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1
Namasivayam, M. "Entropy numbers, s-numbers and embeddings". Thesis, University of Sussex, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.356519.
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Allagan, Julian Apelete D. Johnson Peter D. "Choice numbers, Ohba numbers and Hall numbers of some complete k-partite graphs". Auburn, Ala, 2009. http://hdl.handle.net/10415/1780.
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Fransson, Jonas. "Generalized Fibonacci Series Considered modulo n". Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-26844.
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In this thesis we are investigating identities regarding Fibonacci sequences. In particular we are examiningthe so called Pisano period, which is the period for the Fibonacci sequence considered modulo n to repeatitself. The theory shows that it suces to compute Pisano periods for primes. We are also looking atthe same problems for the generalized Pisano period, which can be described as the Pisano period forthe generalized Fibonacci sequence.
4
Anderson, Crystal Lynn. "An Introduction to Number Theory Prime Numbers and Their Applications". Digital Commons @ East Tennessee State University, 2006. https://dc.etsu.edu/etd/2222.
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The author has found, during her experience teaching students on the fourth grade level, that some concepts of number theory haven't even been introduced to the students. Some of these concepts include prime and composite numbers and their applications. Through personal research, the author has found that prime numbers are vital to the understanding of the grade level curriculum. Prime numbers are used to aide in determining divisibility, finding greatest common factors, least common multiples, and common denominators. Through experimentation, classroom examples, and homework, the author has introduced students to prime numbers and their applications.
5
Chipatala, Overtone. "Polygonal numbers". Kansas State University, 2016. http://hdl.handle.net/2097/32923.
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Master of ScienceDepartment of Mathematics
Todd Cochrane
Polygonal numbers are nonnegative integers constructed and represented by geometrical arrangements of equally spaced points that form regular polygons. These numbers were originally studied by Pythagoras, with their long history dating from 570 B.C, and are often referred to by the Greek mathematicians. During the ancient period, polygonal numbers were described by units which were expressed by dots or pebbles arranged to form geometrical polygons. In his "Introductio Arithmetica", Nicomachus of Gerasa (c. 100 A.D), thoroughly discussed polygonal numbers. Other Greek authors who did remarkable work on the numbers include Theon of Smyrna (c. 130 A.D), and Diophantus of Alexandria (c. 250 A.D). Polygonal numbers are widely applied and related to various mathematical concepts. The primary purpose of this report is to define and discuss polygonal numbers in application and relation to some of these concepts. For instance, among other topics, the report describes what triangle numbers are and provides many interesting properties and identities that they satisfy. Sums of squares, including Lagrange's Four Squares Theorem, and Legendre's Three Squares Theorem are included in the paper as well. Finally, the report introduces and proves its main theorems, Gauss' Eureka Theorem and Cauchy's Polygonal Number Theorem.
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Tomasini, Alejandro. "Wittgensteinian Numbers". Pontificia Universidad Católica del Perú - Departamento de Humanidades, 2013. http://repositorio.pucp.edu.pe/index/handle/123456789/112986.
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In this paper I reconstruct the tractarian view of natural numbers. i show how Wittgenstein uses his conceptual apparatus (operatlon, formal concept, internal property, logical form) to elaborate analternative to the logicist definition of number. Finally, I briefly examine sorneof the criticisms that have been raised against it.En este trabajo reconstruyo la concepción tractariana de los números naturales. Muestro cómo Wittgenstein usa su aparato conceptual (operación, conceptoformal, propiedad interna, forma lógica) para elaborar una definición de número alternativa a la logicista. Por último, examino brevemente algunas de lascríticas que se han elevado en su contra.
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Hostetler, Joshua. "Surreal Numbers". VCU Scholars Compass, 2012. http://scholarscompass.vcu.edu/etd/2935.
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The purpose of this thesis is to explore the Surreal Numbers from an elementary, con- structivist point of view, with the intention of introducing the numbers in a palatable way for a broad audience with minimal background in any specific mathematical field. Created from two recursive definitions, the Surreal Numbers form a class that contains a copy of the real numbers, transfinite ordinals, and infinitesimals, combinations of these, and in- finitely many numbers uniquely Surreal. Together with two binary operations, the surreal numbers form a field. The existence of the Surreal Numbers is proven, and the class is constructed from nothing, starting with the integers and dyadic rationals, continuing into the transfinite ordinals and the remaining real numbers, and culminating with the infinitesimals and uniquely surreal numbers. Several key concepts are proven regarding the ordering and containment properties of the numbers. The concept of a surreal continuum is introduced and demonstrated. The binary operations are explored and demonstrated, and field properties are proven, using many methods, including transfinite induction.
8
Ho, Kwan-hung, e 何君雄. "On the prime twins conjecture and almost-prime k-tuples". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2002. http://hub.hku.hk/bib/B29768421.
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Chan, Ching-yin, e 陳靖然. "On k-tuples of almost primes". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hdl.handle.net/10722/195967.
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Ketkar, Pallavi S. (Pallavi Subhash). "Primitive Substitutive Numbers are Closed under Rational Multiplication". Thesis, University of North Texas, 1998. https://digital.library.unt.edu/ark:/67531/metadc278637/.
