Dissertations / Theses: 'Numbus'

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Ho, Kwan-hung, and 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, and 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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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.

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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.

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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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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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Bronder, Justin S. "The AKS Class of Primality Tests: A Proof of Correctness and Parallel Implementation." Fogler Library, University of Maine, 2006. http://www.library.umaine.edu/theses/pdf/BronderJS2006.pdf.

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Kong, Yafang, and 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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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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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 Matemática
In 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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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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Loveless, Andrew David. "Extensions in the theory of Lucas and Lehmer pseudoprimes." Online access for everyone, 2005. http://www.dissertations.wsu.edu/Dissertations/Summer2005/a%5Floveless%5F070705.pdf.

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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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Shahabi, Majid. "The distribution of the classical error terms of prime number theory." Thesis, Lethbridge, Alta. : University of Lethbridge, Dept. of Mathematics and Computer Science, c2012, 2012. http://hdl.handle.net/10133/3252.

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Wodzak, Michael A. "Entire functions and uniform distribution /." free to MU campus, to others for purchase, 1996. http://wwwlib.umi.com/cr/mo/fullcit?p9823328.

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Maynard, James. "Topics in analytic number theory." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:3bf4346a-3efe-422a-b9b7-543acd529269.

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In this thesis we prove several different results about the number of primes represented by linear functions. The Brun-Titchmarsh theorem shows that the number of primes which are less than x and congruent to a modulo q is less than (C+o(1))x/(phi(q)log{x}) for some value C depending on log{x}/log{q}. Different authors have provided different estimates for C in different ranges for log{x}/log{q}, all of which give C>2 when log{x}/log{q} is bounded. We show in Chapter 2 that one can take C=2 provided that log{x}/log{q}> 8 and q is sufficiently large. Moreover, we also produce a lower bound of size x/(q^{1/2}phi(q)) when log{x}/log{q}>8 and is bounded. Both of these bounds are essentially best-possible without any improvement on the Siegel zero problem. Let k>1 and Pi(n) be the product of k linear functions of the form a_in+b_i for some integers a_i, b_i. Suppose that Pi(n) has no fixed prime divisors. Weighted sieves have shown that for infinitely many integers n, the number of prime factors of Pi(n) is at most r_k, for some integer r_k depending only on k. In Chapter 3 and Chapter 4 we introduce two new weighted sieves to improve the possible values of r_k when k>2. In Chapter 5 we demonstrate a limitation of the current weighted sieves which prevents us proving a bound better than r_k=(1+o(1))klog{k} for large k. Zhang has shown that there are infinitely many intervals of bounded length containing two primes, but the problem of bounded length intervals containing three primes appears out of reach. In Chapter 6 we show that there are infinitely many intervals of bounded length containing two primes and a number with at most 31 prime factors. Moreover, if numbers with up to 4 prime factors have `level of distribution' 0.99, there are infinitely many integers n such that the interval [n,n+90] contains 2 primes and an almost-prime with at most 4 prime factors.

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Borba, Rute Elizabete de Souza Rosa. "The effect of number meanings, conceptual invariants and symbolic representations on children's reasoning about directed numbers." Thesis, Oxford Brookes University, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.247603.

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Escardó, Martín H. "PCF extended with real numbers : a domain-theoretic approach to higher-order exact real number computation." Thesis, Imperial College London, 1997. http://hdl.handle.net/1842/509.

