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1
Waller, Bradley A. "Properties of p-adic C^k Distributions." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1385485834.
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Kou, Kit Ian. "Paley-Wiener theorem and Shannon sampling with the Clifford analysis setting." Thesis, University of Macau, 2005. http://umaclib3.umac.mo/record=b2492153.
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Butler, Pieter-Willem. "The transfer of distributions by LULU smoothers." Thesis, Link to the online version, 2008. http://hdl.handle.net/10019/2030.
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Begum, Munni. "Estimating posterior expectation of distributions belonging to exponential and non exponential families." Virtual Press, 2001. http://liblink.bsu.edu/uhtbin/catkey/1244863.
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Bayesian principle is conceptually simple and intuitively plausible to carry out but its numerical implementation is not always straightforward. Most of the times we have posterior distributions in terms of complicated analytical funs ions and be known only up to a multiplicative constant. Hence it becomes computationally difficult to attain the marginal densities and the moments of the posterior distributions in closed form. In the present study the leading methods, both analytical and numerical, for implementing Bayesian inference has been explored. In particular, the non-iterative Monte Carlo method known as Importance Sampling has been applied to approximate the posterior expectations of the Lognormal and Cauchy distributions, belonging to the Exponential family and the non-Exponential family of distributions respectively. Sample values from these distributions have been simulated through computer programming. Calculations are done mostly by C++ programming language and Mathematica.<br>Department of Mathematical Sciences
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Kim, Jongchul. "Generalized Function Solutions to Nonlinear Wave Equations with Distribution Initial Data." Thesis, University of North Texas, 1996. https://digital.library.unt.edu/ark:/67531/metadc278853/.
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In this study, we consider the generalized function solutions to nonlinear wave equation with distribution initial data. J. F. Colombeau shows that the initial value problem u_tt - Δu = F(u); m(x,0) = U_0; u_t (x,0) = i_1 where the initial data u_0 and u_1 are generalized functions, has a unique generalized function solution u. Here we take a specific F and specific distributions u_0, u_1 then inspect the generalized function representatives for the initial value problem solution to see if the generalized function solution is a distribution or is more singular. Using the numerical technics, we show for specific F and specific distribution initial data u_0, u_1, there is no distribution solution.
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Hasan, Abeer. "A Study of non-central Skew t Distributions and their Applications in Data Analysis and Change Point Detection." Bowling Green State University / OhioLINK, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1371055538.
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Engelke, Sebastian. "Brown-Resnick Processes: Analysis, Inference and Generalizations." Doctoral thesis, Niedersächsische Staats- und Universitätsbibliothek Göttingen, 2012. http://hdl.handle.net/11858/00-1735-0000-000D-F1B3-2.
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Kong, Fanhui. "Asymptotic distributions of Buckley-James estimator." Online access via UMI:, 2005.
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Lai, Pik-ying, and 黎碧瑩. "Lp regression under general error distributions." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2004. http://hub.hku.hk/bib/B30287844.
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Chan, Chun-man, and 陳俊文. "On a topic of Bayesian analysis using scale mixtures distributions." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2001. http://hub.hku.hk/bib/B31223989.
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Chan, Chun-man. "On a topic of Bayesian analysis using scale mixtures distributions." Hong Kong : University of Hong Kong, 2001. http://sunzi.lib.hku.hk/hkuto/record.jsp?B22665183.
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Matsumoto, K., and A. Laurinčikas. "Joint value-distribution theorems on Lerch zeta-functions. II." Kluwer Academic Publishers-Consultants Bureau, 2006. http://hdl.handle.net/2237/20426.
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Sun, Yannan. "Extremal dependence of multivariate distributions and its applications." Pullman, Wash. : Washington State University, 2010. http://www.dissertations.wsu.edu/Dissertations/Spring2010/Y_SUN_041610.pdf.
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Pihnastyi, O. M., and K. V. Likhno. "About the kinetic models of controlled production processes." Thesis, Національний технічний університет "Харківський політехнічний інститут", 2017. http://repository.kpi.kharkov.ua/handle/KhPI-Press/42512.
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Jones, Graeme Stephen. "Instantaneous frequency, time-frequency distributions and the analysis of multicomponent signals." Thesis, Queensland University of Technology, 1992.
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潘成達 and Shing-Tat Poon. "Measuring the degree of dependence of lifetimes in some bivariate survival distributions." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1993. http://hub.hku.hk/bib/B31977443.
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Poon, Shing-Tat. "Measuring the degree of dependence of lifetimes in some bivariate survival distributions." [Hong Kong] : University of Hong Kong, 1993. http://sunzi.lib.hku.hk/hkuto/record.jsp?B13787421.
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Stewart, Ian James. "Functional analysis and electroacoustic composition : theory, extensions and implications." Thesis, City University London, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.442116.
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Bottazzi, Emanuele. "Nonstandard Models in Measure Theory and in functional Analysis." Doctoral thesis, Università degli studi di Trento, 2017. https://hdl.handle.net/11572/368322.
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This thesis is concerned with the study of nonstandard models in measure theory and in functional analysis.
In measure theory, we define elementary numerosities, that are additive measures that take on values in a non-archimedean field and for which the measure of every singleton is 1. We have shown that, by taking the ratio with a suitable unit of measurement, from a numerosity it can be defined a non-atomic real-valued measure, and that every non-atomic measure can be obtained from a numerosity by this procedure. We then used numerosities to develop
a model for the probability of infinite sequences of coin tosses coherent with the original ideas of Laplace.
In functional analysis, we introduce a space of functions of nonstandard analysis with a formally finite domain, that extends both the space of distributions and the space of Young measures. Among the applications of this
space of functions, we develop a continuous-in-time, discrete-in-space nonstandard formulation for a class of ill-posed forward-backward parabolic equations, and on the study of the regularity and asymptotic behaviour of its nonstandard solutions. This approach proved to be a viable alternative to the study of the vanishing viscosity limit of the solution of a pseudoparabolic regularization of the original problem.
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Bottazzi, Emanuele. "Nonstandard Models in Measure Theory and in functional Analysis." Doctoral thesis, University of Trento, 2017. http://eprints-phd.biblio.unitn.it/2056/1/Tesi.pdf.
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This thesis is concerned with the study of nonstandard models in measure theory and in functional analysis.
In measure theory, we define elementary numerosities, that are additive measures that take on values in a non-archimedean field and for which the measure of every singleton is 1. We have shown that, by taking the ratio with a suitable unit of measurement, from a numerosity it can be defined a non-atomic real-valued measure, and that every non-atomic measure can be obtained from a numerosity by this procedure. We then used numerosities to develop
a model for the probability of infinite sequences of coin tosses coherent with the original ideas of Laplace.
In functional analysis, we introduce a space of functions of nonstandard analysis with a formally finite domain, that extends both the space of distributions and the space of Young measures. Among the applications of this
space of functions, we develop a continuous-in-time, discrete-in-space nonstandard formulation for a class of ill-posed forward-backward parabolic equations, and on the study of the regularity and asymptotic behaviour of its nonstandard solutions. This approach proved to be a viable alternative to the study of the vanishing viscosity limit of the solution of a pseudoparabolic regularization of the original problem.