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Lehr (1991) proved that, if M(q, r) denotes the set of real numbers whose expansion in base-r is q-automatic i.e., is recognized by an automaton A = (Aq, Ar, ao, δ, φ) (or is the image under a letter to letter morphism of a fixed point of a substitution of constant length q) then M(q, r) is closed under addition and rational multiplication. Similarly if we let M(r) denote the set of real numbers α whose base-r digit expansion is ultimately primitive substitutive, i.e., contains a tail which is the image (under a letter to letter morphism) of a fixed point of a primitive substitution then in an attempt to generalize Lehr's result we show that the set M(r) is closed under multiplication by rational numbers. We also show that M(r) is not closed under addition.
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Ewers-Rogers, Jennifer. "Very young children's understanding and use of numbers and number symbols". Thesis, University College London (University of London), 2002. http://discovery.ucl.ac.uk/10007376/.
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Children grow up surrounded by numerals reflecting various uses of number. In their primary school years they are expected to grasp arithmetical symbols and use measuring devices. While much research on number development has examined children's understanding of numerical concepts and principles, little has investigated their understanding of these symbols. This thesis examines studies of understanding and use of number symbols in a range of contexts and for a variety of purposes. It reports several studies on the use of numerals by children aged between 3 and 5 years in Nursery settings in England, Japan and Sweden and their understanding of the meanings of these symbols. 167 children were observed and interviewed individually in the course of participating in a range of practical activities; the activities were designed for the study and considered to be appropriate and interesting for young children. The results are discussed in terms of how they complement existing theories of number development and their relevance to early years mathematics education.
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Allen, Emily. "Combinatorial Interpretations Of Generalizations Of Catalan Numbers And Ballot Numbers". Research Showcase @ CMU, 2014. http://repository.cmu.edu/dissertations/366.
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The super Catalan numbers T(m,n) = (2m)!(2n)!=2m!n!(m+n)! are integers which generalize the Catalan numbers. Since 1874, when Eugene Catalan discovered these numbers, many mathematicians have tried to find their combinatorial interpretation. This dissertation is dedicated to this open problem. In Chapter 1 we review known results on T (m,n) and their q-analog polynomials. In Chapter 2 we give a weighted interpretation for T(m,n) in terms of 2-Motzkin paths of length m+n2 and a reformulation of this interpretation in terms of Dyck paths. We then convert our weighted interpretation into a conventional combinatorial interpretation for m = 1,2. At the beginning of Chapter 2, we prove our weighted interpretation for T(m,n) by induction. In the final section of Chapter 2 we present a constructive combinatorial proof of this result based on rooted plane trees. In Chapter 3 we introduce two q-analog super Catalan numbers. We also define the q-Ballot number and provide its combinatorial interpretation. Using our q-Ballot number, we give an identity for one of the q-analog super Catalan numbers and use it to interpret a q-analog super Catalan number in the case m= 2. In Chapter 4 we review problems left open and discuss their difficulties. This includes the unimodality of some of the q-analog polynomials and the conventional combinatorial interpretation of the super Catalan numbers and their q-analogs for higher values of m.
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Bento, Antonio Jorge Gomes. "Interpolation, measures of non-compactness, entropy numbers and s-numbers". Thesis, University of Sussex, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.344067.
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Lin, Wensong. "Circular chromatic numbers and distance two labelling numbers of graphs". HKBU Institutional Repository, 2004. http://repository.hkbu.edu.hk/etd_ra/591.
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Magnusson, Tobias. "Counting Class Numbers". Thesis, KTH, Matematik (Avd.), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-223643.
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The following thesis contains an extensive account of the theory of class groups. First the form class group is introduced through equivalence classes of certain integral binary quadratic forms with a given discriminant. The sets of classes is then turned into a group through an operation referred to as "composition''. Then the ideal class group is introduced through classes of fractional ideals in the ring of integers of quadratic fields with a given discriminant. It is then shown that for negative fundamental discriminants, the ideal class group and form class group are isomorphic. Some concrete computations are then done, after which some of the most central conjectures concerning the average behaviour of class groups with discriminant less than $X$ -- the Cohen-Lenstra heuristics -- are stated and motivated. The thesis ends with a sketch of a proof by Bob Hough of a strong result related to a special case of the Cohen-Lenstra heuristics.Följande mastersuppsats innehåller en utförlig redogörelse av klassgruppsteori. Först introduceras formklassgruppen genom ekvivalensklasser av en typ av binära kvadratiska former med heltalskoefficienter och en given diskriminant. Mängden av klasser görs sedan till en grupp genom en operation som kallas "komposition''. Därefter introduceras idealklassgruppen genom klasser av kvotideal i heltalsringen till kvadratiska talkroppar med given diskriminant. Det visas sedan att formklassgruppen och idealklassgruppen är isomorfa för negativa fundamentala diskriminanter. Några konkreta beräkningar görs sedan, efter vilka en av de mest centrala förmodandena gällande det genomsnittliga beteendet av klassgrupper med diskriminant mindre än $X$ -- Cohen-Lenstra heuristiken -- formuleras och motiveras. Uppsatsen avslutas med en skiss av ett bevis av Bob Hough av ett starkt resultat relaterat till ett specialfall av Cohen-Lenstra heuristiken.
