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Rigid Quasilocal FramesMcGrath, Paul January 2014 (has links)
This thesis begins by introducing the concept of a rigid quasilocal frame (RQF) as a geometrically natural way to define an extended system in the context of the dynamical spacetime of general relativity. An RQF is defined as a two-parameter family of timelike worldlines comprising the worldtube boundary of the history of a finite spatial volume with the rigidity conditions that the congruence of worldlines is expansion-free (the ``size'' of the system is not changing) and shear-free (the ``shape'' of the system is not changing). We demonstrate that this frame exists in flat and arbitrary curved spacetimes and, moreover, exhibits the full six motional time-dependent degrees of freedom we are familiar with from Newtonian mechanics. The latter result is intimately connected with the fact that a spatial slice through the RQF - having a two-sphere topology - always admits precisely six conformal Killing vector (CKV) fields (three boosts and three rotations) associated with the action of the Lorentz group on a two-sphere. These CKVs, along with the four-velocity of observers on the RQF, are then used to quasilocally define the energy, momentum, and angular momentum inside an RQF without relying on the pre-general relativistic practice of appealing to spacetime symmetries. These quasilocal definitions for energy, momentum, and angular momentum also involve replacing the local matter-only stress-energy-momentum (SEM) tensor with the Brown-York matter plus gravity boundary SEM tensor. This allows for the construction of completely general conservation laws which describe the changes in a system in terms of fluxes across the boundary. Furthermore, since an RQF is a congruence with zero expansion and shear only relevant fluxes appear in these conservation laws - that is, fluxes due merely to changes in the size or shape of the boundary are eliminated.
These resulting fluxes are simple, exact, and quantified in terms of operationally-defined geometrical quantities on the boundary and we show that they explain at a deeper level the mechanisms behind gravitational energy and momentum transfer by way of the equivalence principle. In particular, when we accelerate relative to a mass, the energy changes at a rate proportional to our acceleration times the momentum (and we propose an exact gravitational analogue of the electromagnetic Poynting vector to capture this idea). Similarly, the momentum of that object changes at a rate proportional to our acceleration times the energy. This new insight has fascinating consequences for how we should understand everyday occurrences like a falling apple - that is, the change in energy of the apple involves frame dragging while the change in momentum involves extrinsic curvature effects near the apple. Our naive general relativistic intuition tells us that these quantities should be so tiny that they should be negligible and, indeed, they are tiny but they are multiplied by huge numbers to give rise to macroscopic effects. This is how general relativity universally explains the transfer of energy and momentum but we needed rigid quasilocal frames to uncover this beautiful property of nature.
Using the RQF formalism we also investigate a variety of specific problems. In particular, while looking at time-dependent rotations we discover that the reason Ehrenfest's rigid rotating disk paradox has gone unsolved for so long is that rotation introduces a subtle non-locality in time. By this we mean that, in order to maintain rigidity while undergoing time-dependent rotation, one needs to know, not only the instantaneous rotation rate, but the entire history of the motion. This makes it impossible to keep a volume of observers rigid but is doable with an RQF. We also consider RQFs in the small-sphere limit to derive many of our results and one example with particularly interesting consequences involves Bell's spaceship accelerating through an electromagnetic field. Here, we show that the change in electromagnetic energy inside the spaceship is made up of two pieces: the usual electromagnetic Poynting flux accounts for half the change while the gravitational Poynting vector equally contributes to make up the other half. This means that electromagnetism in flat spacetime generically does not tell you what is actually going on. Rather, the curvature due to the electromagnetic field necessitates a fully general relativistic treatment to get the whole story. We also use the RQF linear momentum conservation law in the context of stationary observers and fields to derive, for the first time, an exact fully general relativistic analogue of Archimedes' law. In essence, this law demonstrates that the weight of the matter and gravitational fields contained in a finite region of space is supported by the stresses (buoyant forces) acting on the boundary of that region. Furthermore, in a post-Newtonian approximation, we derive a simple set of quasilocal conservation laws which describe non-relativistic systems bound by mutual gravitational attraction. In turn, we use these laws to obtain expressions for the rates of gravitational energy and angular momentum transfer between two tidally interacting bodies - that is, the tidal heating and tidal torque - without the need to define unphysical pseudotensors. Moreover, the RQF approach explains these transfers of energy and momentum again, not as the difference of forces acting on a tidal bulge, but instead more fundamentally in the language of the equivalence principle in terms of ``accelerations relative to mass''.
