Macaulay style formulas for sparse resultants

We present formulas for computing the resultant of sparse polyno- mials as a quotient of two determinants, the denominator being a minor of the numerator. These formulas extend the original formulation given by Macaulay for homogeneous polynomials.

Strategic behaviours in healthcare : evidence from primary care and pharmaceutical markets

We analyse the strategic behaviours of agents in a market through the appropriate¬ness of their skills to the market. If agents' skills are well adapted to market and they can reach their target, they will not need to adopt strategic behaviours. The agents will behave as selfish individuals. However, if their skills are not well adapted and they cannot attain their target alone, they will adopt strategic behaviours to reach their objectives. These behaviours will have a different impact on the utilities of other agents, depending on the skills and the objectives of the agent. If these agents need other agents to reach their objectives, they will behave as altruistic individuals who internalise the utilities of other agents in reaching their objectives and will adopt cooperative behaviours. However, if these agents fear that other agents could prevent them from reaching their target because they can foresee that the skills of other agents are better adapted than their own skills, the agents will then behave as predator individuals and will adopt destructive behaviours to attain their objective. It is in the interests of these agents to manipulate information to increase disorder and dissimulate their lack of skills. They will reproduce the strategies of animals that modify their appearance to escape predators or simulate being bait to attract their prey. These agents will seek to induce chaos into the behaviours of other agents to amplify the impact of their strategies. The appropriateness of skills to the market allows an understanding of the emer-gence of networks and associated strategies. The members of a networks are inputs who are excluded when their costs are higher than their benefits. A network simul-taneously allows cooperation and selfish, predatory behaviours among its members. A network may adopt informational strategies when seeking to become the leader in a market or when it cannot survive. The creation of networks and the manipulation of information are two overlapping evolutionary strategies, with the first strategy favouring the second. In our model, an agent does not behave like a firm that aims only to maximise the profits of the firm but rather as a member of a network who adopts strategic behaviours as a function of the interests of this network. If his skills are well adapted to the market and he can innovate, he will not invest in erroneous input; in contrast, if his skills are not adapted, the agent will invest in the erroneous input of information into the market in order to survive. Therefore, when any informational asymmetries between the agents and their principals characterise the market, the price cannot be the main element that allows equilibrium to be reached in the market; instead, the appropriateness of skills to the market enables equilibrium. We will now apply these hypotheses to explain the strategic behaviours of physicians and pharmaceutical companies.

Epoxyeicosanoids stimulate multiorgan metastasis and tumor dormancy escape in mice.

Epoxyeicosatrienoic acids (EETs) are small molecules produced by cytochrome P450 epoxygenases. They are lipid mediators that act as autocrine or paracrine factors to regulate inflammation and vascular tone. As a result, drugs that raise EET levels are in clinical trials for the treatment of hypertension and many other diseases. However, despite their pleiotropic effects on cells, little is known about the role of these epoxyeicosanoids in cancer. Here, using genetic and pharmacological manipulation of endogenous EET levels, we demonstrate that EETs are critical for primary tumor growth and metastasis in a variety of mouse models of cancer. Remarkably, we found that EETs stimulated extensive multiorgan metastasis and escape from tumor dormancy in several tumor models. This systemic metastasis was not caused by excessive primary tumor growth but depended on endothelium-derived EETs at the site of metastasis. Administration of synthetic EETs recapitulated these results, while EET antagonists suppressed tumor growth and metastasis, demonstrating in vivo that pharmacological modulation of EETs can affect cancer growth. Furthermore, inhibitors of soluble epoxide hydrolase (sEH), the enzyme that metabolizes EETs, elevated endogenous EET levels and promoted primary tumor growth and metastasis. Thus, our data indicate a central role for EETs in tumorigenesis, offering a mechanistic link between lipid signaling and cancer and emphasizing the critical importance of considering possible effects of EET-modulating drugs on cancer.