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Ishii, Minoru 1945. "Small Ramsey numbers". Thesis, McGill University, 1985. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=63235.
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Shi, Lingsheng. "Numbers and topologies". Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät II, 2003. http://dx.doi.org/10.18452/14871.
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In der Ramsey Theorie fuer Graphen haben Burr und Erdos vor nunmehr fast dreissig Jahren zwei Vermutungen formuliert, die sich als richtungsweisend erwiesen haben. Es geht darum diejenigen Graphen zu charakterisieren, deren Ramsey Zahlen linear in der Anzahl der Knoten wachsen. Diese Vermutungen besagen, dass Ramsey Zahlen linear fuer alle degenerierten Graphen wachsen und dass die Ramsey Zahlen von Wuerfeln linear wachsen. Ein Ziel dieser Dissertation ist es, abgeschwaechte Varianten dieser Vermutungen zu beweisen. In der topologischen Ramseytheorie bewies Kojman vor kurzem eine topologische Umkehrung des Satzes von Hindman und fuehrte gleichzeitig sogenannte Hindman-Raeume und van der Waerden-Raeume ein (beide sind eine Teilmenge der folgenkompakten Raeume), die jeweils zum Satz von Hindman beziehungsweise zum Satz von van der Waerden korrespondieren. In der Dissertation wird zum einen eine Verstaerkung der Umkehrung des Satzes von van der Waerden bewiesen. Weiterhin wird der Begriff der Differentialkompaktheit eingefuehrt, der sich in diesem Zusammenhang ergibt und der eng mit Hindman-Raeumen verknuepft ist. Dabei wird auch die Beziehung zwischen Differentialkompaktheit und anderen topologischen Raeumen untersucht. Im letzten Abschnitt des zweiten Teils werden kompakte dynamische Systeme verwendet, um ein klassisches Ramsey-Ergebnis von Brown und Hindman et al. ueber stueckweise syndetische Mengen ueber natuerlichen Zahlen und diskreten Halbgruppen auf lokal zusammenhaengende Halbgruppen zu verallgemeinern.In graph Ramsey theory, Burr and Erdos in 1970s posed two conjectures which may be considered as initial steps toward the problem of characterizing the set of graphs for which Ramsey numbers grow linearly in their orders. One conjecture is that Ramsey numbers grow linearly for all degenerate graphs and the other is that Ramsey numbers grow linearly for cubes. Though unable to settle these two conjectures, we have contributed many weaker versions that support the likely truth of the first conjecture and obtained a polynomial upper bound for the Ramsey numbers of cubes that considerably improves all previous bounds and comes close to the linear bound in the second conjecture. In topological Ramsey theory, Kojman recently observed a topological converse of Hindman's theorem and then introduced the so-called Hindman space and van der Waerden space (both of which are stronger than sequentially compact spaces) corresponding respectively to Hindman's theorem and van der Waerden's theorem. In this thesis, we will strengthen the topological converse of Hindman's theorem by using canonical Ramsey theorem, and introduce differential compactness that arises naturally in this context and study its relations to other spaces as well. Also by using compact dynamical systems, we will extend a classical Ramsey type theorem of Brown and Hindman et al on piecewise syndetic sets from natural numbers and discrete semigroups to locally connected semigroups.
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Schwartzkopff, Robert. "The numbers of the marketplace : commitment to numbers in natural language". Thesis, University of Oxford, 2015. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.711821.
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Slavic, Aida. "Call numbers, book numbers and collection arrangements in European library traditions". Ess Ess Pub, 2009. http://hdl.handle.net/10150/111798.
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Throughout the long history of the library, there have been many examples of methodical approaches to creating techniques, tools and knowledge that contribute to creating the library profession as we know it today. Collection arrangement and book labelling represent skills that are built into the very foundations of librarianship.With the opening of each new library, with collection merging or moving, or when building open access to a collection from scratch, librarians continue to question the methods they inherited. Librarians have to have a good understanding of the details and functions of book labelling in order to make an informed decision on how much of the work required for book labelling and re-shelving can be saved or replaced by other methods of locating and presenting documents.
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Brown, Bruce J. L. "Numbers: a dream or reality? A return to objects in number learning". Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-82378.
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Simmons, Jill. "CO-irredundant Ramsey numbers". Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0005/MQ36621.pdf.
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Hey, Jessica L. ""Coming out" by numbers". Ohio : Ohio University, 2007. http://www.ohiolink.edu/etd/view.cgi?ohiou1189022132.
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Megyesi, Gabor. "Inequalities between Chern numbers". Thesis, University of Cambridge, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.308243.
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Rivard-Cooke, Martin. "Parametric Geometry of Numbers". Thesis, Université d'Ottawa / University of Ottawa, 2019. http://hdl.handle.net/10393/38871.
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This thesis is primarily concerned in studying the relationship between different exponents of Diophantine approximation, which are quantities arising naturally in the study of rational approximation to a fixed n-tuple of real irrational numbers.
