Mucolipidosis type IV (MLIV) is a rare, autosomal recessive, neurodegenerative, lysosomal storage disorder. MLIV is caused by mutations in a gene (MCOLN1) encoding a TRP channel family member known as Mucolipin 1 or TRPML1. TRPML1 is a lysosomal transmembrane protein that appears to be required for normal lysosomal pH regulation, recycling of molecules and membrane reorganisation including lysosomal biogenesis, fusion and exocytosis. The exact function of the channel is unknown but it is permeable to multiple ions including Ca²⁺, Na⁺ and K⁺, possibly also Fe²⁺ and Zn²⁺. How normal TRPML1 function regulates lysosomal processes is not clearly understood. Mutations in the MCOLN1 gene can lead to complete loss of TRPML1 function, partial loss of function or mislocalisation, all of which lead to lysosomal dysfunction, lysosomal lipid storage and ultimately neurodegeneration. The disease processes that lead to neurodegeneration are poorly understood and at present no therapy exists for MLIV. We have discovered that TRPML1 results in regulating lysosomal Ca²⁺ homeostasis that is the opposite of the Ca²⁺ dysregulation associated with Niemann-Pick type C disease (NPC). Our findings indicate that disrupted function of TRPML1 leads to enhanced Ca²⁺ release via the NAADP receptor, recently shown to be the lysosomal two-pore channel TPC2. This indicates that TRPML1 is not the NAADP receptor as suggested by others, indeed NAADP mediated Ca²⁺ release is enhanced with multiple NAADP induced lysosomal Ca²⁺ release events occurring in TRPML1 null cells compared to single releases in normal cells. This phenotype appears to be responsible for the cellular dysfunction associated with MLIV disease cells, enhanced lysosomal fusion, defective endocytosis and potentially even altered lysosomal pH. Several of these phenotypes are normalised by the NAADP receptor specific antagonist Ned-19. These findings illustrate that the NAADP receptor is central to MLIV disease pathology and may be a novel candidate for disease therapy.

Thesis (MBA)--Stellenbosch University, 2002. / ENGLISH ABSTRACT: Ongoing business sustainability today is one of the major issues facing the management of organizations. How to remain in the profit zone, that area where a company will be allowed to make high profit in its industry, is a constant challenge. Continued profitability in a fast changing industry, where the profit zone moves as competitors offer the same solutions, requires constant innovation, implementation of new ideas and heavy financial commitments. The key is to identify clear and rational business design choices that are responsive to customers and that will ensure profitability. This document will illustrate how the four major food retail companies in South Africa, and their visionary leaders, have reinvented their business designs in ways that kept or returned them to the profit zone. Shoprite's target market is the middle to lower income group. The company has built up core competencies within its business to serve this segment. There are currently a number of issues facing Shoprite's core market, and as a result the company is diversifying its income streams to be less dependant on a vulnerable target market. . The visionary leadership of Raymond Ackerman, who applied principles of customer sovereignty long before his peers, has resulted in one of the best-run companies in South Africa. Pick 'n Pay's ability lies within the middle to upper segment of the market. The company has built its business on one core element - the customer, and has adapted the company business design to meet the needs of the customer and capture value . .Spars' philosophy of giving the small retailer the power to compete with the larger retailer, who buys in bulk, has proved to be a successful formula and is threatening the traditional hierarchy. Owners who are in close contact to customers have the flexibility to align their businesses with the customer requirements. 