Title: Optimal pairs of function spaces for weighted Hardy operators Author: Rastislav Ol'hava Department: Department of Mathematical Analysis Supervisor of the master thesis: Prof. RNDr. Luboš Pick, CSc., DSc., Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Prague 8, Czech Republic Abstrakt: We focus on a certain weighted Hardy operator, with a continuous, quasi- concave weight, defined on a rearrangement-invariant Banach function spaces. The op- erators of Hardy type are of great use to the theory of function spaces. The mentioned operator is a more general version of the Hardy operator, whose boundedness was shown to be equivalent to a Sobolev-type embedding inequality. This thesis is con- cerned with the proof of existence of domain and range spaces of our Hardy operator that are optimal. This optimality should lead to the optimality in the Sobolev-type embedding equalities. Our another aim is to study supremum operators, which are also closely related to this issue, and establish some of their basic properties. Keywords: optimality, weighted Hardy operator, supremum operator

On propose d'analyser la gestion de la dette publique pour montrer que, si l’on tient compte des critères d’optimalité, la dette publique peut être un choix de financement du déficit public plus judicieux par rapport à la hausse des prélèvements obligatoires ou au seigneuriage. Pour ce faire, une étude comparative entre ces trois modes de financement est menée en tenant compte de leur faisabilité institutionnelle et en revisitant la notion d’optimalité d’un point de vue financier, i.e. compte-tenu des impacts sur la santé financière de l’Etat et d’un point de vue économique, i.e. par rapport à la performance économique du pays. Il est montré que la sous optimalité ou la non optimalité de la hausse des prélèvements obligatoires ou du seigneuriage peut être un motif incitant le Gouvernement à financer le déficit public par endettement. Toutefois, il est montré également que ce dernier doit répondre à des critères d’optimalité sinon il ne peut être considéré comme efficace. Par la suite, on montre que pour atteindre l’optimalité de la dette publique, le Gouvernement doit veiller à sa soutenabilité. Autrement dit, le Gouvernement doit éviter que la dette publique ne suive une tendance explosive qui risque de la rendre non optimale. Enfin, on met en avant le rôle que jouent les risques financiers dans la gestion de la dette publique pour montrer que c’est en partie la mauvaise prise en change de ces risques qui rend la dette publique non soutenable et non optimale. / The objective of this thesis is to analyze public debt management in order to show that, based on optimality criteria, public debt could be a more judicial financing choice in comparison with taxation or seigniorage. A comparative study between these three financing strategies is conducted by taking into consideration their respective institutional feasability and by revisiting the concept of optimality from a financial viewpoint, i.e. regarding the potential impacts on public finance soundness, and from an economic aspect, i.e. regarding the potential impacts on the economic performance of the country. The non optimality of taxation and seigniorage could be a motive for the Governement to finance public deficit by indebtedness. However, it must be highlighted that public debt must also comply with optimality criteria, otherwise it will be considered inefficient. Subsequently, it is shown that Government must aim at public debt sustainability in order to ensure its optimality. In other words, Governement must avoid public debt to follow an explosive path, which is likely to lead to its non optimality. Finally, the role of financial risks in public debt management is put forth in order to suggest that non optimal or non sustainable public debt is partly due to failing financial risk management. The case study is conducted in the member countries of the Indian Ocean Commission.

<p>A significant hurdle for analyzing big data is the lack of effective technology and statistical inference methods. A popular approach for analyzing data with large sample is subsampling. Many subsampling probabilities have been introduced in literature (Ma, \emph{et al.}, 2015) for linear model. In this dissertation, we focus on generalized estimating equations (GEE) with big data and derive the asymptotic normality for the estimator without resampling and estimator with resampling. We also give the asymptotic representation of the bias of estimator without resampling and estimator with resampling. we show that bias becomes significant when the data is of high-dimensional. We also present a novel subsampling method called A-optimal which is derived by minimizing the trace of some dispersion matrices (Peng and Tan, 2018). We derive the asymptotic normality of the estimator based on A-optimal subsampling methods. We conduct extensive simulations on large sample data with high dimension to evaluate the performance of our proposed methods using MSE as a criterion. High dimensional data are further investigated and we show through simulations that minimizing the asymptotic variance does not imply minimizing the MSE as bias not negligible. We apply our proposed subsampling method to analyze a real data set, gas sensor data which has more than four millions data points. In both simulations and real data analysis, our A-optimal method outperform the traditional uniform subsampling method.</p>