As Khinchin observed, these exponents are not independent of each other, spurring interest in the study of the spectrum of a given family of exponents, which is the set of all possible values that can be taken by said family of exponents.
Introduced in 2009-2013 by Schmidt and Summerer and completed by Roy in 2015, the parametric geometry of numbers provides strong tools with regards to the study of exponents of Diophantine approximation and their associated spectra by the introduction of combinatorial objects called n-systems. Roy proved the very surprising result that the study of spectra of exponents is equivalent to the study of certain quantities attached to n-systems. Thus, the study of rational approximation can be replaced by the study of n-systems when attempting to determine such spectra.
Recently, Roy proved two new results for the case n=3, the first being that spectra are semi-algebraic sets, and the second being that spectra are stable under the minimum with respect to the product ordering. In this thesis, it is shown that both of these results do not hold in general for n>3, and examples are given.
This thesis also provides non-trivial examples for n=4 where the spectra is stable under the minimum.
An alternate and much simpler proof of a recent result of Marnat-Moshchevitin proving an important conjecture of Schmidt-Summerer is also given, relying only on the parametric geometry of numbers instead. Further, a conjecture which generalizes this result is also established, and some partial results are given towards its validity. Among these results, the simplest, but non-trivial, new case is also proven to be true.
In a different vein, this thesis considers certain generalizations theta(q) of the classical theta q-series. We show under conditions on the coefficients of the series that theta(q) is neither rational nor quadratic irrational for each integer q>1.
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Fornasiero, Antongiulio. "Integration on surreal numbers". Thesis, University of Edinburgh, 2004. http://hdl.handle.net/1842/12194.
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The thesis concerns the (class) structure No of Conway’s surreal numbers. The main concern is the behaviour on No of some of the classical functions of real analysis, and a definition of integral for such functions. In the main texts on No, most definitions and proofs are done by transfinite recursion and induction on the complexity of elements. In the thesis I consider a general scheme of definition for functions on No, generalising those for sum, product and exponential. If a function has such a definition, and can live in a Hardy field, and satisfies some auxiliary technical conditions, one can obtain in No a substantial analogue of real analysis for that function. One example is the sign-change property, and this (applied to polynomials) gives an alternative treatment of the basic fact that No is real closed. I discuss the analogue for the exponential. Using these ideas one can define a generalization of Riemann integration (the indefinite integral falling under the recursion scheme). The new integral is linear, monotone, and satisfies integration by parts. For some classical functions (eg polynomials) the integral yields the traditional formulas of analysis. There are, however, anomalies for the exponential function. But one can show that the logarithm, defined as the inverse of the exponential, is the integral of 1/x as usual.
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Anicama, Jorge. "Prime numbers and encryption". Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/95565.
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In this article we will deal with the prime numbers and its current use in encryption algorithms. Encryption algorithms make possible the exchange of sensible data in internet, such as bank transactions, email correspondence and other internet transactions where privacy is important.
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Shah, Sunil. "The white man's numbers". Master's thesis, University of Cape Town, 2012. http://hdl.handle.net/11427/12498.
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Palladino, Chiara. "Numbers, winds and stars". Universitätsbibliothek Leipzig, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-221565.
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Jonsson, Helena. "Bimodules over dual numbers". Thesis, Uppsala universitet, Algebra och geometri, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-325502.
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McNamara, James N. "Two new Ramsey numbers /". Online version of thesis, 1992. http://hdl.handle.net/1850/11146.
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Warren, Erin. "How we understand numbers". View electronic thesis, 2008. http://dl.uncw.edu/etd/2008-3/warrene/erinwarren.pdf.
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Yamada, Tomohiro. "Unitary super perfect numbers". 京都大学 (Kyoto University), 2009. http://hdl.handle.net/2433/124385.
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Chakmak, Ryan. "Eigenvalues and Approximation Numbers". Scholarship @ Claremont, 2019. https://scholarship.claremont.edu/cmc_theses/2167.
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While the spectral theory of compact operators is known to many, knowledge regarding the relationship between eigenvalues and approximation numbers might be less known. By examining these numbers in tandem, one may develop a link between eigenvalues and l^p spaces. In this paper, we develop the background of this connection with in-depth examples.
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Goldoni, Luca. "Prime Numbers and Polynomials". Doctoral thesis, Università degli studi di Trento, 2010. https://hdl.handle.net/11572/368684.
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This thesis deals with the classical problem of prime numbers represented by polynomials. It consists of three parts. In the first part I collected many results about the problem. Some of them are quite recent and this part can
be considered as a survey of the state of the art of the subject. In the second part I present two results due to P. Pleasants about the cubic polynomials with integer coefficients in several variables. The aim of this part is to simplify the works of Pleasants and modernize the notation employed. In such a way these important theorems are now in a more readable form. In the third part I present some original results related with some algebraic invariants which are the key-tools in the works of Pleasants. The hidden diophantine nature of these invariants makes them very difficult to study. Anyway some
results are proved. These results make the results of Pleasants somewhat more effective.
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Goldoni, Luca. "Prime Numbers and Polynomials". Doctoral thesis, University of Trento, 2010. http://eprints-phd.biblio.unitn.it/384/1/Thesis.pdf.