Mastectomy, Body De-Construction and Impact on Identity: A qualitative study

Objectives: This qualitative study aims at understanding the consequences of body deconstruction through mastectomy on corporality and identity in women with breast cancer. Design: Nineteen women were contacted through the hospital. All had to undergo mastectomy. Some were offered immediate breast reconstruction, others, because of cancer treatments, had no planned reconstruction. A qualitative reflexive methodological background was chosen. Method: Women were invited to participate in three semi-structured interviews, one shortly before or after mastectomy, and the other interviews later in their illness courses, after surgery. All interviews were transcribed verbatim. Thematic analysis was performed. The analysis of the first interview of each woman is presented in this article. Results: Mastectomy provokes a painful experience of body deconstruction. Even when immediate reconstruction is proposed, contrasted feelings and dissonance are expressed when comparing the former healthy body to the present challenged body entity. Body transformations are accompanied with experiences of mutilation, strangeness, and modify the physical, emotional social, symbolic and relational dimensions of the woman's gendered identity. Although the opportunity of breast reconstruction is seen as a possible recovery of a lost physical symmetry and body integrity, grieving the past body and integrating a new corporality leads to a painful identity crisis. Conclusion: With mastectomy, the roots of the woman's identity are challenged, leading to a re-evaluation of her existential values. The consequences of mastectomy transform the woman's corporality and embodiment, and question her identity. Psychological support is discussed in the perspective of our results.

Entropic transport in confined media: a challenge for computational studies in biological and soft-matter systems

Transport in small-scale biological and soft-matter systems typically occurs under confinement conditions in which particles proceed through obstacles and irregularities of the boundaries that may significantly alter their trajectories. A transport model that assimilates the confinement to the presence of entropic barriers provides an efficient approach to quantify its effect on the particle current and the diffusion coefficient. We review the main peculiarities of entropic transport and treat two cases in which confinement effects play a crucial role, with the appearance of emergent properties. The presence of entropic barriers modifies the mean first-passage time distribution and therefore plays a very important role in ion transport through micro- and nano-channels. The functionality of molecular motors, modeled as Brownian ratchets, is strongly affected when the motor proceeds in a confined medium that may constitute another source of rectification. The interplay between ratchet and entropic rectification gives rise to a wide variety of dynamical behaviors, not observed when the Brownian motor proceeds in an unbounded medium. Entropic transport offers new venues of transport control and particle manipulation and new ways to engineer more efficient devices for transport at the nanoscale.

Methods and Models for Accelerating Dynamic Simulation of Fluid Power Circuits

The objective of this dissertation is to improve the dynamic simulation of fluid power circuits. A fluid power circuit is a typical way to implement power transmission in mobile working machines, e.g. cranes, excavators etc. Dynamic simulation is an essential tool in developing controllability and energy-efficient solutions for mobile machines. Efficient dynamic simulation is the basic requirement for the real-time simulation. In the real-time simulation of fluid power circuits there exist numerical problems due to the software and methods used for modelling and integration. A simulation model of a fluid power circuit is typically created using differential and algebraic equations. Efficient numerical methods are required since differential equations must be solved in real time. Unfortunately, simulation software packages offer only a limited selection of numerical solvers. Numerical problems cause noise to the results, which in many cases leads the simulation run to fail. Mathematically the fluid power circuit models are stiff systems of ordinary differential equations. Numerical solution of the stiff systems can be improved by two alternative approaches. The first is to develop numerical solvers suitable for solving stiff systems. The second is to decrease the model stiffness itself by introducing models and algorithms that either decrease the highest eigenvalues or neglect them by introducing steady-state solutions of the stiff parts of the models. The thesis proposes novel methods using the latter approach. The study aims to develop practical methods usable in dynamic simulation of fluid power circuits using explicit fixed-step integration algorithms. In this thesis, twomechanisms whichmake the systemstiff are studied. These are the pressure drop approaching zero in the turbulent orifice model and the volume approaching zero in the equation of pressure build-up. These are the critical areas to which alternative methods for modelling and numerical simulation are proposed. Generally, in hydraulic power transmission systems the orifice flow is clearly in the turbulent area. The flow becomes laminar as the pressure drop over the orifice approaches zero only in rare situations. These are e.g. when a valve is closed, or an actuator is driven against an end stopper, or external force makes actuator to switch its direction during operation. This means that in terms of accuracy, the description of laminar flow is not necessary. But, unfortunately, when a purely turbulent description of the orifice is used, numerical problems occur when the pressure drop comes close to zero since the first derivative of flow with respect to the pressure drop approaches infinity when the pressure drop approaches zero. Furthermore, the second derivative becomes discontinuous, which causes numerical noise and an infinitely small integration step when a variable step integrator is used. A numerically efficient model for the orifice flow is proposed using a cubic spline function to describe the flow in the laminar and transition areas. Parameters for the cubic spline function are selected such that its first derivative is equal to the first derivative of the pure turbulent orifice flow model in the boundary condition. In the dynamic simulation of fluid power circuits, a tradeoff exists between accuracy and calculation speed. This investigation is made for the two-regime flow orifice model. Especially inside of many types of valves, as well as between them, there exist very small volumes. The integration of pressures in small fluid volumes causes numerical problems in fluid power circuit simulation. Particularly in realtime simulation, these numerical problems are a great weakness. The system stiffness approaches infinity as the fluid volume approaches zero. If fixed step explicit algorithms for solving ordinary differential equations (ODE) are used, the system stability would easily be lost when integrating pressures in small volumes. To solve the problem caused by small fluid volumes, a pseudo-dynamic solver is proposed. Instead of integration of the pressure in a small volume, the pressure is solved as a steady-state pressure created in a separate cascade loop by numerical integration. The hydraulic capacitance V/Be of the parts of the circuit whose pressures are solved by the pseudo-dynamic method should be orders of magnitude smaller than that of those partswhose pressures are integrated. The key advantage of this novel method is that the numerical problems caused by the small volumes are completely avoided. Also, the method is freely applicable regardless of the integration routine applied. The superiority of both above-mentioned methods is that they are suited for use together with the semi-empirical modelling method which necessarily does not require any geometrical data of the valves and actuators to be modelled. In this modelling method, most of the needed component information can be taken from the manufacturer’s nominal graphs. This thesis introduces the methods and shows several numerical examples to demonstrate how the proposed methods improve the dynamic simulation of various hydraulic circuits.