21
Yaskina, Maryna. "Topics in functional analysis and convex geometry." Diss., Columbia, Mo. : University of Missouri-Columbia, 2006. http://hdl.handle.net/10355/4346.
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Thesis (Ph.D.)--University of Missouri-Columbia, 2006.<br>The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (March 1, 2007) Vita. Includes bibliographical references.
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Vernon, Denis Wesley. "The functional analysis of shoe wear patterns : theory and application." Thesis, Sheffield Hallam University, 2000. http://shura.shu.ac.uk/3106/.
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Shoe wear patterns have potential value in clinical diagnosis and forensic identification, although they lack rigorous study. Podiatrists have claimed understanding of shoe wear patterns, associating foot pathologies with characteristic patterns and implying a "onecondition, one wear pattern" hypothesis. This project was commenced to understand and clarify this relationship. Round one of an initial Delphi exercise to seek agreements over such wear pattern associations however indicated that, many different patterns could be associated with single named foot pathologies with round three agreements appearing to relate to the most common pattern associations. Analysis of the patterns in the Delphi exercise produced an instrument to describe and compare shoe wear patterns using focal points - points from which areas of shoe wear would spread. A following survey questionnaire suggested that podiatrists were most familiar with wear patterns associated with four foot pathologies - pronation, hallux rigidus, pes cavus and rearfoot varus. Patterns associated with these pathologies were collected from U. K. podiatrists in a single round questionnaire. Inductive analysis of these patterns from a hermeneutic phenomenological perspective using the focal point concept suggested that if the pathological context is known, wear patterns could be classified on the basis of causative function. A theoretical model was proposed of factors important in wear pattern production, suggesting that primary walking intention (the intended walking function of the foot) was more influential than foot pathologies in wear pattern formation and that "external" factors could also influence shoe wear. Validation and grounding of the focal point concept and model of shoe wear influence was planned, involving paired podiatry observers, to determine whether focal points could clarify, differentiate and show similarities between shoe wear patterns in reality and whether the model of wear influence was justified. To reduce the potential for observer error, two prior exercises were undertaken. A Delphi exercise focused participants on the required task and produced statements for the recognition of variables, which may influence shoe wear patterns. Inter-observer reliability tests demonstrated that clinical observation agreement levels were acceptable for the validation. In the validation, three subjects exhibiting pathologies, including hallux rigidus, and their owned footwear (22 items) were studied. The presence, level and effect of variables potentially influencing the wear patterns present, were determined by paired observations of foot pathologies, shoe fit and function, video analysis of foot function and subject interview for the footwear history. The focal point concept showed similarities and differences between shoe wear patterns, although wear pattern clarity limitations occurred. Within the pathological context the patterns predicted the related functions. The model of wear influence was supported with external influences needing to be major to override primary walking intention and foot pathology effects. A method to describe and compare shoe wear patterns and a model to explain the link between function and wear, showing the relationship of factors important in wear pattern production have been produced. This model provides an alternative perspective on foot function to that of biomechanical theory and could represent the basis of a new taxonomy for podiatry. This greater understanding of shoe wear patterns should improve their potential value in forensic identification and in clinical diagnosis.
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Diallo, Ibrahima Castillo. "Analysis of defects in GaN using Hybrid Density Functional Theory." VCU Scholars Compass, 2013. http://scholarscompass.vcu.edu/etd/3130.
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In this thesis, we first present a brief overview of various theoretical approaches used to examine the electronic structure of defects in GaN. Using the recently developed hybrid density functional theory (HSE06) along with the experimental measurements, we propose a new explanation of the nature of the yellow luminescence band in carbon-doped GaN. We conduct a systematic study of electronic and optical properties of defects (Carbon, Oxygen, Silicon related) that are candidates for the origin of yellow luminescence. We show that the CN-ON complex is significantly more likely to form compared to isolated carbon configurations. In contrast to the properties of the isolated carbon acceptor, calculated defect levels and optical transitions involving deep level of the CN-ON complex agree quite well with our thermal luminescence quenching data as well as with the experimentally measured C-doped GaN luminescence spectra. Hence, the CN-ON complex, rather than isolated C impurity, is more likely to resolve a long-standing problem of the yellow luminescence in GaN.
24
欒世武 and Shiwu Luan. "Structural inference of linear models for some families of error distributions." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1998. http://hub.hku.hk/bib/B31237502.
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Luan, Shiwu. "Structural inference of linear models for some families of error distributions /." Hong Kong : University of Hong Kong, 1998. http://sunzi.lib.hku.hk/hkuto/record.jsp?B19979368.
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Pescim, Rodrigo Rossetto. "The new class of Kummer beta generalized distributions: theory and applications." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/11/11134/tde-30012014-112231/.
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In this study, a new class of generalized distributions was developed, based on the Kummer beta distribution (NG; KOTZ, 1995), which contains as particular cases the exponentiated and beta generators of distributions. The main feature of the new family of distributions is to provide greater flexibility to the extremes of the density function and therefore, it becomes suitable for analyzing data sets with high degree of asymmetry and kurtosis. Also, two new distributions belonging to the new class of distributions, based on the Birnbaum-Saunders and generalized gamma distributions, that has as main characteristic the hazard function which assumes different forms (unimodal, bathtub shape, increase, decrease) were studied. In all studies, general mathematical properties such as ordinary and incomplete moments, generating function, mean deviations, reliability, entropies, order statistics and their moments were discussed. The estimation of parameters is approached by the method of maximum likelihood and Bayesian analysis and the observed information matrix is derived. It is also considered the likelihood ratio statistics and formal goodness-of-fit tests to compare all the proposed distributions with some of its sub-models and non-nested models. The developed results for all studies were applied to six real data sets.<br>Neste trabalho, foi proposta uma nova classe de distribuições generalizadas, baseada na distribuição Kummer beta (NG; KOTZ, 1995), que contém como casos particulares os geradores exponencializado e beta de distribuições. A principal característica da nova família de distribuições é fornecer grande flexibilidade para as extremidades da função densidade e portanto, ela torna-se adequada para a análise de conjuntos de dados com alto grau de assimetria e curtose. Também foram estudadas duas novas distribuições que pertencem à nova família de distribuições, baseadas nas distribuições Birnbaum-Saunders e gama generalizada, que possuem função de taxas de falhas que assumem diferentes formas (unimodal, forma de banheira, crescente e decrescente). Em todas as pesquisas, propriedades matemáticas gerais como momentos ordinários e incompletos, função geradora, desvios médio, confiabilidade, entropias, estatísticas de ordem e seus momentos foram discutidas. A estimação dos parâmetros é abordada pelo método da máxima verossimilhança e pela análise bayesiana e a matriz de informação observada foi derivada. Considerou-se, também, a estatística de razão de verossimilhanças e testes formais de qualidade de ajuste para comparar todas as distribuições propostas com alguns de seus submodelos e modelos não encaixados. Os resultados desenvolvidos foram aplicados a seis conjuntos de dados.
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Negash, Efrem Ocubamicael. "Risk and admissibility for a Weibull class of distributions." Thesis, Stellenbosch : Stellenbosch University, 2004. http://hdl.handle.net/10019.1/50086.