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This thesis deals with the classical problem of prime numbers represented by polynomials. It consists of three parts. In the first part I collected many results about the problem. Some of them are quite recent and this part can
be considered as a survey of the state of the art of the subject. In the second part I present two results due to P. Pleasants about the cubic polynomials with integer coefficients in several variables. The aim of this part is to simplify the works of Pleasants and modernize the notation employed. In such a way these important theorems are now in a more readable form. In the third part I present some original results related with some algebraic invariants which are the key-tools in the works of Pleasants. The hidden diophantine nature of these invariants makes them very difficult to study. Anyway some
results are proved. These results make the results of Pleasants somewhat more effective.
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Müller, Dana. "The representation of numbers in space : a journey along the mental number line". Phd thesis, Universität Potsdam, 2006. http://opus.kobv.de/ubp/volltexte/2007/1294/.
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The present thesis deals with the mental representation of numbers in space. Generally it is assumed that numbers are mentally represented on a mental number line along which they ordered in a continuous and analogical manner. Dehaene, Bossini and Giraux (1993) found that the mental number line is spatially oriented from left-to-right. Using a parity-judgment task they observed faster left-hand responses for smaller numbers and faster right-hand responses for larger numbers. This effect has been labelled as Spatial Numerical Association of Response Codes (SNARC) effect.
The first study of the present thesis deals with the question whether the spatial orientation of the mental number line derives from the writing system participants are adapted to. According to a strong ontogenetic interpretation the SNARC effect should only obtain for effectors closely related to the comprehension and production of written language (hands and eyes). We asked participants to indicate the parity status of digits by pressing a pedal with their left or right foot. In contrast to the strong ontogenetic view we observed a pedal SNARC effect which did not differ from the manual SNARC effect. In the second study we evaluated whether the SNARC effect reflects an association of numbers and extracorporal space or an association of numbers and hands. To do so we varied the spatial arrangement of the response buttons (vertical vs. horizontal) and the instruction (handrelated vs. button-related). For vertically arranged buttons and a buttonrelated instruction we found a button-related SNARC effect. In contrast, for a hand-related instruction we obtained a hand-related SNARC effect. For horizontally arranged buttons and a handrelated instruction, however, we found a buttonrelated SNARC effect. The results of the first to studies were interpreted in terms of weak ontogenetic view.
In the third study we aimed to examine the functional locus of the SNARC effect. We used the psychological refractory period paradigm. In the first experiment participants first indicated the pitch of a tone and then the parity status of a digit (locus-of-slack paradigma). In a second experiment the order of stimulus presentation and thus tasks changed (effect-propagation paradigm). The results led us conclude that the SNARC effect arises while the response is centrally selected.
In our fourth study we test for an association of numbers and time. We asked participants to compare two serially presented digits. Participants were faster to compare ascending digit pairs (e.g., 2-3) than descending pairs (e.g., 3-2). The pattern of our results was interpreted in terms of forwardassociations (“1-2-3”) as formed by our ubiquitous cognitive routines to count of objects or events.Die vorliegende Arbeit beschäftigt sich mit der räumlichen Repräsentation von Zahlen. Generell wird angenommen, dass Zahlen in einer kontinuierlichen und analogen Art und Weise auf einem mentalen Zahlenstrahl repräsentiert werden. Dehaene, Bossini und Giraux (1993) zeigten, dass der mentale Zahlenstrahl eine räumliche Orientierung von links-nach-rechts aufweist. In einer Paritätsaufgabe fanden sie schnellere Links-hand Antworten auf kleine Zahlen und schnellere Rechts-hand Antworten auf große Zahlen. Dieser Effekt wurde Spatial Numerical Association of Response Codes (SNARC) Effekt genannt. In der ersten Studie der vorliegenden Arbeit ging es um den Einfluss der Schriftrichtung auf den SNARC Effekt. Eine strenge ontogenetische Sichtweise sagt vorher, dass der SNARC Effekt nur mit Effektoren, die unmittelbar in die Produktion und das Verstehen von Schriftsprache involviert sind, auftreten sollte (Hände und Augen). Um dies zu überprüfen, forderten wir Versuchspersonen auf, die Parität dargestellter Ziffern durch Tastendruck mit ihrem rechten oder linken Fuß anzuzeigen. Entgegen der strengen ontogenetischen Hypothese fanden wir den SNARC Effekt auch für Fußantworten, welcher sich in seiner Charakteristik nicht von dem manuellen SNARC Effekt unterschied. In der zweiten Studie gingen wir der Frage nach, ob dem SNARC Effekt eine Assoziation des nicht-körperbezogenen Raumes und Zahlen oder der Hände und Zahlen zugrunde liegt. Um dies zu untersuchen, variierten wir die räumliche Orientierung der Tasten zueinander (vertikal vs. horizontal) als auch die Instruktionen (hand-bezogen vs. knopf-bezogen). Bei einer vertikalen Knopfanordnung und einer knopf-bezogenen Instruktion fanden wir einen knopfbezogenen SNARC Effekt. Bei einer hand-bezogenen Instruktion fanden wir einen hand-bezogenen SNARC Effekt. Mit horizontal angeordneten Knöpfen gab es unabhängig von der Instruktion einen knopf-bezogenen SNARC Effekt. Die Ergebnisse dieser beiden ersten Studien wurden im Sinne einer schwachen ontogenetischen Sichtweise interpretiert. In der dritten Studie befassten wir uns mit dem funktionalen Ursprung des SNARC Effekts. Hierfür nutzten wir das Psychological Refractory Period (PRP) Paradigma. In einem ersten Experiment hörten Versuchspersonen zuerst einen Ton nach welchem eine Ziffer visuell präsentiert wurde (locus-of-slack Paradigma). In einem zweiten Experiment wurde die Reihenfolge der Stimuluspräsentation/Aufgaben umgedreht (effect-propagation Paradigma). Unsere Ergebnisse lassen vermuten, dass der SNARC Effekt während der zentralen Antwortselektion generiert wird. In unserer vierten Studie überprüften wir, ob Zahlen auch mit Zeit assoziiert werden. Wir forderten Versuchspersonen auf zwei seriell dargebotene Zahlen miteinander zu vergleichen. Versuchspersonen waren schneller zeitlich aufsteigende Zahlen (z.B. erst 2 dann 3) als zeitlich abfolgenden Zahlen (z.B. erst 3 dann 2) miteinander zu vergleichen. Unsere Ergebnisse wurden im Sinne unseres vorwärtsgerichteten Mechanismus des Zählens („1-2-3“) interpretiert.
