Multipliers for Continuous Frames in Hilbert Spaces

In this paper we examine the general theory of continuous frame multipliers in Hilbert space. These operators are a generalization of the widely used notion of (discrete) frame multipliers. Well-known examples include Anti-Wick operators, STFT multipliers or Calder\'on- Toeplitz operators. Due to the possible peculiarities of the underlying measure spaces, continuous frames do not behave quite as well as their discrete counterparts. Nonetheless, many results similar to the discrete case are proven for continuous frame multipliers as well, for instance compactness and Schatten class properties. Furthermore, the concepts of controlled and weighted frames are transferred to the continuous setting

Bilinear time-frequency distributions and pseudodifferential operators

Diese Dissertation verfolgt zwei Zielsetzungen. Erstens wird versucht, wohlbekannte Zeit-Frequenz-Verteilungen wie etwa die Kurzzeit-Fouriertransformation oder die Wigner-Verteilung zu verallgemeinern und in einen einheitlichen Rahmen einzufügen. Insbesondere werden die zugehörigen Pseudodifferentialoperator-Kalküle und deren wesentliche Eigenschaften untersucht und mit bereits bestehenden Kalkülen wie etwa der Kohn-Nirenberg-Korrespondenz oder dem Weyl-Kalkül verglichen. Die Leitfrage besteht darin, ob sich die recht schönen Eigenschaften der erwähnten Kalküle auf die allgemeinere Situation übertragen lassen. Zweitens wird, basierend auf den Ergebnissen des ersten Teils, ein spezieller Typus von Pseudodifferentialoperatoren, nämlich Zeit-Frequenz-Lokalsationsoperatoren, genauer analysiert. Ihre grundlegenden Eigenschaften, besonders Abbildungseigenschaften des Symbols, werden in einheitlichem Rahmen präsentiert. Der Zusammenhang mit der Berezin-Transformation erlaubt es, neue Dichtheitsresultate für die Menge der Lokalisationsoperatoren als Teilmengen größerer Operatorklassen sowohl bezüglich verschiedener Symbolkalssen als auch verschiedener Topologien zu beweisen.The purpose of this doctoral thesis is twofold. First, an attempt is made to generalize well-known time-frequency distributions, such as the short-time Fourier transform or the Wigner distribution, and integrate them into a unified framework. In particular, the associated pseudodifferential calculi and their properties are investigated and compared to already existing calculi, such as the Kohn-Nirenberg correspondence or the Weyl calculus. The guiding question is which of the rather nice properties of the mentioned calculi carry over to the more general situation. Second, based on the first part, a specific type of pseudodifferential operators, namely the time-frequency localization operators, are analyzed more closely. Their basic properties, in particular mapping properties of the symbol, are reviewed in a unified way. The connection with the Berezin transform allows to prove new density results of the set of localization operators as subsets of larger classes of operators, for different symbol classes and with respect to different topologies

High resolution multi-facies realizations of sedimentary reservoir and aquifer analogs

Geological structures are by nature inaccessible to direct observation. This can cause difficulties in applications where a spatially explicit representation of such structures is required, in particular when modelling fluid migration in geological formations. An increasing trend in recent years has been to use analogs to palliate this lack of knowledge, i.e., exploiting the spatial information from sites where the geology is accessible (outcrops, quarry sites) and transferring the observed properties to a study site deemed geologically similar. While this approach is appealing, it is difficult to put in place because of the lack of access to well-documented analog data. In this paper we present comprehensive analog data sets which characterize sedimentary structures from important groundwater hosting formations in Germany and Brazil. Multiple 2-D outcrop faces are described in terms of hydraulic, thermal and chemical properties and interpolated in 3-D using stochastic techniques. These unique data sets can be used by the wider community to implement analog approaches for characterizing reservoir and aquifer formations

Prevalence of findings compatible with carotid artery calcifications on dental panoramic radiographs

Cerebrovascular accidents are responsible for killing or disabling more than half a million Americans every year. They are the third leading cause of death in this country. In Germany, the annual stroke incidence reaches 182 cases per 100,000 inhabitants. Stroke there is the fourth leading cause of death. There is a need of finding cost-effective means of decreasing stroke mortality and morbidity. Instruments for early diagnosis are of great humanitarian and economic importance. All possible clinical findings should be taken into account. It is not the demand of this study to present the panoramic radiograph as a screening test method for early diagnosis of atherosclerosis. The aim is to show the potential of this radiograph used in everyday clinical dental practice by the prevalence of radiopaque findings in the carotid region. This study included panoramic dental radiographs of 2,557 patients older than 30years of age. Fifty-nine percent of the patients were women and 41% were men. The radiographs were adjudged for signs compatible with carotid arterial calcifications appearing as a radiopaque nodular mass adjacent to the cervical vertebrae at or below the intervertebral space C3-4. Of all these radiographs, 4.8% showed radiopaque findings compatible with atherosclerotic lesions. The proportion of women reached 64.8% and that of men reached 35.2%. In accordance to recent literature, the results of this study show that about 5% of the patients show radiological findings compatible with carotid arterial calcifications. Some of these patients at risk for a cerebrovascular accident may be identified in the dentist's office by appropriate review of the panoramic dental radiograph. The suspicion of carotid artery calcifications demands an impetuous referral to an appropriate practitioner who can assist in the control of risk factors and if necessary arrange surgical removal of the carotid arterial plaque. So, the dentist should be aware of this problem and able to make a contribution to stroke preventio

Clinical retention force development of double crowns

This study deals with the development of the retentive forces of double crowns intraorally measured. Twenty-five combined fixed-removable prostheses with a total of 84 double crowns were included in the study. The intraoral measurement was performed at 72 defined measuring points directly adjacent to the double crowns of the dentures. The measurement was performed 4-6weeks (baseline), 6months (recall 1), and 18months (recall 2) after the insertion of the restoration. A specifically designed measuring device was used. The median values for the single measuring points reached 4.705N at the baseline, 5.190N after 6months, and 3.740N after 18months. The measured values were analyzed according to differences between the median retention forces at the three defined points in time. The statistical analysis of the median values showed no statistical difference for the retention force change after 6months but for the decrease until the second recall (Mann-Whitney test). The retention force per denture was calculated by a summation of the single measuring points. At the baseline, 12.9N was reached. The forces did only decrease slightly and were not statistically significant. The results indicate that retention force values of double crowns, measured intraorally at the patient, do not relevantly change clinically within the first 1.5years. Within the limitations of this study, it can be stated that wear does not influence the retentive forces of double crowns within the first 18months. After this period the retention force should be still sufficient for denture retentio