Potential Analysis for Hypoelliptic Second Order PDEs with Nonnegative Characteristic Form

In this Thesis we consider a class of second order partial differential operators with non-negative characteristic form and with smooth coefficients. Main assumptions on the relevant operators are hypoellipticity and existence of a well-behaved global fundamental solution. We first make a deep analysis of the L-Green function for arbitrary open sets and of its applications to the Representation Theorems of Riesz-type for L-subharmonic and L-superharmonic functions. Then, we prove an Inverse Mean value Theorem characterizing the superlevel sets of the fundamental solution by means of L-harmonic functions. Furthermore, we establish a Lebesgue-type result showing the role of the mean-integal operator in solving the homogeneus Dirichlet problem related to L in the Perron-Wiener sense. Finally, we compare Perron-Wiener and weak variational solutions of the homogeneous Dirichlet problem, under specific hypothesis on the boundary datum.

Robust Nonlinear Output Regulation by Identification Tools

The present thesis focuses on the problem of robust output regulation for minimum phase nonlinear systems by means of identification techniques. Given a controlled plant and an exosystem (an autonomous system that generates eventual references or disturbances), the control goal is to design a proper regulator able to process the only measure available, i.e the error/output variable, in order to make it asymptotically vanishing. In this context, such a regulator can be designed following the well known “internal model principle” that states how it is possible to achieve the regulation objective by embedding a replica of the exosystem model in the controller structure. The main problem shows up when the exosystem model is affected by parametric or structural uncertainties, in this case, it is not possible to reproduce the exact behavior of the exogenous system in the regulator and then, it is not possible to achieve the control goal. In this work, the idea is to find a solution to the problem trying to develop a general framework in which coexist both a standard regulator and an estimator able to guarantee (when possible) the best estimate of all uncertainties present in the exosystem in order to give “robustness” to the overall control loop.

Dynamic wetting of complex liquids

A simple dependency between contact angle θ and velocity or surface tension has been predicted for the wetting and dewetting behavior of simple liquids. According to the hydrodynamic theory, this dependency was described by Cox and Voinov as θ ∼ Ca^(1/3) (Ca: Capillary number). For more complex liquids like surfactant solutions, this prediction is not directly given.rnHere I present a rotating drum setup for studying wetting/dewetting processes of surfactant solutions on the basis of velocity-dependent contact angle measurements. With this new setup I showed that surfactant solutions do not follow the predicted Cox-Voinov relation, but showed a stronger contact angle dependency on surface tension. All surfactants independent of their charge showed this difference from the prediction so that electrostatic interactions as a reason could be excluded. Instead, I propose the formation of a surface tension gradient close to the three-phase contact line as the main reason for the strong contact angle decrease with increasing surfactant concentration. Surface tension gradients are not only formed locally close to the three-phase contact line, but also globally along the air-liquid interface due to the continuous creation/destruction of the interface by the drum moving out of/into the liquid. By systematically hindering the equilibration routes of the global gradient along the interface and/or through the bulk, I was able to show that the setup geometry is also important for the wetting/dewetting of surfactant solutions. Further, surface properties like roughness or chemical homogeneity of the wetted/dewetted substrate influence the wetting/dewetting behavior of the liquid, i. e. the three-phase contact line is differently pinned on rough/smooth or homogeneous/inhomogeneous surfaces. Altogether I showed that the wetting/dewetting of surfactant solutions did not depend on the surfactant type (anionic, cationic, or non-ionic) but on the surfactant concentration and strength, the setup geometry, and the surface properties.rnSurfactants do not only influence the wetting/dewetting behavior of liquids, but also the impact behavior of drops on free-standing films or solutions. In a further part of this work, I dealt with the stability of the air cushion between drop and film/solution. To allow coalescence between drop and substrate, the air cushion has to vanish. In the presence of surfactants, the vanishing of the air is slowed down due to a change in the boundary condition from slip to no-slip, i. e. coalescence is suppressed or slowed down in the presence of surfactant.