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Lozier, Stephane. "On simultaneous approximation to a real number and its cube by rational numbers". Thesis, University of Ottawa (Canada), 2010. http://hdl.handle.net/10393/28701.
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One of the fundamental problems in Diophantine approximation is approximation to real numbers by algebraic numbers of bounded degree. In 1969, H. Davenport and W. M. Schmidt developed a new method to approach the problem. This method combines a result on simultaneous approximation to successive powers of a real number xi with geometry of numbers. For now, the only case where the estimates are optimal is the case of two consecutive powers. Davenport and Schmidt show that if a real number xi is such that 1, xi, xi² are linearly independent over Q , then the exponent of simultaneous approximation to xi and xi² by rational numbers with the same denominator is at most ( 5 - 1}/2 = 0.618..., the inverse of the Golden ratio. In this thesis, we consider the case of a number and its cube. Our main result is that if a real number xi is such that 1, xi, xi³ are linearly independent over Q , then the exponent of simultaneous approximation to xi and xi³ by rational numbers with the same denominator is at most 5/7 = 0.714.... As corollaries, we deduce a result on approximation by algebraic numbers and a version of Gel'fond's lemma for polynomials of the form a + bT + cT³.
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Kong, Yafang, e 孔亚方. "On linear equations in primes and powers of two". Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hub.hku.hk/bib/B50533769.
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It is known that the binary Goldbach problem is one of the open problems on linear equations in primes, and it has the Goldbach-Linnik problem, that is, representation of an even integer in the form of two odd primes and powers of two, as its approximate problem. The theme of my research is on linear equations in primes and powers of two. Precisely, there are two cases: one pair of linear equations in primes and powers of two, and one class of pairs of linear equations in primes and powers of two, in this thesis.
In 2002, D.R. Heath-Brown and P.C. Puchta obtained that every sufficiently large even integer is the sum of two odd primes and k powers of two. Here k = 13, or = 7 under the generalized Riemann hypothesis. In 2010, B. Green and T. Tao obtained that every pair of linear equations in four prime variables with coefficients matrix A = (a_ij)s×t with s ≤ t, satisfying nondegenerate condition, that is, A has full rank and the only elements of the row-space of A over Q with two or fewer nonzero entries is the zero vector, is solvable. The restriction on the coefficient matrix means that they excluded the case of the binary Goldbach problem. Motivated by the above results, it is obtained that for every pair of sufficiently large positive even integers B1, B2, the simultaneous equation
{█({B1 = p1 + p2 + 2v1 + 2v2 + · · · + 2vk ,@B2 = p3 + p4 + 2v1 + 2v2 + · · · + 2vk ,)┤ (1)
is solvable, where p1, · · · , p4 are odd primes, each vi is a positive integer, and the positive integer k ≥ 63 or ≥ 31 under the generalized Riemann
hypothesis. Note that, in 1989, M.C. Liu and K.M. Tsang have obtained that subject to some natural conditions on the coefficients, every pair of linear equations in five prime variables is solvable. Therefore one class of pairs of linear equations in four prime variables with special coefficient matrix and powers of two is considered. Indeed, it is deduced that every pair of integers B1 and B2 satisfying B1 ≡ 0 (mod 2), 3BB1 > e^(eB^48 ), B2 ≡ ∑_1^4▒= 1^(a_i ) (mod 2) and |B2| < BB1, where B = max1≤j≤4(2, |aj|), can be represented as
{█(B1 = 〖p1〗_1 + p2 + 2^(v_1 ) + 2^(v_2 )+ · · · + 2^(v_k )@B2 = a1p1 + a2p2 + a3p3 + a4p4 + 2^(v_1 )+ 2^(v_2 )+ · · · + 2^(v_k ) )┤ (2)
with k being a positive integer. Here p1, · · · p4 are odd primes, each 〖v 〗_iis a positive integer and the integral coefficients ai (i = 1, 2, 3, 4) satisfy
{█((〖a 〗_1- 〖a 〗_2, 〖a 〗_3, 〖a 〗_4) = 1,@〖a 〗_1 〖a 〗_2< 0, 〖a 〗_3 〖a 〗_4<0,)┤