Throughout this work we demonstrate that the RQF approach always gives very simple, geometrical descriptions of the physical mechanisms at work in general relativity. Given that this approach also includes both matter and gravitational energy, momentum, and angular momentum and does not rely on spacetime symmetries to define these quantities, we argue that we are seeing here strong evidence that the universe is actually quasilocal in nature. We are really deeply ingrained with a local way of thinking, so shifting to a quasilocal mindset will require great effort, but we contend that it ultimately leads to a deeper understanding of the universe.
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The cross-cultural application of the adapted Schwartz values instrument in South Africa / G.C. WelthagenWelthagen, Gerrit Cornelius January 2005 (has links)
Different value systems are a major source of diversity between people and culture groups. A
better understanding of these differences can be a valuable tool when a diverse work force, as
found in South Africa, has to be managed. Values can act as a unifying theory for the field of
human motivation, as a way of organising the different needs, motives and goals proposed in
other theories. The values theory describes aspects of the human psychological structure that
are fundamental, aspects presumably common to all humankind.
The objective of this study was to investigate the construct equivalence of the values as
measured by the Work and Organizational Values Scale for new applicants from different
language groups in the South African Police Service (SAPS), and to investigate the
relationship between the value patterns of the different language and gender groups.
A cross-sectional survey design was used. The study population consisted of two groups who
applied for jobs in the South African Police Services (SAPS). The first group consisted of
civilians (N=3 400), while the second group consisted of police applicants (N=1 800). The
Work and Organizational Values Scale was administered. Descriptive statistics, exploratory
factor analyses, and multivariate analysis of variance were used to analyse the results.
Principal component analysis with a direct oblimin rotation resulted in two factors. The first
factor was interpreted as self-enhancement (power, materialism and prestige) versus
conservation (conformity and security). The second factor was interpreted as collectivism
(social commitment, relations, and environment) versus individualism (goal-orientedness.
stimulation and self-direction). These factors were found to be equivalent for four language
groups. Statistically significant differences were found between the value priorities of
different language groups as well as genders. However, larger practically significant
differences were found between males and females than between different language groups.
Recommendations for future research were made. / Thesis (M.A. (Industrial Psychology))--North-West University, Potchefstroom Campus, 2006.
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Statistical method in a comparative study in which the standard treatment is superior to othersIkeda, Mitsuru, Shimamoto, Kazuhiro, Ishigaki, Takeo, Yamauchi, Kazunobu, 池田, 充, 山内, 一信 11 1900 (has links)
No description available.
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The Effects of Using Arbitrary Symbols in Naming Procedures with AdultsJaramillo, Andia 05 1900 (has links)
Naming refers to encountering a new word and subsequently being able to use it both expressively and receptively. Sometimes, this can happen in as little as a single experience. Several recent studies have explored factors that influence the acquisition of naming in adults. However, these studies used familiar stimuli for which the participants already had names. In these studies, preexisting stimulus-response relations with the stimuli could have impeded the acquisition of new names for some participants. In contrast, the present study used unfamiliar ("arbitrary") stimuli. In addition, an equivalence test was used to validate the findings because some theorists have claimed that naming is required for equivalence. The results revealed some advantages to teaching naming with arbitrary stimuli. Interestingly, a subset of participants had high scores on equivalence tests without having high scores on expressive tests. This indicates that, contrary to naming theory, naming may not be necessary for equivalence and match-to-sample tests may not be the best test of equivalence. These findings support the independence of the expressive and receptive repertoires both in the development of naming and equivalence.
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General covariance, artificial gauge freedom and empirical equivalence :Pitts, James Brian. January 2008 (has links)
Thesis (Ph. D.)--University of Notre Dame, 2008. / Thesis directed by Don Howard for the Department of History and Philosophy of Science. "July 2008." Includes bibliographical references (leaves 196-233).
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Using the Stimulus Equivalence Paradigm to Teach Course Material in an Undergraduate Rehabilitation CourseWalker, Brooke 01 January 2009 (has links)
The current research study examined the formation of derived stimulus relations consisting of course content material in an undergraduate rehabilitation class. Specifically, the study examined the degree to which the stimulus equivalence instructional paradigm could be effectively used to teach the relationships between the names, definitions, causes, and common treatments for disabilities using a paper-and-pencil training format. Twenty-two participants were pre and post-tested on definition-to-name, cause-to-name, and treatment-to-name relations by the experimenter in a flashcard-style fashion. Training was conducted using an instructional package consisting of multiple-choice questionnaires in which name-to-definition, name-to-cause, and cause-to-treatment relations were taught and feedback was delivered from the experimenter until mastery. Results suggest that the stimulus equivalence paradigm can be effectively trained in a paper-and-pencil training format with great ease.
