We give a review of classical and recent results on maximization of expected utility for an investor who has the possibility of trading in a financial market. Emphasis will be given to the duality theory related to this convex optimization problem. For expository reasons we first consider the classical case where the underlying probability space is finite. This setting has the advantage that the technical diffculties of the proofs are reduced to a minimum, which allows for a clearer insight into the basic ideas, in particular the crucial role played by the Legendre-transform. In this setting we state and prove an existence and uniqueness theorem for the optimal investment strategy, and its relation to the dual problem; the latter consists in finding an equivalent martingale measure optimal with respect to the conjugate of the utility function. We also discuss economic interpretations of these theorems. We then pass to the general case of an arbitrage-free financial market modeled by an R^d-valued semi-martingale. In this case some regularity conditions have to be imposed in order to obtain an existence result for the primal problem of finding the optimal investment, as well as for a proper duality theory. It turns out that one may give a necessary and sufficient condition, namely a mild condition on the asymptotic behavior of the utility function, its so-called reasonable asymptotic elasticity. This property allows for an economic interpretation motivating the term "reasonable". The remarkable fact is that this regularity condition only pertains to the behavior of the utility function, while we do not have to impose any regularity conditions on the stochastic process modeling the financial market (to be precise: of course, we have to require the arbitrage-freeness of this process in a proper sense; also we have to assume in one of the cases considered below that this process is locally bounded; but otherwise it may be an arbitrary R^d-valued semi-martingale). (author's abstract) / Series: Report Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"

Dans cette thèse nous explorons le diagramme de phase des fullerènes intercalées avec des métaux alcalins lourds, Rb6C60 et Cs6C60, à très haute pression (<50 GPa) et à très haute température (de l'ambiante à 1500 K).<br /><br />Ce travail inclue des expériences d'absorption de rayons X, de diffraction de rayons X, de spectroscopie Raman, ainsi que des calculs DFT ab initio à haute pression.<br /><br />Le couplage entre expériences et calculs permet d'observer que la présence de la forte interaction ionique entre chaque molécule et les ions alcalins, empêche la polymérisation des fullerènes sous pression. Dans le cas de Cs6C60, ceci a permis d'étendre le domaine de stabilité en pression des molécules de C60 d'au moins un facteur deux par rapport aux cristaux de C60 non-intercalés. Dans le cas de Rb6C60 une transition réversible est observée à 35 GPa.<br /><br />Nous avons mis en évidence la déformation progressive de la molécule de fullerène sous pression dans les systèmes étudiés. La compressibilité des deux cristaux a été mesurée et calculée.

Cette thèse présente une étude quantitative des modes de fragmentation du fullerène C60 en collision avec des ions légers (Hn=1,2,3+ , Heq=1,2+) dans le domaine de vitesse 0,1 - 2,3 u.a.. La technique de multicorrélation (ions, électrons, énergie des électrons) employée a permis de dégager certaines dépendances et propriétés des mécanismes de fragmentation (sections efficaces, spectroscopie d'électrons, distributions de taille, énergies cinétiques des fragments, tracé de Campi, énergies d'activation). L'énergie déposée s'est ainsi révélée comme un paramètre important. Les sections efficaces ont été mesurées pour la première fois sur l'ensemble des processus collisionnels. L'ionisation et la capture ne dépendent que de la vitesse de collision. Une loi d'échelle avec l'énergie déposée a été observée pour les sections efficaces de multifragmentation. L'énergie déposée est aussi apparue comme le paramètre principal dans l'évolution des distributions de taille des fragments chargés émis. La spectroscopie des électrons (inédite sur un agrégat), réalisée à un angle d'émission de 35°, a montré des spectres piqués à des énergies d'électron importantes (de 5 à 20 eV). La forme de ces spectres dépend de la vitesse de collision. Un début d'analyse théorique semble montrer que cette structure particulière est liée à la présence d'une barrière de potentiel centrifuge. Enfin, les corrélations ions produits et énergie des électrons mettent en évidence que l'énergie des électrons augmente avec l'énergie interne.

