In this work we study properties of spacetimes with a high degree of symme- try. Particularly, we focus on geometries related to higher-dimensional rotating black-hole spacetimes described by the Kerr-NUT-(A)dS metric. In the first part, we examine spacetimes admitting a separable Klein-Gordon equation. Motivated by Carter's work in four dimensions, we introduce a separable met- ric ansatz in higher dimensions. Analyzing Einstein's equations, we obtain the Kerr-NUT-(A)dS and specific Einstein-K¨ahler metrics. Then we consider a metric ansatz in the form of warped geometries of two Klein-Gordon separable metrics and classify the corresponding solutions. In the second part, we in- vestigate a class of limits of the Kerr-NUT-(A)dS spacetimes where particular roots of metric functions degenerate. Our limiting procedure results in various NUT-like and near-horizon geometries such as the higher-dimensional Taub- NUT-(A)dS spacetime. We demonstrate that the symmetries of the resulting geometries are enhanced, which is manifested by decomposition of Killing ten- sors into Killing vectors. The third part of this work deals with generalized symmetry axes of the Kerr-NUT-(A)dS spacetimes that are formed by fixed points of isometries. We show that some parts of the symmetry axes are sin- gular for nonzero NUT charges....

<p>In computational science it is common to describe dynamic systems by mathematical models in forms of differential or integral equations. These models may contain parameters that have to be computed for the model to be complete. For the special type of ordinary differential equations studied in this thesis, the resulting parameter estimation problem is a separable nonlinear least squares problem with equality constraints. This problem can be solved by iteration, but due to complicated computations of derivatives and the existence of several local minima, so called short-cut methods may be an alternative. These methods are based on simplified versions of the original problem. An algorithm, called the modified Kaufman algorithm, is proposed and it takes the separability into account. Moreover, different kinds of discretizations and formulations of the optimization problem are discussed as well as the effect of ill-conditioning.</p><p>Computation of parameters often includes as a part solution of linear system of equations <i>Ax = b</i>. The corresponding pseudoinverse solution depends on the properties of the matrix <i>A</i> and vector <i>b</i>. The singular value decomposition of <i>A</i> can then be used to construct error propagation matrices and by use of these it is possible to investigate how changes in the input data affect the solution <i>x</i>. Theoretical error bounds based on condition numbers indicate the worst case but the use of experimental error analysis makes it possible to also have information about the effect of a more limited amount of perturbations and in that sense be more realistic. It is shown how the effect of perturbations can be analyzed by a semi-experimental analysis. The analysis combines the theory of the error propagation matrices with an experimental error analysis based on randomly generated perturbations that takes the structure of <i>A</i> into account</p>

In computational science it is common to describe dynamic systems by mathematical models in forms of differential or integral equations. These models may contain parameters that have to be computed for the model to be complete. For the special type of ordinary differential equations studied in this thesis, the resulting parameter estimation problem is a separable nonlinear least squares problem with equality constraints. This problem can be solved by iteration, but due to complicated computations of derivatives and the existence of several local minima, so called short-cut methods may be an alternative. These methods are based on simplified versions of the original problem. An algorithm, called the modified Kaufman algorithm, is proposed and it takes the separability into account. Moreover, different kinds of discretizations and formulations of the optimization problem are discussed as well as the effect of ill-conditioning. Computation of parameters often includes as a part solution of linear system of equations Ax = b. The corresponding pseudoinverse solution depends on the properties of the matrix A and vector b. The singular value decomposition of A can then be used to construct error propagation matrices and by use of these it is possible to investigate how changes in the input data affect the solution x. Theoretical error bounds based on condition numbers indicate the worst case but the use of experimental error analysis makes it possible to also have information about the effect of a more limited amount of perturbations and in that sense be more realistic. It is shown how the effect of perturbations can be analyzed by a semi-experimental analysis. The analysis combines the theory of the error propagation matrices with an experimental error analysis based on randomly generated perturbations that takes the structure of A into account