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Thesis (MSc)--Stellenbosch University, 2004.<br>ENGLISH ABSTRACT: The Bayesian approach to decision-making is considered in this thesis for reliability/survival
models pertaining to a Weibull class of distributions. A generalised right censored sampling
scheme has been assumed and implemented. The Jeffreys' prior for the inverse mean lifetime
and the survival function of the exponential model were derived. The consequent posterior distributions
of these two parameters were obtained using this non-informative prior. In addition
to the Jeffreys' prior, the natural conjugate prior was considered as a prior for the parameter
of the exponential model and the consequent posterior distribution was derived. In many
reliability problems, overestimating a certain parameter of interest is more detrimental than underestimating
it and hence, the LINEX loss function was used to estimate the parameters and
their consequent risk measures. Moreover, the same analogous derivations have been carried
out relative to the commonly-used symmetrical squared error loss function. The risk function,
the posterior risk and the integrated risk of the estimators were obtained and are regarded in
this thesis as the risk measures. The performance of the estimators have been compared relative
to these risk measures. For the Jeffreys' prior under the squared error loss function, the
comparison resulted in crossing-over risk functions and hence, none of these estimators are
completely admissible. However, relative to the LINEX loss function, it was found that a correct
Bayesian estimator outperforms an incorrectly chosen alternative. On the other hand for
the conjugate prior, crossing-over of the risk functions of the estimators were evident as a result.
In comparing the performance of the Bayesian estimators, whenever closed-form expressions
of the risk measures do not exist, numerical techniques such as Monte Carlo procedures were
used. In similar fashion were the posterior risks and integrated risks used in the performance
compansons.
The Weibull pdf, with its scale and shape parameter, was also considered as a reliability model.
The Jeffreys' prior and the consequent posterior distribution of the scale parameter of the
Weibull model have also been derived when the shape parameter is known. In this case, the estimation process of the scale parameter is analogous to the exponential model. For the case
when both parameters of the Weibull model are unknown, the Jeffreys' and the reference priors
have been derived and the computational difficulty of the posterior analysis has been outlined.
The Jeffreys' prior for the survival function of the Weibull model has also been derived, when
the shape parameter is known. In all cases, two forms of the scalar estimation error have been
t:. used to compare as much risk measures as possible. The performance of the estimators were
compared for acceptability in a decision-making framework. This can be seen as a type of
procedure that addresses robustness of an estimator relative to a chosen loss function.<br>AFRIKAANSE OPSOMMING: Die Bayes-benadering tot besluitneming is in hierdie tesis beskou vir betroubaarheids- / oorlewingsmodelle
wat behoort tot 'n Weibull klas van verdelings. 'n Veralgemene regs gesensoreerde
steekproefnemingsplan is aanvaar en geïmplementeer. Die Jeffreyse prior vir die
inverse van die gemiddelde leeftyd en die oorlewingsfunksie is afgelei vir die eksponensiële
model. Die gevolglike aposteriori-verdeling van hierdie twee parameters is afgelei, indien hierdie
nie-inligtingge-wende apriori gebruik word. Addisioneel tot die Jeffreyse prior, is die
natuurlike toegevoegde prior beskou vir die parameter van die eksponensiële model en ooreenstemmende
aposteriori-verdeling is afgelei. In baie betroubaarheidsprobleme het die oorberaming
van 'n parameter meer ernstige nagevolge as die onderberaming daarvan en omgekeerd
en gevolglik is die LINEX verliesfunksie gebruik om die parameters te beraam tesame met
ooreenstemmende risiko maatstawwe. Soortgelyke afleidings is gedoen vir hierdie algemene
simmetriese kwadratiese verliesfunksie. Die risiko funksie, die aposteriori-risiko en die integreerde
risiko van die beramers is verkry en word in hierdie tesis beskou as die risiko maatstawwe.
Die gedrag van die beramers is vergelyk relatief tot hierdie risiko maatstawwe. Die
vergelyking vir die Jeffreyse prior onder kwadratiese verliesfunksie het op oorkruisbare risiko
funksies uitgevloei en gevolglik is geeneen van hierdie beramers volkome toelaatbaar nie. Relatief
tot die LINEX verliesfunksie is egter gevind dat die korrekte Bayes-beramer beter vaar
as die alternatiewe beramer. Aan die ander kant is gevind dat oorkruisbare risiko funksies van
die beramers verkry word vir die toegevoegde apriori-verdeling. Met hierdie gedragsvergelykings
van die beramers word numeriese tegnieke toegepas, soos die Monte Carlo prosedures,
indien die maatstawwe nie in geslote vorm gevind kan word nie. Op soortgelyke wyse is die
aposteriori-risiko en die integreerde risiko's gebruik in die gedragsvergelykings.
Die Weibull waarskynlikheidsverdeling, met skaal- en vormingsparameter, is ook beskou as 'n
betroubaarheidsmodel. Die Jeffreyse prior en die gevolglike aposteriori-verdeling van die skaalparameter
van die Weibull model is afgelei, indien die vormingsparameter bekend is. In hierdie geval is die beramingsproses van die skaalparameter analoog aan die afleidings van die eksponensiële
model. Indien beide parameters van die Weibull modelonbekend is, is die Jeffreyse
prior en die verwysingsprior afgelei en is daarop gewys wat die berekeningskomplikasies is
van 'n aposteriori-analise. Die Jeffreyse prior vir die oorlewingsfunksie van die Weibull model
is ook afgelei, indien die vormingsparameter bekend is. In al die gevalle is twee vorms van
die skalaar beramingsfoute gebruik in die vergelykings, sodat soveel as moontlik risiko maatstawwe
vergelyk kan word. Die gedrag van die beramers is vergelyk vir aanvaarbaarheid binne
die besluitnemingsraamwerk. Hierdie kan gesien word as 'n prosedure om die robuustheid van
'n beramer relatief tot 'n gekose verliesfunksie aan te spreek.
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Nathanson, Ekaterina Sergeyevna. "Path integration with non-positive distributions and applications to the Schrödinger equation." Diss., University of Iowa, 2014. https://ir.uiowa.edu/etd/1370.
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In 1948, Richard Feynman published the first paper on his new approach to non-relativistic quantum mechanics. Before Feynman's work there were two mathematical formulations of quantum mechanics. Schrödinger's formulation was based on PDE (the Schrödinger equation) and states representation by wave functions, so it was in the framework of analysis and differential equations. The other formulation was Heisenberg's matrix algebra. Initially, they were thought to be competing. The proponents of one claimed that the other was “ wrong. ” Within a couple of years, John von Neumann had proved that they are equivalent.
Although Feynman's theory was not fundamentally new, it nonetheless offered an entirely fresh and different perspective: via a precise formulation of Bohr's correspondence principle, it made quantum mechanics similar to classical mechanics in a precise sense. In addition, Feynman's approach made it possible to explain physical experiments, and, via diagrams, link them directly to computations. What resulted was a very powerful device for computing energies and scattering amplitudes - the famous Feynman's diagrams.
In his formulation, Feynman aimed at representing the solution to the non-relativistic Schrödinger equation in the form of an “ average ” over histories or paths of a particle. This solution is commonly known as the Feynman path integral. It plays an important role in the theory but appears as a postulate based on intuition coming from physics rather than a justified mathematical object. This is why Feynman's vision has caught the attention of many mathematicians as well as physicists.