Moreover it is calculated that the positive integer k ≥ g(〖a 〗_1- 〖a 〗_2, 〖a 〗_3, 〖a 〗_4) where g(〖a 〗_21- 〖a 〗_22, 〖a 〗_23, 〖a 〗_24) = [(log〖G(〖a 〗_21, …, 〖a 〗_24 〗)-log〖F (〖a 〗_21, …, 〖a 〗_24)〗)/log0.975805-84.0285], (3)
G(〖a 〗_21, 〖a 〗_22, 〖a 〗_23, 〖a 〗_24) = (min(1/(|a_24 |), 1/(|a_23 |)) - (〖|a〗_(21 )- a_22 |)/(|〖a_23 a〗_24 |) 〖(3B)〗^(-1) ×〖(3B)〗^(-1) (1-0.000001)- 〖(3B)〗^(-1-4), with B = max1≤j≤4(2, |a2j|), and
F(a_21, …, a_24) = √(f(a_21)f〖(a〗_22 ))
with
f(a_2i) = {█(4414.15h (a_21-1)+5.088331 if a_21≠1@59.8411 if a_21=1,)┤
for i = 1, 2, and h(n) =∏_(p|n,p>2)▒(p-1)/(p-2). This result, if without the powers of
two, can make up some of the cases excluded in Green and Tao’s paper.published_or_final_version
Mathematics
Doctoral
Doctor of Philosophy
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Spolaor, Silvana de Lourdes Gálio. "Números irracionais: e e". Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/55/55136/tde-02102013-160720/.
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Nesta dissertação são apresentadas algumas propriedades de números reais. Descrevemos de maneira breve os conjuntos numéricos N, Z, Q e R e apresentamos demonstrações detalhadas da irracionalidade dos números \'pi\' e e. Também, apresentamos um texto sobre o número e, menos técnico e mais intuitivo, na tentativa de auxiliar o professor no preparo de aulas sobre o número e para alunos do Ensino Médio, bem como, alunos de cursos de Licenciatura em MatemáticaIn this thesis we present some properties of real numbers. We describe briefly the numerical sets N, Z, Q and R, and we present detailed proofs of irrationality of numbers \'pi\' and e. We also present a text about the number e less technical and more intuitive in an attempt to assist the teacher in preparing lessons about number e for High School students as well as for Teaching degree in Mathematics students
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Munter, Johan. "Number Recognition of Real-world Images in the Forest Industry : a study of segmentation and recognition of numbers on images of logs with color-stamped numbers". Thesis, Mittuniversitetet, Institutionen för informationssystem och –teknologi, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:miun:diva-39365.
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Analytics such as machine learning are of big interest in many types of industries. Optical character recognition is essentially a solved problem, whereas number recognition on real-world images which can be one form of machine learning are a more challenging obstacle. The purpose of this study was to implement a system that can detect and read numbers on given dataset originating from the forest industry being images of color-stamped logs. This study evaluated accuracy of segmentation and number recognition on images of color-stamped logs when using a pre-trained model of the street view house numbers dataset. The general approach of preprocessing was based on car number plate segmentation because of the similar problem of identifying an object to then locate individual digits. Color segmentation were the biggest asset for the preprocessing because of the distinct red color of digits compared to the rest of the image. The accuracy of number recognition was significantly lower when using the pre-trained model on color-stamped logs being 26% in comparison to street view house numbers with 95% but could still reach over 80% per digit accuracy rate for some image classes when excluding accuracy of segmentation. The highest segmentation accuracy among classes was 93% and the lowest was 32%. From the results it was concluded that unclear digits on images lessened the number recognition accuracy the most. There are much to consider for future work, but the most obvious and impactful change would be to train a more accurate model by basing it on the dataset of color-stamped logs.
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Meinke, Ashley Marie. "Fibonacci Numbers and Associated Matrices". Kent State University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=kent1310588704.
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Iuculano, T. "Good and bad at numbers : typical and atypical development of number processing and arithmetic". Thesis, University College London (University of London), 2012. http://discovery.ucl.ac.uk/1355958/.
