouts n'ont pas le même axe. Enfin, nous décrivons les invariants de Nœther correspondant aux isométries des espaces homogènes pour les surfaces minimales et de courbure moyenne constante. Nous utilisons le formalisme de la géométrie de contact qui permet l'écriture de formules explicites en toute généralité, et nous étudions l'évolution des formes de Nœther sous l'action des isométries des espaces homogènes. Nous calculons ces invariants dans le cas des anneaux déformés de H^2xR, et dans celui des anneaux horizontaux du groupe de Heisenberg

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