1 resultado para Musical intervals and scales.
em CaltechTHESIS
Filtro por publicador
- Repository Napier (1)
- Aberdeen University (1)
- Aberystwyth University Repository - Reino Unido (1)
- Adam Mickiewicz University Repository (3)
- AMS Tesi di Dottorato - Alm@DL - Università di Bologna (6)
- Aquatic Commons (11)
- ArchiMeD - Elektronische Publikationen der Universität Mainz - Alemanha (2)
- Archimer: Archive de l'Institut francais de recherche pour l'exploitation de la mer (1)
- Archivo Digital para la Docencia y la Investigación - Repositorio Institucional de la Universidad del País Vasco (1)
- Aston University Research Archive (10)
- Biblioteca Digital | Sistema Integrado de Documentación | UNCuyo - UNCUYO. UNIVERSIDAD NACIONAL DE CUYO. (2)
- Biblioteca Digital da Produção Intelectual da Universidade de São Paulo (15)
- Biblioteca Digital da Produção Intelectual da Universidade de São Paulo (BDPI/USP) (1)
- Biblioteca Digital de Teses e Dissertações Eletrônicas da UERJ (7)
- Bioline International (1)
- BORIS: Bern Open Repository and Information System - Berna - Suiça (29)
- Boston University Digital Common (4)
- Brock University, Canada (3)
- Bucknell University Digital Commons - Pensilvania - USA (9)
- Bulgarian Digital Mathematics Library at IMI-BAS (2)
- CaltechTHESIS (1)
- Cambridge University Engineering Department Publications Database (2)
- CentAUR: Central Archive University of Reading - UK (30)
- Center for Jewish History Digital Collections (1)
- Central European University - Research Support Scheme (1)
- Chinese Academy of Sciences Institutional Repositories Grid Portal (11)
- Cochin University of Science & Technology (CUSAT), India (2)
- Collection Of Biostatistics Research Archive (1)
- Comissão Econômica para a América Latina e o Caribe (CEPAL) (1)
- CORA - Cork Open Research Archive - University College Cork - Ireland (5)
- Dalarna University College Electronic Archive (2)
- Deakin Research Online - Australia (46)
- DI-fusion - The institutional repository of Université Libre de Bruxelles (1)
- Digital Archives@Colby (2)
- Digital Commons at Florida International University (7)
- Digital Repository at Iowa State University (1)
- DigitalCommons@The Texas Medical Center (4)
- DigitalCommons@University of Nebraska - Lincoln (3)
- Doria (National Library of Finland DSpace Services) - National Library of Finland, Finland (1)
- DRUM (Digital Repository at the University of Maryland) (17)
- Duke University (6)
- Ecology and Society (1)
- eResearch Archive - Queensland Department of Agriculture; Fisheries and Forestry (3)
- FAUBA DIGITAL: Repositorio institucional científico y académico de la Facultad de Agronomia de la Universidad de Buenos Aires (1)
- Glasgow Theses Service (4)
- Greenwich Academic Literature Archive - UK (7)
- Harvard University (2)
- Helda - Digital Repository of University of Helsinki (13)
- Helvia: Repositorio Institucional de la Universidad de Córdoba (1)
- Illinois Digital Environment for Access to Learning and Scholarship Repository (1)
- Indian Institute of Science - Bangalore - Índia (16)
- Instituto de Engenharia Nuclear, Brazil - Carpe dIEN (4)
- Instituto Politécnico de Castelo Branco - Portugal (2)
- Instituto Politécnico de Viseu (2)
- Instituto Politécnico do Porto, Portugal (4)
- Instituto Superior de Psicologia Aplicada - Lisboa (1)
- Lume - Repositório Digital da Universidade Federal do Rio Grande do Sul (2)
- Massachusetts Institute of Technology (3)
- Memoria Académica - FaHCE, UNLP - Argentina (12)
- Plymouth Marine Science Electronic Archive (PlyMSEA) (1)
- Portal de Revistas Científicas Complutenses - Espanha (2)
- Publishing Network for Geoscientific & Environmental Data (60)
- QUB Research Portal - Research Directory and Institutional Repository for Queen's University Belfast (34)
- Queensland University of Technology - ePrints Archive (51)
- RCAAP - Repositório Científico de Acesso Aberto de Portugal (1)
- Repositório Aberto da Universidade Aberta de Portugal (2)
- Repositorio Académico de la Universidad Nacional de Costa Rica (1)
- Repositório Alice (Acesso Livre à Informação Científica da Embrapa / Repository Open Access to Scientific Information from Embrapa) (3)
- Repositório Científico da Universidade de Évora - Portugal (3)
