SG-classes, singular symplectic geoemtry, and order preserving isomorphisms

Die geometrischen Kalküle von Pseudo-differenzial- und Fourier-Integraloperatoren beruhen auf den symplektischen Eigenschaften des Kotangentialbündels. Um neue Kalküle zu entwickeln, die an eine besondere Geometrie angepasst sind, ist es nötig, singulär-symplektische Mannigfaltigkeiten zu betrachten. Diese müssen zuerst verstanden werden, bevor man die zugehorigen Operatorkalküle konstruieren kann. In dieser Dissertation geben wir neue Einblicke in die singulär-symplektischen Strukturen, die aus asymptotisch-Euklidischen Mannigfaltigkeiten entstehen. Insbesondere rechnen wir aus, wie die Poisson-Klammer auf SG-Pseudo-Differenzialoperatoren wirkt, und definieren eine neue Klasse symplektischer Abbildungen, die an die geometrischen Besonderheiten angepasst sind. Wir betrachten außerdem die ordnungserhaltenden Isomorphismen der SG-Algebra und zeigen, dass unser Konzept von singulär-symplektischen Abbildungen natürlich in diesem Zusammenhang auftaucht. Wir benutzen es, um diese Isomorphismen als Konjugation mit einem SG-Fourier-Integraloperator zu charakterisieren.The geometric theory of pseudo-differential and Fourier Integral Operators relies on the symplectic structure of cotangent bundles. If one is to study calculi with some specific feature adapted to a geometric situation, the corresponding notion of cotangent bundle needs to be adapted as well and leads to spaces with a singular symplectic structure. Analysing these singularities is a necessary step in order to construct the calculus itself. In this thesis we provide some new insights into the symplectic structures arising from asymptotically Euclidean manifolds. In particular, we study the action of the Poisson bracket on SG-pseudo-differential operators and define a new class of singular symplectomorphisms, taking into account the geometric picture. We then consider this notion in the context of the characterisation of order-preserving isomorphisms of the SG-algebra, and show that these are in fact given by conjugation with a Fourier Integral Operator of SG-type

Synthesis of phenylacetaldehyde amidines and their intramolecular cyclization

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Calorimetric investigations of a series of energetic polyphosphazenes

Energetic, fluorinated, linear polyphosphazenes are currently under investigation as potential, high-density binders for new, polymer bonded explosive compositions. A series of such polymers was synthesised and the enthalpy of combustion of each member of the series was measured by static bomb calorimetry. This was performed after combusting appropriate secondary thermochemical standards to model the combustion stoichiometry of the heteroatoms nitrogen, fluorine and phosphorus. The water-soluble combustion products were identified and quantified using 19F NMR spectroscopy and Ion Chromatography. Since some of the combustion products are hydrolytically unstable, it was found necessary to stabilise the initial combustion product mixtures by using a buffer solution instead of pure water in the bomb, and then to determine the composition of the stabilised product mixtures in order to obtain meaningful values for the enthalpies of combustion and thence enthalpies of formation. The thermochemical measurements themselves were made with pure water in the bomb. The composition and structures of the various polyphosphazenes were correlated with their energies of combustion and enthalpies of formation. The latter were calculated using the latest CODATA values of enthalpy of formation of the combustion products. The ‘combustion’ of the polyphosphazenes under a nitrogen atmosphere was also investigated with the view to calculating the enthalpies of detonation of each member of the series. Three conference papers which include the results of this work have been published and are included in Appendices C-E.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Reliable Fast (20 Hz) Acquisition Rate by a TD fNIRS Device: Brain Resting-State Oscillation Studies

A high power setup for multichannel time-domain (TD) functional near infrared spectroscopy (fNIRS) measurements with high efficiency detection system was developed. It was fully characterized based on international performance assessment protocols for diffuse optics instruments, showing an improvement of the signal-to-noise ratio (SNR) with respect to previous analogue devices, and allowing acquisition of signals with sampling rate up to 20 Hz and source-detector distance up to 5 cm. A resting-state measurement on the motor cortex of a healthy volunteer was performed with an acquisition rate of 20 Hz at a 4 cm source-detector distance. The power spectrum for the cortical oxy- and deoxyhemoglobin is also provided