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We develop a theory of higher-order exact real number computation based on Scott domain theory. Our main object of investigation is a higher-order functional programming language, Real PCF, which is an extension of PCF with a data type for real numbers and constants for primitive real functions. Real PCF has both operational and denotational semantics, related by a computational adequacy property. In the standard interpretation of Real PCF, types are interpreted as continuous Scott domains. We refer to the domains in the universe of discourse of Real PCF induced by the standard interpretation of types as the real numbers type hierarchy. Sequences are functions defined on natural numbers, and predicates are truth-valued functions. Thus, in the real numbers types hierarchy we have real numbers, functions between real numbers, predicates defined on real numbers, sequences of real numbers, sequences of sequences of real numbers, sequences of functions, functionals mapping sequences to numbers (such as limiting operators), functionals mapping functions to numbers (such as integration and supremum operators), functionals mapping predicates to truth-values (such as existential and universal quantification operators), and so on. As it is well-known, the notion of computability on a domain depends on the choice of an effective presentation. We say that an effective presentation of the real numbers type hierarchy is sound if all Real PCF definable elements and functions are computable with respect to it. The idea is that Real PCF has an effective operational semantics, and therefore the definable elements and functions should be regarded as concretely computable. We then show that there is a unique sound effective presentation of the real numbers type hierarchy, up to equivalence with respect to the induced notion of computability. We can thus say that there is an absolute notion of computability for the real numbers type hierarchy. All computable elements and all computable first-order functions in the real numbers type hierarchy are Real PCF definable. However, as it is the case for PCF, some higher-order computable functions, including an existential quantifier, fail to be definable. If a constant for the existential quantifier (or, equivalently, a computable supremum operator) is added, the computational adequacy property remains true, and Real PCF becomes a computationally complete programming language, in the sense that all computable functions of all orders become definable. We introduce induction principles and recursion schemes for the real numbers domain, which are formally similar to the so-called Peano axioms for natural numbers. These principles and schemes abstractly characterize the real numbers domain up to isomorphism, in the same way as the so-called Peano axioms for natural numbers characterize the natural numbers. On the practical side, they allow us to derive recursive definitions of real functions, which immediately give rise to correct Real PCF programs (by an application of computational adequacy). Also, these principles form the core of the proof of absoluteness of the standard effective presentation of the real numbers type hierarchy, and of the proof of computational completeness of Real PCF. Finally, results on integration in Real PCF consisting of joint work with Abbas Edalat are included.

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Andersson, Carina. "Taluppfattning : En undersökning av elevers förståelse av decimaltal." Thesis, Linköping University, Department of Mathematics, 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-5820.

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I detta examensarbete har jag studerat hur elever i år 6 tänker vid decimalform inom taluppfattningens område. Begreppet taluppfattning är ett mycket brett område där det dessutom finns många olika uppfattningar om vad som ingår i begreppet. Därför har jag fokuserat mitt arbete på övergången från heltal till decimaltal. Syftet med undersökningen är att belysa vikten av att lärare har goda matematiska och metodiska kunskaper, hur elever utvecklar sin taluppfattning och förhoppningsvis ge lite tips och idéer som kan användas i undervisningen med elever. Studien omfattar en litteraturgenomgång som behandlar begreppet taluppfattning där jag delat upp kapitlet i tre underrubriker: Vad innebär det att elever har en grundläggande taluppfattning? Hur utvecklar elever en god taluppfattning? Vilka speciella svårigheter finns vid övergången från heltal till decimaltal? Under metoddelen skriver jag om hur pilot- och huvudundersökningen gjordes innan läsaren får ta del av undersökningarnas resultat. Resultatet av undersökningen är att många elever har svårt för övergången från heltal till decimaltal. Det finns tre moment i förståelsen av positionssystemet som tycks orsaka större svårigheter och det är platssiffrans värde, multiplikation med tal mindre än ett och uppskattning av rimligheten av svaret i en beräkning. Uppsatsen innehåller också ett avsnitt om vad vi lärare kan göra för att underlätta elevers förståelse för övergången från heltal till decimaltal.

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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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Deb, Dibyajyoti. "DIAGONAL FORMS AND THE RATIONALITY OF THE POINCARÉ SERIES." UKnowledge, 2010. http://uknowledge.uky.edu/gradschool_diss/25.

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The Poincaré series, Py(f) of a polynomial f was first introduced by Borevich and Shafarevich in [BS66], where they conjectured, that the series is always rational. Denef and Igusa independently proved this conjecture. However it is still of interest to explicitly compute the Poincaré series in special cases. In this direction several people looked at diagonal polynomials with restrictions on the coefficients or the exponents and computed its Poincaré series. However in this dissertation we consider a general diagonal polynomial without any restrictions and explicitly compute its Poincaré series, thus extending results of Goldman, Wang and Han. In a separate chapter some new results are also presented that give a criterion for an element to be an mth power in a complete discrete valuation ring.

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Mahmood, Muhammad Yasir. "Inexact Programming." Thesis, Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-4351.

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Two types of fuzzy linear programming i.e. fuzzy number linear programming and interval number linear programming are used for optimization problems. In interval form of linear programming we convert the inequalities from the feasible region, containing intervals as coefficients, to two groups of inequalities characterized by real, exact coefficients values. Then classical programming has been used to achieve an optimal solution in the feasible region. In fuzzy number linear programming, α‐cuts and LR forms of fuzzy numbers as coefficients have been used to find optimal solution in the feasible region. Finally the numerical examples and their solutions are attached to provide explanations of procedures.

