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Dissertations / Theses on the topic 'Mappings (Mathematics)'

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Weigt, Martin. "Spectrum preserving linear mappings between Banach algebras." Thesis, Stellenbosch : Stellenbosch University, 2003. http://hdl.handle.net/10019.1/53597.

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Thesis (MSc)--University of Stellenbosch, 2003.
ENGLISH ABSTRACT: Let A and B be unital complex Banach algebras with identities 1 and I' respectively. A linear map T : A -+ B is invertibility preserving if Tx is invertible in B for every invertible x E A. We say that T is unital if Tl = I'. IfTx2 = (TX)2 for all x E A, we call T a Jordan homomorphism. We examine an unsolved problem posed by 1. Kaplansky: Let A and B be unital complex Banach algebras and T : A -+ B a unital invertibility preserving linear map. What conditions on A, Band T imply that T is a Jordan homomorphism? Partial motivation for this problem are the Gleason-Kahane-Zelazko Theorem (1968) and a result of Marcus and Purves (1959), these also being special instances of the problem. We will also look at other special cases answering Kaplansky's problem, the most important being the result stating that if A is a von Neumann algebra, B a semi-simple Banach algebra and T : A -+ B a unital bijective invertibility preserving linear map, then T is a Jordan homomorphism (B. Aupetit, 2000). For a unital complex Banach algebra A, we denote the spectrum of x E A by Sp (x, A). Let a(x, A) denote the union of Sp (x, A) and the bounded components of AFRIKAANSE OPSOMMING: Gestel A en B is unitale komplekse Banach algebras met identiteite 1 en I' onderskeidelik. 'n Lineêre afbeelding T : A -+ B is omkeerbaar-behoudend as Tx omkeerbaar in B is vir elke omkeerbare element x E A. Ons sê dat T unitaal is as Tl = I'. As Tx2 = (TX)2 vir alle x E A, dan noem ons T 'n Jordan homomorfisme. Ons ondersoek 'n onopgeloste probleem wat deur I. Kaplansky voorgestel is: Gestel A en B is unitale komplekse Banach algebras en T : A -+ B is 'n unitale omkeerbaar-behoudende lineêre afbeelding. Watter voorwaardes op A, B en T impliseer dat T 'n Jordan homomorfisme is? Gedeeltelike motivering vir hierdie probleem is die Gleason-Kahane-Zelazko Stelling (1968) en 'n resultaat van Marcus en Purves (1959), wat terselfdertyd ook spesiale gevalle van die probleem is. Ons salook na ander spesiale gevalle kyk wat antwoorde lewer op Kaplansky se probleem. Die belangrikste van hierdie resultate sê dat as A 'n von Neumann algebra is, B 'n semi-eenvoudige Banach algebra is en T : A -+ B 'n unitale omkeerbaar-behoudende bijektiewe lineêre afbeelding is, dan is T 'n Jordan homomorfisme (B. Aupetit, 2000). Vir 'n unitale komplekse Banach algebra A, dui ons die spektrum van x E A aan met Sp (x, A). Laat cr(x, A) die vereniging van Sp (x, A) en die begrensde komponente van

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Fahlberg-Stojanovska, Linda Dianne. "Stochastic stability of Lozi mappings." Diss., The University of Arizona, 1989. http://hdl.handle.net/10150/184748.

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We study the Lozi mapping f(x,y) = (1+by-a|x|,x) acting on a compact trapping region in R² and prove that its Sinai-Bowen-Ruelle measure is stable under small random perturbations. This extends the results of Kifer and Young [Y2] for Axiom A attractors to a piecewise hyperbolic setting.

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Adamowicz, Tomasz. "On the geometry of p-harmonic mappings." Related electronic resource: Current Research at SU : database of SU dissertations, recent titles available full text, 2008. http://wwwlib.umi.com/cr/syr/main.

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Jeganathan, P. "Fixed points for nonexpansive mappings in Banach spaces." Master's thesis, University of Cape Town, 1991. http://hdl.handle.net/11427/17067.

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Sarantopoulos, I. C. "Polynomials and multilinear mappings in Banach spaces." Thesis, Brunel University, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.376057.

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Chin, Wai-yi, and 錢慧儀. "Linear maps preserving the spectrum?" Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B31225834.

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Wang, Mingxi. "Factorizations of finite mappings on riemann surfaces." Click to view the E-thesis via HKUTO, 2007. http://sunzi.lib.hku.hk/HKUTO/record/B39557789.

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Wang, Mingxi, and 汪明晰. "Factorizations of finite mappings on riemann surfaces." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2007. http://hub.hku.hk/bib/B39557789.

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Villanueva, Segovia Cristina. "Properties of Lipschitz quotient mappings on the plane." Thesis, University of Birmingham, 2018. http://etheses.bham.ac.uk//id/eprint/8266/.