'Woolworths has one of the strongest brands in the South African retail industry. However, the company has in recent years been in serious trouble having lost its way because it lost touch with its customers. Concentrating back on the core customers and building back confidence in its goods, have taken considerable focus. Each of the business designs are built on a deep understanding of what the customer needs are of the target market they serve and how they will be allowed to make a profit. / AFRIKAANSE OPSOMMING: Een van die grootste knelpunte vir organisasies vandag is volhoubare besigheidsbestuur. Die uitdaging is om in die area te bly waar die organisasie toegelaat sal word om hoë wins te maak. Voortgesette winsgewendheid in 'n industrie waar die wins area veskuif as gevolg van mededingers wat oplossings naboots, vereis voortdurende vernuwing en strawwe finansiële verpligtinge. Die sleutel is om duidelike en rasionele besigheidsontwerpbesluite te neem wat kliente behoeftes aanspreek en wat na 'n wins sal lei. Hierdie dokument beskryf hoe die vier groot voedselhandelaars en hulle leiers hul besighede herontwerp het sodat hulle winsgewend kan bly. Shoprite se teiken mark is die middel - tot lae inkomste groep. Die firma het kern bevoegdhede binne sy besigheid ontwikkel om hierdie segment te bedien. Shoprite diversifeer huidiglik sy inkomste stroom as gevolg van die kwesbaarheid van sy teiken mark. Pick 'n Pay word as een van Suid Afrika se beste bestuurde firmas beskou. Die sukses word toegeskryf aan die leierskap van Raymond Ackerman wat die beginsels van kliënte soewereiniteit lank voor sy portuurgroep geïmplimenteer het. Pick 'n Pay se fokus is die middel - tot hoë inkomste groep. Die firma is op een kern element gebou, die kliënt, en sy besigheids ontwerp is aangepas om die behoeftes van die kliënt te bevredig. Spar se filosofie is om die kleiner handelaar in 'n posisie te stel om met die groot handelaar, wat in grootrnaat aankoop, te kan meeding. Die groei wat Spar toon bedreig die traditionele hiërargie en bewys die sukses van hierdie formule. Winkel eienaars wat noue kontak met kliënte het, kan hulle besighede aanpas om in kliënte se behoeftes te voorsien. Woolworths het een van die sterkste handelsmerke in die Suid Afrikaanse handels industrie. Die firma was in die laaste paar jaar in groot moeilikheid omdat hy tred verloor het met sy kliënte. Deur weer te konsentreer op die kern kliënt en om vertroue op te bou in sy goedere het beduidende fokus vereis. Elk van die besigheids ontwerpe is gebou op 'n intieme begrip van die behoeftes van die teiken mark wat bedien word en hoe die firma toegelaat sal word om 'n wins te maak.

Thesis (MBA)--Stellenbosch University, 2003. / ENGLISH ABSTRACT: The purpose of this report is to create a better understanding of the new pharmacy initiatives in the South African market, with specific reference to the Nuclicks and Pick 'n Pay groups. In order to understand the respective business concepts better the following abstracts from each chapter of the study is given. Chapter one is basically the introduction to the study and describes the events that lead to the above mentioned corporate retailers to enter the pharmacy market place. An introduction to Hamel's business model theory is also discussed and identified as a possible means of evaluating the corporate retailers' business concepts. In Chapter two the strategic analysis of the South African retail pharmacy industry is performed. This analysis is performed to create an understanding of the different forces at work in the industry. Some of the key findings in this chapter are that changes to the pharmacy act and the way dispensing licences are going to be awarded creates uncertainty. The profit outlook of retail pharmacy, though on the decline, still compares favourably to other retailers. In chapter three the core concepts of Hamel's business model are presented in more detail and applied to the retail pharmacy environment. In his view, a strategy needs to change the industry rules. This chapter ends with the concept of wealth potential based on Hamel's teachings. The wealth potential concept is about creating cash flow and profits. A business model that is able to create customer benefits well below the cost of the competitors is regarded as efficient. By utilising the Hamel way the Nuclicks (chapter four) and Pick 'n Pay (chapter five) business concepts is unpacked. Both Nuclicks and Pick 'n Pay pharmacy business models are presented within the corporate framework of the groups. Nuclicks bought an established pharmacy franchise while Pick 'n Pay launched Healthpharm. Nuclicks creates a possible choke