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Narayanan, Ramaswamy Karthik. "ROLLBACK-ABLE RANDOM NUMBER GENERATORS FOR THE SYNCHRONOUS PARALLEL ENVIRONMENT FOR EMULATION AND DISCRETE-EVENT SIMULATION (SPE." Master's thesis, University of Central Florida, 2005. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/4352.

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Random Numbers form the heart and soul of a discrete-event simulation system. There are few situations where the actions of the entities in the process being simulated can be completely predicted in advance. The real world processes are more probabilistic than deterministic. Hence, such chances are represented in the system by using various statistical models, like random number generators. These random number generators can be used to represent a various number of factors, such as length of the queue. However, simulations have grown in size and are sometimes required to run on multiple machines, which share the various methods or events in the simulation among themselves. These Machines can be distributed across a LAN or even the internet. In such cases, to keep the validity of the simulation model, we need rollback-able random number generators. This thesis is an effort to develop such rollback able random number generators for the Synchronous Parallel Environment for Emulation and Discrete-Event Simulation (SPEEDES) environment developed by NASA. These rollback-able random number generators will also add several statistical distribution models to the already rich SPEEDES library.
M.S.
Other
Engineering and Computer Science
Modeling and Simulation

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Roy, George J. "Prospective teachers' development of whole number concepts and operations during a classroom teaching experiment." Orlando, Fla. : University of Central Florida, 2008. http://purl.fcla.edu/fcla/etd/CFE0002398.

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Silva, Bruno Astrolino e. "Números de Fibonacci e números de Lucas." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/55/55136/tde-03032017-143706/.

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Neste trabalho, exploramos os números de Fibonacci e de Lucas. A maioria dos resultados históricos sobre esses números são apresentados e provados. Ao longo do texto, um grande número de identidades a respeito dos números de Fibonacci e de Lucas são mostradas válidas para todos os inteiros. Sequências generalizadas de Fibonacci, a relação entre os números de Fibonacci e de Lucas com as raízes da equação x2 -x -1 = 0 e a conexão entre os números de Fibonacci e de Lucas com uma classe de matrizes em M2(R) são também exploradas.
In this work we explore the Fibonacci and Lucas numbers. The majority of the historical results are stated and proved. Along the text several identities concerning Fibonacci and Lucas numbers are shown valid for all integers. Generalized Fibonacci sequences, the relation between Fibonacci and Lucas numbers with the roots of the equation x2 -x -1 = 0 and the connection between Fibonacci and Lucas numbers with a class of matrices in M2(R) are also explored.

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Henry, Michael A. "Various Old and New Results in Classical Arithmetic by Special Functions." Kent State University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=kent1524583992694218.

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Sixtus, Elena [Verfasser], and Martin H. [Akademischer Betreuer] Fischer. "Subtle fingers – tangible numbers: The influence of finger counting experience on mental number representations / Elena Sixtus ; Betreuer: Martin H. Fischer." Potsdam : Universität Potsdam, 2018. http://d-nb.info/1218404140/34.

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Lesani, Maryam Sadat. "The Correlation between the number of health/fitness club members and health/fitness numbers with Covid-19 prevalence and death." Thesis, Högskolan i Halmstad, Akademin för hälsa och välfärd, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-45088.

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From late of 2019, human is struggling with a new and mutated virus by the name of Covid-19. The speed of prevalence and death caused by it has been very high. It became a trigger to make this area the first and most important issue at this time. Since physical activity can improve immune system, the purpose of this study is the study of the correlation between the number of health/fitness club members and health/fitness numbers with Covid-19 prevalence and death. We assessed 31 European countries from 4 aspects including the number of members of health/fitness clubs, health/fitness club numbers, Covid-19 prevalence, and Covid-19 death. All of the numbers were evaluated per 1 million individuals. To examine the correlation, Person correlation and Linear Regression were used. The results of this study showed that, statistically, there is no relationship between the number of health/fitness club members and Covid-19 prevalence. Also, there is no relationship between the number of clubs and Covid-19 prevalence. However, there was a negative correlation between the number of health/fitness club members and health fitness club numbers with Covid-19 death. In conclusion, based on the results of this study, although physical activity cannot decrease Covid-19 prevalence dramatically, it can surely reduce the number of death caused by Covid-19.

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Giacobello, Matteo. "Wake structure of a transversely rotating sphere at moderate Reynolds numbers." Online version, 2005. http://repository.unimelb.edu.au/10187/2840.