Carbon –based engineered nanoparticles have been widely used due to their small size and uniquephysical and chemical properties. They can dissolve in water, transport through soil and reach drinkingwater resources. The toxic effect of engineered nanoparticles on human and fish cells has beenobserved; therefore, their release and distribution into the environment is a subject of concern. In thisstudy, two types of engineered nanoparticles, multi-walled carbon nano-tubes (MWCNT) and C60 withcylindrical and spherical shapes, respectively, were used. The aim of this study was to investigatetransport and retention of carbon-based engineered and natural nanoparticles through saturated porousmedia. Several laboratory experiments were conducted to observe transport behavior of thenanoparticles through a column packed with sand as a representative porous media. The columnexperiments were intended to monitor the effect of ionic strength, input concentration and the effect ofparticle shape on transport. The results were then interpreted using Derjaguin-Landau-Verwey-Overbeak (DLVO) theory based on the sum of attractive and repulsive forces which exist betweennanoparticles and the porous medium. It was observed that as the ionic strength increased from 1.34mM to 60 mM, the mobility of the nanoparticles was reduced. However, at ionic strength lower than10.89 mM, mobility of C60 was slightly higher than that of MWCNTs. At ionic strength of 60 mMMWCNT particles were significantly more mobile. It is rather difficult to relate this difference to theshape of particle and further studies are required.The effect of input concentration on transport of MWCNTs and C60 was observed in bothmobility of the particle and shape of breakthrough curves while input concentration was elevated from7 mg/l to 100 mg/l. A site-blocking mechanism was suggested to be responsible for the steep andasymmetric shape of the breakthrough curves at the high input concentration.Furthermore inverse modeling was used to calculate parameters such as attachment efficiency,the longitudinal dispersivity, and capacity of the solid phase for the removal of particles. The inversionprocess was performed in a way that the misfit between the observed and simulated breakthroughcurves was minimized. The simulated results were in good agreement with the observed data.

This work presents theoretical background for the investigation of nanostructure formation in alkali-metal doped fullerene layers. A number of computational methods are used to describe structural transformation in the fullerene layer. They include tight-binding molecular dynamics, empirical molecular dynamics, Monte-Carlo calculations as well as other methods. The doped fullerene layers show the highest superconducting critical temperature among organic superconductors. A new electrochemical method of synthesis of potassium and rubidium fullerides has been recently developed by Professor Dunsch and coworkers in the department of electrochemistry and conductive polymers at IFW Dresden. The process of electrochemical doping is accompanied by several side effects, and one of them is nanostructure formation at the surface of the fullerene layer. In the present work an explanation is given for the nanostructure formation observed recently by scanning tunnel microscopy. The corresponding model is based on the concept of spontaneous phase separation that has been realized by kinetic Monte Carlo calculations. These calculations predict instability of initially homogeneous alkali-doped fullerene layers. Due to the significant gap in the Madelung energy formation of an alkali-poor and an alkali-reach phase is expected. The results of the Monte Carlo simulations point out that the particle size of the corresponding phases remains in the nanometer range. Interpretation of experimental data for metal deposition on fullerene substrates can be easily given in the framework of the phase separation concept as well. Metal clusters of the size order 50 to 100 nm emerge in course of electrochemical copper deposition on alkali-doped fullerene layers. The electrically conductive paths through the insulating fullerene layer are probably responsible for the inhomogeneous copper deposition under electrochemical conditions. A novel computer program has been developed in course of this work, which is designed as a distributed application. It can be used for diverse conventional and kinetic Monte Carlo calculations. / Die vorliegende Arbeit präsentiert theoretische Arbeiten, die das Ziel haben, die Nanostrukturbildung in dotierten Fullerenschichten zu verstehen. Diverse Rechenmethoden wurden verwendet, um die strukturellen Umwandlungen in der Fullerenschicht zu beschreiben. Die Tight-Binding-Molekulardynamik, die empirische Molekulardynamik und Monte-Carlo-Berechnungen sowie andere Methoden sind eingeschlossen. Die dotierten Fullerenschichten zeigen die höchste supraleitende kritische Temperatur unter den organischen Supraleitern. Eine neue elektrochemische Methode der Synthese von Kalium- und Rubidium-Fulleriden wurde vor kurzem von Professor Dunsch und Mitarbeitern in der Abteilung Elektrochemie und leitfähigen Polymere am IFW Dresden entwickelt. Der Prozess der elektrochemischen Dotierung wird von mehreren Nebenprozessen begleitet, und einer davon ist die Nanostrukturbildung an der Oberfäche der Fullerenschicht. In der vorliegenden Arbeit wird eine Erklärung für die Herausbildung der Nanostrukturen, die mit Hilfe von Rastertunnelmikroskopie beobachtet wurden, gegeben. Das entsprechende Modell basiert auf dem Konzept der spontanen Phasenentmischung und wird durch kinetische Monte-Carlo-Simulationen realisiert. Diese Simulationen sagen Instabilität der zunächst homogenen Alkali-dotierten Fullerenschichten voraus. Wegen des wesentlichen Unterschieds in der Madelungenergie ist die Herausbildung einer Alkalimetall-armen und einer Alkalimetall-reichen Phase zu erwarten. Die Ergebnisse der Monte-Carlo-Simulationen weisen darauf hin, dass die Teilchengröße der entsprechenden Phasen im Nanometer-Bereich bleibt. Im Rahmen des Phasenentmischungskonzepts können auch experimentelle Daten zur Metallabscheidung auf Fullerensubstraten problemlos interpretiert werden. Bei elektrochemischer Kupferabscheidung auf Alkali-dotierten Fullerenschichten entstehen Metallcluster der Größenordnung von 50 bis 100 nm. Die elektrisch leitfähige Pfade, die in einer isolierenden Matrix auftreten, sind wahrscheinlich für die ungleichmäßige Kupferabscheidung unter elektrochemischen Bedingungen verantwortlich. Ein neuartiges Computerprogramm wurde im Rahmen dieser Arbeit entwickelt, das als eine verteilte Anwendung entworfen ist. Damit können diverse konventionelle und kinetische Monte-Carlo-Simulationen durchgeführt werden.