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Hledání APN permutací ve známých APN funkcích / Hledání APN permutací ve známých APN funkcíchPavlů, Jiří January 2018 (has links)
In the thesis a new way of checking whether a function is CCZ-equivalent to a permutation is given. The results for known families of almost perfect nonlinear (APN) functions are presented for functions defined over GF(2n ), for even n ≤ 12. The ways how to reduce the number of polynomials from each family are studied. For functions of the form x3 + a-1 tr1(a3 x9 ) it is shown, that they cannot be CCZ-equivalent to a permutation on fields GF(24n ) for n ∈ ℕ .
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An Evaluation of High versus Low Preferred Education-Based Stimulus Equivalence Protocols for Adults with Developmental Disabilities outside the Educational SystemRichmond, Ryan Allen 01 May 2015 (has links)
The present study utilized Microsoft Visual Basic 2008 to investigate the role of comparing high and low preferred education-based stimulus equivalence protocols for adults with developmental disabilities outside the educational system. First, participants were exposed to all educational categories and completed a paired choice preference assessment to identify high and low preferred protocols. Next, participants completed high and low preferred protocols following an alternating treatments design, with an initial pretest, training, posttest, and a test for an emergent topography (typing skills). Results showed evidence of higher preference through duration and errors per min measures for two of three participants, with results unclear for a third participant. Furthermore, one participant displayed all equivalence classes expected of the training protocol, while another demonstrated all emergent relations for the high preferred protocol but only one of six for the low preferred protocol, and the last participant exceeded criterion for four of six posttests for the high preferred protocol, and two of six for the low preferred protocol. The results are discussed in terms of measures for preferences, habilitation, modifications to training protocols, the study's limitations, and directions for future research.
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Evaluation of Equivalence Relations: Models of Assessment and Best PracticeSeefeldt, Dawn Amber 01 December 2015 (has links)
Due to changing age demographics in the United States, by 2050, an estimated 62.1 Americans will be over the age of 65 and the number of Americans with cognitive impairment, such as Alzheimer’s disease, will increase drastically as well (Alzheimer’s Association, 2014; Ortman, Velkoff, & Hogan, 2014). Once a diagnosis or behavioral indicators of cognitive impairment are present, it would be beneficial to apply a treatment package that promotes the maintenance or re-establishment of stimulus control in the environment. From a behavioral perspective, stimulus control aids in learning and memory through both respondent and operant conditioning. In the current study, stimulus equivalence training was completed and compared to cognitive and functional assessments scores with older adult participants with and without cognitive impairment as a systematic replication of Gallagher and Keenan (2009). Formation of equivalence relations after exposure to linear series (LS) training with 2 3-member stimulus classes across arbitrary, familiar, and stimuli from Gallagher and Keenan (2009) was compared via trials to criterion, accuracy per relation, and session length to scores on the Mini-Mental Status Exam (MMSE), Saint Louis University State Exam (SLUMS), and Barthel ADL Index. Several methodological changes were applied to a second study to examine the impact of increased programmed stimuli, training changes, and the use of one-to-many (OTM) and many-to-one (MTO) training structures with 3 3-member stimulus classes on equivalence formation. Composite performance scores were created for accuracy during LS, OTM, and MTO training. Non-parametric analyses were conducted between assessment and composite scores. The SLUMS and Barthel ADL Index were not correlated with any composite scores. However, MMSE scores and LS composite scores were correlated. The SLUMS was more sensitive to the detection of cognitive impairment as judged by classification and diagnoses. OTM and MTO composite scores also had a strong, positive correlation. Overall, more participants demonstrated higher levels of accurate responding during LS training than during OTM and MTO training. In contrast to previous research, only 25% of the sample demonstrated equivalence formation. Limitations and future research directions are discussed.
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Evaluating the Effectiveness of the PEAK-E in Teaching Receptive Metonymical Tacts Using Stimulus Equivalence Training ProceduresStanley, Caleb R. 01 August 2016 (has links)
There currently exists limited published literature on methods for teaching complex verbal operants to individuals with autism. The purpose of the current study was to evaluate the effectiveness of the PEAK – E curriculum in teaching receptive metonymical tacts using stimulus equivalence training procedures to children with autism. The procedures described in the PEAK – E program 10P – Equivalence: Metonymical Tacts were replicated across three children diagnosed with autism using a multiple baseline experimental design. The results of the suggest that the procedures were effective in teaching receptive metonymical tacts, with all three participants achieving mastery criteria. The results support and extend on previous studies by providing an empirical demonstration of effective procedures to teach receptive metonymical tacts to children with autism. The current study adds to progress behavior analysis in the direction of a behavior analytic understanding of complex verbal behavior.
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