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Reorganizing a dataset so that its hidden structure can be observed is useful in any data analysis task. For example, detecting a regularity in a dataset helps us to interpret the data, compress the data, and explain the processes behind the data. We study datasets that come in the form of binary matrices (tables with 0s and 1s). Our goal is to develop automatic methods that bring out certain patterns by permuting the rows and columns. We concentrate on the following patterns in binary matrices: consecutive-ones (C1P), simultaneous consecutive-ones (SC1P), nestedness, k-nestedness, and bandedness. These patterns reflect specific types of interplay and variation between the rows and columns, such as continuity and hierarchies. Furthermore, their combinatorial properties are interlinked, which helps us to develop the theory of binary matrices and efficient algorithms. Indeed, we can detect all these patterns in a binary matrix efficiently, that is, in polynomial time in the size of the matrix. Since real-world datasets often contain noise and errors, we rarely witness perfect patterns. Therefore we also need to assess how far an input matrix is from a pattern: we count the number of flips (from 0s to 1s or vice versa) needed to bring out the perfect pattern in the matrix. Unfortunately, for most patterns it is an NP-complete problem to find the minimum distance to a matrix that has the perfect pattern, which means that the existence of a polynomial-time algorithm is unlikely. To find patterns in datasets with noise, we need methods that are noise-tolerant and work in practical time with large datasets. The theory of binary matrices gives rise to robust heuristics that have good performance with synthetic data and discover easily interpretable structures in real-world datasets: dialectical variation in the spoken Finnish language, division of European locations by the hierarchies found in mammal occurrences, and co-occuring groups in network data. In addition to determining the distance from a dataset to a pattern, we need to determine whether the pattern is significant or a mere occurrence of a random chance. To this end, we use significance testing: we deem a dataset significant if it appears exceptional when compared to datasets generated from a certain null hypothesis. After detecting a significant pattern in a dataset, it is up to domain experts to interpret the results in the terms of the application.

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In the thesis I study various quantum coherence phenomena and create some of the foundations for a systematic coherence theory. So far, the approach to quantum coherence in science has been purely phenomenological. In my thesis I try to answer the question what quantum coherence is and how it should be approached within the framework of physics, the metatheory of physics and the terminology related to them. It is worth noticing that quantum coherence is a conserved quantity that can be exactly defined. I propose a way to define quantum coherence mathematically from the density matrix of the system. Degenerate quantum gases, i.e., Bose condensates and ultracold Fermi systems, form a good laboratory to study coherence, since their entropy is small and coherence is large, and thus they possess strong coherence phenomena. Concerning coherence phenomena in degenerate quantum gases, I concentrate in my thesis mainly on collective association from atoms to molecules, Rabi oscillations and decoherence. It appears that collective association and oscillations do not depend on the spin-statistics of particles. Moreover, I study the logical features of decoherence in closed systems via a simple spin-model. I argue that decoherence is a valid concept also in systems with a possibility to experience recoherence, i.e., Poincaré recurrences. Metatheoretically this is a remarkable result, since it justifies quantum cosmology: to study the whole universe (i.e., physical reality) purely quantum physically is meaningful and valid science, in which decoherence explains why the quantum physical universe appears to cosmologists and other scientists very classical-like. The study of the logical structure of closed systems also reveals that complex enough closed (physical) systems obey a principle that is similar to Gödel's incompleteness theorem of logic. According to the theorem it is impossible to describe completely a closed system within the system, and the inside and outside descriptions of the system can be remarkably different. Via understanding this feature it may be possible to comprehend coarse-graining better and to define uniquely the mutual entanglement of quantum systems.