Analysis of the Kohn Laplacian on the Heisenberg Group and on Cauchy-Riemann Manifolds

The purpose of this study is to analyse the regularity of a differential operator, the Kohn Laplacian, in two settings: the Heisenberg group and the strongly pseudoconvex CR manifolds. The Heisenberg group is defined as a space of dimension 2n+1 with a product. It can be seen in two different ways: as a Lie group and as the boundary of the Siegel UpperHalf Space. On the Heisenberg group there exists the tangential CR complex. From this we define its adjoint and the Kohn-Laplacian. Then we obtain estimates for the Kohn-Laplacian and find its solvability and hypoellipticity. For stating L^p and Holder estimates, we talk about homogeneous distributions. In the second part we start working with a manifold M of real dimension 2n+1. We say that M is a CR manifold if some properties are satisfied. More, we say that a CR manifold M is strongly pseudoconvex if the Levi form defined on M is positive defined. Since we will show that the Heisenberg group is a model for the strongly pseudo-convex CR manifolds, we look for an osculating Heisenberg structure in a neighborhood of a point in M, and we want this structure to change smoothly from a point to another. For that, we define Normal Coordinates and we study their properties. We also examinate different Normal Coordinates in the case of a real hypersurface with an induced CR structure. Finally, we define again the CR complex, its adjoint and the Laplacian operator on M. We study these new operators showing subelliptic estimates. For that, we don't need M to be pseudo-complex but we ask less, that is, the Z(q) and the Y(q) conditions. This provides local regularity theorems for Laplacian and show its hypoellipticity on M.

Classical and quantum aspects of black hole dynamics

Il contenuto fisico della Relatività Generale è espresso dal Principio di Equivalenza, che sancisce l'equivalenza di geometria e gravitazione. La teoria predice l'esistenza dei buchi neri, i più semplici oggetti macroscopici esistenti in natura: essi sono infatti descritti da pochi parametri, le cui variazioni obbediscono a leggi analoghe a quelle della termodinamica. La termodinamica dei buchi neri è posta su basi solide dalla meccanica quantistica, mediante il fenomeno noto come radiazione di Hawking. Questi risultati gettano una luce su una possibile teoria quantistica della gravitazione, ma ad oggi una simile teoria è ancora lontana. In questa tesi ci proponiamo di studiare i buchi neri nei loro aspetti sia classici che quantistici. I primi due capitoli sono dedicati all'esposizione dei principali risultati raggiunti in ambito teorico: in particolare ci soffermeremo sui singularity theorems, le leggi della meccanica dei buchi neri e la radiazione di Hawking. Il terzo capitolo, che estende la discussione sulle singolarità, espone la teoria dei buchi neri non singolari, pensati come un modello effettivo di rimozione delle singolarità. Infine il quarto capitolo esplora le ulteriori conseguenze della meccanica quantistica sulla dinamica dei buchi neri, mediante l'uso della nozione di entropia di entanglement.

Le partecipazioni azionarie degli enti locali tra dismissione ed esigenze di governo dei servizi pubblici