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In the present work, we are concerned with the relation between the Lipschitz and co-Lipschitz constants of a mapping f : R2 → R2 and the cardinality of the inverse image of a point under the mapping f, depending on the norm on R2. It is known that there is a scale of real numbers 0 < ... < Pn <...< P1 < 1 such that for any Lipschitz quotient mapping from the Euclidean plane to itself, if the ratio between the co-Lipschitz and Lipschitz constants of f is bigger than Pn, then the cardinality of any fibre of f is less than or equal to n. Furthermore, it is proven that for the Euclidean case the values of this scale are Pn = 1/n + 1) for each n ∈ N and that these are sharp. A natural question is: given a normed space (R2 , II · II) whether it is possible to find the values of the scale 0 < . . . < pn II · II < ... < p1 II · II < 1 such that for any Lipschitz quotient mapping from (R2, II · II) to itself, with Lipschitz and co-Lipschitz constants equal to L and c respectively, the relation c/L > pn II · II implies #f- 1 (x) ≤ n for all x ∈ R2. In this work we prove that the same "Euclidean scale", Pn = 1/(n+1), works for any norm on the plane. Here we follow the general idea in a previous paper by Maleva but verify details carefully. On the other hand, the question whether this scale is sharp leads to different conclusions. We show that for some non-Euclidean norms the "Euclidean scale" is not sharp, but there are also non-Euclidean norms for which a Lipschitz quotient exists satisfying max# f - 1(x) = 2 and c/L = 1/2.

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Boyd, Zachary M. "Convolutions and Convex Combinations of Harmonic Mappings of the Disk." BYU ScholarsArchive, 2014. https://scholarsarchive.byu.edu/etd/5238.

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Let f_1, f_2 be univalent harmonic mappings of some planar domain D into the complex plane C. This thesis contains results concerning conditions under which the convolution f_1 ∗ f_2 or the convex combination tf_1 + (1 − t)f_2 is univalent. This is a long-standing problem, and I provide several partial solutions. I also include applications to minimal surfaces.

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Wilmhurst, Alan Stephen. "Complex harmonic mappings and the valence of harmonic polynomials." Thesis, University of York, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.259748.

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Stover, Derrick D. "Continuous Mappings and Some New Classes of Spaces." View abstract, 2009. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:3371579.

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Al-Nayef, Anwar Ali Bayer, and mikewood@deakin edu au. "Semi-hyperbolic mappings in Banach spaces." Deakin University. School of Computing and Mathematics, 1997. http://tux.lib.deakin.edu.au./adt-VDU/public/adt-VDU20051208.110247.

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The definition of semi-hyperbolic dynamical systems generated by Lipschitz continuous and not necessarily invertible mappings in Banach spaces is presented in this thesis. Like hyperbolic mappings, they involve a splitting into stable and unstable spaces, but a slight leakage from the strict invariance of the spaces is possible and the unstable subspaces are assumed to be finite dimensional. Bi-shadowing is a combination of the concepts of shadowing and inverse shadowing and is usually used to compare pseudo-trajectories calculated by a computer with the true trajectories. In this thesis, the concept of bi-shadowing in a Banach space is defined and proved for semi-hyperbolic dynamical systems generated by Lipschitz mappings. As an application to the concept of bishadowing, linear delay differential equations are shown to be bi-shadowing with respect to pseudo-trajectories generated by nonlinear small perturbations of the linear delay equation. This shows robustness of solutions of the linear delay equation with respect to small nonlinear perturbations. Complicated dynamical behaviour is often a consequence of the expansivity of a dynamical system. Semi-hyperbolic dynamical systems generated by Lipschitz mappings on a Banach space are shown to be exponentially expansive, and explicit rates of expansion are determined. The result is applied to a nonsmooth noninvertible system generated by delay differential equation. It is shown that semi-hyperbolic mappings are locally φ-contracting, where -0 is the Hausdorff measure of noncompactness, and that a linear operator is semi-hyperbolic if and only if it is φ-contracting and has no spectral values on the unit circle. The definition of φ-bi-shadowing is given and it is shown that semi-hyperbolic mappings in Banach spaces are φ-bi-shadowing with respect to locally condensing continuous comparison mappings. The result is applied to linear delay differential equations of neutral type with nonsmooth perturbations. Finally, it is shown that a small delay perturbation of an ordinary differential equation with a homoclinic trajectory is chaotic.

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Romney, Matthew Daniel. "A Class of Univalent Convolutions of Harmonic Mappings." BYU ScholarsArchive, 2013. https://scholarsarchive.byu.edu/etd/4169.

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A planar harmonic mapping is a complex-valued function ƒ : D → C of the form ƒ(x+iy) = u(x,y) + iv(x,y), where u and v are both real harmonic. Such a function can be written as ƒ = h+g where h and g are both analytic; the function w = g'/h' is called the dilatation of ƒ. This thesis considers the convolution or Hadamard product of planar harmonic mappings that are the vertical shears of the canonical half-plane mapping p;(z) = z/(1-z) with respective dilatations e^iθz and e^ipz, θ, p ∈ R. We prove that any such convolution is univalent. We also derive a convolution identity that extends this result to shears of p(z) = z/(1-z) in other directions.

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Beane, Robbie Allen. "Inverse limits of permutation maps." Diss., Rolla, Mo. : Missouri University of Science and Technology, 2008. http://scholarsmine.mst.edu/thesis/pdf/Beane_09007dcc804f93c9.pdf.