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In the first decade of the 21st century, national notables were a significant theme in the Finnish theatre. The lives of artists, in particular, inspired the performances that combined historical and fictional elements. In this study, I focus on the characters of female artists in 18 Finnish plays or performances from the first decade of the 21st century. The study pertains to the field of performance analysis. I approach the characters from three points of view. Firstly, I examine them through the action of performances at the thematic level. Secondly, I concentrate on the forms of relationships between the audience and the half-historical character. Thirdly, I examine the representations of characters and their relationships to the audience using myth as a tool. I approach characters from the frame of feminist phenomenological theatre study but also combine the points of view of other traditions. As a model, I adapt the approach of the theatre researcher Bert O. States, which concentrates on the relation between a play s text and an actor, and between an actor and the public. Furthermore, I use the analysing tools of performance art in an examination of performances counted among the contemporary performance genre. The biographical plays about these artists are concentrated in the domestic sphere and take part in the conversation about the position of women in both the community and private life. They represent the heroines work, love, temptations and hardships. The artists do not carry out heroic acts, being more like everyday heroines whose lives and art were shared with the audience in an aphoristic atmosphere. In the examined performances, criticism of the heterosexual matrix was mainly conservative and the myths of female and male artists differed from each other: the woman artist was presented as a super heroine whose strength often meant sacrifices; the male artist was a weaker figure primarily pursuing his individualistic objectives. The performances proved to be a kind of documentary theatre, a hybrid of truth and fiction. Nonetheless, the constructions of subject and identity mainly represented the characters of the mythical stories and only secondarily gave a faithful rendition of the artists lives. Although these performances were addressed to the general and heterogeneous public, their audience proved to be a strictly predefined group, for which the national myths and the experience of a collective identity emerged as an important theme. The heroine characters offered the audience "safe" idols who ensured the solidity of the community. These performances contained common, shared values and gave the audience an opportunity to feel empathy and to be charmed by the confessions of well-known national characters.

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Foreign compounds, such as drugs are metabolised in the body in numerous reactions. Metabolic reactions are divided into phase I (functionalisation) and phase II (conjugation) reactions. Uridine diphosphoglucuronosyltransferase enzymes (UGTs) are important catalysts of phase II metabolic system. They catalyse the transfer of glucuronic acid to small lipophilic molecules and convert them to hydrophilic and polar glucuronides that are readily excreted from the body. Liver is the main site of drug metabolism. Many drugs are racemic mixtures of two enantiomers. Glucuronidation of a racemic compound yields a pair of diastereomeric glucuronides. Stereoisomers are interesting substrates in glucuronidation studies since some UGTs display stereoselectivity. Diastereomeric glucuronides of O-desmethyltramadol (M1) and entacapone were selected as model compounds in this work. The investigations of the thesis deal with enzymatic glucuronidation and the development of analytical methods for drug metabolites, particularly diastereomeric glucuronides. The glucuronides were analysed from complex biological matrices, such as urine or from in vitro incubation matrices. Various pretreatment techniques were needed to purify, concentrate and isolate the analytes of interest. Analyses were carried out by liquid chromatography (LC) with ultraviolet (UV) or mass spectrometric (MS) detection or with capillary electromigration techniques. Commercial glucuronide standards were not available for the studies. Enzyme-assisted synthesis with rat liver microsomes was therefore used to produce M1 glucuronides as reference compounds. The glucuronides were isolated by LC/UV and ultra performance liquid chromatography (UPLC)/MS, while tandem mass spectrometry (MS/MS) and nuclear magnetic resonance (NMR) spectroscopy were employed in structural characterisation. The glucuronides were identified as phenolic O-glucuronides of M1. To identify the active UGT enzymes in (±)-M1 glucuronidation recombinant human UGTs and human tissue microsomes were incubated with (±)-M1. The study revealed that several UGTs can catalyse (±)-M1 glucuronidation. Glucuronidation in human liver microsomes like in rat liver microsomes is stereoselective. The results of the studies showed that UGT2B7, most probably, is the main UGT responsible for (±)-M1 glucuronidation in human liver. Large variation in stereoselectivity of UGTs toward (±)-M1 enantiomers was observed. Formation of M1 glucuronides was monitored with a fast and selective UPLC/MS method. Capillary electromigration techniques are known for their high resolution power. A method that relied on capillary electrophoresis (CE) with UV detection was developed for the separation of tramadol and its free and glucuronidated metabolites. The suitability of the method to identify tramadol metabolites in an authentic urine samples was tested. Unaltered tramadol and four of its main metabolites were detected in the electropherogram. A micellar electrokinetic chromatography (MEKC) /UV method was developed for the separation of the glucuronides of entacapone in human urine. The validated method was tested in the analysis of urine samples of patients. The glucuronides of entacapone could be quantified after oral entacapone dosing.

