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Dissertations / Theses on the topic 'Tropical mathematics'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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1

Wise, William D. "Tropical Linear Algebra: Notions of Rank Over the Tropical Semiring." Oberlin College Honors Theses / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=oberlin1432052601.

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2

Taylor, Matthew. "On upper triangular tropical matrix semigroups, tropical matrix identities and T-modules." Thesis, University of Manchester, 2017. https://www.research.manchester.ac.uk/portal/en/theses/on-upper-triangular-tropical-matrix-semigroups-tropical-matrix-identities-and-tmodules(d470a4a1-4eca-46c8-b9b8-4377affcc6fe).html.

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3

Hlavacek, Magda L. "Random Tropical Curves." Scholarship @ Claremont, 2017. http://scholarship.claremont.edu/hmc_theses/95.

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In the setting of tropical mathematics, geometric objects are rich with inherent combinatorial structure. For example, each polynomial $p(x,y)$ in the tropical setting corresponds to a tropical curve; these tropical curves correspond to unbounded graphs embedded in $\R^2$. Each of these graphs is dual to a particular subdivision of its Newton polytope; we classify tropical curves by combinatorial type based on these corresponding subdivisions. In this thesis, we aim to gain an understanding of the likeliness of the combinatorial type of a randomly chosen tropical curve by using methods from po

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4

O'Neill, Kevin. "Lines in Tropical Quadrics." Scholarship @ Claremont, 2013. http://scholarship.claremont.edu/hmc_theses/43.

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Classical algebraic geometry is the study of curves, surfaces, and other varieties defined as the zero set of polynomial equations. Tropical geometry is a branch of algebraic geometry based on the tropical semiring with operations minimization and addition. We introduce the notions of projective space and tropical projective space, which are well-suited for answering enumerative questions, like ours. We attempt to describe the set of tropical lines contained in a tropical quadric surface in $\mathbb{TP}^3$. Analogies with the classical problem and computational techniques based on the idea of

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5

Wade, Darryl Gene. "The Tropical Jacobian of a Tropical Elliptic Curve Is S^1(Q)." BYU ScholarsArchive, 2008. https://scholarsarchive.byu.edu/etd/1868.

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We establish consistent deﬁnitions for divisors, principal divisors, and Jacobians of a tropical elliptic curve and show that for a tropical elliptic cubic C , the associated Jacobian (or zero divisor class group) is the group S^1(Q).

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6

Hoyt, Christopher. "On the Landscape of Random Tropical Polynomials." Scholarship @ Claremont, 2018. https://scholarship.claremont.edu/hmc_theses/114.

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Tropical polynomials are similar to classical polynomials, however addition and multiplication are replaced with tropical addition (minimums) and tropical multiplication (addition). Within this new construction, polynomials become piecewise linear curves with interesting behavior. All tropical polynomials are piecewise linear curves, and each linear component uniquely corresponds to a particular monomial. In addition, certain monomial in the tropical polynomial can be trivial due to the fact that tropical addition is the minimum operator. Therefore, it makes sense to consider a graph of connec

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7

Tripoli, Paolo. "Chow hypersurfaces and realizability problems in tropical geometry." Thesis, University of Warwick, 2017. http://wrap.warwick.ac.uk/99839/.

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Tropical geometry is an area of mathematics between algebraic geometry, polyhedral geometry and combinatorics. The basic principle of tropical geometry is to associate to an algebraic variety X a polyhedral complex Trop(X) called the tropicalization of X. The tropicalization of X can be studied by means of polyhedral geometry and combinatorics and reflects many properties of the original variety X. Given a projective variety X . Pn of codimension k+1, the Chow hypersurface ZX is the hypersurface of the Grassmannian Gr(k; n) parametrizing k-dimensional linear subspaces of Pn that intersect X. I

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8

Rimmasch, Gretchen. "Complete Tropical Bezout's Theorem and Intersection Theory in the Tropical Projective Plane." Diss., CLICK HERE for online access, 2008. http://contentdm.lib.byu.edu/ETD/image/etd2507.pdf.

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9

Lamboglia, Sara. "Toric degenerations, Fano schemes and computations in tropical geometry." Thesis, University of Warwick, 2018. http://wrap.warwick.ac.uk/106943/.