Low hazard small-scale synthesis and chemical analysis of high purity nitroglycerine (NG)

A previously reported two-phase (99.5% fuming nitric acid/dichloromethane) batch method to prepare high purity 1,2,3-propanetriyl trinitrate (nitroglycerine, NG) was evaluated, simplified and adapted specifically for low hazard small-scale synthesis. The purity of the product, as determined by NMR spectroscopy, HPLC and IR spectroscopic analysis was found to be greater than 99%. The quick synthetic method is highly recommended when small amounts of highly pure NG are required for analytical and related purposes in the absence of a microreactor

Effect of a thin superficial layer on the estimate of hemodynamic changes in a two-layer medium by time domain NIRS

In order to study hemodynamic changes involved in muscular metabolism by means of time domain fNIRS, we need to discriminate in the measured signal contributions coming from different depths. Muscles are, in fact, typically located under other tissues, e.g. skin and fat. In this paper, we study the possibility to exploit a previously proposed method for analyzing time-resolved fNIRS measurements in a two-layer structure with a thin superficial layer. This method is based on the calculation of the timedependent mean partial pathlengths. We validated it by simulating venous and arterial arm cuff occlusions and then applied it on in vivo measurements

New frontiers in time-domain diffuse optics, a review

The recent developments in time-domain diffuse optics that rely on physical concepts (e.g., time-gating and null distance) and advanced photonic components (e.g., vertical cavity source-emitting laser as light sources, single photon avalanche diode, and silicon photomultipliers as detectors, fast-gating circuits, and time-to-digital converters for acquisition) are focused. This study shows how these tools could lead on one hand to compact and wearable time-domain devices for point-of-care diagnostics down to the consumer level and on the other hand to powerful systems with exceptional depth penetration and sensitivity

Clinical and Laboratory Findings in Tick-Borne Encephalitis Virus Infection.

Purpose: Tick-Borne Encephalitis (TBE), a disease caused by Tick-Borne Encephalitis Virus (TBEV), is emerging in Italy. This study aimed to characterize the epidemiological, clinical, laboratory, imaging and electroencephalogram characteristics in Belluno, North-East Italy. Results: 76% were males, mean age 53 years; 50% did not report tick bite. 72% had a biphasic course, 42% a monophasic one, 8 cases of abortive TBE. Mostly no specific symptoms were observed, together with neurological signs and symptoms. None died, but 35% had sequelae at the one-month follow-up. Men had a higher risk of having neurological/neurocognitive sequelae; paresthesia or tremors were associated independently with sequelae. In terms of laboratory data, thrombocytopenia, neutropenia and lymphocytosis were associated with the first phase (p < .01), while monocytosis, lymphocytopenia, high levels of ESR and CRP with the second (p < .05). Other abnormal laboratory data were observed: high levels of transaminases, bilirubin, GGT, fibrinogen, amylase, LDH, CPK and electrolyte disorders. Most of the liquor showed pleocytosis and increased protein levels. No specific findings characterized imaging; electroencephalogram mainly reported general and focal anomalies in the temporal lobe. Conclusions: Although patients have not reported a tick bite, TBEV infection should be considered for diagnosis. Usually no specific symptoms are reported along with neurological signs and symptoms. The biphasic course is more often described than the monophasic course; abortive TBE is sometimes present. Paresthesia and tremors are independently associated with neurological/neurocognitive sequelae; men have a higher risk of having sequelae. The first phase is probably associated with thrombocytopenia, neutropenia and lymphocytosis; the second with monocytosis, lymphocytopenia, high levels of CRP and ESR. Electrolyte disorders, high levels of transaminases, GGT, bilirubin, CPK, LDH, fibrinogen and amylase may characterize TBEV infection. © 202