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.

Zeta and L-functions of elliptic curves

In questa tesi si studiano alcune proprietà fondamentali delle funzioni Zeta e L associate ad una curva ellittica. In particolare, si dimostra la razionalità della funzione Zeta e l'ipotesi di Riemann per due famiglie specifiche di curve ellittiche. Si studia poi il problema dell'esistenza di un prolungamento analitico al piano complesso della funzione L di una curva ellittica con moltiplicazione complessa, attraverso l'analisi diretta di due casi particolari.

Molecular plating of thin lanthanide layers with improved material properties for nuclear applications

In der vorliegenden Arbeit werden Experimente beschrieben, die zu einem vertieften Verständnis fundamentaler Prozesse bei der elektrochemischen Herstellung von Dünnschichten, sog. Targets, für kernphysikalische und -chemische Studien führten. Targets wurden mittels 'Molecular Plating' (MP) hergestellt, indem eine Elektrodeposition aus organischem Medium in der Regel bei konstantem Strom in Zwei-Elektroden-Zellen. Die Resultate erlaubten, optimierte Herstellungs-bedingungen zu ermitteln, welche die Produktion deutlich verbesserter Targets erlaubten. MP bei konstantem Strom ist ein massentransportkontrollierter Prozess. Der angelegte Strom wird durch einen konstanten Fluss elektroaktiver Spezies zur Kathode – auf der die Schicht wächst – und Anode aufrechterhalten. Die Untersuchungen zeigten, dass das Zellenpotential des Elektrodepositionsystems immer durch den Ohm'schen Spannungsabfall auf Grund des Widerstandes der verwendeten Lösung dominiert wurde. Dies erlaubte die Herleitung einer Beziehung zwischen dem Zellenpotential und der Konzentration der elektroaktiven Spezies. Die Beziehung erlaubt die Erklärung des gemessenen zeitlichen Verlaufs des Zellenpotentials während der Abscheidung als Funktion der Elektrolytkonzentration. Dies dient als Basis, auf der nun ein umfassenderes Bild der Prozesse, die für die charakteristischen Minima im Potentialverlauf einer Abscheidung verantwortlich sind, gewonnen werden kann. Es konnte gezeigt werden, dass die Minima mit der fast vollständigen Entfernung (durch Abscheidung) der aus einem gelösten Salz erzeugten Nd-Ionen korrespondieren. Die abgeschiedene Spezies wurde als Nd3+ identifiziert, vermutlich als Carboxylat, Oxid oder Hydroxid, was auf Grund der hohen negative Werte des Standardredoxpotentials der Lanthanide verständlich erscheint. Von den vorliegenden elektroaktiven Spezies tragen die Nd3+ Ionen nur zu knapp 20% zum Gesamtstrom bei. Durch Elektrolyse tragen auch die Lösungsmittelkomponenten zu diese Strom bei. Die Gegenwart von elektrolysiertem Lösungsmittel wurde in Analysen der Dünnschichten bestätigt. Diese waren immer mit chemi- und physisorbierten Lösungsmittelmolekülen bedeckt. Die Analyse der Dünnschichten zeigte, dass die Oberflächen von einem furchenartiges Netz durchzogen waren, und dass diese während des Trocknen der Schichten nach dem MP entstanden. Ob die Schichten an Luft oder in inerter Atmosphäre trockneten, hatte keinen Einfluss. Es wurden Experimente mit mehreren Lösungsmitteln durchgeführt, die sich deutlich in ihren physikalischen Eigenschaften, v.a. dem Siedepunkt, unterschieden. Furchenfreie Dünnschichten konnten insbesondere bei MP in N,N-dimethylformamide (DMF) erzeugt werden. Die Verwendung von DMF in Kombination mit einer Abscheidung auf sehr glatten Substraten erlaubte die Produktion von sehr homogenen, glatten und defektfreien Schichten. Diese waren vermutlich geringeren inneren Spannungen während des Trocknens ausgesetzt, als Schichten auf raueren Substraten oder solche, die aus flüchtigeren Lösungsmitteln hergestellt wurden. Die Oberflächenrauigkeit des Substrats und das gewählte Lösungsmittel wurden so als Schlüsselfaktoren für die Produktion hochqualitativer Schichten identifiziert. Es konnte gezeigt werden, dass mit MP eine sehr effiziente Methode zur Herstellung homogener Schichten mit exzellenter Ausbeute ist. In weiteren Experimenten mit dem primordialen Alpha-Emitter 147Sm als Modellisotop wurde die Eignung solcher Schichten als Alpha-Quelle untersucht. Sowohl die Energieauflösung als auch der Anteil der Alpha-Teilchen, die den Detektor erreichten, waren von den Quelleneigenschaften abhängig. Die Effekte wurden verschiedenen Variablen der Dünnschicht zugeordnet, welche die Alpha-Spektren beeinflussten. Dominant war die Wahl des Lösungsmittels und die Rauigkeit des Substrats. Dies beeinflusste Schichtdicke und -morphologie sowie die Art des Schichtwachstums und veränderte die Detektionseffizienz in Alpha-Messungen bis zu 15%. Nur homogene, ebene Schichten, die aus DMF auf glatten Substraten abgeschieden wurden, eignen sich optimal als Alpha-Quelle. Die gewonnenen Ergebnisse erlauben die optimierte Herstellung nuklearer Targets durch MP. Künftige Anwendungen beinhalten insbesondere die Herstellung von Targets für neutroneninduzierte Spaltexperimente und untergrundarmeAlpha-Messungen sehr kleiner Aktivitäten.