Made available in DSpace on 2014-06-11T19:22:18Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-02-28Bitstream added on 2014-06-13T20:48:40Z : No. of bitstreams: 1 costa_tm_me_sjrp.pdf: 1425800 bytes, checksum: f5b08954e14201ee5211145299b1e813 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho, estamos interessados em apresentar uma abordagem relacionando a análise não suave com a otimização. Primeiramente, é realizado um estudo sobre conceitos da análise não suave, como cones normais, cone tangente de Bouligand, subdiferenciais proximal, estrita, limite e de clarke. Com esses conceitos exibimos uma série de resultados, por exemplo, uma caracterização par funções de Lipschitz, subdiferencais da soma, produto e máximo de funções semi-contínuas inferior, uma versão não suave dos multiplicadores de Lagrange, i.e., condições de primeira ordem para otimalidade de problemas de otimização não suaves. Também é feito um estudo sobre as condições de segunda ordem para otimalidade em problemas de otimização não suaves e para isso, foi necessário a apresentação de outros conceitos e propriedades como os de Hessiana generalizada, Jacobiana aproximada a Hessiana proximada. Após a apresentação desses resultados, é feita uma análise sobre dois Teoremas que fornecem, com abordagens distintas, condições suficiente de segunda ordem para problemas de otimização não suaves e este trabalho é finalizado com a aprsentação de um resultado que é considerado uma unificação desses dois Teoremas / In this work we are interested in the presentation of an approach relating Nonsmooth Analysis to Optimization. First we make a study about concepts of nonsmooth analysis such as, normal cone, Bouligand's tangent cone, proximal, strict and limiting Subdiferential, as well as Clarke's Suddifferential. After these, we exhibit a series of results, for example, a characterization of Lipschitz functions, Subdifferential sum, product and maxium rules of lower semicontinuous functions and a nonsmooth version of Lagrange's multiplier rule, that is, a first order necessary condition of optimality for nonsmooth optimization problems. We also made a study about second order optimality conditions for nonsmooth optimization problems. In order to do that, it was necessary to present other concepts and properties about generalized Hessian, approximate Jacobian and approximate Hessian. After presenting these concepts and results, an analysis of two theorems that provide, with different approches, second order conditions for optimality for nonsmooth problems is made. Finally, this dissertation is completed with the exposition of a result that is considered a unification of these two theorems

This study is an examination of how English courts have approached, or are likely to approach - and therefore, the effectiveness of - attempts by the parties to oil and gas contracts to allocate risks arising from the activities which form the subject matter of their respective contracts inter se. The study utilises petroleum industry standard form offshore drilling contracts in the United Kingdom, Canada and the United States of America as the context for this analysis, and examines the risks associated with drilling and other incidental operations, in the light of catastrophic events such as the Macondo disaster in the Gulf of Mexico and the Montara disaster in the Timor Sea. Drawing from the Economic Theory of Law espoused by Richard Posner, which correlates market behaviour, resource allocation and the legal system, and so conceptualises risk from a cost and utility perspective, the study will show that it is actually the economic consequences of the occurrence of an event that are being allocated, and that the entire notion of risk allocation is a determination of how the economic cost of the occurrence of the particular consequence will be borne by the parties to the contract. The study will conclude with a comparative analysis of risk allocation in the different model contracts, and an opinion on the success/effectiveness of the model contracts, as tools used by parties for risk allocation inter se, in response to the challenges created by legislative and judicial intervention. Justification for this opinion will be given, with reference to relevant case law and statutes in the different jurisdictions. Recommendations will be made on how the risk allocation structure can be improved, either by reference to other approaches the parties could adopt, or by clarifying ambiguities in the current approach (where applicable), and proposing a balance in the instances in which, from the study's perspective, the allocation formula is skewed, either due to the imbalance of power between the parties or by the interference of external forces such as the courts and legislature.