Au cours de ce travail nous avons étudié la réalisation de couches moléculaires d’accroche terminées amine. Sur l’oxyde de silicium l’aminopropyletriméthoxysilane (APTMS) a été déposé à partir d’une solution, et via une méthode originale par voie sèche qui nous a permis de mettre en évidence les temps caractéristiques de greffage et d’organisation de la couche d’APTMS. Sur l’or, les monocouches d’aminoéthanethiol (AET) et d’aminothiophénol (ATP) ont été réalisées à partir d’une solution. Nous avons ensuite étudié les aspects structuraux et cinétiques du greffage des fullerènes C60 sur de telles couches d’accroche, constituées de terminaisons amines soit sur toute la surface soit en des zones isolées (couches binaires). Les techniques de spectroscopie UV-Visible, IRTF, Raman, et XPS ont permis d’observer le greffage des C60 sur les couches aminées. La spectroscopie Raman en mode exalté (SERS) a mis en lumière que les molécules d’ATP étaient plus inclinées après le greffage à reflux des C60. Les analyses des diverses couches à l’échelle moléculaire ont été menées par microscopie à sondes locales (AFM, STM), et les mesures électriques réalisées sur or à l’aide de la pointe STM ont montré le caractère isolant de la couche d’accroche seule et un gap proche de celui du C60 après greffage des fullerènes. Elles ont également mis en évidence que le C60 était greffé sélectivement sur les zones terminées amines des couches d’accroche binaires. Enfin, une application potentielle des couches de C60 étant les mémoires moléculaires, les propriétés électriques des diverses couches réalisées ont été mesurées à l’aide de contacts électriques évaporés. / In this work we studied the preparation of sticking amine- terminated molecular layers. On silicon dioxide, 3-aminopropyltrimethoxysilane (APTMS) was de- posited from a solution, and using an original dry method that allowed us to determine time constants of APTMS layer grafting and organization. On gold surfaces, monolayers of aminoethanethiol (AET) and aminothiophenol (ATP) molecules were prepared from a solution. Then, we studied structural and kinetic aspects of ullerene C60 grafting on such sticking layers, terminated by amines either all over the surface or on isolated areas (binary layers). UV-visible, FTIR, Raman and XPS spectroscopy techniques enabled to observe that C60 was grafted on the amine-terminated layers. Exalted Raman spec- troscopy (SERS) revealed ATP molecules were more tilted after C60 grafting under reflux. Analyses of all the layers were made at a molecular level by local probe microscopy (AFM, STM), and electrical measurements performed on gold using the STM tip showed the in- sulating nature of the sticking layer whereas a gap close to that of C60 appeared after grafting of fullerenes. They also highlighted that C60 was selectively grafted on amine- terminated zones within binary sticking layers. At last, one of potential applications of C60 layers being molecular memory cells, electrical properties of the various studied layers were measured through evaporated electrical contact pads.