Spin-Dynamics in Cold Gases of 87Rb and Atomic Hydrogen. The spins they are a-changin’

In this thesis the dynamics of cold gaseous atoms is studied. Two different atomic species and two different experimental techniques have been used. In the first part of the thesis experiments with Bose-Einstein condensates of Rb-87 are presented. In these experiments the methods of laser cooling and magnetic trapping of atoms were utilized. An atom chip was used as the experimental technique for implementation of magnetic trapping. The atom chip is a small integrated instrument allowing accurate and detailed manipulation of the atoms. The experiments with Rb-87 probed the behaviour of a falling beam of atoms outcoupled from the Bose-Einstein condensate by electromagnetic field induced spin flips. In the experiments a correspondence between the phases of the outcoupling radio frequency field and the falling beam of atoms was found. In the second part of the thesis experiments of spin dynamics in cold atomic hydrogen gas are discussed. The experiments with atomic hydrogen are conducted in a cryostat using a dilution refrigerator as the cooling method. These experiments concentrated on explaining and quantifying modulations in the electron spin resonance spectra of doubly polarized atomic hydrogen. The modifications to the previous experimental setup are described and the observation of electron spin waves is presented. The observed spin wave modes were caused by the identical spin rotation effect. These modes have a strong dependence on the spatial profile of the polarizing magnetic field. We also demonstrated confinement of these modes in regions of strong magnetic field and manipulated their spatial distribution by changing the position of the field maximum.

The encounter with the real and post-Soviet trauma : fantasy construction in Russian popular cinema /