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Previous research has been inconclusive regarding the impact of those who invest in entrepreneurs. Consider for a moment how potentially important they are to entrepreneurs. They for example decide who deserves funding, how much time they contribute to their portfolio firms, how they grant entrepreneurs access to their networks, and help entrepreneurs acquire additional funding. In sum, investors potentially have a great impact on the success of entrepreneurs. It is therefore important that we better understand the environment, relationships and context in which parties operate. This thesis contains five articles that explore investors’ and entrepreneurs’ relationships from various viewpoints, in theoretical frameworks, and use a variety of data and research methods. The first article is a literature review that summarises what we know of venture capital, business angel and corporate venture capital funding. The second article studies the entrepreneurs’ investor selection process, its consequences, and identifies key factors that influence the process. Earlier, the common approach has been to concentrate research on the investors’ selection policy, not the entrepreneurs’. The data and conclusions are based on multiple case studies. The article analyses how entrepreneurs can ensure that they get the best possible investor, when it is possible for an entrepreneur to select an investor, and what are the consequences of investor selection. The third article employs power constructs (dependency, power balance/imbalance, power sources) and analyses their applicability in the investor-entrepreneur relationship. Power constructs are extensively studied and utilised in the management and organisation literature. In entrepreneur investor relationships, power aspects are rarely analysed. However, having the ability to “get others to do things they would not otherwise do” is a very common factor in the investor-entrepreneur relationship. Therefore, employing and analysing the applicability of power constructs in this setting is well founded. The article is based on a single case study but suggests that power constructs could be applicable and consequently provide additional insights into the investor-entrepreneur relationship. The fourth article studies the role of advisors in the venture capital investment process and analyses implications for research and practice, particularly from the entrepreneurs’ perspective. The common entrepreneurial finance literature describes the entrepreneur-investor relationship as linear and bilateral. However, it was discovered that advisors may influence the relationship. In this article, the role of advisors, operating procedures and advisors’ impact on different parties is analysed. The fifth article concentrates on investors’ certification effect. The article measures and demonstrates that venture capital investment is likely to increase the credibility (in terms of media attention) of early stage firms, those that most often need additional credibility. Understanding investor certification can affect how entrepreneurs evaluate investment offers and how investors can make their offers appear more lucrative.

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The purpose of this master´s thesis is to analyze how NATO Secretary General Anders Fogh Rasmussen is trying to justify the existence of the military alliance through the use of security arguments. I am puzzled by the question: why does NATO still exist – what is NATO’s raison d'être. The New Strategic Concept (2010) forms the base for his argumentation. This thesis focuses on the security argumentation of NATO which is examined by analyzing the speeches the Secretary General. The theoretical framework of this study is based on constructivist approach to international security examining the linguistic process of securitization. Issues become securitized after Anders Fogh Rasmussen names them as threats. This thesis focuses on the securitization process relating to NATO and analyses what issues Rasmussen raises to the security agenda. Research data consists of the speeches by Anders Fogh Rasmussen. They are analyzed through J.L. Austin’s speech act taxonomy and Chaïm Perelman’s argumentation theories. The thesis will concentrate on the formulation and articulation of these threats which are considered and coined as “new threats” in contemporary international relations. I am conducting this research through the use of securitization theory. This study illustrates that the threats are constructed by NATO’s member-states in unison, but the resolutions are sounded through Rasmussen’s official speeches and transcripts. . Based on the analysis it can be concluded that Rasmussen is giving reasons for the existence of NATO. This takes place by making use of speech acts and different rhetorical techniques. The results of the analysis indicate that NATO remains an essential organization for the West and the rest of the world according to the Secretary General.