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Tropical geometry is a developing area of mathematics in between algebraic geometry, combinatorics and polyhedral geometry. The main objects of study are tropical varieties which can be seen as polyhedral and combinatorial shadows of classical algebraic varieties. These simpler geometric objects keep important geometric information. They can be used to tackle problems in algebraic geometry but also to develop a purely tropical theory which has connection to different areas of research. In Chapter 3 we study toric degenerations of the full flag varieties Fl4 and Fl5 using their tropicalization

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10

Turner, Nicole. "Tropical Arithmetics and Dot Product Representations of Graphs." DigitalCommons@USU, 2015. https://digitalcommons.usu.edu/etd/4460.

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In tropical algebras we substitute min or max for the typical addition and then substitute addition for multiplication. A dot product representation of a graph assigns each vertex of the graph a vector such that two edges are adjacent if and only if the dot product of their vectors is greater than some chosen threshold. The resultS of creating dot product representations of graphs using tropical algebras are examined. In particular we examine the tropical dot product dimensions of graphs and establish connections to threshold graphs and the threshold dimension of a graph.

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11

Herold, Matthias. "Tropical orbit spaces and moduli spaces of tropical curves." Phd thesis, Université de Strasbourg, 2011. http://tel.archives-ouvertes.fr/tel-00550370.

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Un principal résultat de la thèse est une preuve conceptionnelle du fait que le nombre pondéré de courbes tropicales de degré et genre donnés qui passent par le bon nombre de points en position générale dans $\RR^2$ (resp., qui passent par le bon nombre de points en position générale dans $ \RR^r $ et représentent un point fixé dans l'espace de modules de courbes tropicales abstraites de genre g ) ne dépend pas du choix de points. Un autre principal résultat est un nouveau théorème de correspondance entre les cycles tropicaux plans et les courbes algébriques elliptiques planes.

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12

Ellis, Amanda. "Classifcation of Conics in the Tropical Projective Plane." BYU ScholarsArchive, 2005. https://scholarsarchive.byu.edu/etd/697.

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This paper defines tropical projective space, TP^n, and the tropical general linear group TPGL(n). After discussing some simple examples of tropical polynomials and their hypersurfaces, a strategy is given for finding all conics in the tropical projective plane. The classification of conics and an analysis of the coefficient space corresponding to such conics is given.

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13

Chan, Andrew John. "Gröbner bases over fields with valuation and tropical curves by coordinate projections." Thesis, University of Warwick, 2013. http://wrap.warwick.ac.uk/59163/.

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In the emerging field of tropical geometry, algebraic varieties are replaced by polyhedral objects called tropical varieties. The algebraic and tropical variety share many invariants, but due to its polyhedral structure the tropical variety is often easier to work with. In this thesis, we look at two problems related to constructing tropical varieties. In the first, we extend the theory of Grobner bases to the case where we are looking over a field with a valuation. The motivation is that we can use these Grobner bases in order to compute tropical varieties over fields with valuations. We disc

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14

Wade, Darryl Gene. "The tropical Jacobian of an elliptic curve is the group S¹(Q) /." Diss., CLICK HERE for online access, 2008. http://contentdm.lib.byu.edu/ETD/image/etd2521.pdf.

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15

Kutler, Max B. "Group Actions and Divisors on Tropical Curves." Scholarship @ Claremont, 2011. http://scholarship.claremont.edu/hmc_theses/5.

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Tropical geometry is algebraic geometry over the tropical semiring, or min-plus algebra. In this thesis, I discuss the basic geometry of plane tropical curves. By introducing the notion of abstract tropical curves, I am able to pass to a more abstract metric-topological setting. In this setting, I discuss divisors on tropical curves. I begin a study of $G$-invariant divisors and divisor classes.

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16

Lin, Yu-Shen. "Open Gromov-Witten Invariants on Elliptic K3 Surfaces and Wall-Crossing." Thesis, Harvard University, 2013. http://dissertations.umi.com/gsas.harvard:10802.

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17

Salazar, Ramon L. II. "Leaf Functional Traits and Forest Structure of Tropical Dry Forest Species Along a Rainfall Gradient in Florida and Puerto Rico." FIU Digital Commons, 2015. http://digitalcommons.fiu.edu/etd/1754.

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This study examined how different rainfall regimes affect a set of leaf functional traits related to plant stress and forest structure in tropical dry forest (TDF) species on limestone substrate. One hundred fifty eight individuals of four tree species were sampled in six ecological sites in south Florida and Puerto Rico, ranging in mean annual rainfall from 858 to 1933 mm yr-1. Leaf nitrogen content, specific leaf area (SLA), and N:P ratio of evergreen species, but not deciduous species, responded positively to increasing rainfall. Phosphorus content was unaffected in both groups. Canopy heig

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18

Hook, James Louis. "Topics in dynamical systems." Thesis, University of Manchester, 2012. https://www.research.manchester.ac.uk/portal/en/theses/topics-in-dynamical-systems(427b5d98-197d-4b53-876e-a81142f72375).html.