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Thesis (Ph. D.)--Missouri University of Science and Technology, 2008.
Vita. The entire thesis text is included in file. Title from title screen of thesis/dissertation PDF file (viewed May 9, 2008) Includes bibliographical references (p. 71-73).

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Pederson, Steven M. "Homoclinic tangencies and families of interval maps with non-constant topological entropy." Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/29167.

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Fryer, Robert Neil. "Dynamics of degree two quasiregular mappings of the plane of constant dilatation." Thesis, University of Warwick, 2012. http://wrap.warwick.ac.uk/54680/.

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Let h : C ! C be an R-linear map. In this thesis, we explore the dynamics of the quasiregular mapping h(z)2 + c. It is well-known that a polynomial can be conjugated by a holomorphic map to w 7! wd in a neighbourhood of infinity. This map is called a Böttcher coordinate for f near infinity. We construct a Böttcher type coordinate for compositions of h and polynomials, a class of mappings first studied in [19]. As an application, we prove that if h is affne and c 2 C, then h(z)2 + c is not uniformly quasiregular. Via the Böttcher type coordinate, we are able to obtain results for any degree two mapping of the plane with constant complex dilatation. We show that any such mapping has either one, two or three fixed external rays, that all cases can occur, and exhibit how the dynamics changes in each case. We use results from complex dynamics to prove that these mappings are nowhere uniformly quasiregular in a neighbourhood of infinity. Finally, we show that in most cases, two such mappings are not quasiconformally conjugate on a neighbourhood of infinity.

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Duda, Jakub. "Aspects of delta-convexity /." free to MU campus, to others for purchase, 2003. http://wwwlib.umi.com/cr/mo/fullcit?p3115539.

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Potter, Harrison D. P. "On Conformal Mappings and Vector Fields." Marietta College Honors Theses / OhioLINK, 2008. http://rave.ohiolink.edu/etdc/view?acc_num=marhonors1210888378.

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Brucks, Karen M. (Karen Marie) 1957. "Dynamics of One-Dimensional Maps: Symbols, Uniqueness, and Dimension." Thesis, North Texas State University, 1988. https://digital.library.unt.edu/ark:/67531/metadc332102/.

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This dissertation is a study of the dynamics of one-dimensional unimodal maps and is mainly concerned with those maps which are trapezoidal. The trapezoidal function, f_e, is defined for eΣ(0,1/2) by f_e(x)=x/e for xΣ[0,e], f_e(x)=1 for xΣ(e,1-e), and f_e(x)=(1-x)/e for xΣ[1-e,1]. We study the symbolic dynamics of the kneading sequences and relate them to the analytic dynamics of these maps. Chapter one is an overview of the present theory of Metropolis, Stein, and Stein (MSS). In Chapter two a formula is given that counts the number of MSS sequences of length n. Next, the number of distinct primitive colorings of n beads with two colors, as counted by Gilbert and Riordan, is shown to equal the number of MSS sequences of length n. An algorithm is given that produces a bisection between these two quantities for each n. Lastly, the number of negative orbits of size n for the function f(z)=z^2-2, as counted by P.J. Myrberg, is shown to equal the number of MSS sequences of length n. For an MSS sequence P, let H_ϖ(P) be the unique common extension of the harmonics of P. In Chapter three it is proved that there is exactly one J(P)Σ[0,1] such that the itinerary of λ(P) under the map is λ(P)f_e is H_ϖ(P). In Chapter four it is shown that only period doubling or period halving bifurcations can occur for the family λf_e, λΣ[0,1]. Results concerning how the size of a stable orbit changes as bifurcations of the family λf_e occur are given. Let λΣ[0,1] be such that 1/2 is a periodic point of λf_e. In this case 1/2 is superstable. Chapter five investigates the boundary of the basin of attraction of this stable orbit. An algorithm is given that yields a graph directed construction such that the object constructed is the basin boundary. From this we analyze the Hausdorff dimension and measure in that dimension of the boundary. The dimension is related to the simple β-numbers, as defined by Parry.

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Stofile, Simfumene. "Fixed points of single-valued and multi-valued mappings with applications." Thesis, Rhodes University, 2013. http://hdl.handle.net/10962/d1002960.

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The relationship between the convergence of a sequence of self mappings of a metric space and their fixed points, known as the stability (or continuity) of fixed points has been of continuing interest and widely studied in fixed point theory. In this thesis we study the stability of common fixed points in a Hausdorff uniform space whose uniformity is generated by a family of pseudometrics, by using some general notations of convergence. These results are then extended to 2-metric spaces due to S. Gähler. In addition, a well-known theorem of T. Suzuki that generalized the Banach Contraction Principle is also extended to 2-metric spaces and applied to obtain a coincidence theorem for a pair of mappings on an arbitrary set with values in a 2-metric space. Further, we prove the existence of coincidence and fixed points of Ćirić type weakly generalized contractions in metric spaces. Subsequently, the above result is utilized to discuss applications to the convergence of modified Mann and Ishikawa iterations in a convex metric space. Finally, we obtain coincidence, fixed and stationary point results for multi-valued and hybrid pairs of mappings on a metric space.