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Biological membranes are tightly linked to the evolution of life, because they provide a way to concentrate molecules into partially closed compartments. The dynamic shaping of cellular membranes is essential for many physiological processes, including cell morphogenesis, motility, cytokinesis, endocytosis, and secretion. It is therefore essential to understand the structure of the membrane and recognize the players that directly sculpt the membrane and enable it to adopt different shapes. The actin cytoskeleton provides the force to push eukaryotic plasma membrane in order to form different protrusions or/and invaginations. It has now became evident that actin directly co-operates with many membrane sculptors, including BAR domain proteins, in these important events. However, the molecular mechanisms behind BAR domain function and the differences between the members of this large protein family remain largely unresolved. In this thesis, the structure and functions of the I-BAR domain family members IRSp53 and MIM were thoroughly analyzed. By using several methods such as electron microscopy and systematic mutagenesis, we showed that these I-BAR domain proteins bind to PI(4,5)P2-rich membranes, generate negative membrane curvature and are involved in the formation of plasma membrane protrusions in cells e.g. filopodia. Importantly, we characterized a novel member of the BAR-domain superfamily which we named Pinkbar. We revealed that Pinkbar is specifically expressed in kidney and epithelial cells, and it localizes to Rab13-positive vesicles in intestinal epithelial cells. Remarkably, we learned that the I-BAR domain of Pinkbar does not generate membrane curvature but instead stabilizes planar membranes. Based on structural, mutagenesis and biochemical work we present a model for the mechanism of the novel membrane deforming activity of Pinkbar. Collectively, this work describes the mechanism by which I-BAR domain proteins deform membranes and provides new information about the biological roles of these proteins. Intriguingly, this work also gives evidence that significant functional plasticity exists within the I-BAR domain family. I-BAR proteins can either generate negative membrane curvature or stabilize planar membrane sheets, depending on the specific structural properties of their I-BAR domains. The results presented in this thesis expand our knowledge on membrane sculpting mechanisms and shows for the first time how flat membranes can be generated in cells.

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Energiataseen mallinnus on osa KarjaKompassi-hankkeeseen liittyvää kehitystyötä. Tutkielman tavoitteena oli kehittää lypsylehmän energiatasetta etukäteen ennustavia ja tuotoskauden aikana saatavia tietoja hyödyntäviä matemaattisia malleja. Selittävinä muuttujina olivat dieetti-, rehu-, maitotuotos-, koelypsy-, elopaino- ja kuntoluokkatiedot. Tutkimuksen aineisto kerättiin 12 Suomessa tehdyistä 8 – 28 laktaatioviikon pituisesta ruokintakokeesta, jotka alkoivat heti poikimisen jälkeen. Mukana olleista 344 lypsylehmästä yksi neljäsosa oli friisiläis- ja loput ayshire-rotuisia. Vanhempien lehmien päätiedosto sisälsi 2647 havaintoa (koe * lehmä * laktaatioviikko) ja ensikoiden 1070. Aineisto käsiteltiin SAS-ohjelmiston Mixed-proseduuria käyttäen ja poikkeavat havainnot poistettiin Tukeyn menetelmällä. Korrelaatioanalyysillä tarkasteltiin energiataseen ja selittävien muuttujien välisiä yhteyksiä. Energiatase mallinnettiin regressioanalyysillä. Laktaatiopäivän vaikutusta energiataseeseen selitettiin viiden eri funktion avulla. Satunnaisena tekijänä mallissa oli lehmä kokeen sisällä. Mallin sopivuutta aineistoon tarkasteltiin jäännösvirheen, selitysasteen ja Bayesin informaatiokriteerin avulla. Parhaat mallit testattiin riippumattomassa aineistossa. Laktaatiopäivän vaikutusta energiataseeseen selitti hyvin Ali-Schaefferin funktio, jota käytettiin perusmallina. Kaikissa energiatasemalleissa vaihtelu kasvoi laktaatioviikosta 12. alkaen, kun havaintojen määrä väheni ja energiatase muuttui positiiviseksi. Ennen poikimista käytettävissä olevista muuttujista dieetin väkirehuosuus ja väkirehun syönti-indeksi paransivat selitysastetta ja pienensivät jäännösvirhettä. Ruokinnan onnistumista voidaan seurata maitotuotoksen, maidon rasvapitoisuuden ja rasva-valkuaissuhteen tai EKM:n sisältävillä malleilla. EKM:n vakiointi pienensi mallin jäännösvirhettä. Elopaino ja kuntoluokka olivat heikkoja selittäjiä. Malleja voidaan hyödyntää karjatason ruokinnan suunnittelussa ja seurannassa, mutta yksittäisen lehmän energiataseen ennustamiseen ne eivät sovellu.