point by buying UPD. The Nuclicks pharmacy strategy is a more comprehensive health strategy, while Pick 'n Pay follows a more cautious approach. As franchising will playa major role in both pharmacy concepts, the theory of franchising is presented in chapter six. Telephonic interviews with Link franchisees are conducted and the possible reasons for the ambiguity that crept into the Link business model are discussed. As the Healthpharm franchise is a new concept, it is evaluated based on information gathered from press releases and the Healthpharm web-site. In chapter seven universal conclusions and recommendations, based upon the literature study and this investigation, are presented. One of the key findings are, success in the face of changes requires more than the current way of doing business. It requires an innovative thinking process. New business models have to be formulated that allows retail pharmacists to establish a focused and well-differentiated value proposition. This value proposition needs to be meaningful for consumers and must strengthen a pharmacy outlet's competitive position. / AFRIKAANSE OPSOMMING: Die doel van hierdie verslag is om 'n beter begrip vir die nuwe apteek inisiatiewe in die Suid-Afrikaanse mark te ontwikkel, met spesifieke verwysing na die Nuclicks en Pick 'n Pay groepe. Om die onderskeie besiqheidskonsepte beter te verstaan, word die volgende opsomming van elke hoofstuk van die studie uiteengesit. Hoofstuk een is 'n inleiding tot die studie en beskryf die gebeure wat aanleiding gegee het tot die bogenoemde korporatiewe kleinhandelaars se toetrede tot die apteek mark. 'n Inleiding van Hamel se besigheidsmodel teorie is ook bespreek en is geïdentifiseer as evaluering van die korporatiewe kleinhandelaars se besigheidskonsepte. Hoofstuk twee bied 'n strategiese analise van die Suid-Afrikaanse kleinhandelaars apteek industrie. Hierdie analise is geskep om beter begrip te ontwikkel vir die verskillende kragte wat inwerk in die industrie. Van die bevindinge in die hoofstuk is die veranderinge in die apteek wetgewing en die wyse waarop resepteer lisensies toegeken gaan word, en hoeveel onsekerhede dit tot gevolg het. Die wins vooruitsigte van kleinhandelaars apteke, alhoewel aan die afneem, vergelyk steeds gunstig met ander kleinhandelaars. In Hoofstuk drie is die kern konsepte van Hamel se besigheidsmodel in meer detail uiteengesit en toegepas op die kleinhandelaar apteek omgewing. Uit sy oogpunt, is 'n strategie nodig om veranderinge te weeg te bring in die industrie reëls. Hierdie hoofstuk eindig met die konsep van waarde potensiaal wat gebaseer is op Hamel se teorie. Hierdie waarde potensiaal konsep is gebaseer op die skep van kontantvloei en 'n Besigheidsmodel wat in staat is om die kliënt te begunstig heelwat laer as die koste van die teenstander, word beskou as effektief. Hamel se teorie is gebruik om Nuclicks (hoofstuk vier) en Pick 'n Pay (hoofstuk vyf) se besigheidskonsepte te analiseer. Beide Nuclicks en Pick 'n Pay se besigheidsmodelle word aangebied binne die korporatiewe raakwerke van die groepe. Nuclicks het 'n gevestigde apteek konsessie gekoop terwyl Pick 'n Pay vir Healthpharm begin het. Nuclicks het 'n moontlike 'wurgpunt" geskep deur die aankoop van UPD. Die Nuclicks apteek strategie is 'n meer omvattende gesondheidstrategie, terwyl Pick 'n Pay 'n meer versigtige benadering volg. Aangesien besigheid konsessie 'n belangrike rol speel in beide apteek konsepte, word die teorie van konsessie in hoofstuk ses behandel. Telefoniese onderhoude is gevoer met Link konsessiehouers en die moontlike redes vir die twyfelagtigheid van die Link besigheidsmodel word bespreek. Aangesien die Healthpharm konsessie 'n nuwe konsep is, word dit geëvalueer op grond van inligting wat versamel is uit die media en die Healthpharm webtuiste. In Hoofstuk sewe word universele afleidings en aanbevelings, gebaseer op die literatuurstudie en die ondersoek, uiteengesit. Een van die hoof bevindings was dat sukses benodig meer as die huidige manier van besigheid doen. Nuwe besigheidsmodelle moet geformuleer word, wat dit vir kleinhandelaar apteke moontlik sal maak om 'n gefokusde en goed gedifferensieerde waarde voorstel tot stand te bring. Hierdie voorstel moet betekenisvol wees vir die verbruiker en moet die apteek kompeterende posisie versterk.