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Rogers, John Gilbert. "Life-long mapping of objects and places in domestic environments." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/47736.

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In the future, robots will expand from industrial and research applications to the home. Domestic service robots will work in the home to perform useful tasks such as object retrieval, cleaning, organization, and security. The tireless support of these systems will not only enable able bodied people to avoid mundane chores; they will also enable the elderly to remain independent from institutional care by providing service, safety, and companionship. Robots will need to understand the relationship between objects and their environments to perform some of these tasks. Structured indoor environments are organized according to architectural guidelines and convenience for their residents. Utilizing this information makes it possible to predict the location of objects. Conversely, one can also predict the function of a room from the detection of a few objects within a given space. This thesis introduces a framework for combining object permanence and context called the probabilistic cognitive model. This framework combines reasoning about spatial extent of places and the identity of objects and their relationships to one another and to the locations where they appear. This type of reasoning takes into account the context in which objects appear to determine their identity and purpose. The probabilistic cognitive model combines a mapping system called OmniMapper with a conditional random field probabilistic model for context representation. The conditional random field models the dependencies between location and identity in a real-world domestic environment. This model is used by mobile robot systems to predict the effects of their actions during autonomous object search tasks in unknown environments.

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Rotter, Harald. "Konjugationsinvarianten in der Umgebung invarianter Kreise von Twist-Abbildungen." Bonn : [s.n.], 1999. http://catalog.hathitrust.org/api/volumes/oclc/41464667.html.

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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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Cadavid, Carlos Alberto. "On a remarkable set of words in the mapping class group /." Digital version accessible at:, 1998. http://wwwlib.umi.com/cr/utexas/main.

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Shrivastava, Vikram M. "Mapping conceptual graphs to primitive VHDL processes." Thesis, This resource online, 1994. http://scholar.lib.vt.edu/theses/available/etd-05022009-040536/.

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O'Bannon, Terry Robert. "A comparison of interpolative methods for cell mapping analyses of nonlinear systems." Thesis, Georgia Institute of Technology, 1988. http://hdl.handle.net/1853/16394.

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Lau, Chi-hin, and 劉智軒. "Holomorphic maps from rational homogeneous spaces onto projective manifolds." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2003. http://hub.hku.hk/bib/B3124550X.

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Niyitegeka, Jean Marie Vianney. "Generalizations of some fixed point theorems in banach and metric spaces." Thesis, Nelson Mandela Metropolitan University, 2015. http://hdl.handle.net/10948/5265.

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A fixed point of a mapping is an element in the domain of the mapping that is mapped into itself by the mapping. The study of fixed points has been a field of interests to mathematicians since the discovery of the Banach contraction theorem, i.e. if is a complete metric space and is a contraction mapping (i.e. there exists such that for all ), then has a unique fixed point. The Banach contraction theorem has found many applications in pure and applied mathematics. Due to fixed point theory being a mixture of analysis, geometry, algebra and topology, its applications to other fields such as physics, economics, game theory, chemistry, engineering and many others has become vital. The theory is nowadays a very active field of research in which many new theorems are published, some of them applied and many others generalized. Motivated by all of this, we give an exposition of some generalizations of fixed point theorems in metric fixed point theory, which is a branch of fixed point theory about results of fixed points of mappings between metric spaces, where certain properties of the mappings involved need not be preserved under equivalent metrics. For instance, the contractive property of mappings between metric spaces need not be preserved under equivalent metrics. Since metric fixed point theory is wide, we limit ourselves to fixed point theorems for self and non-self-mappings on Banach and metric spaces. We also take a look at some open problems on this topic of study. At the end of the dissertation, we suggest our own problems for future research.

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Andersson, Anders. "Numerical Conformal mappings for regions Bounded by Smooth Curves." Licentiate thesis, Växjö University, School of Mathematics and Systems Engineering, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-1190.

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Inom många tillämpningar används konforma avbildningar för att transformera tvådimensionella områden till områden med enklare utseende. Ett exempel på ett sådant område är en kanal av varierande tjocklek begränsad av en kontinuerligt deriverbar kurva. I de tillämpningar som har motiverat detta arbete, är det viktigt att dessa egenskaper bevaras i det område en approximativ konform avbildning producerar, men det är också viktigt att begränsningskurvans riktning kan kontrolleras, särkilt i kanalens båda ändar.

Denna avhandling behandlar tre olika metoder för att numeriskt konstruera konforma avbildningar mellan ett enkelt standardområde, företrädesvis det övre halvplanet eller enhetscirkeln, och ett område begränsat av en kontinuerligt deriverbar kurva, där begränsningskurvans riktning kan kontrolleras, exakt eller approximativt.

Den första metoden är en utveckling av en idé, först beskriven av Peter Henrici, där en modifierad Schwarz-Christoffel-avbildning avbildar det övre halvplanet konformt på en polygon med rundade hörn.

Med utgångspunkt i denna idé skapas en algoritm för att konstruera avbildningar på godtyckliga områden med släta randkurvor.