The heart of Pentecostal practice has always been an experience of the Holy Spirit. These experiences are often claimed to have the direct guidance of the Spirit and form the decisions and actions that result in the ongoing of the development of practices and doctrine. It is my contention that the third and fourth so-called waves of the Spirit are not truly waves of the Spirit, neither are they new. They are the rebirth, albeit in a new manner, of three disappointing and tragic movements of past Pentecostal history, namely the (New) Latter Rain, the Shepherding Movement, and the Prosperity Movement. I maintain that these two waves do not follow a solid Pentecostal doctrinal stand of an experience in the Holy Spirit of separability and subsequence, neither do they draw their doctrinal stand from the book of Acts, but rather the Synoptic gospels. Unfortunately, even though Pentecostal scholarship is on the rise, the majority of the prolific writers of these last two waves are extremely eisegetical in regards to their dealing with the Word of God. They claim vision and direction from Heaven, as opposed to an exegesis of the canon of Scripture. I maintain that these two, so called waves of the Spirit are not Heaven sent but man conceived and thus dangerous heresy to the church. `I believe that courage is the most important virtue, the foundation that underlies and gives realty to all other virtues and personal values. Without courage we become conformists. Conformity is not the fibre good and courageous leaders are made of… Do not be frightened by the aloneness that may come with your holding unpopular positions. It is in aloneness that wisdom will visit you and smile upon you'. These are not, as a theologian might be entitled to expect, the words of Elijah or Jeremiah. They are quoted from a speech given in 1999 by Mamphela Ramphele, vice chancellor of the University of Cape Town. Her context was the silence that has so often fallen on African societies once liberation has taken place. It is just such silent acquiescence, she insists, that allow former `heroes of the struggle' to become despots and dictators. Her words are challenging to Pentecostal theologians for at least two reasons. The first and more mundane is that Pentecostalism is most vibrant today in precisely those countries, which can be termed `postcolonial'. The second, and to my mind the most relevant to the movement, is that Pentecostalism was at its beginning a powerful spiritual force because it inherited an ethos of radical difference and because its proponents were unflinching in refusing to be co-opted into any other agenda than the one for which they knew they had been empowered by the Spirit of Jesus Christ. In this sense it was a prophetic religion, a religion similar to that of Elijah and Jeremiah. It is my plea then in this presentation that the so-called `postcolonial' countries will not swallow this new error, which has been called the new Pentecostal rhema from Heaven, which stems, as do so many new theological trends from the Western world. The new emerging Pentecostal Charismatic churches, particularly of the Third World need to have the courage not to be conformists, for such is not the fiber good and courageous leaders have. The hermeneutical pneumatology of the Pentecostal tradition has always been questioned. The early Pentecostals did not even bother to develop a theological hermeneutical position of a subsequent experience of the Spirit; they accepted their experience as from God . When they did begin to develop a Pentecostal theology it was often ridiculed as being primarily experiential, thus in the minds of most, devoid of Biblical theology. Fifty years after the outpouring of the Spirit at Azusa Street many Pentecostal scholars began to re-examine the pneumatology of Luke's writing. In the latter part of the 20th Century many Pentecostal scholars came into their own, examining and challenging many of the previously accepted conclusions of theologians, in regards to the Classical Pentecostal doctrinal position . Their position was that there was a separable and subsequent experience of the Spirit following salvation, which was accompanied by the initial evidence of speaking with other tongues. The initial evidence was for a few, and still is for some, questionable evidence. Such a position stood in opposition to those who declared that there was no second experience of the Holy Spirit for any person other than salvation. If those who believed in the `conversion-initiation, which included the baptism in the Holy Spirit' were indeed correct, then everything that Luke talks about in relation to pneumatology in his two-volume work is totally in relation to salvation. This was the theological