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Separation of molybdenite from chalcopyrite from the bulk concentrate of a low grade molybdenite ore from Chintamani, Kolar District, Karnataka, has been attempted in a modified Hallimond tube microflotation set-up. The flotation parameters studied are, sodium sulphide and potassium cyanide as depressants for chalcopyrite, pH, depressant concentration, steaming time and time of flotation. Selectivity index was used as a separation parameter. Steaming for 25 min followed by flotation for 7 min at 80 mg/l concentration of potassium cyanide and pH 9 gave the best results for separation of molybdenite. 19 ref.--AA

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Tutkielman tarkoituksena on rakentaa malli, jolla voidaan arvioida maitotilan toimintaa monipuolisesti ravinnehuuhtouman kannalta. Tavoitteena on ennen muuta analyyttinen tarkastelu siten, että kuitenkin huomioiden maidontuotannon ominaispiirteet, keskeisinä esimerkkeinä ravinnon, maidontuotannon ja lannan ominaisuuksien väliset riippuvuudet. Analyysissa tarkastellaan tilanomistajan yksityisen hyödynmaksimoinnin ja yhteiskunnan tavoitteiden eroavaisuutta. Lisäksi johdetaan optimaaliset ohjauskeinot ja arvioidaan eräiden yksinkertaisten ohjauskeinojen vaikuttavuutta. Mallin analysoinnin perusteella yksityinen ja yhteiskunnallinen optimiratkaisu eroavat toisistaan kaikkien päätösmuuttujien osalta. Ei voida kuitenkaan yleispätevästi sanoa muutosten merkittävyyttä tai suuntaa ottamatta kantaa mallin funktiomuotoihin ja parametriarvoihin. Optimaaliset ohjauskeinot tulisi asettaa keinolannoitteen ja lannan levitykselle, väkirehuruokinnalle ja säilörehun viljelylle, mutta ei eläinten määrälle. Toisaalta optimaaliset ohjauskeinot ovat hyvin monimutkaisia. Tarkasteltujen yksinkertaisempien ohjauskeinojen vaikuttavuutta ei voida tarkasti arvioida analyyttisella tasolla. Numeeristen tulosten perusteella yhteiskunnallisessa optimissa eläinmäärä olisi hieman yksityistä optimia pienempi, väkirehun käyttö vähäisempää, enemmän peltoa allokoitaisiin säilörehun viljelyyn ja lannoitustasot olisivat kautta linjan hieman pienemmät. Lannanlevitykset eroavat etäisyyden suhteen: molemmissa tapauksissa lannanlevityksen intensiteetti kasvaa kohti tilan keskusta kuljettaessa, mutta yksityisessä optimissa lähimmälle pellolle dumpataan kaikki ylimääräinen lanta, kun taas yhteiskunnallisessa optimissa lanta levitetään tasaisemmin eri pelloille. Ero kokonaishyvinvoinnissa jää pieneksi, mutta eläinmäärän kasvu kärjistäisi lannan dumppauksen aiheuttamia huuhtoumahaittoja. Yksinkertaisista ohjauskeinoista lannoitusrajoitus sekä ravinne- ja keinolannoitevero osoittautuivat kohtalaisen käyttökelpoisiksi numeeristen tulosten perusteella. Sen sijaan eläinmäärän rajoittaminen ja lannan kuljetuskustannuksia kompensoivat tuet vaikuttavat tulosten perusteella huonoilta ratkaisuilta.

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Belief revision systems aim at keeping a database consistent. They mostly concentrate on how to record and maintain dependencies. We propose an axiomatic system, called MFOT, as a solution to the problem of belief revision. MFOT has a set of proper axioms which selects a set of most plausible and consistent input beliefs. The proposed nonmonotonic inference rule further maintains consistency while generating the consequences of input beliefs. It also permits multiple property inheritance with exceptions. We have also examined some important properties of the proposed axiomatic system. We also propose a belief revision model that is object-centered. The relevance of such a model in maintaining the beliefs of a physician is examined.