This thesis examines the impact of the Soviet Union's collapse on the Russian Symbolic as represented through popular cinema of the post-Soviet period. The disintegration of the USSR in 1991 became one of the most traumatic experiences for many Russian people. The trauma of the collapse of the Soviet Union penetrated the everyday reality of the Russian Symbolic, leaving the traces-symptoms in different cultural fonns like literature, arts, television and cinema. Because popular culture usually reacts very quickly to any social, political and economical shifts in society, it is an excellent barometer for deeper changes in society. Focusing on postSoviet popular cinema, this thesis analyzes the symptoms of cultural and individual trauma occasioned by the momentous changes of the 1990's. This study is grounded in post-analytic theory of Jacques Lacan and its interpretation by Slavoj Zizek, which emphases the traumatic encounter with the Real as a "hard core" of our reality. According to this paradigm, a new chain of signifiers is structured around the traumatic breach in the Symbolic, initiating a process of fantasy construction to deal with consequences of trauma and, thus, to support our Symbolic order. This thesis examines three major fantasy constructions - drinking, traveling to a "happy land" and family reunion and money - in popular films by Alexander Rogozhkin, Yurij Mamin, Georgij Shengelia, Dmitrij Astrakhan, Valerij Todorovskij, Alexej Balabanov, Sergej Bodrov Jr. and Petr Buslov. According to Zizek, enjoyment underlies any fantasy constructions, and that is why after the intrusion of the Real every individual and culture should go through the process of fantasizing about some substitutes which can help to minimize the traumatic effect and which can lead to a partial enjoyment. By analyzing the fantasies about drinking, "happy land", reconstruction of the family bonds and money in Russian popular cinema since 1991, this thesis demonstrates how the traumatic engagement with the Real affected the everyday lives of Russian people, and how individuals tried to fill the gap, the lack, in the post-Soviet Symbolic and "return" the lost feeling of unity and plenitude.

Region Connection Calculus: Composition Tables and Constraint Satisfaction Problems

Qualitative spatial reasoning (QSR) is an important field of AI that deals with qualitative aspects of spatial entities. Regions and their relationships are described in qualitative terms instead of numerical values. This approach models human based reasoning about such entities closer than other approaches. Any relationships between regions that we encounter in our daily life situations are normally formulated in natural language. For example, one can outline one's room plan to an expert by indicating which rooms should be connected to each other. Mereotopology as an area of QSR combines mereology, topology and algebraic methods. As mereotopology plays an important role in region based theories of space, our focus is on one of the most widely referenced formalisms for QSR, the region connection calculus (RCC). RCC is a first order theory based on a primitive connectedness relation, which is a binary symmetric relation satisfying some additional properties. By using this relation we can define a set of basic binary relations which have the property of being jointly exhaustive and pairwise disjoint (JEPD), which means that between any two spatial entities exactly one of the basic relations hold. Basic reasoning can now be done by using the composition operation on relations whose results are stored in a composition table. Relation algebras (RAs) have become a main entity for spatial reasoning in the area of QSR. These algebras are based on equational reasoning which can be used to derive further relations between regions in a certain situation. Any of those algebras describe the relation between regions up to a certain degree of detail. In this thesis we will use the method of splitting atoms in a RA in order to reproduce known algebras such as RCC15 and RCC25 systematically and to generate new algebras, and hence a more detailed description of regions, beyond RCC25.

Informing the structure of subjective well-being through examining changes in life satisfaction, positive affect, and negative affect

Subjective well-being (SWB) refers to how individuals evaluate and experience their lives in positive ways, and encompasses global judgments of life satisfaction (LS), as well as the frequency of positive and negative affect (PA and NA, respectively) in one’s life. To inform the current ambiguity concerning the structure of SWB, the aim of this Masters thesis was to evaluate the structure of SWB based on whether the three components of SWB change together or independently naturally, over time and following experimental manipulation. In Study 1, associations among changes in LS, PA, and NA were evaluated using a longitudinal approach tracking natural changes in the components over periods of three months and three years. Results indicated that change in one component was related to change in the other two components. In Study 2, an experimental design was used to manipulate each SWB component individually, and evaluate changes in all three components following each manipulation. Manipulation materials designed to target LS only were effective (i.e., led to heightened focus on LS, and not PA or NA) and created an increase in both LS and PA. Manipulation materials designed to target PA and NA only were not effective (i.e., led to heightened focus on the target component, as well as on LS). Furthermore, in both studies the strength of an individual’s SWB (assessed in terms of structural consistency and structural ambivalence in Study 1 and Study 2, along with subjective ambivalence in Study 2) did not consistently moderate the degree to which changes in the components were associated with one another. Together, these findings indicate that the structure of SWB may be complex and dynamic, rather than static. Alternatively, the components of SWB may not be easily manipulated in isolation of one another. Implications for existing structural models of SWB are discussed.