pneumatological position prior to Classical Pentecostalism. It did and has resulted in many theological challenges. Scholars who take this position do so on the premise that Pentecost is more of a historical situation for the church. However scholars convinced of the Classical Pentecostal position are refusing to accept this position and have and are continuing to develop an exegetical position for a secondary work of the Holy Spirit in a person's life. This is my personal position made vitally real for me since I did not grow up in a Pentecostal church setting, but rather came into the Pentecostal experience in my early 20's. It is my contention that the theological impact of Christ's ascension prior to the public ascension witnessed in Acts 1 has not been fully examined. Few scholars have dealt with the typological fulfillment firstly, of the work of the High Priest as seen completed in the life of Jesus Christ, or secondly, of His fulfillment of the first four feasts which the Jews were commanded to keep. Both of these aspects very clearly enhance and form a clear indication that the classical Pentecostal theology was and is correct in speaking of a separable and subsequent work of the Spirit following a clear salvation experience. I will seek to elucidate this by an examining the historical background of the first two waves of the Spirit, followed by a preview of the work of the Holy Spirit as seen in the canon of Scripture with emphasis on the New Testament. I will follow this by the development of the idea of regeneration in the New Testament. Finally I will examine Lukan writing in regards to the experience known as the baptism of the Holy Spirit. These chapters will then serve as a base for comparison with the material, which will follow. In the late 20th and early 21st century the Classical Pentecostal doctrine has been challenged by the last two charismatic waves of the Spirit, both of which have spawned a plethora of writings. It is my contention first; that the traditional Pentecostal understanding of the authority of Scripture has been abandoned in that now experience takes precedence over Scripture. Secondly it is clear that these last two waves do not fall within the same parameters as the first two waves in their understanding of a doctrine of separability and subsequence, since they revert to a pre-Classical Pentecostal theological position of only one experience of the Holy Spirit. Thirdly, in a day when Pentecostal scholarship is seeking to become acceptable in their exegesis, the authors of these waves are almost totally eisegetical. The question needs to be asked `Have they subtly taken on a title to glean a following?' It is thus my contention that a survey of these waves shows that they have no common ground with the initial two waves of the Spirit. The indication is that they have deliberately chosen a different Biblical basis and thus disqualify themselves from the Pentecostal Charismatic stream. I will seek to elucidate this by examining the historical background of the last two waves of the Spirit, followed by an examination of the Pentecostal hermeneutic and their lack of hermeneutics, as seen so clearly in their writings. This will be done by pointing out the comparisons to the latter two waves of the Spirit both in theory and in the voluminous writing, which are largely based on eisegesis. The stated desire to `have church without making anyone sick' has broached and taken the movements far into left field. Finally, it is my contention that the third and fourth waves of the Spirit are not new at all. They are simply a rebirth of three disappointing and tragic movements in Pentecostal history. Thus I hope to clearly substantiate that the third and fourth wave of the Spirit are not really waves of the Spirit at all. They are not such in terms of their Biblical theological basis, neither are they such exegetically. They are simply the result of those desirous of the moving of the Holy Spirit who have reached back into the past and reintroduced past aspects of renewal, which unfortunately were man centered and resulted later in much havoc among Christians. I will seek to elucidate these facts by an examination of the history and practice of the (New) Latter Rain, which still haunts Saskatchewan, Canada where tragedies still exist, and the Shepherding movement out of Florida, which after a few years was denounced even by the leaders and finally totally disbanded. Then, finally the Prosperity Movement, which rose and fell as an unacceptable, illegitimate deduction of so called truth of the canon. One hopes and prays that the tragedies in lives will not live to haunt the church if Jesus tarries. We do not want the "heroes of spiritual struggles" to become the despots and dictators of the Pentecostal churches in the Third World. / Christian Spirituality, Church History and Missiology / D.Th. (Church History)

No description available.