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Over the last century, the problem of a viscous flow past a sphere has received on-going attention due to its many engineering applications. These include combustion processes, sediment transport processes and atmospheric flow problems, where the sphere serves as a good model for more general bluff body particles. In these environments, particles may be subjected to both translational and rotational velocities. The objective of this study was to investigate the effect that sphere rotation, about an axis transverse to the freestream flow, has on the characteristics or the vertical wake structure and the forces exerted on the sphere. That was achieved by solving the time-dependant, incompressible Navier Stokes equations, using a highly accurate Fourier Chebyshev spectral collation method.

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Shaughnessy, John F. "Finding Zeros of Rational Quadratic Forms." Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/cmc_theses/849.

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In this thesis, we introduce the notion of quadratic forms and provide motivation for their study. We begin by discussing Diophantine equations, the field of p-adic numbers, and the Hasse-Minkowski Theorem that allows us to use p-adic analysis determine whether a quadratic form has a rational root. We then discuss search bounds and state Cassels' Theorem for small-height zeros of rational quadratic forms. We end with a proof of Cassels' Theorem and suggestions for further reading.

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Vlasic, Andrew. "A Detailed Proof of the Prime Number Theorem for Arithmetic Progressions." Thesis, University of North Texas, 2004. https://digital.library.unt.edu/ark:/67531/metadc4476/.

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We follow a research paper that J. Elstrodt published in 1998 to prove the Prime Number Theorem for arithmetic progressions. We will review basic results from Dirichlet characters and L-functions. Furthermore, we establish a weak version of the Wiener-Ikehara Tauberian Theorem, which is an essential tool for the proof of our main result.

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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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34

Nyqvist, Robert. "Algebraic Dynamical Systems, Analytical Results and Numerical Simulations." Doctoral thesis, Växjö : Växjö University Press, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-1142.

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35

Björkström, Angela. "Is it all in their heads? : A study of the strategies used in mental arithmetic by Swedish pupils in their last years of the obligatory school and in the upper secondary school." Thesis, Mälardalen University, School of Education, Culture and Communication, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-4615.

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Competence in mental arithmetic is recognised by many as essential to be active participants in the fast flowing, high technological society we live in today. Many have noticed pupils’ unwillingness to set their calculators aside and practice this aspect of mathematics when possible. Furthermore, some studies show that pupils’ ability to compute mentally deteriorates as they pass through the school system. Through testing classes in a Swedish obligatory school and an upper secondary school, the aim of this thesis is to see if the goals set by The National [Swedish] Agency for Education regarding mental arithmetic, are being fulfilled. Through using questionnaires to collect the strategies and ideas of the pupils, a wide range of problematic mathematical misconceptions became evident. These are highlighted since they are important aspects teachers should be aware of. The results of this study show that the obligatory school classes are far from reaching the goals set for them whereas the upper secondary classes show good results. Furthermore, there is an apparent improvement in their progression, resulting in a fulfilment the official goals. Many pupils however, seem reluctant to rely on their mental arithmetic capabilities and resort to algorithmic strategies. Other problems to emerge are in carrying out table calculations and in a lack of number sense when deeming if the answers are reasonable.

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Wilson, Keith Eirik. "Factoring Semiprimes Using PG2N Prime Graph Multiagent Search." PDXScholar, 2011. https://pdxscholar.library.pdx.edu/open_access_etds/219.

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In this thesis a heuristic method for factoring semiprimes by multiagent depth-limited search of PG2N graphs is presented. An analysis of PG2N graph connectivity is used to generate heuristics for multiagent search. Further analysis is presented including the requirements on choosing prime numbers to generate 'hard' semiprimes; the lack of connectivity in PG1N graphs; the counts of spanning trees in PG2N graphs; the upper bound of a PG2N graph diameter and a conjecture on the frequency distribution of prime numbers on Hamming distance. We further demonstrated the feasibility of the HD2 breadth first search of PG2N graphs for factoring small semiprimes. We presented the performance of different multiagent search heuristics in PG2N graphs showing that the heuristic of most connected seedpick outperforms least connected or random connected seedpick heuristics on small PG2N graphs of size N

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Mance, Bill. "Normal Numbers with Respect to the Cantor Series Expansion." The Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1274431587.

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38

Yelle, Céline. "Stack Number, Track Number, and Layered Pathwidth." Thesis, Université d'Ottawa / University of Ottawa, 2020. http://hdl.handle.net/10393/40348.