A Categorical Framework for the Specification and the Verification of Aspect Oriented Systems

Un objectif principal du génie logiciel est de pouvoir produire des logiciels complexes, de grande taille et fiables en un temps raisonnable. La technologie orientée objet (OO) a fourni de bons concepts et des techniques de modélisation et de programmation qui ont permis de développer des applications complexes tant dans le monde académique que dans le monde industriel. Cette expérience a cependant permis de découvrir les faiblesses du paradigme objet (par exemples, la dispersion de code et le problème de traçabilité). La programmation orientée aspect (OA) apporte une solution simple aux limitations de la programmation OO, telle que le problème des préoccupations transversales. Ces préoccupations transversales se traduisent par la dispersion du même code dans plusieurs modules du système ou l’emmêlement de plusieurs morceaux de code dans un même module. Cette nouvelle méthode de programmer permet d’implémenter chaque problématique indépendamment des autres, puis de les assembler selon des règles bien définies. La programmation OA promet donc une meilleure productivité, une meilleure réutilisation du code et une meilleure adaptation du code aux changements. Très vite, cette nouvelle façon de faire s’est vue s’étendre sur tout le processus de développement de logiciel en ayant pour but de préserver la modularité et la traçabilité, qui sont deux propriétés importantes des logiciels de bonne qualité. Cependant, la technologie OA présente de nombreux défis. Le raisonnement, la spécification, et la vérification des programmes OA présentent des difficultés d’autant plus que ces programmes évoluent dans le temps. Par conséquent, le raisonnement modulaire de ces programmes est requis sinon ils nécessiteraient d’être réexaminés au complet chaque fois qu’un composant est changé ou ajouté. Il est cependant bien connu dans la littérature que le raisonnement modulaire sur les programmes OA est difficile vu que les aspects appliqués changent souvent le comportement de leurs composantes de base [47]. Ces mêmes difficultés sont présentes au niveau des phases de spécification et de vérification du processus de développement des logiciels. Au meilleur de nos connaissances, la spécification modulaire et la vérification modulaire sont faiblement couvertes et constituent un champ de recherche très intéressant. De même, les interactions entre aspects est un sérieux problème dans la communauté des aspects. Pour faire face à ces problèmes, nous avons choisi d’utiliser la théorie des catégories et les techniques des spécifications algébriques. Pour apporter une solution aux problèmes ci-dessus cités, nous avons utilisé les travaux de Wiels [110] et d’autres contributions telles que celles décrites dans le livre [25]. Nous supposons que le système en développement est déjà décomposé en aspects et classes. La première contribution de notre thèse est l’extension des techniques des spécifications algébriques à la notion d’aspect. Deuxièmement, nous avons défini une logique, LA , qui est utilisée dans le corps des spécifications pour décrire le comportement de ces composantes. La troisième contribution consiste en la définition de l’opérateur de tissage qui correspond à la relation d’interconnexion entre les modules d’aspect et les modules de classe. La quatrième contribution concerne le développement d’un mécanisme de prévention qui permet de prévenir les interactions indésirables dans les systèmes orientés aspect.

Carbon metabolism in transgenic roots with altered levels of hexokinase and triosephosphate isomerase and growing under different nitrogen status

Ce projet a pour but d’évaluer la capacité de la voie des pentoses phosphates (VPP) dans les racines transgéniques de pomme de terre (Solanum tuberosum) modifiées pour exprimer différents niveaux de l'hexokinase (HK) et de la triosephosphate isomérase cytosolique (cTPI). Dans les racines, la VPP alimente la voie de l’assimilation de l’azote en equivalents réducteurs et permet donc la biosynthèse des acides aminés. Le glucose-6-phosphate produit par l’HK est consommé par la partie oxydative de la VPP catalysée par la glucose-6-phosphate déshydrogénase (G6PDH) et la 6-phosphogluconate déshydrogénase (6PGDH). Les changements dans l'expression de HK et cTPI peuvent affecter le fonctionnement de la VPP et les mécanismes qui sont liés à l’utilisation des équivalents réducteurs produits par la VPP, comme l'assimilation de l’azote et la synthèse des acides aminés. Afin d’évaluer l’effet des manipulations génétiques de l’HK et de la cTPI sur l’assimilation de l’azote, nous avons cultivé les racines transgéniques sur des milieux contenant des concentrations élevées (7 mM) ou basses (0,7 mM) de nitrate d’ammonium comme source d’azote. Les résultats montrent que la culture sur un milieu riche en azote induit les activités G6PDH et 6PGDH. Les données montrent que la capacité de la VPP est plus grande avec des niveaux élevés en HK ou en cTPI. Nous avons aussi pu démontrer une plus grande activité spécifique de l’HK dans les conditions pauvres en azote. Ces données ont été complémentées par des mesures des pools d’acides aminés dans les racines transgéniques cultivées sur différents niveaux d’azote. Aucune tendance notable des pools d’acides aminés n’a été remarquée dans les racines modifiées pour leur contenu en HK suggèrant que la manipulation de HK n’affecte pas l'assimilation de l’azote. Dans les racines transgéniques modifiées pour la cTPI, les ratios Gln/Glu et Asn/Asp sont plus élevés chez les clones antisens, indiquant une assimilation de l’azote plus élevée. Ces résultats ont démontré l'activation de l'assimilation de l’azote chez les clones antisens cTPI dans les conditions élevées et basses d’azote alors que la manipulation de l’HK n’affecte pas l’assimilation de l’azote.