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In this thesis I explore three new topics in Dynamical Systems. In Chapters 2 and 3 I investigate the dynamics of a family of asynchronous linear systems. These systems are of interest as models for asynchronous processes in economics and computer science and as novel ways to solve linear equations. I find a tight sandwich of bounds relating the Lyapunov exponents of these asynchronous systems to the eigenvalue of their synchronous counterparts. Using ideas from the theory of IFSs I show how the random behavior of these systems can be quickly sampled and go some way to characterizing the assoc

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19

Nash, Evan D. Nash. "Extended Tropicalization of Spherical Varieties." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1523979975350178.

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20

Will, Etienne. "Constructions tropicales de noeuds algébriques dans IRP3." Phd thesis, Université de Strasbourg, 2012. http://tel.archives-ouvertes.fr/tel-00733721.

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Cette thèse présente la construction de courbes tropicales réelles dans R^3 dont la projectivisation, qui est un entrelacs projectif dans IRP^3, est constituée de 2 composantes, I'une étant isotope à un noeud donné au départ. Dans le cas de certains noeuds toriques, il est possible de modifier cette construction pour que I'entrelacs projectif correspondant ait une seule composante isotope au noeud torique considéré. Pour chacune de ces courbes tropicales réelles, nous faisons appel au théorème récent de G. Mikhalkin, qui affirme l'existence d'une algébrique réelle non singulière dans IRP^3, de

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21

Sharify, Meisam. "Algorithmes de mise à l'échelle et méthodes tropicales en analyse numérique matricielle." Phd thesis, Ecole Polytechnique X, 2011. http://pastel.archives-ouvertes.fr/pastel-00643836.

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L'Algèbre tropicale peut être considérée comme un domaine relativement nouveau en mathématiques. Elle apparait dans plusieurs domaines telles que l'optimisation, la synchronisation de la production et du transport, les systèmes à événements discrets, le contrôle optimal, la recherche opérationnelle, etc. La première partie de ce manuscrit est consacrée a l'étude des applications de l'algèbre tropicale à l'analyse numérique matricielle. Nous considérons tout d'abord le problème classique de l'estimation des racines d'un polynôme univarié. Nous prouvons plusieurs nouvelles bornes pour la valeur

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22

Maude, Richard James. "Malaria elimination modelling in the context of antimalarial drug resistance." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:3a5321ca-f8fc-45b2-a002-363d982d3cc5.

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Introduction: Antimalarial resistance, particularly artemisinin resistance, is a major threat to P. falciparum malaria elimination efforts worldwide. Urgent intervention is required to tackle artemisinin resistance but field data on which to base planning of strategies are limited. The aims were to collect available field data and develop population level mathematical models of P. falciparum malaria treatment and artemisinin resistance in order to determine the optimal strategies for elimination of artemisinin resistant malaria in Cambodia and treatment of pre-hospital and severe malaria in Ca

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23

Usatine, Jeremy. "Arithmetical Graphs, Riemann-Roch Structure for Lattices, and the Frobenius Number Problem." Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/hmc_theses/57.

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If R is a list of positive integers with greatest common denominator equal to 1, calculating the Frobenius number of R is in general NP-hard. Dino Lorenzini defines the arithmetical graph, which naturally arises in arithmetic geometry, and a notion of genus, the g-number, that in specific cases coincides with the Frobenius number of R. A result of Dino Lorenzini's gives a method for quickly calculating upper bounds for the g-number of arithmetical graphs. We discuss the arithmetic geometry related to arithmetical graphs and present an example of an arithmetical graph that arises in this contex

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24

François, Georges [Verfasser], and Andreas [Akademischer Betreuer] Gathmann. "Tropical Intersection Products and Families of Tropical Curves / Georges Francois. Betreuer: Andreas Gathmann." Kaiserslautern : Technische Universität Kaiserslautern, 2012. http://d-nb.info/1028236794/34.

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25

Meyer, Henning [Verfasser]. "Intersection Theory on Tropical Toric Varieties and Compactifications of Tropical Parameter Spaces / Henning Meyer." Kaiserslautern : Universitätsbibliothek Kaiserslautern, 2011. http://d-nb.info/1011911965/34.