Identification of adequate neurally adjusted ventilatory assist (NAVA) during systematic increases in the NAVA level

Neurally adjusted ventilatory assist (NAVA) delivers airway pressure (P(aw)) in proportion to the electrical activity of the diaphragm (EAdi) using an adjustable proportionality constant (NAVA level, cm·H(2)O/μV). During systematic increases in the NAVA level, feedback-controlled down-regulation of the EAdi results in a characteristic two-phased response in P(aw) and tidal volume (Vt). The transition from the 1st to the 2nd response phase allows identification of adequate unloading of the respiratory muscles with NAVA (NAVA(AL)). We aimed to develop and validate a mathematical algorithm to identify NAVA(AL). P(aw), Vt, and EAdi were recorded while systematically increasing the NAVA level in 19 adult patients. In a multistep approach, inspiratory P(aw) peaks were first identified by dividing the EAdi into inspiratory portions using Gaussian mixture modeling. Two polynomials were then fitted onto the curves of both P(aw) peaks and Vt. The beginning of the P(aw) and Vt plateaus, and thus NAVA(AL), was identified at the minimum of squared polynomial derivative and polynomial fitting errors. A graphical user interface was developed in the Matlab computing environment. Median NAVA(AL) visually estimated by 18 independent physicians was 2.7 (range 0.4 to 5.8) cm·H(2)O/μV and identified by our model was 2.6 (range 0.6 to 5.0) cm·H(2)O/μV. NAVA(AL) identified by our model was below the range of visually estimated NAVA(AL) in two instances and was above in one instance. We conclude that our model identifies NAVA(AL) in most instances with acceptable accuracy for application in clinical routine and research.

Changes in cell proliferation, but not in vascularisation are characteristic for human endometrium in different reproductive failures--a pilot study

Reproductive failure, determined as recurrent spontaneous abortions (RSA) or recurrent implantation failure (RIF) in women is not well understood. Several factors, including embryo quality, and cellular and molecular changes in endometrium may contribute to the insufficient feto-maternal interaction resulting in reproductive failure. Prior clinical studies suggest an inadequate endometrial growth and development of the endometrium, leading to a lesser endometrial thickness.

Different Learning Curves for Axillary Brachial Plexus Block: Ultrasound Guidance versus Nerve Stimulation

Little is known about the learning of the skills needed to perform ultrasound- or nerve stimulator-guided peripheral nerve blocks. The aim of this study was to compare the learning curves of residents trained in ultrasound guidance versus residents trained in nerve stimulation for axillary brachial plexus block. Ten residents with no previous experience with using ultrasound received ultrasound training and another ten residents with no previous experience with using nerve stimulation received nerve stimulation training. The novices' learning curves were generated by retrospective data analysis out of our electronic anaesthesia database. Individual success rates were pooled, and the institutional learning curve was calculated using a bootstrapping technique in combination with a Monte Carlo simulation procedure. The skills required to perform successful ultrasound-guided axillary brachial plexus block can be learnt faster and lead to a higher final success rate compared to nerve stimulator-guided axillary brachial plexus block.

Closed Time-like Curves and Inertial Frame Dragging: How to Time Travel via Spacetime Rotation

As the number of solutions to the Einstein equations with realistic matter sources that admit closed time-like curves (CTC's) has grown drastically, it has provoked some authors [10] to call for a physical interpretation of these seemingly exotic curves that could possibly allow for causality violations. A first step in drafting a physical interpretation would be to understand how CTC's are created because the recent work of [16] has suggested that, to follow a CTC, observers must counter-rotate with the rotating matter, contrary to the currently accepted explanation that it is due to inertial frame dragging that CTC's are created. The exact link between inertialframe dragging and CTC's is investigated by simulating particle geodesics and the precession of gyroscopes along CTC's and backward in time oriented circular orbits in the van Stockum metric, known to have CTC's that could be traversal, so the van Stockum cylinder could be exploited as a time machine. This study of gyroscopeprecession, in the van Stockum metric, supports the theory that CTC's are produced by inertial frame dragging due to rotating spacetime metrics.