La ricerca indaga le relazioni che si sono instaurate nel corso degli anni tra il principio di legalità, inteso nella sua declinazione di principio di funzionalizzazione, e principio di concorrenza nell’ambito delle società per la gestione dei servizi pubblici locali. Più precisamente, lo scopo del lavoro è valutare le evoluzioni di tale rapporto, dal momento in cui gli enti locali sono stati ufficialmente autorizzati a costituire società per la gestione dei servizi pubblici locali nel 1990. Lo stimolo a sviluppare queste considerazioni trova la sua ragione nelle pressioni provenienti dalle istituzioni europee, che hanno gradualmente imposto una qualificazione prettamente economica ai servizi a favore della collettività, ritenuti un ambito in cui possa naturalmente imporsi una competizione economica tra operatori economici, indipendentemente dalla loro natura giuridica. Il problema del vincolo funzionale nella partecipazione in società degli enti locali è certamente l’oggetto principale del lavoro. Tuttavia, la questione non può essere analizzata separatamente dalle politiche di dismissione promosse dal legislatore nell’ultimo decennio. L’obiettivo principale delle riforme avviate è stato quello di frenare la proliferazione di società costituite dagli enti locali, così da garantire sia un risparmio di risorse pubbliche sia una maggiore facilità per gli imprenditori privati ad affacciarsi su mercati tradizionalmente appannaggio delle amministrazioni. Stona però con le intenzioni il fatto che gli obblighi ex lege di cessione delle partecipazioni azionarie detenute dagli enti locali non siano stati generalmente imposti per le società di gestione dei servizi pubblici (resi in favore della collettività), bensì per quelle che svolgono servizi strumentali (in favore dell’amministrazione stessa). La scelta appare contraddittoria, in quanto il distacco tra vincolo funzionale e partecipazione degli enti locali nella compagine societaria si ravvisa in particolar modo nel primo dei due moduli menzionati. Si assiste dunque ad una frammentazione del principio di legalità.

Direct and inverse transient eddy current problems

Die vorliegende Arbeit behandelt Vorwärts- sowie Rückwärtstheorie transienter Wirbelstromprobleme. Transiente Anregungsströme induzieren elektromagnetische Felder, welche sogenannte Wirbelströme in leitfähigen Objekten erzeugen. Im Falle von sich langsam ändernden Feldern kann diese Wechselwirkung durch die Wirbelstromgleichung, einer Approximation an die Maxwell-Gleichungen, beschrieben werden. Diese ist eine lineare partielle Differentialgleichung mit nicht-glatten Koeffizientenfunktionen von gemischt parabolisch-elliptischem Typ. Das Vorwärtsproblem besteht darin, zu gegebener Anregung sowie den umgebungsbeschreibenden Koeffizientenfunktionen das elektrische Feld als distributionelle Lösung der Gleichung zu bestimmen. Umgekehrt können die Felder mit Messspulen gemessen werden. Das Ziel des Rückwärtsproblems ist es, aus diesen Messungen Informationen über leitfähige Objekte, also über die Koeffizientenfunktion, die diese beschreibt, zu gewinnen. In dieser Arbeit wird eine variationelle Lösungstheorie vorgestellt und die Wohlgestelltheit der Gleichung diskutiert. Darauf aufbauend wird das Verhalten der Lösung für verschwindende Leitfähigkeit studiert und die Linearisierbarkeit der Gleichung ohne leitfähiges Objekt in Richtung des Auftauchens eines leitfähigen Objektes gezeigt. Zur Regularisierung der Gleichung werden Modifikationen vorgeschlagen, welche ein voll parabolisches bzw. elliptisches Problem liefern. Diese werden verifiziert, indem die Konvergenz der Lösungen gezeigt wird. Zuletzt wird gezeigt, dass unter der Annahme von sonst homogenen Umgebungsparametern leitfähige Objekte eindeutig durch die Messungen lokalisiert werden können. Hierzu werden die Linear Sampling Methode sowie die Faktorisierungsmethode angewendet.

The dynamics of ultra-thin polymer films in different confinements studied by resonance enhanced dynamic light scattering

Die Kontroverse über den Glasübergang im Nanometerbereich, z. B. die Glas¬über¬gangs-temperatur Tg von dünnen Polymerfilmen, ist nicht vollständig abgeschlossen. Das dynamische Verhalten auf der Nanoskala ist stark von den einschränkenden Bedingungen abhängig, die auf die Probe wirken. Dünne Polymerfilme sind ideale Systeme um die Dynamik von Polymerketten unter der Einwirkung von Randbedingungen zu untersuchen, wie ich sie in dieser Arbeit variiert habe, um Einblick in dieses Problem zu erhalten.rnrnResonanzverstärkte dynamische Lichtstreuung ist eine Methode, frei von z.B. Fluoreszenzmarkern, die genutzt werden kann um in dünnen Polymerfilmen dynamische Phänomene