Distributed computing is an approach where computationally heavy problems are broken down into more manageable sub-tasks, which can then be distributed across a number of different computers or servers, allowing for increased efficiency through parallelization. This thesis explores an established distributed computing setting, in which the computationally heavy task involves a number of users requesting a linearly separable function to be computed across several servers. This setting results in a condition for feasible computation and communication that can be described by a matrix factorization problem. Moreover, the associated costs with computation and communication are directly related to the number of nonzero elements of the matrix factors, making sparse factors desirable for minimal costs. The Alternating Direction Method of Multipliers (ADMM) is explored as a possible method of solving the sparse matrix factorization problem. To obtain convergence results, extensive convex analysis is conducted on the ADMM iterates, resulting in a theorem that characterizes the limiting points of the iterates as KKT points for the sparse matrix factorization problem. Using the results of the analysis, an algorithm is devised from the ADMM iterates, which can be applied to the sparse matrix factorization problem. Furthermore, an additional implementation is considered for a noisy scenario, in which existing theoretical results are used to justify convergence. Finally, numerical implementations of the devised algorithms are used to perform sparse matrix factorization. / Distribuerad beräkning är en metod där beräkningstunga problem bryts ner i hanterbara deluppgifter, som sedan kan distribueras över ett antal olika beräkningsenheter eller servrar, vilket möjliggör ökad effektivitet genom parallelisering. Denna avhandling undersöker en etablerad distribuerad beräkningssmiljö, där den beräkningstunga uppgiften involverar ett antal användare som begär en linjärt separabel funktion som beräknas över flera servrar. Denna miljö resulterar i ett villkor för tillåten beräkning och kommunikation som kan beskrivas genom ett matrisfaktoriseringsproblem. Dessutom är det möjligt att relatera kostanderna associerade med beräkning och kommunikation till antalet nollskilda element i matrisfaktorerna, vilket gör glesa matrisfaktorer önskvärda. Alternating Direction Method of Multipliers (ADMM) undersöks som en möjlig metod för att lösa det glesa matrisfaktoriseringsproblemet. För att erhålla konvergensresultat genomförs omfattande konvex analys på ADMM-iterationerna, vilket resulterar i ett teorem som karakteriserar de begränsande punkterna för iterationerna som KKT-punkter för det glesa matrisfaktoriseringsproblemet. Med hjälp av resultaten från analysen utformas en algoritm från ADMM-iterationerna, vilken kan appliceras på det glesa matrisfaktoriseringsproblemet. Dessutom övervägs en ytterligare implementering för ett brusigt scenario, där befintliga teoretiska resultat används för att motivera konvergens. Slutligen används numeriska implementeringar av de framtagna algoritmerna för att utföra gles matrisfaktorisering.

The quadratic class of time-frequency distributions (TFDs) forms a set of tools which allow to effectively extract important information from a nonstationary signal. To determine which TFD best represents the given signal, it is a common practice to visually compare different TFDs' time-frequency plots, and select as best the TFD with the most appealing plot. This visual comparison is not only subjective, but also difficult and unreliable especially when signal components are closely-spaced in the time-frequency plane. To objectively compare TFDs, a quantitative performance measure should be used. Several measures of concentration/complexity have been proposed in the literature. However, those measures by being derived with certain theoretical assumptions about TFDs are generally not suitable for the TFD selection problem encountered in practical applications. The non-existence of practically-valuable measures for TFDs' resolution comparison, and hence the non-existence of methodologies for the signal optimal TFD selection, has significantly limited the use of time-frequency tools in practice. In this thesis, by extending and complementing the concept of spectral resolution to the case of nonstationary signals, and by redefining the set of TFDs' properties desirable for practical applications, we define an objective measure to quantify the quality of TFDs. This local measure of TFDs' resolution performance combines all important signal time-varying parameters, along with TFDs' characteristics that influence their resolution. Methodologies for automatically selecting a TFD which best suits a given signal, including real-life signals, are also developed. The optimisation of the resolution performances of TFDs, by modifying their kernel filter parameters to enhance the TFDs' resolution capabilities, is an important prerequisite in satisfying any additional application-specific requirements by the TFDs. The resolution performance measure and the accompanying TFDs' comparison criteria allow to improve procedures for designing high-resolution quadratic TFDs for practical time-frequency analysis. The separable kernel TFDs, designed in this way, are shown to best resolve closely-spaced components for various classes of synthetic and real-life signals that we have analysed.