The papers of Gelfand, Cameron, and Nelson are among the first, and more substantial, attempts to supply Feynman's theory with a rigorous mathematical foundation. These attempts were followed by many others, but unfortunately all of them were not quite satisfactory. The difficulty comes from a need to define a measure on an infinite-dimensional space of continuous functions that represent all possible paths of a particle. This Feynman's measure has to produce an integral with the properties requested by Feynman. In particular, the expression for the Feynman measure has to involve the non-absolutely integrable Fresnel integrands. The non-absolute integrability of the Fresnel integrands makes the measure fail to be positive and to have the countably additive property. Thus, a well-defined measure in the case of the Feynman path integral does not exist.
Extensive research has been done on the methods of relating the Feynman path integral to the integral with respect to the Wiener measure. The method of analytic continuation in mass defines the Feynman path integral as a certain limit of the Wiener integrals. Unfortunately, this method can be used as definition for only almost all values of the mass parameter in the Schrödinger equation. For physicists, this is not a satisfactory result and needs to be improved.
In this work we examine those questions which originally led to the Feynman path integral. By now we know that Feynman's “ dream ” cannot be realized as a positive and countably additive measure on the path-space. Here, we offer a new way out by modifying Feynman's question, and thereby achieving a solution to the Schrödinger equation via a different kind of averages in the path-space.
We give our version of the question that Feynman “ should have asked ” in order to realize the elusive path integral. In our formulation, we get a Feynman path integral as a limit of linear functionals, as opposed to the more familiar inductive limits of positive measures, traditionally used for constructing the Wiener measure, and related Gaussian families. We adapt here an approach pioneered by Patrick Muldowney. In it, Muldowney suggested a Henstock integration technique in order to deal with the non-absolute integrability of the kind of Fresnel integrals which we need in our solution to Feynman's question. By applying Henstock's theory to Fresnel integrals, we construct a complex-valued “ probability distribution functions ” on the path-space. Then we use this “ probability ” distribution function to define the Feynman path integral as an inductive limit. This establishes a mathematically rigorous Feynman limit, and at the same time, preserves Feynman's intuitive idea in resulting functional. In addition, our definition, and our solution, do not place any restrictions on any of the parameters in the Schrödinger equation, and have a potential to offer useful computational experiments, and other theoretical insights.
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Hu, Zonghui. "Semiparametric functional data analysis for longitudinal/clustered data: theory and application." Texas A&M University, 2004. http://hdl.handle.net/1969.1/3088.
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Semiparametric models play important roles in the field of biological statistics. In this dissertation, two types of semiparametic models are to be studied. One is the partially linear model, where the parametric part is a linear function. We are to investigate the two common estimation methods for the partially linear models when the data is correlated  longitudinal or clustered. The other is a semiparametric model where a latent covariate is incorporated in a mixed effects model. We will propose a semiparametric approach for estimation of this model and apply it to the study on colon carcinogenesis.
First, we study the profilekernel and backfitting methods in partially linear models for clustered/longitudinal data. For independent data, despite the potential rootn inconsistency of the backfitting estimator noted by Rice (1986), the two estimators have the same asymptotic variance matrix as shown by Opsomer and Ruppert (1999). In this work, theoretical comparisons of the two estimators for multivariate responses are investigated. We show that, for correlated data, backfitting often produces a larger asymptotic variance than the profilekernel method; that is, in addition to its bias problem, the backfitting estimator does not have the same asymptotic efficiency as the profilekernel estimator when data is correlated. Consequently, the common practice of using the backfitting method to compute profilekernel estimates is no longer advised. We illustrate this in detail by following Zeger and Diggle (1994), Lin and Carroll (2001) with a working independence covariance structure for nonparametric estimation and a correlated covariance structure for parametric estimation. Numerical performance of the two estimators is investigated through a simulation study. Their application to an ophthalmology dataset is also described.
Next, we study a mixed effects model where the main response and covariate variables are linked through the positions where they are measured. But for technical reasons, they are not measured at the same positions. We propose a semiparametric approach for this misaligned measurements problem and derive the asymptotic properties of the semiparametric estimators under reasonable conditions. An application of the semiparametric method to a colon carcinogenesis study is provided. We find that, as compared with the corn oil supplemented diet, fish oil supplemented diet tends to inhibit the increment of bcl2 (oncogene) gene expression in rats when the amount of DNA damage increases, and thus promotes apoptosis.
30
Li, Ben. "Müller Density-Matrix-Functional Theory: Existence of Solutions and their Properties." Thesis, Uppsala universitet, Analys och tillämpad matematik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-190518.
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Schluter, Christian. "Topics in distributional analysis : the importance of intermediate institutions for income distributions, inequality and intra-distributional mobility." Thesis, London School of Economics and Political Science (University of London), 1999. http://etheses.lse.ac.uk/1487/.
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The unifying theme of this dissertation is the importance of intermediate institutions for income distributions, inequality and intra-distributional mobility. First, we analyse the effects of informational problems in a general equilibrium model with dynamically evolving wealth distributions. Poor agents need to borrow funds but a non-commitment problem on the capital market leads to persistent inequality. The next important institution to be examined is the tax-benefit system. The third chapter investigates the relative performance of alternative unemployment benefit regimes in a search-theoretic general equilibrium model of the labour market. Policy objectives such as the reduction in inequality or the alleviation of poverty are considered and the incentive problems are examined. Prior to the empirical analysis, the fourth chapter develops the large sample distribution of a number of inequality and mobility indices. Moreover, the relative performance of these (asymptotic) approximations and various bootstrap estimators is examined. The data is described in chapter five. The sixth chapter analyses the distributional consequences of the German tax-benefit system using the German Socio-Economic Panel. Two dimensions income dynamics are investigated by distinguishing between shape dynamics and intra-distributional mobility. The complementarity between various tools such as non-parametric stochastic kernel density estimates and transition matrices is explored. As the transition probabilities are found to be time-varying, several statistical models of income mobility are estimated (and a new mover-stayer model is proposed) in the last chapter. In order to give an economic explanation of the observed mobility patterns various duration models (with duration dependent hazards and unobserved heterogeneity) are estimated.
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Cunha, Ana Torre do Valle de Arriaga e. "Cumulative prospect theory : a parametric analysis of the functional forms and applications." Master's thesis, Instituto Superior de Economia e Gestão, 2012. http://hdl.handle.net/10400.5/10990.
Full textAbstract:
Mestrado em Finanças<br>Este trabalho apresenta um estudo empírico sobre cumulative prospect theory através do estudo da função de utilidade e a função de probabilidade distorcida.
Os resultados obtidos estão de acordo com a literatura, que mostra que a função da utilidade é côncava no domínio dos ganhos, e quase linear no domínio das perdas.
Não só mostra que a função da probabilidade distorcida tem a forma de um "S" inverso tanto no domínio dos ganhos como no domínio das perdas. Também aborda o estudo de variáveis demográficas relacionando-as com os coeficientes das funções mencionadas anteriormente, concluindo assim que os homens estão mais dispostos a correr riscos do que as mulheres.
Por fim, através dos coeficientes calculados, foi possível aplicar os resultados ao mercado financeiro.
Primeiro criando uma ponte entre o coeficiente de loss aversion e a escala de DOSPERT, o que irá facilitar a determinação do carteira mais adequado para cada individuo.