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26

Gleitsmann, Anke. "Exploiting the spatial information in high resolution satellite data and utilising multi-source data for tropical mountain forest and land cover mapping." Doctoral thesis, Stuttgart Ibidem-Verl, 2005. http://deposit.d-nb.de/cgi-bin/dokserv?id=2852171&prov=M&dok_var=1&dok_ext=htm.

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27

Shahari, Nor Azni. "Mathematical modelling of drying food products : application to tropical fruits." Thesis, University of Nottingham, 2012. http://eprints.nottingham.ac.uk/12485/.

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Drying is an old traditional method of removing liquid from inside material, suchas wood, food, paper, ceramics, building materials, textiles, granular products, pharmaceutical and electronic devices. The kinetics of this liquid removal depends on the material properties of the solid phase as well as on cellular structure. The aim of this project is to understand the effect of complex interaction of heat, moisture and shrinkage to create a detailed mathematical modelling to quantify the drying of a food product and tropical fruits in particular, which typically have high water content. To this

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28

Ochse, Dennis [Verfasser], and Andreas [Akademischer Betreuer] Gathmann. "Moduli spaces of rational tropical stable maps into smooth tropical varieties / Dennis Ochse. Betreuer: Andreas Gathmann." Kaiserslautern : Technische Universität Kaiserslautern, 2013. http://d-nb.info/1035637820/34.

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29

Kulas, Katja [Verfasser]. "Combinatorics of Tropical Polytopes / Katja Kulas." München : Verlag Dr. Hut, 2013. http://d-nb.info/1037286804/34.

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30

Horn, Silke [Verfasser]. "Tropical Oriented Matroids and Cubical Complexes / Silke Horn." München : Verlag Dr. Hut, 2012. http://d-nb.info/1028784643/34.

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31

Tewari, Ayush Kumar [Verfasser], Michael [Akademischer Betreuer] Joswig, Michael [Gutachter] Joswig, Hannah [Gutachter] Markwig, and Dhruv [Gutachter] Ranganathan. "Realizability of tropical plane curves and tropical incidence geometry / Ayush Kumar Tewari ; Gutachter: Michael Joswig, Hannah Markwig, Dhruv Ranganathan ; Betreuer: Michael Joswig." Berlin : Technische Universität Berlin, 2021. http://d-nb.info/1226217400/34.

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32

Ren, Yue [Verfasser], and Thomas [Akademischer Betreuer] Markwig. "Tropical Geometry in Singular / Yue Ren. Betreuer: Thomas Markwig." Kaiserslautern : Technische Universität Kaiserslautern, 2015. http://d-nb.info/1076503047/34.

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33

Smacka, Jascha [Verfasser], and Walter [Akademischer Betreuer] Gubler. "Differential Forms on Tropical Spaces / Jascha Smacka ; Betreuer: Walter Gubler." Regensburg : Universitätsbibliothek Regensburg, 2017. http://d-nb.info/1143948874/34.

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34

Wall, Steven E. "Structure and evolution of thermohaline staircases in tropical North Atlantic." Thesis, Monterey, Calif. : Naval Postgraduate School, 2007. http://bosun.nps.edu/uhtbin/hyperion-image.exe/07Dec%5FWall.pdf.

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Thesis (M.S. in Physical Oceanography)--Naval Postgraduate School, December 2007.<br>Thesis Advisor(s): Radko, Timour. "December 2007." Description based on title screen as viewed on January 24, 2008. Includes bibliographical references (p. 83-86). Also available in print.

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35

Hampe, Simon [Verfasser], and Andreas [Akademischer Betreuer] Gathmann. "Algorithmic aspects of tropical intersection theory / Simon Hampe. Betreuer: Andreas Gathmann." Kaiserslautern : Technische Universität Kaiserslautern, 2014. http://d-nb.info/1053326181/34.

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36

Böhm, Janko [Verfasser], and Frank-Olaf [Akademischer Betreuer] Schreyer. "Mirror symmetry and tropical geometry / Janko Böhm. Betreuer: Frank-Olaf Schreyer." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2011. http://d-nb.info/1051094968/34.

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37

Jürgens, Christian Verfasser], and Hannah [Akademischer Betreuer] [Markwig. "(Real) Tropical Singularities and Bergman Fans / Christian Jürgens ; Betreuer: Hannah Markwig." Tübingen : Universitätsbibliothek Tübingen, 2018. http://d-nb.info/1168804574/34.