- Repositório Científico do Instituto Politécnico de Lisboa - Portugal (8)
- Repositorio de la Universidad de Cuenca (1)
- Repositório Digital da UNIVERSIDADE DA MADEIRA - Portugal (1)
- Repositório Institucional da Universidade de Aveiro - Portugal (11)
- Repositório Institucional da Universidade de Brasília (1)
- Repositório Institucional da Universidade Federal do Rio Grande do Norte (2)
- Repositorio Institucional de la Universidad de Málaga (1)
- Repositório Institucional UNESP - Universidade Estadual Paulista "Julio de Mesquita Filho" (132)
- Royal College of Art Research Repository - Uninet Kingdom (1)
- RUN (Repositório da Universidade Nova de Lisboa) - FCT (Faculdade de Cienecias e Technologia), Universidade Nova de Lisboa (UNL), Portugal (3)
- SAPIENTIA - Universidade do Algarve - Portugal (2)
- School of Medicine, Washington University, United States (2)
- Universidad de Alicante (7)
- Universidad del Rosario, Colombia (8)
- Universidad Politécnica de Madrid (11)
- Universidade Complutense de Madrid (2)
- Universidade de Lisboa - Repositório Aberto (3)
- Universidade de Madeira (1)
- Universidade Estadual Paulista "Júlio de Mesquita Filho" (UNESP) (1)
- Universidade Federal de Uberlândia (4)
- Universidade Federal do Pará (6)
- Universidade Federal do Rio Grande do Norte (UFRN) (22)
- Universidade Metodista de São Paulo (6)
- Universidade Técnica de Lisboa (5)
- Universitat de Girona, Spain (3)
- Universitätsbibliothek Kassel, Universität Kassel, Germany (2)
- Université de Montréal (4)
- Université de Montréal, Canada (47)
- University of Michigan (46)
- University of Queensland eSpace - Australia (11)
- University of Southampton, United Kingdom (1)
- University of Washington (7)
- WestminsterResearch - UK (3)
Resumo:
Let E be a compact subset of the n-dimensional unit cube, 1n, and let C be a collection of convex bodies, all of positive n-dimensional Lebesgue measure, such that C contains bodies with arbitrarily small measure. The dimension of E with respect to the covering class C is defined to be the number
dC(E) = sup(β:Hβ, C(E) > 0),
where Hβ, C is the outer measure
inf(Ʃm(Ci)β:UCi Ↄ E, Ci ϵ C) .
Only the one and two-dimensional cases are studied. Moreover, the covering classes considered are those consisting of intervals and rectangles, parallel to the coordinate axes, and those closed under translations. A covering class is identified with a set of points in the left-open portion, 1’n, of 1n, whose closure intersects 1n - 1’n. For n = 2, the outer measure Hβ, C is adopted in place of the usual:
Inf(Ʃ(diam. (Ci))β: UCi Ↄ E, Ci ϵ C),
for the purpose of studying the influence of the shape of the covering sets on the dimension dC(E).
If E is a closed set in 11, let M(E) be the class of all non-decreasing functions μ(x), supported on E with μ(x) = 0, x ≤ 0 and μ(x) = 1, x ≥ 1. Define for each μ ϵ M(E),
dC(μ) = lim/c → inf/0 log ∆μ(c)/log c , (c ϵ C)
where ∆μ(c) = v/x (μ(x+c) – μ(x)). It is shown that
dC(E) = sup (dC(μ):μ ϵ M(E)).
This notion of dimension is extended to a certain class Ӻ of sub-additive functions, and the problem of studying the behavior of dC(E) as a function of the covering class C is reduced to the study of dC(f) where f ϵ Ӻ. Specifically, the set of points in 11,
(*) {dB(F), dC(f)): f ϵ Ӻ}
is characterized by a comparison of the relative positions of the points of B and C. A region of the form (*) is always closed and doubly-starred with respect to the points (0, 0) and (1, 1). Conversely, given any closed region in 12, doubly-starred with respect to (0, 0) and (1, 1), there are covering classes B and C such that (*) is exactly that region. All of the results are shown to apply to the dimension of closed sets E. Similar results can be obtained when a finite number of covering classes are considered.
In two dimensions, the notion of dimension is extended to the class M, of functions f(x, y), non-decreasing in x and y, supported on 12 with f(x, y) = 0 for x · y = 0 and f(1, 1) = 1, by the formula
dC(f) = lim/s · t → inf/0 log ∆f(s, t)/log s · t , (s, t) ϵ C
where
∆f(s, t) = V/x, y (f(x+s, y+t) – f(x+s, y) – f(x, y+t) + f(x, t)).
A characterization of the equivalence dC1(f) = dC2(f) for all f ϵ M, is given by comparison of the gaps in the sets of products s · t and quotients s/t, (s, t) ϵ Ci (I = 1, 2).