Segundo, aplicando a cumulative prospect theory à modern portfolio theory para o mercado Português. Isto irá permitir que as instituições financeiras consigam determinar a carteira óptima do mercado, tendo em conta as probabilidades distorcidas.<br>This work presents an empirical study of the cumulative prospect theory using a Portuguese sample. We estimate the value function and the probability weighting function with positive and negative outcomes. The results confirm previous works that the value function is concave in the gain domain and almost linear in the loss domain. Our results also show an inverse S-shape for the probability weighting function in both loss and gain domain.
We also look into the relation of the coefficient from the already mentioned functions with some demographic variables. It was possible to conclude that males are more willing to take risks than females.
Finally, using the calculated coefficients we discuss the applicability of the results in the context of financial markets. First we establish a bridge between the loss aversion coefficient and the DOSPERT-scale, which will provide an easier way for financial institutions to present the correct efficient portfolio for each individual. Second we apply the cumulative prospect theory to the modern portfolio theory, for the Portuguese market. This will allow the financial institutions to create an efficient portfolio of the market, taking into account the probabilities distortions
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Dimakou, Sofia. "Waiting time distributions and national targets for elective surgery in UK : theoretical modelling and duration analysis." Thesis, City University London, 2013. http://openaccess.city.ac.uk/2947/.
Full textAbstract:
Waiting times for elective surgery constitute a key performance indicator for the NHS. The principal policy response has been to introduce maximum waiting time targets against which performance is measured and rewarded. The aim of this thesis is to shed light on the mechanism of patients’ admittance for elective surgery in UK by examining the whole distribution of their waiting times from an empirical and theoretical perspective. In Chapter 2, we empirically investigate the effect of government targets on the distribution of patients’ waiting times by applying duration analysis techniques to waiting time data from 2001/02 and 2002/03 for three specialties: general surgery, trauma & orthopaedics and ophthalmology. In Chapter 3, we examine further the variation in the way hospitals and surgeons manage their waiting lists by exposing detailed patterns regarding the shape of the survival and hazard curves of patients’ waits. We use an expanded dataset (1997/98 to 2005/06) both in a cross-sectional and across time framework controlling for factors such as size, type and performance rating for hospitals and activity level for doctors. We also address the issue of the evolution of waiting time distributions over time. Chapter 4 provides a theoretical supply model on how a hospital manages its stock of patients given its objective function and the constraints it is faced with. We derive the optimal waiting time distribution and identify important factors that could explain the differences between the observed empirical patterns.
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Kucherenko, Tamara. "The absolute functional calculus for sectorial operators." Diss., Columbia, Mo. : University of Missouri-Columbia, 2005. http://hdl.handle.net/10355/4155.
Full textAbstract:
Thesis (Ph. D.)--University of Missouri-Columbia, 2005.<br>The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (July 18, 2006) Vita. Includes bibliographical references.
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Umunoza, Gasana Emelyne. "Misclassification Probabilities through Edgeworth-type Expansion for the Distribution of the Maximum Likelihood based Discriminant Function." Licentiate thesis, Linköpings universitet, Tillämpad matematik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-175873.
Full textAbstract:
This thesis covers misclassification probabilities via an Edgeworth-type expansion of the maximum likelihood based discriminant function. When deriving misclassification errors, first the expectation and variance in the population are assumed to be known where the variance is the same across populations and thereafter we consider the case where those parameters are unknown. Cumulants of the discriminant function for discriminating between two multivariate normal populations are derived. Approximate probabilities of the misclassification errors are established via an Edgeworth-type expansion using a standard normal distribution.
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Swartz, Horn Rebecca. "CT3 as an Index of Knowledge Domain Structure: Distributions for Order Analysis and Information Hierarchies." Thesis, University of North Texas, 2002. https://digital.library.unt.edu/ark:/67531/metadc3306/.
Full textAbstract:
The problem with which this study is concerned is articulating all possible CT3 and KR21 reliability measures for every case of a 5x5 binary matrix (32,996,500 possible matrices). The study has three purposes. The first purpose is to calculate CT3 for every matrix and compare the results to the proposed optimum range of .3 to .5. The second purpose is to compare the results from the calculation of KR21 and CT3 reliability measures. The third purpose is to calculate CT3 and KR21 on every strand of a class test whose item set has been reduced using the difficulty strata identified by Order Analysis. The study was conducted by writing a computer program to articulate all possible 5 x 5 matrices. The program also calculated CT3 and KR21 reliability measures for each matrix. The nonparametric technique of Order Analysis was applied to two sections of test items to stratify the items into difficulty levels. The difficulty levels were used to reduce the item set from 22 to 9 items. All possible strands or chains of these items were identified so that both reliability measures (CT3 and KR21) could be calculated. One major finding of this study indicates that .3 to .5 is a desirable range for CT3 (cumulative p=.86 to p=.98) if cumulative frequencies are measured. A second major finding is that the KR21 reliability measure produced an invalid result more than half the time. The last major finding is that CT3, rescaled to range between 0 and 1, supports De Vellis' guidelines for reliability measures. The major conclusion is that CT3 is a better measure of reliability since it considers both inter- and intra-item variances.
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Paneah, B. "On the general theory of the cauchy type functional equations with applications in analysis." Universität Potsdam, 2005. http://opus.kobv.de/ubp/volltexte/2009/3000/.
Full textAbstract:
Contents:
1 The main notations and definitions.
2 Statement of the problems and main results.
2.1 The case of a Z-configuration.
2.2 The case of a P-configuration.
3 Proofs of Theorems 1-7.
4 Applications.
4.1 Multiplicative Cauchy type functional equation.
4.2 On some integral equations relating to a geometric problem
4.3 On the solvability of boundary problem for hyperbolic differential equations.
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Kröger, Viktor. "Classification in Functional Data Analysis : Applications on Motion Data." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-184963.
