Thesis (Ph. D.)--University of Wisconsin--Madison, 1969. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

Inaug.-diss.--Göttingen. / Lebenslauf.

Thesis (M.A.)--Boston University

Thesis (M.A.)--Boston University. / In Chapter 1 of this thesis we give some elementary definitions and prove the following three theorems: 1.1 Every positive integer n greater than one can be expressed in the form n=p1p2...pk where each of the pi is a prime number. 1.2 Every integer n greater than one can be expressed in standard form in one and only one way. If we write n=(p1^a1)(p2^a2).....(pj^aj), where p1< p2 <...< pj and each ai is greater than 0, then n is expressed in standard form. 1.3 The number of prime numbers is infinite [TRUNCATED]

TORRES, Máro Règis Rebouças. Números algébricos e transcendentes. 66 f. Dissertação (Mestrado Profissional em Matemática) - Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017. / Submitted by Jessyca Silva (jessyca@mat.ufc.br) on 2017-09-15T05:05:08Z No. of bitstreams: 1 2017_dis_mrrtorres.pdf: 1191154 bytes, checksum: bcb31593bd1a02e84caee6bd47906dab (MD5) / Approved for entry into archive by Rocilda Sales (rocilda@ufc.br) on 2017-09-15T11:00:00Z (GMT) No. of bitstreams: 1 2017_dis_mrrtorres.pdf: 1191154 bytes, checksum: bcb31593bd1a02e84caee6bd47906dab (MD5) / Made available in DSpace on 2017-09-15T11:00:00Z (GMT). No. of bitstreams: 1 2017_dis_mrrtorres.pdf: 1191154 bytes, checksum: bcb31593bd1a02e84caee6bd47906dab (MD5) Previous issue date: 2017 / The present work deals with algebraic and transcendent numbers characterizing them under different aspects. In particular we bring some demonstrations of the irrationality of the number π and the number of Euler, base of the natural logarithm. We will also present a demonstration of the transcendence of the number and based on the script of exercises proposed by D.G. de Figueiredo, in addition to a small historical survey on π, and, algebraic and transcendent numbers. / O presente trabalho trata sobre números algébricos e transcendentes caracterizando-os sob diferentes aspectos. Em particular trazemos algumas demonstrações da irracionalidade do número π e do número de Euler, base do logaritmo natural. Também apresentaremos uma demonstração da transcendência do número e baseada no roteiro de exercícios propostos por D.G. de Figueiredo em [4], além de um pequeno apanhado histórico sobre π, e, números algébricos e transcendentes.

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This thesis investigates several theoretical and practical problems in index numbers. In Chapter 2 a hedonic elementary price index for accessing the Internet in Canada is constructed. We find that the quality-adjusted price index declines at about 15% per year. Detailed data are readily available on-line. We discuss the use of different functional forms in the regression, their ease of use and performance, and compare the result with the matched model approach. Problems in using the Box-Cox transformation and in handling packages with unlimited access are also discussed. Chapter 3 studies the problems associated with the treatment of seasonal commodities in a consumer price index. Economic assumptions behind various commonly used methods are examined from the cost-of-living perspective. A new theoretical justification based on the theory of preference change is provided for the maximum overlap method. Empirical studies using a particular data set show that indices based on various approaches give substantially different results. Direct measurement techniques have recently been employed by some statistical agencies for government output components in the SNA. These methods use proxies and indicators for outputs due to the inherent lack of market valuations. Chapter 4 investigates the pros and cons of these new approaches and compares them with the traditional cost method. This leads us to take a deeper look at the purposes, objectives, and uses of the SNA. The current method can be justified from a collective household point of view, but the lack of direct output data frustrates students of productivity analysis. By taking the economic approach in index number theory, some direct measurement methods can be compatible with the cost-of-living approach in the CPI. Using implicit expected utility theory, a money metric for utility derived from playing a lottery game is developed in Chapter 5. Using a kinked parametric functional form, outputs of the Canadian Lotto 6/49 are estimated. Results show that this direct economic approach yields an average output three times that of the official GDP. The estimated price elasticity of demand -0.67 closely resembles results for the U.K. in previous studies. / Arts, Faculty of / Vancouver School of Economics / Graduate

1 volume

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