This work presents theoretical background for the investigation of nanostructure formation in alkali-metal doped fullerene layers. A number of computational methods are used to describe structural transformation in the fullerene layer. They include tight-binding molecular dynamics, empirical molecular dynamics, Monte-Carlo calculations as well as other methods. The doped fullerene layers show the highest superconducting critical temperature among organic superconductors. A new electrochemical method of synthesis of potassium and rubidium fullerides has been recently developed by Professor Dunsch and coworkers in the department of electrochemistry and conductive polymers at IFW Dresden. The process of electrochemical doping is accompanied by several side effects, and one of them is nanostructure formation at the surface of the fullerene layer. In the present work an explanation is given for the nanostructure formation observed recently by scanning tunnel microscopy. The corresponding model is based on the concept of spontaneous phase separation that has been realized by kinetic Monte Carlo calculations. These calculations predict instability of initially homogeneous alkali-doped fullerene layers. Due to the significant gap in the Madelung energy formation of an alkali-poor and an alkali-reach phase is expected. The results of the Monte Carlo simulations point out that the particle size of the corresponding phases remains in the nanometer range. Interpretation of experimental data for metal deposition on fullerene substrates can be easily given in the framework of the phase separation concept as well. Metal clusters of the size order 50 to 100 nm emerge in course of electrochemical copper deposition on alkali-doped fullerene layers. The electrically conductive paths through the insulating fullerene layer are probably responsible for the inhomogeneous copper deposition under electrochemical conditions. A novel computer program has been developed in course of this work, which is designed as a distributed application. It can be used for diverse conventional and kinetic Monte Carlo calculations. / Die vorliegende Arbeit präsentiert theoretische Arbeiten, die das Ziel haben, die Nanostrukturbildung in dotierten Fullerenschichten zu verstehen. Diverse Rechenmethoden wurden verwendet, um die strukturellen Umwandlungen in der Fullerenschicht zu beschreiben. Die Tight-Binding-Molekulardynamik, die empirische Molekulardynamik und Monte-Carlo-Berechnungen sowie andere Methoden sind eingeschlossen. Die dotierten Fullerenschichten zeigen die höchste supraleitende kritische Temperatur unter den organischen Supraleitern. Eine neue elektrochemische Methode der Synthese von Kalium- und Rubidium-Fulleriden wurde vor kurzem von Professor Dunsch und Mitarbeitern in der Abteilung Elektrochemie und leitfähigen Polymere am IFW Dresden entwickelt. Der Prozess der elektrochemischen Dotierung wird von mehreren Nebenprozessen begleitet, und einer davon ist die Nanostrukturbildung an der Oberfäche der Fullerenschicht. In der vorliegenden Arbeit wird eine Erklärung für die Herausbildung der Nanostrukturen, die mit Hilfe von Rastertunnelmikroskopie beobachtet wurden, gegeben. Das entsprechende Modell basiert auf dem Konzept der spontanen Phasenentmischung und wird durch kinetische Monte-Carlo-Simulationen realisiert. Diese Simulationen sagen Instabilität der zunächst homogenen Alkali-dotierten Fullerenschichten voraus. Wegen des wesentlichen Unterschieds in der Madelungenergie ist die Herausbildung einer Alkalimetall-armen und einer Alkalimetall-reichen Phase zu erwarten. Die Ergebnisse der Monte-Carlo-Simulationen weisen darauf hin, dass die Teilchengröße der entsprechenden Phasen im Nanometer-Bereich bleibt. Im Rahmen des Phasenentmischungskonzepts können auch experimentelle Daten zur Metallabscheidung auf Fullerensubstraten problemlos interpretiert werden. Bei elektrochemischer Kupferabscheidung auf Alkali-dotierten Fullerenschichten entstehen Metallcluster der Größenordnung von 50 bis 100 nm. Die elektrisch leitfähige Pfade, die in einer isolierenden Matrix auftreten, sind wahrscheinlich für die ungleichmäßige Kupferabscheidung unter elektrochemischen Bedingungen verantwortlich. Ein neuartiges Computerprogramm wurde im Rahmen dieser Arbeit entwickelt, das als eine verteilte Anwendung entworfen ist. Damit können diverse konventionelle und kinetische Monte-Carlo-Simulationen durchgeführt werden.