Ce travail a pour objectif d'étudier les effets d’une supplémentation en acides gras polyinsaturés (AGPI) n-3 à longues chaines sur la production d’embryons chez les vaches laitières. Le régime enrichi en AGPI n-3 a eu tendance à augmenter le nombre moyen des complexes ovocyte-cumulus récupérés par vache par session d’OPU par rapport au groupe témoin AGPI n-6. Une tendance à augmenter le nombre moyen par vache par session d’OPU de blastocystes et de blastocystes expansés avec une augmentation significative de blastocystes de qualité 1 et 2 ont été notés dans le groupe n-3. De même, les taux de blastocystes, de blastocystes expansés et de blastocystes de qualité 1 et 2 ont été significativement augmentés dans le groupe n-3. Nous avons aussi montré que l’addition d’acide docosahexaénoïque (DHA, C22:6 n-3) à une faible concentration (1μM) pendant la maturation in vitro des ovocytes bovins augmente significativement le taux de clivage et le taux et la qualité de blastocyste. La stimulation de FFAR4 (free fatty acid receptor 4), au cours de la MIV, par un agoniste spécifique (TUG 891), a entrainé des effets bénéfiques similaires à ceux du DHA (1μM) sur la compétence ovocytaire. Cela suggère que l’effet bénéfique du DHA pourrait passer, au moins partiellement, par l’activation du FFAR4. / We aimed to investigate whether dietary n-3 PUFA, in Prim‘Holstein dairy cattle in lactation, could influence reproductive performance in terms of embryo production. We showed that n-3 PUFA-enriched diet had a tendency to increase the average number of oocyte-cumulus complexes recovered per cow per OPU session. A tendency to increase the average numbers per cow per OPU session of blastocysts and expanded blastocysts with significantly increase of blastocysts of quality 1 and 2 were noted in the n-3 group compared to the n-6 group. Similarly, the rate of blastocysts, expanded blastocysts and blastocysts of quality 1 and 2 were significantly increased in the n-3 group compared to the n-6 group. We also showed that the addition of docosahexaenoic acid (DHA, C22:6 n-3) at low concentration (1μM) during IVM of bovine oocytes increased cleavage rate, blastocyst rate and embryo quality. DHA and free fatty acid receptor 4 (FFAR4) agonist TUG- 891 (1 or 5 μM) supplied during IVM similarly improved in vitro embryo development, suggesting that FFAR4 may, at least partially, mediate DHA beneficial effects on OCC, through activation of signaling pathways.

La thèse est consacrée à une étude d'interpolation complexe "semi-libre" dans le sens suivant: étant donné un ensemble "sigma" dans le disque unité D et une fonction f holomorphe dans D appartenant à une certaine classe X, on cherche g dans une autre classe Y (plus petite que X) qui minimise la norme de g dans Y parmi toutes les fonctions g satisfaisant g=f sur l'ensemble "sigma". Plus précisément, nous nous intéressons aux estimations de la constante d'interpolation suivante: c(sigma, X, Y ) = sup{ inf{||g||_Y: g=f sur sigma}: ||f||_X<=1} Dans la thèse, nous étudions le cas où Y = H^infini et où l'espace des contraintes X est choisi parmi les espaces suivants: les espaces de Hardy, les espaces de Bergman pondérés à poids radial ou encore les espaces de fonctions holomorphes ayant leurs coefficients de Taylor dans lp(w) (w étant un poids). La thèse contient également certaines applications aux nombres conditionnés des matrices de Toeplitz. / The thesis is devoted to a "semi-free" interpolation problem in the following way. Let sigma be a finite set of the unit disc D and f an holomorphic function in D which belongs to a certain class X, we search for g in another class Y (smaller than X) which minimize the norm of g in Y among all the functions g such that g=f on the set "sigma". More precisely, we are interested in the following interpolation constant : c(sigma, X, Y ) = sup{ inf{||g||_Y: g=f sur sigma}: ||f||_X<=1}. We study in the thesis the case where Y=H^\infinity and the space of constrains X is chosen among the following spaces: Hardy spaces, weighted Bergman spaces (with radial waights), and holomorphic functions which Taylor coefficients are in lp(w) (w being a weight). The thesis also contains an application to the condition numbers of Toeplitz matrices.

