307,159 research outputs found

    Volumes, áreas e outros problemas do tipo-Falconer

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    In this thesis, we investigate the Falconer-type problems about point configurations and in different dimensions. It is well-known the concept of the Hausdorff measure is a generalization of the Lebesgue measure and the Falconer distance problem aims to relate these two topics when it asks how large does the Hausdorff dimension of a compact set need to be to ensure the Lebesgue measure of the distance set. In the first moment, we consider a k-point configurations in Rd and we prove that a compact set E EUR Rd determines a positive measure of such volume types if the Hausdorff dimension of E is greater than d d1 2kd generalizing some results in this field. This portion of the work represents joint work with Dr. Alex McDonald. In the second moment, we study a Falconer-type problem on a 4-point configuration in the plane and we prove that a compact set E EUR R2 determines a positive measure of such Galo area types if the Hausdorff dimension of E is greater than 3 2 extending some results from A. McDonald in [22].Nessa tese, investigamos alguns problemas do tipo-Falconer sobre específicas configurações e em diferentes dimensões. O conceito de medida de Hausdorff é bem conhecido por todos pois se trata de uma generalização da medida de Lebesgue e o problema da distância de Falconer tem o objetivo de alinhar estes dois conceitos quando perguntado quão grande precisamos atribuir a dimensão de Hausdorff de um conjunto compacto a fim de que a medida de Lebesgue do conjunto de distancias seja positiva. No primeiro momento, consideramos uma configuração de k-pontos em mathbbd\\mathbb^d e provamos que se um conjunto compacto EsubsetmathbbdE\\subset \\mathbb^d então conseguimos determinar que o conjunto do tipo-volumes possui medida de Lebesgue positiva quando a dimensão de Hausdorff de E é maior do que dfracd-\\frac generalizando assim alguns resultados existentes neste campo. Uma porção destes resultados representa um trabalho feito em parceria com Dr. Alex McDonald. No segundo momento, estudamos outros problemas do tipi-Falconer sendo uma configuração de 4 pontos no plano e provamos que um conjunto compacto Esubsetmathbb2E\\subset \\mathbb^2 determina que o conjuntos do tipo area de Galo possui medida de Lebesgue positiva se a dimensão de Hausdorff de EEé maior do que frac\\frac extendendo alguns resultados de A. McDonald

    Falconer, E J, NX29123

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    This record was harvested from a previous catalogue system and will be withdrawn in 2025. Information in this record may be superseded or incomplete. Visit this record in UMA's new catalogue at: https://archives.library.unimelb.edu.au/nodes/view/384480Surname: FALCONER. Given Name(s) or Initials: E J. Military Service Number or Last Known Location: NX29123. Missing, Wounded and Prisoner of War Enquiry Card Index Number: 2795.230222 Item: [2016.0049.16773] "Falconer, E J, NX29123

    Palaeontological memoirs and notes / von Murchison, Charles / 2 Mastodon, elephant, rhinoceros, ossiferous caves, primeval man and his contemporaries

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    of the late Hugh Falconer ; compiled and edited by Charles MurchinsonExlibrisetikette: "Legat von Herrn Professor Oswald Heer" 002320143_0002 Exemplar der ETH-BI

    Palaeontological memoirs and notes

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    of the late Hugh Falconer ; compiled and edited by Charles Murchiso

    Palaeontological memoirs and notes / von Murchison, Charles / 1 Fauna antiqua sivalensis

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    of the late Hugh Falconer ; compiled and edited by Charles MurchisonExlibrisetikette: "Legat von Herrn Professor Oswald Heer" 002320143_0002 Exemplar der ETH-BIBHandschriftliches Geschenkexlibris: "To Professor Oswald Heer with W. Charles Falconer's compts." 002320101_0001 Exemplar der ETH-BI

    A singular variant of the Falconer distance problem

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    In this paper we study the following variant of the Falconer distance problem. Let EE be a compact subset of Rd{\mathbb{R}}^d, d1d \ge 1, and define (E)={xy2+xz2:x,y,zE,yz}. \Box(E)=\left\{\sqrt{{|x-y|}^2+{|x-z|}^2}: x,y,z \in E,\, y\neq z \right\}. We shall prove using a variety of methods that if the Hausdorff dimension of EE is greater than d2+14\frac{d}{2}+\frac{1}{4}, then the Lebesgue measure of (E)\Box(E) is positive. This problem can be viewed as a singular variant of the classical Falconer distance problem because considering the diagonal (x,x)(x,x) in the definition of (E)\Box(E) poses interesting complications stemming from the fact that the set {(x,x):xE}R2d\{(x,x): x \in E\}\subseteq \mathbb{R}^{2d} is much smaller than the sets for which the Falconer type results are typically established. We also prove a finite field variant of the Euclidean results for (E)\Box(E) and indicate both the similarities and the differences between the two settings.Comment: A new approach has been added. 25 page

    Assessment of motivational states in performance environments

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    The development of a new measure of operator motivational state is described, within the framework of a model of subjective stress that distinguishes Task Engagement, Distress and Worry as fundamental aspects of state (Matthews et al., 1999). Previous work on task motivation suggests that strivings for success should be distinguished from interest in the task. Factor analysis of items representing these constructs in a sample of 880 supported the development of reliable, psychometrically distinct scales for Success and Interest Motivation. Both dimensions relate to Task Engagement, but Success Motivation, perhaps surprisingly, is also associated with negative emotions and self-beliefs. The two scales showed different patterns of dependence on task factors. They were also distinguished by differing associations with workload and coping measures, although both related to higher effort and use of task-focused coping. It is concluded that the scales are promising for use in human factors research that addresses the need to structure tasks for greater operator interest and engagement

    IS Falconer

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    Research School of Physical Sciences - Research Scholars (Small Photos) - Dr. F. D. Stacey, J. R. Sherwood, Ian McDougall, I. S. Falconer, E. W. Godbole, P. W. Seymore, Dr. R. N. Glover, Mr. B. F. Wadsworth, Dr. F. C. Barker, Dr. Germaine A. Joplin, Mr. H. Johnson, Mr. R. A. Marshall, Mr. H. Doyle & other

    Going Beyond Counting First Authors in Author Co-citation Analysis

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    The present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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