Engendered Conversations: Gender Subversion Through Fictional Dialogue in Lawrence, Hemingway and Forster

This dissertation examines gendered fictional dialogue in popular works by D.H. Lawrence, Ernest Hemingway and E.M. Forster, including Howards End (1910), The Sun Also Rises (1926) and Lady Chatterley’s Lover (1928). I apply Judith Halberstam’s notion of female masculinity to direct speech, to explore how speech traits inform modernist literary aesthetics. My introduction frames this discussion in sociolinguistics, Judith Butler’s theory of performativity, M.M. Bakhtin’s discourse theory, and gender studies. It provides an opportunity to establish experimental dialogue techniques, and the manipulation of gendered talk, in transgressive texts including James Joyce’s Ulysses (1922), Virginia Woolf’s Orlando (1928) and Radcyffe Hall’s The Well of Loneliness (1928). The first chapter discusses taboos and dialect in D.H. Lawrence’s fictional dialogue. The second chapter establishes gender subversion as a crucial element in Ernest Hemingway’s dialogue style. The third chapter contrasts Forster’s latently gendered speech with his techniques of dialect emphasis and dialect suppression. Finally, my conclusion discusses gender identity in the poetry of Dorothy Parker and Baroness Elsa von Freytag Loringhoven, and the temporality of gender in “Time Passes” from Virginia Woolf’s To the Lighthouse (1927). New Woman characters like Lady Brett Ashley typified a crucial moment in women’s liberation. They not only subverted stereotypes of womanhood through their dress or sexual freedom, they also adopted/adapted masculine idiom to shock, to rebel against and challenge male dominance. Different speech acts incited fashionable slang, became a political protest symbol or inspired psychoanalytic theory. The intriguing functions of women’s masculine speech in early twentieth century fiction establishes the need to examine additional connections between gender and talk in literary studies.