Full textAbstract:
Anterior cruciate knee ligament injuries are common and well known, especially amongst athletes.These injuries often require surgeries and long rehabilitation programs, and can lead to functionloss and re-injuries (Marshall et al., 1977). This work aims to explore the possibility of applyingsupervised classification on knee functionality, using different types of models, and testing differentdivisions of classes. The data used is gathered through a performance test, where individualsperform one-leg hops with motion sensors attached to their bodies. The obtained data representsthe position over time, and is considered functional data.With functional data analysis (FDA), a process can be analysed as a continuous function of time,instead of being reduced to finite data points. FDA includes many useful tools, but also somechallenges. A functional observation can for example be differentiated, a handy tool not found inthe multivariate tool-box. The speed, and acceleration, can then be calculated from the obtaineddata. How to define "similarity" is, on the other hand, not as obvious as with points. In this work,an FDA-approach is taken on classifying knee kinematic data, from a long-term follow-up studyon knee ligament injuries.This work studies kernel functional classifiers, and k-nearest neighbours models, and performssignificance tests on the model accuracy, using re-sampling methods. Additionally, depending onhow similarity is defined, the models can distinguish different features of the data. Attempts atutilising more information through incorporation of ensemble-methods, does not exceed the singlemodels it is created from. Further, it is shown that classification on optimised sub-domains, canbe superior to classifiers using the full domain, in terms of predictive power.<br>Främre korsbandsskador är vanliga och välkända skador, speciellt bland idrottsutövare. Skadornakräver ofta operationer och långa rehabiliteringsprogram, och kan leda till funktionell nedsättningoch återskador (Marshall et al., 1977). Målet med det här arbetet är att utforska möjligheten attklassificera knän utifrån funktionalitet, där utfallet är känt. Detta genom att använda olika typerav modeller, och genom att testa olika indelningar av grupper. Datat som används är insamlatunder ett prestandatest, där personer hoppat på ett ben med rörelsesensorer på kroppen. Deninsamlade datan representerar position över tid, och betraktas som funktionell data.Med funktionell dataanalys (FDA) kan en process analyseras som en kontinuerlig funktion av tid,istället för att reduceras till ett ändligt antal datapunkter. FDA innehåller många användbaraverktyg, men även utmaningar. En funktionell observation kan till exempel deriveras, ett händigtverktyg som inte återfinns i den multivariata verktygslådan. Hastigheten och accelerationen kandå beräknas utifrån den insamlade datan. Hur "likhet" är definierat, å andra sidan, är inte likauppenbart som med punkt-data. I det här arbetet används FDA för att klassificera knärörelsedatafrån en långtidsuppföljningsstudie av främre korsbandsskador.I detta arbete studeras både funktionella kärnklassificerare och k-närmsta grannar-metoder, och ut-för signifikanstest av modellträffsäkerheten genom omprovtagning. Vidare kan modellerna urskiljaolika egenskaper i datat, beroende på hur närhet definieras. Ensemblemetoder används i ett försökatt nyttja mer av informationen, men lyckas inte överträffa någon av de enskilda modellerna somutgör ensemblen. Vidare så visas också att klassificering på optimerade deldefinitionsmängder kange en högre förklaringskraft än klassificerare som använder hela definitionsmängden.
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Dean, Nema. "Variable selection and other extensions of the mixture model clustering framework /." Thesis, Connect to this title online; UW restricted, 2006. http://hdl.handle.net/1773/8943.
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Sakurai, Kazuhiro, and 櫻井和裕. "An OT-LFG analysis of language change." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2011. http://hub.hku.hk/bib/B46732482.
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Wang, Yunli. "Mass Spectrum Analysis of a Substance Sample Placed into Liquid Solution." Thesis, North Dakota State University, 2011. https://hdl.handle.net/10365/28881.
Full textAbstract:
Mass spectrometry is an analytical technique commonly used for determining elemental composition in a substance sample. For this purpose, the sample is placed into some liquid solution called liquid matrix. Unfortunately, the spectrum of the sample is not observable separate from that of the solution. Thus, it is desired to distinguish the sample spectrum. The analysis is usually based on the comparison of the mixed spectrum with the one of the sole solution. Introducing the missing information about the origin of observed spectrum peaks, the author obtains a classic set up for the Expectation-Maximization (EM) algorithm. The author proposed a mixture modeling the spectrum of the liquid solution as well as that of the sample. A bell-shaped probability mass function obtained by discretization of the univariate Gaussian probability density function was proposed or serving as a mixture component. The E- and M- steps were derived under the proposed model. The corresponding R program is written and tested on a small but challenging simulation example. Varying the number of mixture components for the liquid matrix and sample, the author found the correct model according to Bayesian Information Criterion. The initialization of the EM algorithm is a difficult standalone problem that was successfully resolved for this case. The author presents the findings and provides results from the simulation example as well as corresponding illustrations supporting the conclusions.
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Mondino, Andrea. "The Willmore functional and other L^p curvature functionals in Riemannian manifolds." Doctoral thesis, SISSA, 2011. http://hdl.handle.net/20.500.11767/4840.
Full textAbstract:
Using techniques both of non linear analysis and geometric measure theory, we prove existence of minimizers and more generally of critical points for the Willmore functional and other $L^p$ curvature functionals for immersions in Riemannian manifolds.
More precisely, given a $3$-dimensional Riemannian manifold $(M,g)$ and an immersion of a sphere $f:\Sp^2 \hookrightarrow (M,g)$ we study the following problems.
1) The Conformal Willmore functional in a perturbative setting: consider $(M,g)=(\Rtre,\eu+\epsilon h)$ the euclidean $3$-space endowed with a perturbed metric ($h=h_{\mu\nu}$ is a smooth field of symmetric bilinear forms); we prove, under assumptions on the trace free Ricci tensor and asymptotic flatness, existence of critical points for the Conformal Willmore functional $I(f):=\frac{1}{2}\int |A^\circ|^2 $ (where $A^\circ:=A-\frac{1}{2}H$ is the trace free second fundamental form). The functional is conformally invariant in curved spaces. We also establish a non existence result in general Riemannian manifolds. The technique is perturbative and relies on a Lyapunov-Schmidt reduction.
\\
2) The Willmore functional in a semi-perturbative setting: consider $(M,g)=(\Rtre, \eu+h)$ where $h=h_{\mu\nu}$ is a $C^{\infty}_0(\Rtre)$ field of symmetric bilinear forms with compact support and small $C^1$ norm. Under a general assumption on the scalar curvature we prove existence of a smooth immersion of $\Sp^2$ minimizing the Willmore functional $W(f):=\frac{1}{4} \int |H|^2$ (where $H$ is the mean curvature). The technique is more global and relies on the direct method in the calculus of variations.
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3) The functionals $E:=\frac{1}{2} \int |A|^2 $ and $W_1:=\int\left( \frac{|H|^2}{4}+1 \right)$ in compact ambient manifolds: consider $(M,g)$ a $3$-dimensional compact Riemannian manifold. We prove, under global conditions on the curvature of $(M,g)$, existence and regularity of an immersion of a sphere minimizing the functionals $E$ or $W_1$. The technique is global, uses geometric measure theory and regularity theory for higher order PDEs.
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4) The functionals $E_1:=\int \left( \frac{|A|^2}{2} +1 \right) $ and $W_1:=\int\left( \frac{|H|^2}{4}+1 \right)$ in noncompact ambient manifolds: consider $(M,g)$ a $3$-dimensional asymptotically euclidean non compact Riemannian $3$-manifold. We prove, under general conditions on the curvature of $(M,g)$, existence and regularity of an immersion of a sphere minimizing the functionals $E_1$ or $W_1$. The technique relies on the direct method in the calculus of variations.
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5) The supercritical functionals $\int |H|^p$ and $\int |A|^p$ in arbitrary dimension and codimension: consider $(N,g)$ a compact $n$-dimensional Riemannian manifold possibly with boundary. For any $2\leq m<n$ consider the functionals $\int |H|^p$ and $\int |A|^p$ with $p>m$, defined on the $m$-dimensional submanifolds of $N$. We prove, under assumptions on $(N,g)$, existence and partial regularity of a minimizer of such functionals in the framework of varifold theory. During the arguments we prove some new monotonicity formulas and new Isoperimetric Inequalities which are interesting by themselves.
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Wong, Chin Pin. "Kato's Perturbation Theorem and honesty theory." Thesis, University of Oxford, 2015. https://ora.ox.ac.uk/objects/uuid:c72c308b-d96d-4e31-a854-f2a10e99eeb6.