A classificação isomorfa dos espaços de Banach separáveis C(K) é devida a Milutin no caso em que K são não enumeráveis e a Bessaga e Pelczynski no caso em que K são enumeráveis. Neste trabalho apresentamos uma extensão vetorial dessa classificação e tiramos várias consequências, por exemplo, considerando o espaço métrico compacto infinito K e Y um espaço de Banach: &nbsp; &nbsp; 1. Sendo 1 < p < &infin; e &Gamma; um conjunto infinito, classificamos, a menos de isomorfismo, os espaços de Banach C(K, Y &oplus; lp(&Gamma;)), quando o dual de Y contém uma cópia de lq, onde 1/p+ 1/q =1. &nbsp; &nbsp; 2. Classificamos os espaços de Banach C(K, Y &oplus; l&infin;(&Gamma;)), quando a densidade de Y é estritamente menor que 2|&Gamma;|. &nbsp; &nbsp; 3. Classificamos os espaços de Banach C(K &times;(S&oplus; &beta;&Gamma;)) e C(S &oplus; (K&times; &beta;&Gamma;)), onde S é um compacto disperso de Hausdorff arbitrário e &beta;&Gamma; é a compactificação de Stone-Cech de &Gamma;. Obtemos, também, algumas leis de cancelamento para espaços de Banach da forma C(K1,X)&oplus; C(K2,Y), onde K1 e K2 são espaços compactos métricos infinitos de Hausdorff e X, Y espaços de Banach satisfazendo condições adequadas. Estabelecemos também um teorema de quase-dicotomia envolvendo os espaços C(K,X), onde X tem cotipo finito. Finalmente, apresentamos algumas majorações nas distorções de isomorfismos positivos de C([0,&omega;k]) em C([0,&omega;]) e também de C([0,&omega;]) em C([0,&omega;k]), k&isin; N, k &ge; 2. / The isomorphic classification of separable Banach spaces C(K) is due Milutin in the case when K are uncountable and to Bessaga and Pelczynski in the case when K are countable. In this work we prove a vectorial extention of this classification and provide several consequences, for example considering the infinite metric compact space K and Y a Banach space: &nbsp; &nbsp; 1. Let 1 < p < &infin; and &Gamma; a infinite set, we classify, up to an isomorphism, the Banach spaces C(K, Y &oplus; lp(&Gamma;)), in the case where the dual of Y contains no copy of lq, where 1/p+ 1/q =1. &nbsp; &nbsp; 2. We classify the Banach spaces C(K, Y &oplus; l&infin;(&Gamma;)), when the density character of Y is strictly less that 2|&Gamma;|. &nbsp; &nbsp; 3. We classify the Banach spaces C(K &times;(S&oplus; &beta;&Gamma;)) and C(S &oplus; (K&times; &beta;&Gamma;)) where S is an arbitrary dispersed compact and &beta;&Gamma; is the Stone-Cech compactification of &Gamma;. We obtain also some cancellation laws for Banach spaces in the form C(K1,X)&oplus; C(K2,Y), where K1 and K2 are metric compact Hausdorff spaces and X, Y Banach spaces satisfying appropriate conditions. We established also a quasi-dichotomy theorem envolving the C(K,X) spaces, where X is of finite cotype. Finally, we present some upper bounds of distortions of positive isomorphisms of C([0,&omega;k]) on C([0,&omega;]) and also of C([0,&omega;]) on C([0,&omega;k]), k&isin; N, k &ge; 2.

A classificação isomorfa dos espaços de Banach separáveis C(K) é devida a Milutin no caso em que K são não enumeráveis e a Bessaga e Pelczynski no caso em que K são enumeráveis. Neste trabalho apresentamos uma extensão vetorial dessa classificação e tiramos várias consequências, por exemplo, considerando o espaço métrico compacto infinito K e Y um espaço de Banach: &nbsp; &nbsp; 1. Sendo 1 < p < &infin; e &Gamma; um conjunto infinito, classificamos, a menos de isomorfismo, os espaços de Banach C(K, Y &oplus; lp(&Gamma;)), quando o dual de Y contém uma cópia de lq, onde 1/p+ 1/q =1. &nbsp; &nbsp; 2. Classificamos os espaços de Banach C(K, Y &oplus; l&infin;(&Gamma;)), quando a densidade de Y é estritamente menor que 2|&Gamma;|. &nbsp; &nbsp; 3. Classificamos os espaços de Banach C(K &times;(S&oplus; &beta;&Gamma;)) e C(S &oplus; (K&times; &beta;&Gamma;)), onde S é um compacto disperso de Hausdorff arbitrário e &beta;&Gamma; é a compactificação de Stone-Cech de &Gamma;. Obtemos, também, algumas leis de cancelamento para espaços de Banach da forma C(K1,X)&oplus; C(K2,Y), onde K1 e K2 são espaços compactos métricos infinitos de Hausdorff e X, Y espaços de Banach satisfazendo condições adequadas. Estabelecemos também um teorema de quase-dicotomia envolvendo os espaços C(K,X), onde X tem cotipo finito. Finalmente, apresentamos algumas majorações nas distorções de isomorfismos positivos de C([0,&omega;k]) em C([0,&omega;]) e também de C([0,&omega;]) em C([0,&omega;k]), k&isin; N, k &ge; 2. / The