The roles of phonetics (e.g., Jun 1995, Holt 1997, Steriade 2001) and Articulatory Phonology (AP, Browman and Goldstein 1986, et seq.) in both the diachronic evolution of and synchronic analyses for phonological processes are relatively recent incorporations into Optimality Theory (OT) (Prince and Smolensky 1993/2004, McCarthy and Prince 1993/2001). I continue this line of inquiry by offering an AP-based OT proposal of three fricative-vowel assimilations in Latin American Spanish: /f/>[x] velarization (fui [xui] "I went"), /f/>[phi] bilabialization (fumo "I smoke") and /x/>[ç] palatalization (gente [çente] "people"). In this dissertation, I pursue three main objectives: to update and clarify via empirical study and spectral analysis the available data; to account for the crosslinguistically recurrent phonological patterns that affect fricative-vowel sequences; and to explain the above processes' genesis and diffusion in Latin American Spanish by integrating the first two goals into an Optimality Theoretic framework. Concerning the first task, data for the three processes are culled primarily from sociolinguistic corpora (Perissinotto 1975, Resnick 1975, Sanicky 1988, inter alia). Lacking from these accounts are detailed phonetic analyses. To fill this gap, I report on a four-part perception and production study designed to update the descriptive facts and provide spectral analyses for the allophonic variants. Regarding the second goal, I show that fricatives are susceptible to regressive consonant-vowel assimilation given the recurrence of assimilatory patterns nearly identical to the Spanish processes under investigation in disparate languages throughout the world. I argue that articulatory and acoustic facts conspire to render place features in (non-sibilant) fricatives difficult to recover given the vast interspeaker, intraspeaker and crosslinguistic variability in production (e.g., Ladefoged and Maddieson 1996) and the greater reliance on fricative-vowel transitional cues as opposed to cues internal to the frication on the part of the hearer (e.g., Manrique and Massone 1981, Feijóo and Fernández 2003). To that end, I argue that the sound changes originate(d) with the hearer's misperception of a speaker's extremely coarticulated target (Baker, Archangeli and Mielke 2011, inter alia). The dissertation concludes with a proposal adapting Jun (1995) that encodes the above articulatory and acoustic facts into an AP-based, typologically-minded OT approach that accounts both diachronically and synchronically for /f/ velarization, /f/ bilabialization and /x/ palatalization in Spanish (updating previous analyses by Lipski 1995 and Mazzaro 2005, 2011).

The separation of water and fat from multi-echo images is a classic problem in magnetic resonance imaging (MRI) with a wide range of important clinical applications. For example, removal of fat signal can provide better visualization of other signal of interest in MRI scans. In other cases, the fat distribution map can be of great importance in diagnosis. Although many methods have been proposed over the past three decades, robust fat water separation remains a challenge as radiological technology and clinical expectation continue to grow. The problem presents three key difficulties: a) the presence of B0 field inhomogeneities, often large in the state-of-the-art research and clinical settings, which makes the problem non-linear and ill-posed; b) the ambiguity of signal modeling in locations with only one metabolite (either fat or water), which can manifest as spurious fat water swaps in the separation; c) the computational expenditure in fat water separation as the size of the data is increasing along with evolving MRI hardware, which hampers the clinical applicability of the fat water separation. The main focus of this thesis is to develop novel graph based algorithms to estimate the B0 field inhomogeneity maps and separate fat water signals with global accuracy and computational efficiency. We propose a new smoothness constrained framework for the GlObally Optimal Surface Estimation (GOOSE), in which the spatial smoothness of the B0 field is modeled as a finite constraint between adjacent voxels in a uniformly discretized graph. We further develop a new non-equidistant graph model that enables a Rapid GlObally Optimal Surface Estimation (R-GOOSE) in a subset of the fully discretized graph in GOOSE. Extensions of the above frameworks are also developed to achieve high computational efficiency for processing large 3D datasets. Global convergence of the optimization formulation is proven in all frameworks. The developed methods have also been extensively compared to the existing state-of-the-art fat water separation methods on a variety of datasets with consistent performance of high accuracy and efficiency.