O objetivo dessa pesquisa foi avaliar aspectos genéticos que relacionados à produção in vitro de embriões na raça Guzerá. O primeiro estudo focou na estimação de (co) variâncias genéticas e fenotípicas em características relacionadas a produção de embriões e na detecção de possível associação com a idade ao primeiro parto (AFC). Foi detectada baixa e média herdabilidade para características relacionadas à produção de oócitos e embriões. Houve fraca associação genética entre características ligadas a reprodução artificial e a idade ao primeiro parto. O segundo estudo avaliou tendências genéticas e de endogamia em uma população Guzerá no Brasil. Doadoras e embriões produzidos in vitro foram considerados como duas subpopulações de forma a realizar comparações acerca das diferenças de variação anual genética e do coeficiente de endogamia. A tendência anual do coeficiente de endogamia (F) foi superior para a população geral, sendo detectado efeito quadrático. No entanto, a média de F para a sub- população de embriões foi maior do que na população geral e das doadoras. Foi observado ganho genético anual superior para a idade ao primeiro parto e para a produção de leite (305 dias) entre embriões produzidos in vitro do que entre doadoras ou entre a população geral. O terceiro estudo examinou os efeitos do coeficiente de endogamia da doadora, do reprodutor (usado na fertilização in vitro) e dos embriões sobre resultados de produção in vitro de embriões na raça Guzerá. Foi detectado efeito da endogamia da doadora e dos embriões sobre as características estudadas. O quarto (e último) estudo foi elaborado para comparar a adequação de modelos mistos lineares e generalizados sob método de Máxima Verossimilhança Restrita (REML) e sua adequação a variáveis discretas. Quatro modelos hierárquicos assumindo diferentes distribuições para dados de contagem encontrados no banco. Inferência foi realizada com base em diagnósticos de resíduo e comparação de razões entre componentes de variância para os modelos em cada variável. Modelos Poisson superaram tanto o modelo linear (com e sem transformação da variável) quanto binomial negativo à qualidade do ajuste e capacidade preditiva, apesar de claras diferenças observadas na distribuição das variáveis. Entre os modelos testados, a pior qualidade de ajuste foi obtida para o modelo linear mediante transformação logarítmica (Log10 X +1) da variável resposta. / The objective of this research was to evaluate genetic aspects permeating in vitro embryo production in Guzerá cattle. The first study aimed for estimating genetic and phenotypic (co)variances among embryo production traits and detecting possible genetic association with the age at first calving (AFC). Low and medium heritabilities were detected for oocyte and embryo production traits. A weak genetic association between artificial reproduction traits and AFC was identified. The second study evaluated genetic and inbreeding trends in the Brazilian Guzerá population. Female donors and in vitro produced embryos were considered as two subpopulations in order to perform comparisons and infer over differences in inbreeding and genetic annual variations. Embryos\' subpopulation showed higher genetic gains for age at first calving and milk production than donors\' subpopulation and the general population. Higher annual mean inbreeding values were also detected for the embryos\' subpopulation. The third study examined the effects of donor, sire (used for in vitro fertilization) and embryos\' inbreeding coefficient over in vitro embryo production traits in Guzerá cattle. Donors\' and embryos\' inbreeding effects over the analyzed traits were detected. Fourth and final study was designed to compare the performance of Linear and Generalized Linear Mixed Models under Restricted Maximum Likelihood method when fitting discrete variables. Four hierarchical models assuming different distributions for the response variable were fit to the (count) data. Inference was performed upon residual diagnostics and comparison of variance component ratios between models within each trait. Poisson models outperformed both linear (with and without variable transformation) and negative binomial models for goodness of fit and predictive ability despite clear differences in each trait\'s distribution. Logarithmic transformation (Log10 X +1) showed lowest goodness of fit among all models tested.