Den andra metoden bygger också den på Schwarz-Christoffel-avbildningen, och utnyttjar det faktum att om enhetscirkeln eller halvplanet avbildas på en polygon kommer ett område Q i det inre av dessa, som till exempel en cirkel med centrum i origo och radie mindre än 1, eller ett område i övre halvplanet begränsat av två strålar, att avbildas på ett område R i det inre av polygonen begränsat av en slät kurva. Vi utvecklar en metod för att hitta ett polygonalt område P, utanför det Omega som man önskar att skapa en avbildning för, sådant att den Schwarz-Christoffel-avbildning som avbildar enhetscirkeln eller halvplanet på P, avbildar Q på Omega.

I båda dessa fall används tangentpolygoner för att numeriskt bestämma den önskade avbildningen.

Slutligen beskrivs en metod där en av Don Marshalls så kallade zipper-algoritmer används för att skapa en avbildning mellan det övre

halvplanet och en godtycklig kanal, begränsad av släta kurvor, som i båda ändar går mot oändligheten som räta parallella linjer.

In many applications, conformal mappings are used to transform two-dimensional regions into simpler ones. One such region for which conformal mappings are needed is a channel bounded by continuously differentiable curves. In the applications that have motivated this work, it is important that the region an approximate conformal mapping produces, has this property, but also that the direction of the curve can be controlled, especially in the ends of the channel.

This thesis treats three different methods for numerically constructing conformal mappings between the upper half-plane or unit circle and a region bounded by a continuously differentiable curve, where the direction of the curve in a number of control points is controlled, exact or approximately.

The first method is built on an idea by Peter Henrici, where a modified Schwarz-Christoffel mapping maps the upper half-plane conformally on a polygon with rounded corners. His idea is used in an algorithm by which mappings for arbitrary regions, bounded by smooth curves are constructed.

The second method uses the fact that a Schwarz-Christoffel mapping from the upper half-plane or unit circle to a polygon maps a region Q inside the half-plane or circle, for example a circle with radius less than 1 or a sector in the half--plane, on a region Omega inside the polygon bounded by a smooth curve. Given such a region Omega, we develop methods to find a suitable outer polygon and corresponding Schwarz-Christoffel mapping that gives a mapping from Q to Omega.

Both these methods use the concept of tangent polygons to numerically determine the coefficients in the mappings.

Finally, we use one of Don Marshall's zipper algorithms to construct conformal mappings from the upper half--plane to channels bounded by arbitrary smooth curves, with the additional property that they are parallel straight lines when approaching infinity.

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Harris, Jean Elisabeth. "The effects of map type and availability on performance with hypermedia." Thesis, This resource online, 1992. http://scholar.lib.vt.edu/theses/available/etd-10102009-020342/.

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Brink, Willie. "Spherical parameterisation methods for 3D surfaces." Thesis, Stellenbosch : University of Stellenbosch, 2005. http://hdl.handle.net/10019.1/2360.

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Thesis (MSc (Applied Mathematics))--University of Stellenbosch, 2005.
The surface of a 3D model may be digitally represented as a collection of flat polygons in R3. The collection is known as a polygonal mesh. This representation method has become standard in computer graphics.

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Medwid, Mark Edward. "Rigidity of Quasiconformal Maps on Carnot Groups." Bowling Green State University / OhioLINK, 2017. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1497620176117104.

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Kaczynski, Tomasz. "Topological transversality of condensing set-valued maps." Thesis, McGill University, 1986. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=73995.

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Taylor, John (John Allen). "Aspects of Universality in Function Iteration." Thesis, University of North Texas, 1991. https://digital.library.unt.edu/ark:/67531/metadc278799/.

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Shin, Hyunshik. "Algebraic degrees of stretch factors in mapping class groups." Diss., Georgia Institute of Technology, 2014. http://hdl.handle.net/1853/51910.

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Given a closed surface Sg of genus g, a mapping class f in \MCG(Sg) is said to be pseudo-Anosov if it preserves a pair of transverse measured foliations such that one is expanding and the other one is contracting by a number \lambda(f). The number \lambda(f) is called a stretch factor (or dilatation) of f. Thurston showed that a stretch factor is an algebraic integer with degree bounded above by 6g-6. However, little is known about which degrees occur. Using train tracks on surfaces, we explicitly construct pseudo-Anosov maps on Sg with orientable foliations whose stretch factor \lambda has algebraic degree 2g. Moreover, the stretch factor \lambda is a special algebraic number, called Salem number. Using this result, we show that there is a pseudo-Anosov map whose stretch factor has algebraic degree d, for each positive even integer d such that d≤g. Our examples also give a new approach to a conjecture of Penner.

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Ruth, Harry Leonard Jr. "Conformal densities and deformations of uniform loewner metric spaces." Cincinnati, Ohio : University of Cincinnati, 2008. http://www.ohiolink.edu/etd/view.cgi?ucin1210203872.