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The object of this research is to study the mineralogy of the diabase dykes in Suomussalmi and the relevance of the mineralogy to tectonic events, specifically large block movements in the Archaean crust. Sharp tectonic lines separate two anomalies in the dyke swarms, shown on a geomagnetic map as positive anomalies. In one of these areas, the Toravaara anomaly, the diabases seem to contain pyroxenes as a main component. Outside the Toravaara anomaly hornblende is the main ferromagnesian mineral in diabases. The aim of this paper is to research the differences in the diabases inside and outside the anomalies and interpret the processes that formed the anomalies. The data for this sudy consist of field observations, 120 thin sections, 334 electron microprobe analyses, 19 whole-rock chemical analyses, a U-Pb age analysis and geomagnetic low-altitude aerial survey maps. The methods are interpretation of field observations, chemical analyses, microprobe analyses of single minerals and radiometric age determination, microscopic studies of the thin sections, geothermometers and geobarometers. On the basis of field observations and petrographic studies the diabases in the area are divided into pyroxene diabases, hornblende diabases and the Lohisärkkä porphyritic dyke swarm. Hornblende diabases are found in the entire study area, while the pyroxene diabases concentrate on the area of the Toravaara geomagnetic anomaly. The Lohisärkkä swarm transects the whole area as a thin line from east to west. The diabases are fairly homogenous both chemically and by mineral composition. The few exceptions are part of rarer older swarms or are significantly altered. The Lohisärkkä dyke swarm was dated as 2,21 Ga old, significantly older than the most common 1,98 Ga swarm in the area. The geothermometers applied showed that the diabases on the Toravaara anomaly were stabilized at a much higher temperature than the dykes outside the anomaly. The geobarometers showed the pyroxenes to have crystallized at varying depths. The research showed the Toravaara anomaly to have formed by a vertical block movement, and the fault on its west side to have a total lateral transfer of only a few kilometers. The formation of the second anomaly was also interpreted to be tectonic in nature. In addition, the results of the geothermobarometry uncovered necessary conditions for the study of diabase emplacement depth: the minerals for the study must be chosen by minimum crystallization depth, and a geobarometer capable of determining the magmatic temperature must be used. In addition, it would be more suitable to conduct this kind of study in an area where the dykes are more exposed.

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The coherence of the Soviet bloc was seriously tested at the turn of the 1970s, as the Soviet Union and its allies engaged in intensive negotiations over their relations with the European Communities (EC). In an effort to secure their own national economic interests many East European countries began independent manoeuvres against the wishes of their bloc leader. However, much of the intra-bloc controversy was kept out of the public eye, as the battle largely took place behind the scenes, within the organisation for economic cooperation, the Council for Mutual Economic Assistance (CMEA). The CMEA policy-making process vis-à-vis the EC is described in this study with reference to primary archival materials. This study investigates the negotiating positions and powers of the CMEA member states in their efforts to deal with the economic challenge created by the progress of the EC, as it advanced towards the customs union. This entails an analysis of the functioning principles and performance of the CMEA machinery. The study traces the CMEA negotiations that began in 1970 over its policy toward the EC. The policy was finally adopted in 1974, and was followed by the first official meeting between the two organisations in early 1975. The story ends in 1976, when the CMEA s efforts to enter into working relations with the EC were seemingly frustrated by the latter. The first major finding of the study is that, contrary to much of the prior research, the Soviet Union was not in a hegemonic position vis-à-vis its allies. It had to use a lot of its resources to tame the independent manoeuvring of its smaller allies. Thus, the USSR was not the kind of bloc leader that the totalitarian literature has described. Because the Soviet Union had to spend so much attention on its own bloc-politics, it was not able to concentrate on formulating a policy vis-à-vis the EC. Thus, the Soviet leadership was dependent on its allies in those instances when the socialist countries needed to act as a bloc. This consequently opened up the possibility for the USSR s allies to manoeuvre. This study also argues that when the CMEA did manage to find a united position, it was a force that the EC had to reckon with in its policy-making. This was particularly the case in the implementation of the EC Common Commercial Policy. The other main finding of the study is that, although it has been largely neglected in the previous literature on the history of West European integration, the CMEA did in fact have an effect on EC decision-making. This study shows how for political and ideological reasons the CMEA members did not acknowledge the EC s supranational authority. Therefore the EC had no choice but to refrain from implementing its Common Commercial Policy in full.

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Various aspects of coherent states of nonlinear su(2) and su(1,1) algebras are studied. It is shown that the nonlinear su(1,1) Barut-Girardello and Perelomov coherent states are related by a Laplace transform. We then concentrate on the derivation and analysis of the statistical and geometrical properties of these states. The Berry's phase for the nonlinear coherent states is also derived. (C) 2010 American Institute of Physics. doi:10.1063/1.3514118]

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Limestone rejects from Bagalkot mines have been beneficiated by froth flotation with a view to reducing the magnesia content. In order to ascertain the effect of the main parameters such as sodium oleate concentration, sodium silicate concentration and pH on the MgO content, statistically designed experiments have been performed. The results indicate that under the optimum conditions arrived at limestone rejects could be beneficiated to produce a concentrate with magnesia. content meeting the specifications for cement manufacture.