<p>Fullerenes have been shown to constitute a prototypical building block for truly nanometer-sized devices and exotic nanounit-based materials, e.g., high-temperature superconductors. This makes the detailed understanding of fullerene electronic states in compounds and at interfaces of primary importance, since the high symmetry of the molecule greatly </p><p>simplifies the starting point of the analysis. Carbon nanotubes, which combine one macroscopic with two nanoscopic dimensions, are perhaps of even greater practical interest.</p><p>Angle-dependent electron spectroscopies have been employed in the present work to study these materials, characterizing their structure, bonding, and electronic states. For solid C₆₀, the photoelectron angular distribution has been found to be essentially that of the free molecule, modified by solid state scattering; a similar distribution is found for K₃C_60.</p><p>The surface and bulk electronic structure of K₃C₆₀ has been identified by angle-dependent core and valence photoelectron spectroscopy (PES) and x-ray emission spectroscopy. An insulating surface layer has been identified for this high-temperature superconductor.</p><p>Angle-dependent valence PES is used to investigate the electronic states of C₆₀/Al(110). Electron correlations are found to be the origin of the splitting observed in the molecular orbitals, which is quite sensitive to the molecular orientation. The components of the highest occupied molecular orbital are differentiated according to their overlap with the substrate.</p><p>A rigid shift of valence- and core-levels has been observed even for ionic and covalent C₆₀compounds, reflecting the efficient static polarizability screening of the molecule. </p><p>The alignment of multi-walled carbon nanotubes has been investigated by x-ray absorption spectroscopy, using the spectral intensity ratio of π*- and *-resonances. Core level combined with valence PES shows that the degree of defect structure varies from position to position on the sample. Valence photoelectron spectra of defect-free sample spots closely resembles the total DOS of graphite.</p>

Fullerenes have been shown to constitute a prototypical building block for truly nanometer-sized devices and exotic nanounit-based materials, e.g., high-temperature superconductors. This makes the detailed understanding of fullerene electronic states in compounds and at interfaces of primary importance, since the high symmetry of the molecule greatly simplifies the starting point of the analysis. Carbon nanotubes, which combine one macroscopic with two nanoscopic dimensions, are perhaps of even greater practical interest. Angle-dependent electron spectroscopies have been employed in the present work to study these materials, characterizing their structure, bonding, and electronic states. For solid C60, the photoelectron angular distribution has been found to be essentially that of the free molecule, modified by solid state scattering; a similar distribution is found for K3C60. The surface and bulk electronic structure of K3C60 has been identified by angle-dependent core and valence photoelectron spectroscopy (PES) and x-ray emission spectroscopy. An insulating surface layer has been identified for this high-temperature superconductor. Angle-dependent valence PES is used to investigate the electronic states of C60/Al(110). Electron correlations are found to be the origin of the splitting observed in the molecular orbitals, which is quite sensitive to the molecular orientation. The components of the highest occupied molecular orbital are differentiated according to their overlap with the substrate. A rigid shift of valence- and core-levels has been observed even for ionic and covalent C60 compounds, reflecting the efficient static polarizability screening of the molecule. The alignment of multi-walled carbon nanotubes has been investigated by x-ray absorption spectroscopy, using the spectral intensity ratio of π*- and *-resonances. Core level combined with valence PES shows that the degree of defect structure varies from position to position on the sample. Valence photoelectron spectra of defect-free sample spots closely resembles the total DOS of graphite.

Cette thèse s'inscrit dans le contexte de l'électronique de spin. Dans une première partie, nous nous intéressons à l'effet Kondo induit par un atome 3d sur une surface ferromagnétique étudié en spectroscopie à effet tunnel. Nous montrons que la signature spectroscopique observée au-dessus d'atomes uniques de Co adsorbés sur des plots de fer auto-organisés sur une surface d'Au(111) peut se dédoubler sous l'effet du couplage avec les îlots. Un modèle de résonance Fano à deux niveaux en interaction avec un continuum permet d'ajuster les spectres tunnel et d'extraire la température Kondo et le champ magnétique qui induirait le dédoublement s'il s'agissait d'un effet Zeeman. Ce champ de plusieurs dizaines de Teslas est compatible avec la valeur connue du champ d'échange à la surface du fer. Des atomes bistables entre deux sites adjacents ont été observés, montrant de façon réversible un spectre dédoublé ou non. Dans une seconde partie, nous nous intéressons à la polarisation de spin de la densité d'états de molécules uniques de C60 adsorbées sur une surface de Cr(001) observée en microscopie à effet tunnel résolue en spin. Les cartes de conductance différentielle et les spectres tunnel locaux montrent une magnétorésistance tunnel au-dessus des molécules. Des simulations liaisons fortes et ab initio ont permis d'identifier l'état moléculaire impliqué et de montrer que le substrat induit une levée de dégénérescence dépendant du spin. La magnétorésistance mesurée change de signe en fonction de la tension tunnel et atteint plusieurs dizaines de pourcents à des tensions de plusieurs centaines de mV.