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This thesis elucidates the heterogeneous nature of mathematical skills by examining numerical and arithmetical abilities in typical, atypical and exceptional populations. Moreover, it looks at the benefits of intervention for remediating and improving mathematical skills. First, we establish the nature of the ‘number sense’ and assess its contribution to typical and atypical arithmetical development. We confirmed that representing and manipulating numerosities approximately is fundamentally different from the ability to manipulate them exactly. Yet only the exact manipulation of numbers seems to be crucial for the development of arithmetic. These results lead to a better characterization of mathematical disabilities such as Developmental Dyscalculia and Low Numeracy. In the latter population we also investigated more general cognitive functions demonstrating how inhibition processes of working memory and stimulusmaterial interacted with arithmetical attainment. Furthermore, we examined areas of mathematics that are often difficult to grasp: the representation and processing of rational numbers. Using explicit mapping tasks we demonstrated that well-educated adults, but also typically developing 10 year olds and children with low numeracy have a comprehensive understanding of these types of numbers. We also investigated exceptional maths abilities in a population of children with Autism Spectrum Disorder (ASD) demonstrating that this condition is characterized by outstanding arithmetical skills and sophisticated calculation strategies, which are reflected in a fundamentally different pattern of brain activation. Ultimately we looked at remediation and learning. Targeted behavioural intervention was beneficial for children with low numeracy but not in Developmental Dyscalculia. Finally, we demonstrated that adults’ numerical performance can be enhanced by neural stimulation (tDCS) to dedicated areas of the brain. This work sheds light on the entire spectrum of mathematical skills from atypical to exceptional development and it is extremely relevant for the advancing of the field of mathematical cognition and the prospects of diagnosis, education and intervention.
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McNicholas, Aine. "Dickens by Numbers : the 'Christmas Numbers' of 'Household Words' and 'All the Year Round'". Thesis, University of York, 2015. http://etheses.whiterose.ac.uk/10391/.
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This thesis examines the short fiction that makes up the annual Christmas Numbers of Dickens’s journals, Household Words and All the Year Round. Through close reading and with reference to Dickens’s letters, contemporary reviews, and the work of his contributors, this thesis contends that the Christmas Numbers are one of the most remarkable and overlooked bodies of work of the second half of the nineteenth century. Dickens’s short fictions rarely receive sustained or close attention, despite the continuing commitment by critics to bring the whole range of Dickens’s career into focus, from his sketches and journalism, to his late public readings. Through readings of selected texts, this thesis will show that Dickens’s Christmas Number stories are particularly powerful and experimental examples of some of the deepest and most recurrent concerns of his work. They include, for example, three of his four uses of a child narrator and one of his few female narrators, and are concerned with childhood, memory, and the socially marginal figures and distinctive voices that are so characteristic of his longer work. But, crucially, they also go further than his longer work to thematise the very questions raised by their production, including anonymity, authorship, collaboration, and annual return. This thesis takes Dickens’s works as its primary focus, but it will also draw throughout on the work of his contributors, which appeared alongside Dickens’s stories in these Christmas issues. In doing so this thesis aims to acknowledge the original conditions under which these stories were produced and published, but more importantly to underline the rich plurality of the Victorian periodical, which these Numbers demonstrate.
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Coles, Jonathan. "Algorithms for bounding Folkman numbers /". Online version of thesis, 2005. https://ritdml.rit.edu/dspace/handle/1850/2765.
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Mankiewicz, Piotr, Carsten Schuett e schuett@math uni-kiel de. "On the Delone Triangulation Numbers". ESI preprints, 2000. ftp://ftp.esi.ac.at/pub/Preprints/esi952.ps.
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Parra, Rodrigo. "Lelong numbers on projective varieties". Licentiate thesis, KTH, Matematik (Inst.), 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-25285.
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Wolczuk, Dan. "Intervals with few Prime Numbers". Thesis, University of Waterloo, 2004. http://hdl.handle.net/10012/1064.
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In this thesis we discuss some of the tools used in the study of the number of primes in short intervals. In particular, we discuss a large sieve density estimate due to Gallagher and two classical delay equations. We also show how these tools have been used by Maier and Stewart and provide computational data to their result.
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Follon, Derek. "Synthesis from numbers to intentionality". Thesis, University of Ottawa (Canada), 1985. http://hdl.handle.net/10393/4600.
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Guadiana, Juan, James Baird e Curtiss Tackill. "Modeling and Simulation with Numbers!" International Foundation for Telemetering, 2017. http://hdl.handle.net/10150/626946.
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Moore's Law predicts the trends in our technology very well and we have witnessed the relentless march of software solutions deep into the hardware domain. Link models are normally in the realm of scientific software packages like Mathematica, MatLab or Satellite Tool Kit. Here we apply Frii's Transmission equation to perform a link model with a common application like Numbers or Excel. Modeling a single link is easy and a staring antenna Array is modeled as many single links. Creating the model does require planning just as creating any software application does, but the "coding" is fairly straight forward. The results are stunning graphical plots. A simulation is created from the same spread sheet depicts the array's Graphics User Interface (GUI). Very low cost, an excellent way for students to learn to model and simulate their systems. The work serves as a good prototype to experiment with before investing in expensive software or software development. Spreadsheets do break easily so plan to back up your sheets periodically.
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Johnstone, Jennifer Ann. "Congruent numbers and elliptic curves". Thesis, University of British Columbia, 2010. http://hdl.handle.net/2429/26993.
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Throughout this thesis we will be primarily concerned with the area of a rational right angle triangle, also known as a congruent number. The purpose of this thesis is to present a family of congruent number elliptic curves with rank at least three, as well as provide some insight into the distribution of congruent numbers. We provide an in depth background on congruent numbers and elliptic curves, as well as an overview of one of the key methods that will be used in determining the rank of an elliptic curve.