Clinical radiology and postmortem imaging (Virtopsy) are not the same: Specific and unspecific postmortem signs

The aim of this article is to disclose the characteristics of postmortem forensic imaging; give an overview of the several possible findings in postmortem imaging, which are uncommon or new to clinical radiologists; and discuss the possible pitfalls. Unspecific postmortem signs are enlisted and specific signs shall be presented, which are typical for one cause of death. Unspecific signs. Livor mortis may not only be seen from the outside, but also inside the body in the lungs: in chest CT internal livor mortis appear as ground glass opacity in the dependent lower lobes. The aortic wall is often hyperdense in postmortem CT due to wall contraction and loss of luminal pressure. Gas bubbles are very common postmortem due to systemic gas embolism after major open trauma, artificial respiration or initial decomposition; in particular putrefaction produces gas bubbles globally. Specific signs. Intracranial bleeding is hyperattenuating both in radiology and in postmortem imaging. Signs of strangulation are hemorrhage in the soft tissue of the neck like skin, subcutaneous tissue, platysma muscle and lymph nodes. The "vanishing" aorta is indicative for exsanguination. Fluid in the airways with mosaic lung densities and emphysema (aquosum) is typical for fresh-water drowning.

A syntactic realization theorem for justification logics

Justification logics are refinements of modal logics where modalities are replaced by justification terms. They are connected to modal logics via so-called realization theorems. We present a syntactic proof of a single realization theorem that uniformly connects all the normal modal logics formed from the axioms \$mathsfd\$, \$mathsft\$, \$mathsfb\$, \$mathsf4\$, and \$mathsf5\$ with their justification counterparts. The proof employs cut-free nested sequent systems together with Fitting's realization merging technique. We further strengthen the realization theorem for \$mathsfKB5\$ and \$mathsfS5\$ by showing that the positive introspection operator is superfluous.

Macrophage activating syndrome is associated with lobular hepatitis and severe bile duct injury with cholestasis

Macrophage activating syndrome (MAS) is a rare hematological disorder associated with uncontrolled systemic T-cell activation. Persistent fever, fatigue and hepatosplenomegaly are frequent clinical manifestations, whereas hyperferritinemia, elevated serum lactate dehydrogenase levels and cytopenia are key criteria for the diagnosis of MAS. The nature of liver pathology in MAS has been partially elucidated but destructive biliary lesions have been rarely described. This report illustrates four cases of MAS developing marked cholestasis, leading to one case of biliary cirrhosis necessitating liver transplantation. Histologically, liver involvement was characterized in all cases by acute lobular hepatitis, marked hepatocyte apoptosis and small bile duct injury similar to the vanishing bile duct syndrome. Immuno-histological studies showed that the inflammatory changes and bile duct lesions were dominated by the presence of activated macrophages and T-cells, in particular CD8+ lymphocytes, and in part NK-cells. These findings suggest that in MAS, various T-cell triggers such as infection, autoimmune disease and malignancy might result in the release of cytokines, which in turn activate macrophages to trigger a systemic acute phase response and local tissue damage. This communication suggests that a macrophage, T- and NK-cell network is operational in the pathogenesis of the cholangiocyte, hepatocyte and sinus endothelial cell damage in MAS.

Public preferences of the Great Lakes Environment : a Lake Michigan pilot study

The Great Lakes watershed is home to over 40 million people, and the health of the Great Lakes ecosystem is vital to the overall economic, societal, and environmental health of the U.S. and Canada. However, environmental issues related to them are sometimes overlooked. Policymakers and the public face the challenges of balancing economic benefits with the need to conserve and/or replenish regional natural resources to ensure long term prosperity. From the literature review, nine critical stressors of ecological services were delineated, which include pollution and contamination, agricultural erosion, non-native species, degraded recreational resources, loss of wetlands habitat, climate change, risk of clean water shortage, vanishing sand dunes, and population overcrowding; this list was validated through a series of stakeholder discussions and focus groups in Grand Rapids. Focus groups were conducted in Grand Rapids to examine the awareness of, concern with, and willingness to expend resources on these stressors. Stressors that the respondents have direct contact with tend to be the most important. The focus group results show that concern related to pollution and contamination is much higher than for any of the other stressors. Low responses to climate change result in recommendations for outreach programs.