Mannitol dry powder challenge in comparison with exercise testing in children

Rationale Mannitol dry powder (MDP) challenge is an indirect bronchial provocation test, which is well studied in adults but not established for children. Objective We compared feasibility, validity, and clinical significance of MDP challenge with exercise testing in children in a clinical setting. Methods Children aged 6–16 years, referred to two respiratory outpatient clinics for possible asthma diagnosis, underwent standardized exercise testing followed within a week by an MDP challenge (Aridol™, Pharmaxis, Australia). Agreement between the two challenge tests using Cohen's kappa and receiving operating characteristic (ROC) curves was compared. Results One hundred eleven children performed both challenge tests. Twelve children were excluded due to exhaustion or insufficient cooperation (11 at the exercise test, 1 at the MDP challenge), leaving 99 children (mean ± SD age 11.5 ± 2.7 years) for analysis. MDP tests were well accepted, with minor side effects and a shorter duration than exercise tests. The MDP challenge was positive in 29 children (29%), the exercise test in 21 (21%). Both tests were concordant in 83 children (84%), with moderate agreement (κ = 0.58, 95% CI 0.39–0.76). Positive and negative predictive values of the MDP challenge for exercise-induced bronchoconstriction were 68% and 89%. The overall ability of MDP challenge to separate children with or without positive exercise tests was good (area under the ROC curve 0.83). Conclusions MDP challenge test is feasible in children and is a suitable alternative for bronchial challenge testing in childhood. Pediatr. Pulmonol. 2011; 46:842–848. © 2011 Wiley-Liss, Inc.

Prospective comparison of clinical prognostic scores in elderly patients with pulmonary embolism

Background: The Geneva Prognostic Score (GPS), the Pulmonary Embolism Severity Index (PESI), and its simplified version (sPESI) are well known clinical prognostic scores for pulmonary embolism (PE).Objectives: To compare the prognostic performance of these scores in elderly patients with PE. Patients/Methods: In a multicenter Swiss cohort of elderly patients with venous thromboembolism, we prospectively studied 449 patients aged ≥65 years with symptomatic PE. The outcome was 30-day overall mortality. We dichotomized patients as low- vs. higher-risk in all three scores using the following thresholds: GPS scores ≤2 vs. >2, PESI risk classes I-II vs. III-V, and sPESI scores 0 vs. ≥1. We compared 30-day mortality in low- vs. higher-risk patients and the areas under the receiver operating characteristic curve (ROC). Results: Overall, 3.8% of patients (17/449) died within 30 days. The GPS classified a greater proportion of patients as low risk (92% [413/449]) than the PESI (36.3% [163/449]) and the sPESI (39.6% [178/449]) (P<0.001 for each comparison). Low-risk patients based on the sPESI had a mortality of 0% (95% confidence interval [CI] 0-2.1%) compared to 0.6% (95% CI 0-3.4%) for low-risk patients based on the PESI and 3.4% (95% CI 1.9-5.6%) for low-risk patients based on the GPS. The areas under the ROC curves were 0.77 (95%CI 0.72-0.81), 0.76 (95% CI 0.72-0.80), and 0.71 (95% CI 0.66-0.75), respectively (P=0.47). Conclusions: In this cohort of elderly patients with PE, the GPS identified a higher proportion of patients as low-risk but the PESI and sPESI were more accurate in predicting mortality.

Chronotropic incompetence predicts impaired response to exercise training in heart failure patients in sinus rhythm

Background: In most patients with chronic heart failure (CHF), endurance training improves exercise capacity. However, some patients do not respond favourably. The purpose of this study was to explore the reasons of non-response and to determine their predictive value.Methods: We studied a cohort of 120 consecutive CHF patients with sinus rhythm (mean age 57 ± 12 years, ejection fraction 29.3 ± 9.9%, peak VO2 17.3 ± 5.1 ml/min/kg), participating in a 3-month outpatient cardiac rehabilitation programme. Responders were defined as subjects who improved peak VO2 by more than 5%, work load by more than 10%, or VE/VCO2 slope by more than 5%. Subjects who did not fulfil at least one of the above criteria were characterized as non-responders. Multivariate regression analyses were performed to identify parameters that were predictive for a response. Receiver operating characteristic (ROC) analyses were performed for predictive parameters to identify thresholds for response or non-response.Results: Multivariate regression analyses revealed heart rate (HR) reserve, HR recovery at 1 min, and peak HR as significant predictors for a positive training response. ROC curves revealed the optimal thresholds separating responders from non-responders at less than 30 bpm for HR reserve, less than 6 bpm for HR recovery and less than 101 bpm for peak HR.Conclusions: The presence of impaired chronotropic competence is a major predictor of poor training response in CHF patients with sinus rhythm.