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In this thesis, we consider three parameters associated with graphs : stack number, track number, and layered pathwidth. Our first result is to show that the stack number of any graph is at most 4 times its layered pathwidth. This result complements an existing result of Dujmovic et al. that showed that the queue number of a graph is at most 3 times its layered pathwidth minus one (Dujmovic, Morin, and Wood [SIAM J. Comput., 553–579, 2005]). Our second result is to show that graphs of track number at most 3 have layered pathwidth at most 4. This answers an open question posed by Banister et al. (Bannister, Devanny, Dujmovic, Eppstein, and Wood [GD 2016, 499–510, 2016, Algorithmica, 1–23, 2018]).

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Schadeberg, Thilo C. "Number in Swahili grammar." Universitätsbibliothek Leipzig, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-91516.

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Kiswahili hat ein doppeltes System der nominalen Klassifikation. Das erste System ist das aus dem Bantu (Niger-Congo) bekannte System der konkordierenden nominalen und \"pronominalen\" Präfixe; das zweite, jüngere System gründet sich auf das Bedeutungsmerkmal [belebt]. Die grammatische Kategorie NUMERUS (SINGULAR::PLURAL) gilt nur im zweiten System; innerhalb des ersten Systems ist die Bildung der Nominalpaare, z .B. mtulwatu, ein derivationeller Prozeß und bezieht Konkordanz sich ausschlieBlich auf die Kategorie KLASSE.

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40

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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41

Nilsson, Marcus. "Monomial Dynamical Systems in the Fields of p-adic Numbers and Their Finite Extensions." Doctoral thesis, Växjö universitet, Matematiska och systemtekniska institutionen, 2005. http://urn.kb.se/resolve?urn=urn:nbn:se:vxu:diva-403.

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42

Hinkel, Dustin. "Constructing Simultaneous Diophantine Approximations Of Certain Cubic Numbers." Diss., The University of Arizona, 2014. http://hdl.handle.net/10150/338879.

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For K a cubic field with only one real embedding and α, β ϵ K, we show how to construct an increasing sequence {m_n} of positive integers and a subsequence {ψ_n} such that (for some constructible constants γ₁, γ₂ > 0): max{ǁm_nαǁ,ǁm_nβǁ} < [(γ₁)/(m_n^(¹/²))] and ǁψ_nαǁ < γ₂/[ψ_n^(¹/²) log ψ_n] for all n. As a consequence, we have ψ_nǁψ_nαǁǁψ_nβǁ < [(γ₁ γ₂)/(log ψ_n)] for all n, thus giving an effective proof of Littlewood's conjecture for the pair (α, β). Our proofs are elementary and use only standard results from algebraic number theory and the theory of continued fractions.

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Bongiovanni, Alex. "Problems with power-free numbers and Piatetski-Shapiro sequences." Kent State University / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=kent1618331559201676.

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44

Crunk, Anthony Wayne. "A portable C random number generator." Thesis, Virginia Tech, 1985. http://hdl.handle.net/10919/45720.

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Proliferation of computers with varying word sizes has led to increases in software use where random number generation is required. Several techniques have been developed. Criteria of randomness, portability, period, reproducibility, variety, speed, and storage are used to evaluate developed generation methods. The Tausworthe method is the only method to meet the portability requirement, and is chosen to be implemented. A C language implementation is proposed as a possible implementation and test results are presented to confirm the acceptability of the proposed code.
Master of Science

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45

Schmidtke, Maximilian [Verfasser], and Annette [Akademischer Betreuer] Huber. "On the motivic Tamagawa number of number fields." Freiburg : Universität, 2018. http://d-nb.info/1166559335/34.

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Buchanan, Dan Matthews. "Analytic Number Theory and the Prime Number Theorem." Youngstown State University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1525451327211365.

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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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Chipatala, Overtone. "Polygonal numbers." Kansas State University, 2016. http://hdl.handle.net/2097/32923.

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Master of Science
Department 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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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.

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Svanström, Fredrik. "Properties of a generalized Arnold’s discrete cat map." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-35209.

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After reviewing some properties of the two dimensional hyperbolic toral automorphism called Arnold's discrete cat map, including its generalizations with matrices having positive unit determinant, this thesis contains a definition of a novel cat map where the elements of the matrix are found in the sequence of Pell numbers. This mapping is therefore denoted as Pell's cat map. The main result of this thesis is a theorem determining the upper bound for the minimal period of Pell's cat map. From numerical results four conjectures regarding properties of Pell's cat map are also stated. A brief exposition of some applications of Arnold's discrete cat map is found in the last part of the thesis.

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Dissertations / Theses on the topic 'Numbus'

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