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38

Birkmeyer, Anna Lena [Verfasser]. "The Realizability of Tropical Hypersurfaces in Matroid Fans / Anna Lena Birkmeyer." München : Verlag Dr. Hut, 2016. http://d-nb.info/1106592417/34.

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39

Schroeter, Franziska Verfasser], and Hannah [Akademischer Betreuer] [Markwig. "The enumeration of real tropical curves / Franziska Schroeter. Betreuer: Hannah Markwig." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2013. http://d-nb.info/1053030983/34.

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40

Olarte, Jorge Alberto [Verfasser]. "Polytopal subdivisions in Grassmannians, tropical geometry and algebraic curves / Jorge Alberto Olarte." Berlin : Freie Universität Berlin, 2020. http://d-nb.info/1205737103/34.

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41

Gross, Andreas [Verfasser]. "An Intersection-Theoretic Approach to Correspondence Problems in Tropical Geometry / Andreas Gross." München : Verlag Dr. Hut, 2017. http://d-nb.info/1126297224/34.

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42

Buchholz, Arne Verfasser], and Hannah [Akademischer Betreuer] [Markwig. "Tropical covers, moduli spaces & mirror symmetry / Arne Buchholz. Betreuer: Hannah Markwig." Saarbrücken : Saarländische Universitäts- und Landesbibliothek, 2014. http://d-nb.info/1060715953/34.

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43

Torchiani, Carolin [Verfasser]. "Enumerative geometry of rational and elliptic tropical curves in R m / Carolin Torchiani." München : Verlag Dr. Hut, 2014. http://d-nb.info/1055863834/34.

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44

Canesin, Míriam Regina. "Cenários agrícolas futuros para Panicum maximum cv. Tanzânia no estado de São Paulo." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/11/11139/tde-02062014-113142/.

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O presente trabalho teve por objetivo avaliar cenários futuros de produção de forragem em pastagens de Panicum maximum cv. Tanzânia no Estado de São Paulo, baseados nos modelos climáticos ETA-CPTEC e PRECIS, e discutir os impactos potenciais das mudanças climáticas globais sobre a pecuária na região. Foram realizadas simulações de taxa de acúmulo de matéria seca utilizando-se um modelo de estimativa de produção considerando o acúmulo de graus-dia e a introdução da variável armazenamento de água no solo como fator de penalização do modelo para as condições de sequeiro. Os dados gerados foram es

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45

French, Michael Duncan. "Mathematical modelling of neglected tropical disease control with particular reference to schistosomiasis in sub-Saharan Africa." Thesis, Imperial College London, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.550985.

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The overarching aim of the thesis is the use of mathematical models to provide policy-relevant guidance to neglected tropical disease (NTD) control programmes, particularly those against schistosomiasis, identified following discussions with Schistosomiasis Control Initiative (SCI) staff, and utilising the SCl's extensive datasets from sub-Saharan Africa. Firstly, changes are estimated in the force of infection (Fa/) of schistosomes following annual control in Uganda, relative to baseline, expressed as the number of mature parasites acquired per host per year. It is known that praziquantel tre

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46

Baumann, Martin [Verfasser], and V. [Akademischer Betreuer] Heuveline. "Numerical Simulation of Tropical Cyclones using Goal-Oriented Adaptivity / Martin Baumann. Betreuer: V. Heuveline." Karlsruhe : KIT-Bibliothek, 2012. http://d-nb.info/1019790105/34.

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47

Gross, Andreas [Verfasser], and Andreas [Akademischer Betreuer] Gathmann. "An Intersection-Theoretic Approach to Correspondence Problems in Tropical Geometry / Andreas Gross ; Betreuer: Andreas Gathmann." Kaiserslautern : Technische Universität Kaiserslautern, 2016. http://d-nb.info/1138979716/34.

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48

Loho, Georg [Verfasser], Michael [Akademischer Betreuer] Joswig, Michael [Gutachter] Joswig, and Stéphane [Gutachter] Gaubert. "Combinatorics of tropical linear programming / Georg Loho ; Gutachter: Michael Joswig, Stéphane Gaubert ; Betreuer: Michael Joswig." Berlin : Technische Universität Berlin, 2017. http://d-nb.info/1156013437/34.

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49

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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50

Goldner, Christoph Jan [Verfasser]. "Enumerative aspects of Tropical Geometry : Curves with cross-ratio constraints and Mirror Symmetry / Christoph Jan Goldner." Tübingen : Universitätsbibliothek Tübingen, 2021. http://d-nb.info/1233678248/34.

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