Les défis environnementaux et l’augmentation de la population viennent en preuve de l’importance de réfléchir à d’autres moyens de production tout en maintenant la sécurité et la fiabilité du système électrique. La sûreté du système électrique exige à tout moment que la production soit égale à la demande des consommateurs, pour ça, différentes solutions sont déjà mises en place, ces solutions consistent à mettre en marche des moyens de pointes couteux et polluants pendant les périodes de pointes, mais comme les moyens de production son insuffisants et vue la difficulté d’exploitation de nouveaux moyens de production, une nouvelle réflexion sur la gestion de la demande est apparue; celle-ci se base sur la possibilité à gérer la demande du consommateur final au lieu de la satisfaire.L’objectif de la thèse est d’étudier la possibilité à rendre des services au système électrique en appliquant des actions de contrôle dites de DR (Demand Response), sur différents types de charges électriques. Ces actions de DR représentent des interruptions partielles appliquées sur les charges électriques de type thermique. Notre choix s’est basé sur ces types de charges parce que celles-ci emmagasinent de la chaleur respectivement dans l’air et dans l’eau; qui peut être restituée pendant la période de contrôle ou d’interruption. Néanmoins, il existe un effet négatif qui suit le contrôle de ces charges car l’énergie effacée de ces charges est reportée à l’instant de reconnexion de celles-ci; ce report prend la forme d’un pic de consommation nommé CLPU (Cold Load Pick-Up) et qui apparait au moment de la reconnexion. Le CLPU représente un problème qui doit être géré, et sa magnitude dépend des types d’actions de contrôle qu’on veut implanter et aussi des conditions du système électrique (contingence, défaillance d’une unité de production ou besoin de réserve de puissance). Pendant la thèse, le CLPU est contrôlé et optimisé ainsi que la puissance effacée. Un cas d’étude est présenté sur la contribution des actions de gestion de la demande à l‘ajustement entre la demande et la production et l’effet généré sur le réglage secondaire de fréquence. / Environmental challenges and the increasing in electric demand show the importance of considering other form of production while maintaining the safety and reliability of the electrical system. The electrical power systems stability lays on a fundamental constraint: supply and demand must be equal at each instant, so, different solutions are already in place, these solutions include controlling generators’ production during peak periods. But, power units (mainly nuclear, thermal, hydro) capacities are not always sufficient and flexible to follow the demand variations during these periods; an alternative solution to this insufficiency is to make the demand following the electrical power generation by providing bulks of electrical power to the power system by curtailing consumer’s electric load consumption. Such a solution that represents a new organization in the power system industry can be done by Demand Side Management (DSM) actions. The aim of the thesis is to study the possibility to offer services to the electrical system by applying control actions called DR (Demand Response) on different types of electric loads. These DR actions represent partial interruptions of electrical loads’ consumption and especially thermal loads’ consumption.Our choice was based on the thermal electric loads because they store heat respectively in air and water, which can be restored during the control period or interruption. However, there is a negative effect that follows the control of these type of loads because the reduced energy during curtailment period is deferred at the time of reconnection, this deferred power takes the form of a power peak named CLPU (Cold Load Pick-Up), which appears at the time of reconnection. The CLPU is a problem that must be managed, and its magnitude depends on the type of control actions and on the electric system conditions (ie: contingency or failure of a generating unit). In the thesis, the CLPU is controlled and optimized as well as the load reduction during curtailment period. The contribution of control actions in balancing mechanisms and the effect produced on the secondary control of frequency are analyzed.

No description available.