Identifikation spezieller Funktionen, die durch Rodriguesformeln gegeben sind

Es ist allgemein bekannt, dass sich zwei gegebene Systeme spezieller Funktionen durch Angabe einer Rekursionsgleichung und entsprechend vieler Anfangswerte identifizieren lassen, denn computeralgebraisch betrachtet hat man damit eine Normalform vorliegen. Daher hat sich die interessante Forschungsfrage ergeben, Funktionensysteme zu identifizieren, die über ihre Rodriguesformel gegeben sind. Zieht man den in den 1990er Jahren gefundenen Zeilberger-Algorithmus für holonome Funktionenfamilien hinzu, kann die Rodriguesformel algorithmisch in eine Rekursionsgleichung überführt werden. Falls die Funktionenfamilie überdies hypergeometrisch ist, sogar laufzeiteffizient. Um den Zeilberger-Algorithmus überhaupt anwenden zu können, muss es gelingen, die Rodriguesformel in eine Summe umzuwandeln. Die vorliegende Arbeit beschreibt die Umwandlung einer Rodriguesformel in die genannte Normalform für den kontinuierlichen, den diskreten sowie den q-diskreten Fall vollständig. Das in Almkvist und Zeilberger (1990) angegebene Vorgehen im kontinuierlichen Fall, wo die in der Rodriguesformel auftauchende n-te Ableitung über die Cauchysche Integralformel in ein komplexes Integral überführt wird, zeigt sich im diskreten Fall nun dergestalt, dass die n-te Potenz des Vorwärtsdifferenzenoperators in eine Summenschreibweise überführt wird. Die Rekursionsgleichung aus dieser Summe zu generieren, ist dann mit dem diskreten Zeilberger-Algorithmus einfach. Im q-Fall wird dargestellt, wie Rekursionsgleichungen aus vier verschiedenen q-Rodriguesformeln gewonnen werden können, wobei zunächst die n-te Potenz der jeweiligen q-Operatoren in eine Summe überführt wird. Drei der vier Summenformeln waren bislang unbekannt. Sie wurden experimentell gefunden und per vollständiger Induktion bewiesen. Der q-Zeilberger-Algorithmus erzeugt anschließend aus diesen Summen die gewünschte Rekursionsgleichung. In der Praxis ist es sinnvoll, den schnellen Zeilberger-Algorithmus anzuwenden, der Rekursionsgleichungen für bestimmte Summen über hypergeometrische Terme ausgibt. Auf dieser Fassung des Algorithmus basierend wurden die Überlegungen in Maple realisiert. Es ist daher sinnvoll, dass alle hier aufgeführten Prozeduren, die aus kontinuierlichen, diskreten sowie q-diskreten Rodriguesformeln jeweils Rekursionsgleichungen erzeugen, an den hypergeometrischen Funktionenfamilien der klassischen orthogonalen Polynome, der klassischen diskreten orthogonalen Polynome und an der q-Hahn-Klasse des Askey-Wilson-Schemas vollständig getestet werden. Die Testergebnisse liegen tabellarisch vor. Ein bedeutendes Forschungsergebnis ist, dass mit der im q-Fall implementierten Prozedur zur Erzeugung einer Rekursionsgleichung aus der Rodriguesformel bewiesen werden konnte, dass die im Standardwerk von Koekoek/Lesky/Swarttouw(2010) angegebene Rodriguesformel der Stieltjes-Wigert-Polynome nicht korrekt ist. Die richtige Rodriguesformel wurde experimentell gefunden und mit den bereitgestellten Methoden bewiesen. Hervorzuheben bleibt, dass an Stelle von Rekursionsgleichungen analog Differential- bzw. Differenzengleichungen für die Identifikation erzeugt wurden. Wie gesagt gehört zu einer Normalform für eine holonome Funktionenfamilie die Angabe der Anfangswerte. Für den kontinuierlichen Fall wurden umfangreiche, in dieser Gestalt in der Literatur noch nie aufgeführte Anfangswertberechnungen vorgenommen. Im diskreten Fall musste für die Anfangswertberechnung zur Differenzengleichung der Petkovsek-van-Hoeij-Algorithmus hinzugezogen werden, um die hypergeometrischen Lösungen der resultierenden Rekursionsgleichungen zu bestimmen. Die Arbeit stellt zu Beginn den schnellen Zeilberger-Algorithmus in seiner kontinuierlichen, diskreten und q-diskreten Variante vor, der das Fundament für die weiteren Betrachtungen bildet. Dabei wird gebührend auf die Unterschiede zwischen q-Zeilberger-Algorithmus und diskretem Zeilberger-Algorithmus eingegangen. Bei der praktischen Umsetzung wird Bezug auf die in Maple umgesetzten Zeilberger-Implementationen aus Koepf(1998/2014) genommen. Die meisten der umgesetzten Prozeduren werden im Text dokumentiert. Somit wird ein vollständiges Paket an Algorithmen bereitgestellt, mit denen beispielsweise Formelsammlungen für hypergeometrische Funktionenfamilien überprüft werden können, deren Rodriguesformeln bekannt sind. Gleichzeitig kann in Zukunft für noch nicht erforschte hypergeometrische Funktionenklassen die beschreibende Rekursionsgleichung erzeugt werden, wenn die Rodriguesformel bekannt ist.

Museums, memories and social movements

From modernity to the contemporary world, museums have been acknowledged for their power to produce metamorphoses of meanings and functions, for their ability to adapt historic and social determination, and for their calling for cultural mediation. They derive from creating gestures which bind the symbolic and the material, which bind what is sensitive and what is intelligible. For this very reason the bridge metaphor fits them well, a bridge cast between different times, spaces, individuals, social groups and cultures, a bridge that is built with images and which holds a special place in the imaginary.