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Thesis (Ph.D.)--University of Cincinnati, 2008.
Committee/Advisors: David Herron PhD (Committee Chair), David Minda PhD (Committee Member), Nageswari Shanmugalingam PhD (Committee Member). Title from electronic thesis title page (viewed Sep.3, 2008). Keywords: conformal density; uniform spaces; Loewner; quasisymmetry; quasiconofrmal. Includes abstract. Includes bibliographical references.

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Erhardt, Erik Barry. "Bayesian Simultaneous Intervals for Small Areas: An Application to Mapping Mortality Rates in U.S. Health Service Areas." Link to electronic thesis, 2004. http://www.wpi.edu/Pubs/ETD/Available/etd-0105104-195633/.

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Thesis (M.S.) -- Worcester Polytechnic Institute.
Keywords: Poisson-Gamma Regression; MCMC; Bayesian; Small Area Estimation; Simultaneous Inference; Statistics Includes bibliographical references (p. 61-67).

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O'Hea, Adrian Ralph. "Optophone design : optical-to-auditory vision substitution for the blind." Thesis, n.p, 1994. http://ethos.bl.uk/.

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Thompson, Scotty L. "Comparing Topological Spaces Using New Approaches to Cleavability." View abstract, 2009. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:3372574.

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Mujica, Ximena. "Aplicações tau(p;q)-somantes e sigma (p)-nucleares." [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306106.

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Orientador: Mario Carvalho de Matos
Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica
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Resumo: Neste trabalho estendemos os conceitos de operadores t-somantes e s-nucleares apresentados por Pietsch em seu livro Operator Ideals, para aplicações multilineares, polinômios e funções holomorfas, estabelecendo uma relação de dualidade entre os mesmos. Apresentamos também um teorema de dominação para aplicações e polinômios t (p; q)-somantes, mostrando a sua relação com as aplicações e polinômios semi-integrais, bem como um teorema de fatoração para aplicações e polinômios s (p)-nucleares
Abstract: In this work we extend the concepts of t-summing and s-nuclear operators presented by Pietsch in his book Operator Ideals, to multilinear mappings, polynomials and holomorphic functions, thus establishing a duality relation between them. We also present a domination theorem for t(p; q)-summing mappings and polynomials, showing their relation with semi-integral mappings and polynomials, as well as a factorization theorem for s(p)-nuclear mappings and polynomials
Doutorado
Analise Funcional
Doutor em Matemática

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Wong, Alfred Ka Yiu Computer Science &amp Engineering Faculty of Engineering UNSW. "Ontology mapping: a logic-based approach with applications in selected domains." Publisher:University of New South Wales. Computer Science & Engineering, 2008. http://handle.unsw.edu.au/1959.4/41103.

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In advent of the Semantic Web and recent standardization efforts, Ontology has quickly become a popular and core semantic technology. Ontology is seen as a solution provider to knowledge based systems. It facilitates tasks such as knowledge sharing, reuse and intelligent processing by computer agents. A key problem addressed by Ontology is the semantic interoperability problem. Interoperability in general is a common problem in different domain applications and semantic interoperability is the hardest and an ongoing research problem. It is required for systems to exchange knowledge and having the meaning of the knowledge accurately and automatically interpreted by the receiving systems. The innovation is to allow knowledge to be consumed and used accurately in a way that is not foreseen by the original creator. While Ontology promotes semantic interoperability across systems by unifying their knowledge bases through consensual understanding, common engineering and processing practices, it does not solve the semantic interoperability problem at the global level. As individuals are increasingly empowered with tools, ontologies will eventually be created more easily and rapidly at a near individual scale. Global semantic interoperability between heterogeneous ontologies created by small groups of individuals will then be required. Ontology mapping is a mechanism for providing semantic bridges between ontologies. While ontology mapping promotes semantic interoperability across ontologies, it is seen as the solution provider to the global semantic interoperability problem. However, there is no single ontology mapping solution that caters for all problem scenarios. Different applications would require different mapping techniques. In this thesis, we analyze the relations between ontology, semantic interoperability and ontology mapping, and promote an ontology-based semantic interoperability solution. We propose a novel ontology mapping approach namely, OntoMogic. It is based on first order logic and model theory. OntoMogic supports approximate mapping and produces structures (approximate entity correspondence) that represent alignment results between concepts. OntoMogic has been implemented as a coherent system and is applied in different application scenarios. We present case studies in the network configuration, security intrusion detection and IT governance & compliance management domain. The full process of ontology engineering to mapping has been demonstrated to promote ontology-based semantic interoperability.

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Kleeman, R. "Generalized quantization and colour algebras /." Title page, table of contents and abstract only, 1985. http://web4.library.adelaide.edu.au/theses/09PH/09phk635.pdf.

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Saran, Nurdan A. "Time Memory Trade Off Attack On Symmetric Ciphers." Phd thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/12610437/index.pdf.