isomorphic classification of separable Banach spaces C(K) is due Milutin in the case when K are uncountable and to Bessaga and Pelczynski in the case when K are countable. In this work we prove a vectorial extention of this classification and provide several consequences, for example considering the infinite metric compact space K and Y a Banach space: &nbsp; &nbsp; 1. Let 1 < p < &infin; and &Gamma; a infinite set, we classify, up to an isomorphism, the Banach spaces C(K, Y &oplus; lp(&Gamma;)), in the case where the dual of Y contains no copy of lq, where 1/p+ 1/q =1. &nbsp; &nbsp; 2. We classify the Banach spaces C(K, Y &oplus; l&infin;(&Gamma;)), when the density character of Y is strictly less that 2|&Gamma;|. &nbsp; &nbsp; 3. We classify the Banach spaces C(K &times;(S&oplus; &beta;&Gamma;)) and C(S &oplus; (K&times; &beta;&Gamma;)) where S is an arbitrary dispersed compact and &beta;&Gamma; is the Stone-Cech compactification of &Gamma;. We obtain also some cancellation laws for Banach spaces in the form C(K1,X)&oplus; C(K2,Y), where K1 and K2 are metric compact Hausdorff spaces and X, Y Banach spaces satisfying appropriate conditions. We established also a quasi-dichotomy theorem envolving the C(K,X) spaces, where X is of finite cotype. Finally, we present some upper bounds of distortions of positive isomorphisms of C([0,&omega;k]) on C([0,&omega;]) and also of C([0,&omega;]) on C([0,&omega;k]), k&isin; N, k &ge; 2.

Dans le but de faire face aux défis interdépendants en termes d’épuisement des ressources énergétiques, de dégradation environnementale et des préoccupations de santé publique dans le contexte chinois en réponse au développement durable, nous nous concentrons sur l'étude des politiques en matière d’énergie, d’environnement et de santé en Chine. Dans le chapitre 1, nous donnons un aperçu des politiques chinoises en matière d’énergie, d’environnement et de santé au cours des 20 dernières années afin de connaître les orientations politiques futures auxquelles le gouvernement n'a pas donné une attention suffisante. Dans les trois chapitres suivants, nous proposons une série d'études empiriques afin de tirer quelques implications politiques utiles. Dans le chapitre 2, nous étudions l'impact de l'urbanisation, de l'adaptation de la structure industrielle, du prix de l'énergie et de l'exportation sur les intensités énergétiques agrégés et désagrégés des provinces. Dans le chapitre 3, nous étudions les facteurs qui expliquent la transition énergétique vers des combustibles propres des ménages ruraux. Dans le chapitre 4, nous examinons les effets conjoints des risques environnementaux, du revenu individuel, des politiques de santé sur l'état de santé des adultes chinois. En particulier, nos résultats empiriques suggèrent d’intégrer le développement urbain dans la stratégie d'économies d'énergie; de considérer des substitutions/complémentarités complexes parmi les sources d'énergie et entre l'énergie et l’alimentation pour les ménages ruraux; d’aligner les politiques environnementales, énergétiques et alimentaires avec les politiques de santé. / With the purpose of coping with the intertwined challenges of energy depletion, environmental degradation and public health concerns in the Chinese-specific context in response to sustainable development, we focus on investigating China’s energy, environment and health policies. In chapter 1, we provide an overview of China’s energy, environment and health policies over the past 20 years in order to know about the future policy directions to which the government has not given a sufficient attention. In the following three chapters, we provide a series of empirical studies so as to derive some useful policy implications. In chapter 2, we investigate the impact of urbanization, industrial structure adjustment, energy price and export on provincial aggregate and disaggregate energy intensities. In chapter 3, we study the factors explaining the switches from dirty to clean fuel sources in rural households. In chapter 4, we examine the joint effects of environmental hazards, individual income and health policies on the health status of Chinese adults. Our empirical findings particularly suggest integrating urban development into the strategy of energy saving; considering the complex substitutions/complementarities among energy sources and between energy and food for rural households; aligning the environment, energy and food policies with health policies.