Full textAbstract:
We study an additive perturbation theorem for substochastic semigroups which is known as Kato's Theorem. There are two previously-known generalisations of Kato's Theorem, namely for abstract state spaces and for KB-spaces. We prove a version of Kato's Theorem for a class of spaces which encompasses both, namely ordered Banach spaces with generating cone and monotone norm. We also study a property of the perturbed semigroup in Kato's Theorem known as honesty of the semigroup. We add a few results to the fairly extensive existing theory of honesty for Kato's Theorem for abstract state spaces. In light of our new generalisation of Kato's Theorem to ordered Banach spaces with monotone norm, we investigate generalising the theory of honesty to these spaces as well. The results for the general case are less complete as many of the results for the case of abstract state spaces depend on the additive norm structure of the space. We also consider some new applications of honesty theory in abstract state spaces. We begin by applying honesty theory to the study of the heat equation on graphs. We prove that honesty of the heat semigroup coincides with a concept known as stochastic completeness of the graph which has been studied independently of honesty. We then look at the application of honesty theory to quantum dynamical semigroups. We show that honesty is the natural generalisation of the concept of conservativity of quantum dynamical semigroups. Conservative quantum dynamical semigroups are known to have certain "nice" properties. We show that similar properties hold for honest semigroups using honesty theory results. Finally, we consider a form of boundary perturbations in the context of transport semigroups. There exists an analogous theory of honesty for this set-up. We formulate a general result from which honesty results of both Kato's Theorem and transport semigroups can be derived.
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Ngundze, Unathi. "Statistical comparison of international size-based equity index using a mixture distribution." Thesis, Nelson Mandela Metropolitan University, 2011. http://hdl.handle.net/10948/d1012367.
Full textAbstract:
Investors and financial analysts spend an inordinate amount of time, resources and effort in an attempt to perfect the science of maximising the level of financial returns. To this end, the field of distribution modelling and analysis of firm size effect is important as an investment analysis and appraisal tool. Numerous studies have been conducted to determine which distribution best fits stock returns (Mandelbrot, 1963; Fama, 1965 and Akgiray and Booth, 1988). Analysis and review of earlier research has revealed that researchers claim that the returns follow a normal distribution. However, the findings have not been without their own limitations in terms of the empirical results in that many also say that the research done does not account for the fat tails and skewness of the data. Some research studies dealing with the anomaly of firm size effect have led to the conclusion that smaller firms tend to command higher returns relative to their larger counterparts with a similar risk profile (Banz, 1981). Recently, Janse van Rensburg et al. (2009a) conducted a study in which both non- normality of stock returns and firm size effect were addressed simultaneously. They used a scale mixture of two normal distributions to compare the stock returns of large capitalisation and small capitalisation shares portfolios. The study concluded that in periods of high volatility, the small capitalisation portfolio is far more risky than the large capitalisation portfolio. In periods of low volatility they are equally risky. Janse van Rensburg et al. (2009a) identified a number of limitations to the study. These included data problems, survivorship bias, exclusion of dividends, and the use of standard statistical tests in the presence of non-normality. They concluded that it was difficult to generalise findings because of the use of only two (limited) portfolios. In the extension of the research, Janse van Rensburg (2009b) concluded that a scale mixture of two normal distributions provided a more superior fit than any other mixture. The scope of this research is an extension of the work by Janse van Rensburg et al. (2009a) and Janse van Rensburg (2009b), with a view to addressing several of the limitations and findings of the earlier studies. The Janse van rensburg (2009b) study was based on data from the Johannesburg Stock Exchange (JSE); this study seeks to compare their research by looking at the New York Stock Exchange (NYSE) to determine if similar results occur in developed markets. For analysis purposes, this study used the statistical software package R (R Development Core Team 2008) and its package mixtools (Young, Benaglia, Chauveau, Elmore, Hettmansperg, Hunter, Thomas, Xuan 2008). Some computation was also done using Microsoft Excel. This dissertation is arranged as follows: Chapter 2 is a literature review of some of the baseline studies and research that supports the conclusion that earlier research finding had serious limitations. Chapter 3 describes the data used in the study and gives a breakdown of portfolio formation and the methodology used in the study. Chapter 4 provides the statistical background of the methods used in this study. Chapter 5 presents the statistical analysis and distribution fitting of the data. Finally, Chapter 6 gives conclusions drawn from the results obtained in the analysis of data as well as recommendations for future work.
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Heymann, Retha. "Fredholm theory in general Banach algebras." Thesis, Stellenbosch : University of Stellenbosch, 2010. http://hdl.handle.net/10019.1/4265.
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Thesis (MSc (Mathematics))--University of Stellenbosch, 2010.<br>ENGLISH ABSTRACT: This thesis is a study of a generalisation, due to R. Harte (see [9]), of Fredholm
theory in the context of bounded linear operators on Banach spaces
to a theory in a Banach algebra setting. A bounded linear operator T on a
Banach space X is Fredholm if it has closed range and the dimension of its
kernel as well as the dimension of the quotient space X/T(X) are finite. The
index of a Fredholm operator is the integer dim T−1(0)−dimX/T(X). Weyl
operators are those Fredholm operators of which the index is zero. Browder
operators are Fredholm operators with finite ascent and descent. Harte’s generalisation
is motivated by Atkinson’s theorem, according to which a bounded
linear operator on a Banach space is Fredholm if and only if its coset is invertible
in the Banach algebra L(X) /K(X), where L(X) is the Banach
algebra of bounded linear operators on X and K(X) the two-sided ideal of
compact linear operators in L(X). By Harte’s definition, an element a of a
Banach algebra A is Fredholm relative to a Banach algebra homomorphism
T : A ! B if Ta is invertible in B. Furthermore, an element of the form
a + b where a is invertible in A and b is in the kernel of T is called Weyl
relative to T and if ab = ba as well, the element is called Browder. Harte
consequently introduced spectra corresponding to the sets of Fredholm, Weyl
and Browder elements, respectively. He obtained several interesting inclusion
results of these sets and their spectra as well as some spectral mapping
and inclusion results. We also convey a related result due to Harte which
was obtained by using the exponential spectrum. We show what H. du T.
Mouton and H. Raubenheimer found when they considered two homomorphisms.
They also introduced Ruston and almost Ruston elements which led
to an interesting result related to work by B. Aupetit. Finally, we introduce
the notions of upper and lower semi-regularities – concepts due to V. M¨uller.
M¨uller obtained spectral inclusion results for spectra corresponding to upper
and lower semi-regularities. We could use them to recover certain spectral
mapping and inclusion results obtained earlier in the thesis, and some could
even be improved.<br>AFRIKAANSE OPSOMMING: Hierdie tesis is ‘n studie van ’n veralgemening deur R. Harte (sien [9]) van
Fredholm-teorie in die konteks van begrensde lineˆere operatore op Banachruimtes
tot ’n teorie in die konteks van Banach-algebras. ’n Begrensde lineˆere
operator T op ’n Banach-ruimte X is Fredholm as sy waardeversameling geslote
is en die dimensie van sy kern, sowel as di´e van die kwosi¨entruimte
X/T(X), eindig is. Die indeks van ’n Fredholm-operator is die heelgetal
dim T−1(0) − dimX/T(X). Weyl-operatore is daardie Fredholm-operatore
waarvan die indeks gelyk is aan nul. Fredholm-operatore met eindige styging
en daling word Browder-operatore genoem. Harte se veralgemening is gemotiveer
deur Atkinson se stelling, waarvolgens ’n begrensde lineˆere operator op
’n Banach-ruimte Fredholm is as en slegs as sy neweklas inverteerbaar is in die
Banach-algebra L(X) /K(X), waar L(X) die Banach-algebra van begrensde
lineˆere operatore op X is en K(X) die twee-sydige ideaal van kompakte
lineˆere operatore in L(X) is. Volgens Harte se definisie is ’n element a van
’n Banach-algebra A Fredholm relatief tot ’n Banach-algebrahomomorfisme
T : A ! B as Ta inverteerbaar is in B. Verder word ’n Weyl-element relatief
tot ’n Banach-algebrahomomorfisme T : A ! B gedefinieer as ’n element
met die vorm a + b, waar a inverteerbaar in A is en b in die kern van T is.