The percentage of shop fabrication, including pipe spool fabrication, has been increasing on industrial construction projects during the past years. Industrial fabrication has a great impact on construction projects due to the fact that the productivity is higher in a controlled environment than in the field, and therefore time and cost of construction projects are reduced by making use of industrial fabrication. Effective planning and scheduling of the industrial fabrication processes is important for the success of construction projects. This thesis focuses on developing a new framework for optimizing shop scheduling, particularly pipe spool fabrication shop scheduling. The proposed framework makes it possible to capture uncertainty of the pipe spool fabrication shop while accounting for linguistic vagueness of the decision makers preferences using simulation modeling and fuzzy set theory. The implementation of the proposed framework is discussed using a real case study of a pipe spool fabrication shop. In this thesis, first, a simulation based scheduling framework is presented based on the integration of relational database management system, product modeling, process modeling, and heuristic approaches. Next, a framework for optimization of the industrial shop scheduling with respect to multiple criteria is proposed. Fuzzy set theory is used to linguistically assess different levels of satisfaction for the selected criteria. Additionally, an executable scheduling toolkit is introduced as a decision support system for pipe spool fabrication shop. / Construction Engineering and Management

Knowledge has always been a decisive factor of humankind's social evolutions. Collecting the world's knowledge is one of the greatest challenges of our civilization. Knowledge involves the use of information but information is not knowledge. It is a way of acquiring and understanding information. Improving the visibility and the accessibility of information requires to organize it efficiently. This thesis focuses on this general purpose. A fundamental objective of computer science is to store and retrieve information efficiently. This is known as the dictionary problem. A dictionary asks for a data structure which allows essentially the search operation. In general, information that is important and popular at a given time has to be accessed faster than less relevant information. This can be achieved by dynamically managing the data structure periodically such that relevant information is located closer from the search starting point. The second part of this thesis is devoted to the development and the understanding of self-adjusting dictionaries in various models of computation. In particular, we focus our attention on dictionaries which do not have any knowledge of the future accesses. Those dictionaries have to auto-adapt themselves to be competitive with dictionaries specifically tuned for a given access sequence. This approach, which transforms the information structure, is not always feasible. Reasons can be that the structure is based on the semantic of the information such as categorization. In this context, the search procedure is linked to the structure itself and modifying the structure will affect how a search is performed. A solution developed to improve search in static structure is the hotlink assignment. It is a way to enhance a structure without altering its original design. This approach speeds up the search by creating shortcuts in the structure. The first part of this thesis is devoted to this approach.

If we want to compare the explanatory and descriptive adequacy of the MP and OT, the original definitions by Chomsky (1964) are or little direct use. However, a relativized version of both notions can be defined, which can be used to express a number of parallels between the study of individual I-languages and the language faculty. In any version of explanatory and descriptive adequacy, the two notions derive from the research programme and can only be achieved together. They can therefore not be used to characterize the difference in orientation between OT and the MP. Even if ‘OT’ is restricted to a particular theory in Chomskyan linguistics (to the exclusion of, for instance, its use in LFG), it cannot be said to be stronger in descriptive adequacy than in explanatory adequacy in the technical sense of these terms.