(i) We prove that intermediate Banach spaces A, B with respect to arbitrary Hilbert couples H, K are exact interpolation iff they are exact K-monotonic, i.e. the condition f0∊A and the inequality K(t,g0;K)≤K(t,f0;H), t&gt;0 imply g0∊B and ||g0||B≤||f0||A (K is Peetre's K-functional). It is well-known that this property is implied by the following: for each ρ&gt;1 there exists an operator T : H→K such that Tf0=g0, and K(t,Tf;K)≤ρK(t,f;H), f∊H0+H1, t&gt;0.Verifying the latter property, it suffices to consider the "diagonal" case where H=K is finite-dimensional. In this case, we construct the relevant operators by a method which allows us to explicitly calculate them. In the strongest form of the theorem, it is shown that the statement remains valid when substituting ρ=1. (ii) A new proof is given to a theorem of W. F. Donoghue which characterizes certain classes of functions whose domain of definition are finite sets, and which are subject to certain matrix inequalities. The result generalizes the classical Löwner theorem on monotone matrix functions, and also yields some information with respect to the finer study of monotone functions of finite order. (iii) It is shown that with respect to a positive concave function ψ there exists a function h, positive and regular on ℝ+ and admitting of analytic continuation to the upper half-plane and having positive imaginary part there, such that h≤ψ≤ 2h. This fact is closely related to a theorem of Foiaş, Ong and Rosenthal, which states that regardless of the choice of a concave function ψ, and a weight λ, the weighted l2-space l2(ψ(λ)) is c-interpolation with respect to the couple (l2,l2(λ)), where we have c≤√2 for the best c. It turns out that c=√2 is best possible in this theorem; a fact which is implicit in the work of G. Sparr. (iv) We give a new proof and new interpretation (based on the work (ii) above) of Donoghue's interpolation theorem; for an intermediate Hilbert space H* to be exact interpolation with respect to a regular Hilbert couple H it is necessary and sufficient that the norm in H* be representable in the form ||f||*= (∫[0,∞] (1+t-1)K2(t,f;H)2dρ(t))1/2 with some positive Radon measure ρ on the compactified half-line [0,∞]. (v) The theorem of W. F. Donoghue (item (ii) above) is extended to interpolation of tensor products. Our result is related to A. Korányi's work on monotone matrix functions of several variables.

This thesis is divided into two parts. The first part deals with theNevanlinna-Pick interpolation problem, a problem which occursnaturally in several applications such as robust control, signalprocessing and circuit theory. We consider the problem of shaping andapproximating solutions to the Nevanlinna-Pick problem in a systematicway. In the second part, we study distance measures between powerspectra for spectral estimation. We postulate a situation where wewant to quantify robustness based on a finite set of covariances, andthis leads naturally to considering the weak*-topology. Severalweak*-continuous metrics are proposed and studied in this context.In the first paper we consider the correspondence between weighted entropyfunctionals and minimizing interpolants in order to find appropriateinterpolants for, e.g., control synthesis. There are two basic issues that weaddress: we first characterize admissible shapes of minimizers bystudying the corresponding inverse problem, and then we developeffective ways of shaping minimizers via suitable choices of weights.These results are used in order to systematize feedback controlsynthesis to obtain frequency dependent robustness bounds with aconstraint on the controller degree.The second paper studies contractive interpolants obtained as minimizersof a weighted entropy functional and analyzes the role of weights andinterpolation conditions as design parameters for shaping theinterpolants. We first show that, if, for a sequence of interpolants,the values of the corresponding entropy gains converge to theoptimum, then the interpolants converge in H_2, but not necessarily inH-infinity. This result is then used to describe the asymptoticbehaviour of the interpolant as an interpolation point approaches theboundary of the domain of analyticity.A quite comprehensive theory of analytic interpolation with degreeconstraint, dealing with rational analytic interpolants with an apriori bound, has been developed in recent years. In the third paper,we consider the limit case when this bound is removed, and only stableinterpolants with a prescribed maximum degree are sought. This leadsto weighted H_2 minimization, where the interpolants areparameterized by the weights. The inverse problem of determining theweight given a desired interpolant profile is considered, and arational approximation procedure based on the theory is proposed. Thisprovides a tool for tuning the solution for attaining designspecifications. The purpose of the fourth paper is to study the topology and develop metricsthat allow for localization of power spectra, based on second-orderstatistics. We show that the appropriate topology is theweak*-topology and give several examples on how to construct suchmetrics. This allows us to quantify uncertainty of spectra in anatural way and to calculate a priori bounds on spectral uncertainty,based on second-order statistics. Finally, we study identification ofspectral densities and relate this to the trade-off between resolutionand variance of spectral estimates.In the fifth paper, we present an axiomatic framework for seekingdistances between power spectra. The axioms requirethat the sought metric respects the effects of additive andmultiplicative noise in reducing our ability to discriminate spectra.They also require continuity of statistical quantities withrespect to perturbations measured in the metric. We then present aparticular metric which abides by these requirements. The metric isbased on the Monge-Kantorovich transportation problem and iscontrasted to an earlier Riemannian metric based on theminimum-variance prediction geometry of the underlying time-series. Itis also being compared with the more traditional Itakura-Saitodistance measure, as well as the aforementioned prediction metric, ontwo representative examples. / QC 20100817