As ab = ba met a en b soos in die definisie van ’n Weyl-element, dan word
die element Browder relatief tot T genoem. Harte het vervolgens spektra
gedefinieer in ooreenstemming met die versamelings van Fredholm-, Weylen
Browder-elemente, onderskeidelik. Hy het heelparty interessante resultate
met betrekking tot insluitings van die verskillende versamelings en hulle
spektra verkry, asook ’n paar spektrale-afbeeldingsresultate en spektraleinsluitingsresultate.
Ons dra ook ’n verwante resultaat te danke aan Harte
oor, wat verkry is deur van die eksponensi¨ele-spektrum gebruik te maak.
Ons wys wat H. du T. Mouton en H. Raubenheimer verkry het deur twee
homomorfismes gelyktydig te beskou. Hulle het ook Ruston- en byna Rustonelemente
gedefinieer, wat tot ’n interessante resultaat, verwant aan werk van
B. Aupetit, gelei het. Ten slotte stel ons nog twee begrippe bekend, naamlik
’n onder-semi-regulariteit en ’n bo-semi-regulariteit – konsepte te danke
aan V. M¨uller. M¨uller het spektrale-insluitingsresultate verkry vir spektra
wat ooreenstem met bo- en onder-semi-regulariteite. Ons kon dit gebruik
om sekere spektrale-afbeeldingsresultate en spektrale-insluitingsresultate wat
vroe¨er in hierdie tesis verkry is, te herwin, en sommige kon selfs verbeter
word.
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Zhou, Zhengquan. "A theory and analysis of planing catamarans in calm and rough water." ScholarWorks@UNO, 2003. http://louisdl.louislibraries.org/u?/NOD,45.
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Thesis (Ph.D)--University of New Orleans, 2003.<br>Title from electronic submission form. "A dissertation ... in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Engineering and Applied Science"--Dissertation t.p. Vita. Includes bibliographical references.
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Griesenauer, Erin. "Algebras of cross sections." Diss., University of Iowa, 2016. https://ir.uiowa.edu/etd/2086.
Full textAbstract:
My research studies algebras of holomorphic functions from $d$-tuples of $n\times n$- matrices, $M_n(\bC)^d$, to $M_n(\bC)$. In particular, I study the holomorphic functions that can be approximated by \emph{polynomial matrix concomitants}, that is polynomial maps from $M_n(\bC)^d$ to $M_n(\bC)$ that satisfy the relationship
\[
f(g^{-1}\fz g) = g^{-1}f(\fz)g
\]
for every $\fz \in M_n(\bC)^d$ and $g\in GL_n(\bC)$. In a sense, these are the polynomial maps that “remember” the structure of the $d$-tuple $\fz$.
My first result is that these holomorphic matrix concomitants can be identified with holomorphic cross sections of certain matrix bundles. A holomorphic matrix bundle is a fibred space in which every fibre is $M_n(\bC)$ and the fibres are glued together in such a way that the total space has a holomorphic structure.
Once the identification between holomorphic cross sections and holomorphic concomitants is established, the structure of the matrix bundle is used to endow the algebra of continuous cross sections with a $C^*$-algebra structure. Then we study the subalgebra of cross sections that can be approximated by polynomial concomitants. By identifying the matrix concomitants with cross sections, we are able to prove interesting results about these algebras.
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McCabe, Terence W. (Terence William). "Minimization of a Nonlinear Elasticity Functional Using Steepest Descent." Thesis, University of North Texas, 1988. https://digital.library.unt.edu/ark:/67531/metadc331296/.
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Smith, Inna Fausett Donald W. "Controllability, observability and realizability." Click here to access thesis, 2005. http://www.georgiasouthern.edu/etd/archive/fall2005/ismith/smith%5Finna%5Fn%5F200508%5Fms.pdf.
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Thesis (M.S.)--Georgia Southern University, 2005.<br>"A thesis submitted to the Graduate Faculty of Georgia Southern University in partial fulfillment of the requirements for the degree Master of Science" ETD. Includes bibliographical references (p. 131-132)
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Economou, Dorothy. "Photos in the News: appraisal analysis of visual semiosis and verbal-visual intersemiosis." University of Sydney, 2009. http://hdl.handle.net/2123/5740.
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Doctor of Philosophy (PhD)<br>This thesis concerns the intersection of social semiotic theory and critical discourse analysis (CDA), applying systemic-functional (SF) theory to verbal-visual news media texts. The aim of the thesis is to develop social semiotic descriptions of visual meaning in order to facilitate analyses of evaluative stance in visual-verbal text. The texts studied are ‘factual’ daily broadsheet news photos and prominent visual-verbal ‘displays’ that incorporate these photos alongside headlines and captions. Such displays introduce investigative stories on the front page of broadsheet weekly news reviews and are referred to in the thesis as ‘standout’ texts. They are significant because they may also be read as independent texts and play a critical role in positioning a wide readership on the issues investigated in the story. The SF system of verbal appraisal was used in this thesis to develop a corresponding system of visual appraisal. The process involved applying general appraisal options to a corpus of news photos and proceeding to further delicacy in a repeated cycle of analysis and system-building. Once refined in this way the system was applied alongside the verbal appraisal system to account for evaluation in verbal-visual standouts. In the thesis four Australian and four Greek standouts introducing stories on asylum seekers were analysed in order to explore the potential for variation and the impact of context on evaluative meaning choices. The thesis contributes insights into SF theory, media discourse and CDA. The visual systems developed allow appraisal analysis to be extended to images and to verbalvisual texts. Visual appraisal analysis in the thesis provides new evidence for the ideological and evaluative power of news photos. Verbal-visual appraisal analysis shows how each semiotic contributes to evaluative meaning, and to its accumulation and spread across a text. In respect to media discourse, the thesis also provides evidence for the ‘standout’ as an orbital verbal-visual news genre. The comparison of evaluative stance in two sets of standouts demonstrates consistent editorial choices in texts within each context and contrasts across the two sites. The Australian texts display more evaluative complexity, greater emphasis on entertainment and offer two different stances, aligning a diverse target audience. The Greek texts are more straightforward and construct a single stance, aligning a narrower audience. By identifying the semiotic choices involved in the evaluative positioning of readers by visual-verbal texts, the thesis can contribute to more informed and reflective practice. Thus, as well as making theoretical advances, the findings have relevance for journalism and education at a time when the impact of images is changing our conception of literacy.