Edge coloring BIBDS and constructing MOELRs

Chapter 1 is used to introduce the basic tools and mechanics used within this thesis. Some historical uses and background are touched upon as well. The majority of the definitions are contained within this chapter as well. In Chapter 2 we consider the question whether one can decompose λ copies of monochromatic Kv into copies of Kk such that each copy of the Kk contains at most one edge from each Kv. This is called a proper edge coloring (Hurd, Sarvate, [29]). The majority of the content in this section is a wide variety of examples to explain the constructions used in Chapters 3 and 4. In Chapters 3 and 4 we investigate how to properly color BIBD(v, k, λ) for k = 4, and 5. Not only will there be direct constructions of relatively small BIBDs, we also prove some generalized constructions used within. In Chapter 5 we talk about an alternate solution to Chapters 3 and 4. A purely graph theoretical solution using matchings, augmenting paths, and theorems about the edgechromatic number is used to develop a theorem that than covers all possible cases. We also discuss how this method performed compared to the methods in Chapters 3 and 4. In Chapter 6, we switch topics to Latin rectangles that have the same number of symbols and an equivalent sized matrix to Latin squares. Suppose ab = n2. We define an equitable Latin rectangle as an a × b matrix on a set of n symbols where each symbol appears either [b/n] or [b/n] times in each row of the matrix and either [a/n] or [a/n] times in each column of the matrix. Two equitable Latin rectangles are orthogonal in the usual way. Denote a set of ka × b mutually orthogonal equitable Latin rectangles as a k–MOELR(a, b; n). We show that there exists a k–MOELR(a, b; n) for all a, b, n where k is at least 3 with some exceptions.

The effect of projections on dimension in the Heisenberg group

We prove analogs of classical almost sure dimension theorems for Euclidean projection mappings in the first Heisenberg group, equipped with a sub-Riemannian metric.

Laparoscopic computer-navigated ablation of liver metastases

Objective In order to benefit from the obvious advantages of minimally invasive liver surgery there is a need to develop high precision tools for intraoperative anatomical orientation, navigation and safety control. In a pilot study we adapted a newly developed system for computer-assisted liver surgery (CALS) in terms of accuracy and technical feasibility to the specific requirements of laparoscopy. Here, we present practical aspects related to laparoscopic computer assisted liver surgery (LCALS). Methods Our video relates to a patient presenting with 3 colorectal liver metastases in Seg. II, III and IVa who was selected in an appropriate oncological setting for LCALS using the CAScination system combined with 3D MEVIS reconstruction. After minimal laparoscopic mobilization of the liver, a 4- landmark registration method was applied to enable navigation. Placement of microwave needles was performed using the targeting module of the navigation system and correct needle positioning was confirmed by intraoperative sonography. Ablation of each lesion was carried out by application of microwave energy at 100 Watts for 1 minute. Results To acquire an accurate (less 0.5 cm) registration, 4 registration cycles were necessary. In total, seven minutes were required to accomplish precise registration. Successful ablation with complete response in all treated areas was assessed by intraoperative sonography and confirmed by postoperative CT scan. Conclusions This teaching video demonstrates the theoretical and practical key points of LCALS with a special emphasis on preoperative planning, intraoperative registration and accuracy testing by laparoscopic methodology. In contrast to mere ultrasound-guided ablation of liver lesions, LCALS offers a more dimensional targeting and higher safety control. This is currently also in routine use to treat vanishing lesions and other difficult to target focal lesions within the liver.