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Time Memory Trade O (TMTO) is a cryptanalytic method that aims to develop an attack which has a lower memory complexity than lookup table and a lower online time complexity than exhaustive search. TMTO methods are widely studied in the literature and used for inverting various cryptosystems. We focus on the design and the analysis of TMTO on symmetric ciphers in this thesis. Firstly, the summary of the random mapping statistics from the view point of TMTO is presented. We also recalculate some expected values with a simpler approach than the existing proofs. Then, we propose some variant constructions and also present three new distinguishers based on random mappings. Next, we provide a detailed analysis of the success rate of two main improvements of the attack
Distinguished Point Method and Rainbow Method. Finally, we discuss the adjustment of the parameters to achieve a high success rate. To support our theoretical framework, we also present empirical results of our analysis to actual ciphers.

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Wan, Wei. "A New Approach to the Decomposition of Incompletely Specified Functions Based on Graph Coloring and Local Transformation and Its Application to FPGA Mapping." PDXScholar, 1992. https://pdxscholar.library.pdx.edu/open_access_etds/4698.

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The thesis presents a new approach to the decomposition of incompletely specified functions and its application to FPGA (Field Programmable Gate Array) mapping. Five methods: Variable Partitioning, Graph Coloring, Bond Set Encoding, CLB Reusing and Local Transformation are developed in order to efficiently perform decomposition and FPGA (Lookup-Table based FPGA) mapping. 1) Variable Partitioning is a high quality hemistic method used to find the "best" partitions, avoiding the very time consuming testing of all possible decomposition charts, which is impractical when there are many input variables in the input function. 2) Graph Coloring is another high quality heuristic\ used to perform the quasi-optimum don't care assignment, making the program possible to accept incompletely specified function and perform a quasi-optimum assignment to the unspecified part of the function. 3) Bond Set Encoding algorithm is used to simplify the decomposed blocks during the process of decomposition. 4) CLB Reusing algorithm is used to reduce the number of CLBs used in the final mapped circuit. 5) Local Transformation concept is introduced to transform nondecomposable functions into decomposable ones, thus making it possible to apply decomposition method to FPGA mapping. All the above developed methods are incorporated into a program named TRADE, which performs global optimization over the input functions. While most of the existing methods recursively perform local optimization over some kinds of network-like graphs, and few of them can handle incompletely specified functions. Cube calculus is used in the TRADE program, the operations are global and very fast. A short description of the TRADE program and the evaluation of the results are provided at the_ end of the thesis. For many benchmarks the TRADE program gives better results than any program published in the literature.

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Ha, Pham Hoang. "On unicity problems of meromorphic mappings of Cn into PN(C) and the ramification of the Gauss maps of complete minimal surfaces." Phd thesis, Université de Bretagne occidentale - Brest, 2013. http://tel.archives-ouvertes.fr/tel-00871320.

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In 1975, H. Fujimoto generalized Nevanlinna's known results for meromorphic fonctions to the case of meromorphic mappings of Cn into PN(C). He proved that for two linearly nondegenerate meromorphic mappings f and g of C into PN(C). if they have the saine inverse images counted with multiplicities for 3N + 2 hyperplanes in general position in PN(C) then f = g. After that, this problem has been studied intensively by a number of mathematicans as H. Fujimoto, W. Stoll, L. Smiley, M. Ru, G. Dethloff - T. V. Tan, D. D. Thai - S. D. Quang, Chen-Yan and so on. Parallel to the development of Nevanlinna theory, the value distribution theory of the Gauss map of minimal surfaces immersed in Rm vas studied by many mathematicans as R. Osserman, S.S. Chern, F. Xavier, H. Fujimoto, S. J. Kao, M. Ru and many other mathematicans. In this thesis, we continuous studing some problems on these directions. The main goals of the thesis are followings. * Unicity theorems with truncated multiplicities of meromorphic mappings of Cn into PN(C) sharing 2N + 2 fixed hyperplanes.* Unicity theorems with truncated multiplicities of meromorphic mappings of Cn into PN(C) for moving targets, and a small set of identity.

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Buck, Lisa Diane. "The motivational effects of a GPS mapping project on student attitudes toward mathematics and mathematical achievement." Thesis, [Tuscaloosa, Ala. : University of Alabama Libraries], 2009. http://purl.lib.ua.edu/17.

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Tracy, Jacob Dennis, and Jacob Dennis Tracy. "Mapping Pre-Service Teacher Talk: Variations in Talk About Mathematics, Ability, and Themselves as Mathematical Learners." Diss., The University of Arizona, 2017. http://hdl.handle.net/10150/625620.

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It has been argued that teachers do not always teach in the ways their teacher education programs promoted. One cause of this problem has to do with teachers' conceptions about mathematics and ability being incompatible with the visions of mathematics that teacher educators promote. For example, teacher educators may emphasize the need for conceptual understanding but a teacher who equates understanding with being correct and fast will enact this goal differently from someone who expects students to be able to explain and communicate their understanding. The way a teacher understands what it means to do mathematics and be good at mathematics will influence their future teaching. Furthermore, the messages teachers send to their students about who they are as mathematical learners are full of messages about what it means to do and be good at mathematics. Additionally, these messages can have a long-term impact on how those students view themselves and the decisions they make for their future. This study uses qualitative methods to better understand pre-service teacher (PST) talk, how their talk relates, and how their talk changes over time. I describe PST talk as it relates to mathematics (M), ability (A), and themselves as mathematical learners (P) (the three components of the MAP framework). This study took place with the PSTs in two sections of a mathematical content course for elementary school teachers taught by the researcher. First, using grounded theory, I developed codes to understand how these PSTs talked in regards to the three components and applied these codes to written reflections at the beginning and end of our course. After analyzing the data I selected and interviewed 14 PSTs one year after our course. Again, I applied the same codes to their talk in the interview to see how their talk continued to change. Select interview PSTs were then chosen to represent common and uncommon examples of PST talk. Findings from this study show that talk across the MAP framework was related and that this talk became more standards-aligned by the end of the content course. However, the findings also provide a much more nuanced insight into different relationships and changes in talk. One finding shows that when variations in PST talk existed between framework components it was most commonly due to PSTs talking about mathematics in a more traditional way than when they talked about ability or themselves as mathematical learners. Another finding shows that during the interviews (one year after our course) PSTs continued to talk about themselves and abilities in mostly standards-aligned ways but reverted towards more traditional talk when discussing mathematics and how someone demonstrates their mathematical understanding. These findings have important implications for future research and for teacher educators. First, the relationships between the components of the MAP framework suggest that addressing PSTs conceptions of mathematics and their conceptions of ability may affect how they talk about individuals as mathematical learners. Second, the findings show which aspects in the MAP framework PSTs more readily talk about in standards-aligned ways. This provides insights into which areas teacher educators may want to emphasize more in trying to promote changes in PST talk. Lastly, these findings also show which aspects of PST talk maintain over a longer time frame and which aspects need a greater sustained emphasis. All of this is necessary as we support PSTs to think and talk about mathematics and mathematical abilities in standards-aligned ways that are truly supportive of all students.

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Peyron, Marianne. "Quelques problèmes d'analyse géométrique dans les variétés presque complexes à bord." Phd thesis, Université de Grenoble, 2013. http://tel.archives-ouvertes.fr/tel-00989815.

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Nous étudions d'abord l'analyticité des applications CR entre deux hypersurfaces dans des variétés presque complexes. Nous démontrons l'analyticité d'une telle application dans deux cas distincts : premièrement dans le cas où les hypersurfaces de départ et d'arrivée sont le bord d'un domaine modèle et la structure presque complexe est une structure modèle, deuxièmement dans le cas où la structure presque complexe d'arrivée est une déformation d'une structure modèle et lorsque les hypersurfaces sont des petites perturbations de l'hypersurface $partialh$ définie par $partial h={zinC^n,RE(z_n)+|z'|^2=0}$. La preuve utilise la méthode de prolongation des systèmes d'équations aux dérivées partielles ainsi que la théorie des systèmes complets. Nous appliquons ensuite ces résultats pour généraliser le Théorème de Poincaré-Alexander au cas presque complexe. Le Théorème de Poincaré-Alexander stipule qu'une application holomorphe définie sur un ouvert de la boule unité de $C^n$ peut, sous certaines conditions, être prolongée en un biholomorphisme de la boule unité. Dans le cadre presque complexe, la boule unité n'est plus, à biholomorphisme près, le seul domaine strictement pseudoconvexe et homogène. Un domaine strictement pseudoconvexe et homogène est biholomorphe à un domaine modèle. Nous donnons ainsi une genéralisation du Théorème de Poincaré-Alexander pour les domaines modèles. Enfin, nous définissons les applications $J$-quasiconformes et démontrons que les ouverts et les sous variétés totalement réelles incluses dans le bord du domaine constituent des ensembles d'unicité pour les applications $J$-quasiconformes. Nous démontrons aussi qu'une application $J$-quasiconforme qui admet des limites nulles en tout point d'une sous-variété totatemement réelle incluse dans le bord du domaine est identiquement nulle.

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Lucci, Paulo Cesar de Alvarenga 1974. "Descrição matematica de geometrias curvas por interpolação transfinita." [s.n.], 2009. http://repositorio.unicamp.br/jspui/handle/REPOSIP/258706.

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Orientador: Philippe Remy Bernard Devloo
Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Civil, Arquitetura e Urbanismo
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Resumo: Este trabalho é dedicado ao desenvolvimento de uma metodologia específica de mapeamento curvo aplicável a qualquer tipo de elemento geométrico regular. Trata-se de uma generalização do modelo matemático de representação geométrica apresentado em 1967 por Steven Anson Coons, denominado "Bilinearly Blended Coons Patches", o qual ajusta uma superfície retangular em um contorno delimitado por quatro curvas arbitrárias. A generalização proposta permitirá a utilização deste tipo de interpolação geométrica em elementos de qualquer topologia, através de uma sistemática única e consistente.
Abstract: In this work a methodology is developed for mathematical representation of curved domains, applicable to any type of finite element geometry. This methodology is a generalization of the mathematical model of a geometric representation presented in 1967 by Steven Anson Coons, called "Bilinearly Blended Coons Patches", which patch a rectangular surface in four arbitrary boundary curves. The proposed methodology is a kind of geometric transfinite interpolation applicable to elements of any topology, using a single and consistent systematic.
Mestrado
Estruturas
Mestre em Engenharia Civil

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