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In this dissertation we consider complex, projective hypersurfaces with many isolated singularities. The leading questions concern the maximal number of prescribed singularities of such hypersurfaces in a given linear system, and geometric properties of the equisingular stratum. In the first part a systematic introduction to the theory of equianalytic families of hypersurfaces is given. Furthermore, the patchworking method for constructing hypersurfaces with singularities of prescribed types is described. In the second part we present new existence results for hypersurfaces with many singularities. Using the patchworking method, we show asymptotically proper results for hypersurfaces in P^n with singularities of corank less than two. In the case of simple singularities, the results are even asymptotically optimal. These statements improve all previous general existence results for hypersurfaces with these singularities. Moreover, the results are also transferred to hypersurfaces defined over the real numbers. The last part of the dissertation deals with the Castelnuovo function for studying the cohomology of ideal sheaves of zero-dimensional schemes. Parts of the theory of this function for schemes in P^2 are generalized to the case of schemes on general surfaces in P^3. As an application we show an H^1-vanishing theorem for such schemes.

In this text we survey some large deviation results for diffusion processes. The first chapters present results from the literature such as the Freidlin-Wentzell theorem for diffusions with small noise. We use these results to prove a new large deviation theorem about diffusion processes with strong drift. This is the main result of the thesis. In the later chapters we give another application of large deviation results, namely to determine the exponential decay rate for the Bayes risk when separating two different processes. The final chapter presents techniques which help to experiment with rare events for diffusion processes by means of computer simulations.

Materials in general can be divided into insulators, semiconductors and conductors,
depending on their degree of electrical conductivity. Polymers are classified as
electrically insulating materials, having electrical conductivity values lower than 10-12
S/cm. Due to their favourable characteristics, e.g. their good physical characteristics,
their low density, which results in weight reduction, etc., polymers are also
considered for applications where a certain degree of conductivity is required. The
main aim of this study was to develop electrically conductive composite materials
based on epoxy (EP) matrix, and to study their thermal, electrical, and mechanical
properties. The target values of electrical conductivity were mainly in the range of
electrostatic discharge protection (ESD, 10-9-10-6 S/cm).
Carbon fibres (CF) were the first type of conductive filler used. It was established that
there is a significant influence of the fibre aspect ratio on the electrical properties of
the fabricated composite materials. With longer CF the percolation threshold value
could be achieved at lower concentrations. Additional to the homogeneous CF/EP
composites, graded samples were also developed. By the use of a centrifugation
method, the CF created a graded distribution along one dimension of the samples.
The effect of the different processing parameters on the resulting graded structures
and consequently on their gradients in the electrical and mechanical properties were
systematically studied.
An intrinsically conductive polyaniline (PANI) salt was also used for enhancing the
electrical properties of the EP. In this case, a much lower percolation threshold was
observed compared to that of CF. PANI was found out to have, up to a particular
concentration, a minimal influence on the thermal and mechanical properties of the
EP system.
Furthermore, the two above-mentioned conductive fillers were jointly added to the EP
matrix. Improved electrical and mechanical properties were observed by this
incorporation. A synergy effect between the two fillers took place regarding the
electrical conductivity of the composites.
The last part of this work was engaged in the application of existing theoretical
models for the prediction of the electrical conductivity of the developed polymer composites. A good correlation between the simulation and the experiments was
observed.
Allgemein werden Materialien in Bezug auf ihre elektrische Leitfähigkeit in Isolatoren,
Halbleiter oder Leiter unterteilt. Polymere gehören mit einer elektrischen Leitfähigkeit
niedriger als 10-12 S/cm in die Gruppe der Isolatoren. Aufgrund vorteilhafter
Eigenschaften der Polymere, wie z.B. ihren guten physikalischen Eigenschaften,
ihrer geringen Dichte, welche zur Gewichtsreduktion beiträgt, usw., werden Polymere
auch für Anwendungen in Betracht gezogen, bei denen ein gewisser Grad an
Leitfähigkeit gefordert wird. Das Hauptziel dieser Studie war, elektrisch leitende
Verbundwerkstoffe auf der Basis von Epoxidharz (EP) zu entwickeln und deren
elektrische, mechanische und thermische Eigenschaften zu studieren. Die Zielwerte
der elektrischen Leitfähigkeit lagen hauptsächlich im Bereich der Vermeidung
elektrostatischer Aufladungen (ESD, 10-9-10-6 S/cm).
Bei der Herstellung elektrisch leitender Kunststoffen wurden als erstes
Kohlenstofffasern (CF) als leitfähige Füllstoffe benutzt. Bei den durchgeführten
Experimenten konnte man beobachten, dass das Faserlängenverhältnis einen
bedeutenden Einfluss auf die elektrischen Eigenschaften der fabrizierten
Verbundwerkstoffe hat. Mit längeren CF wurde die Perkolationsschwelle bereits bei
einer niedrigeren Konzentration erreicht. Zusätzlich zu den homogenen CF/EP
Verbundwerkstoffen, wurden auch Gradientenwerkstoffe entwickelt. Mit Hilfe einer
Zentrifugation konnte eine gradierte Verteilung der CF entlang der Probenlängeachse
erreicht werden. Die Effekte der unterschiedlichen Zentrifugationsparameter
auf die resultierenden Gradientenwerkstoffe und die daraus
resultierenden, gradierten elektrischen und mechanischen Eigenschaften wurden
systematisch studiert.
Ein intrinsisch leitendes Polyanilin-Salz (PANI) wurde auch für das Erhöhen der
elektrischen Eigenschaften des EP benutzt. In diesem Fall wurde eine viel niedrigere
Perkolationsschwelle verglichen mit der von CF beobachtet. Der Einsatz von PANI hat bis zu einer bestimmten Konzentration nur einen minimalen Einfluß auf die
thermischen und mechanischen Eigenschaften des EP Systems.
In einem dritte Schritt wurden die zwei oben erwähnten, leitenden Füllstoffe
gemeinsam der EP Matrix hinzugefügt. Erhöhte elektrische und mechanische
Eigenschaften wurden in diesem Fall beobachtet, wobei sich ein Synergie-Effekt
zwischen den zwei Füllstoffen bezogen auf die elektrische Leitfähigkeit der
Verbundwerkstoffe ergab.
Im letzten Teil dieser Arbeit fand die Anwendung von theoretischen Modelle zur
Vorhersage der elektrischen Leitfähigkeit der entwickelten Verbundwerkstoffe statt.
Dabei konnte eine gute Übereinstimmung mit den experimentellen Ergebnissen
festgestellt werden .

In the present work, various aspects of the mixed continuum-atomistic modelling of materials are studied, most of which are related to the problems arising due to a development of microstructures during the transition from an elastic to plastic description within the framework of continuum-atomistics. By virtue of the so-called Cauchy-Born hypothesis, which is an essential part of the continuum-atomistics, a localization criterion has been derived in terms of the loss of infinitesimal rank-one convexity of the strain energy density. According to this criterion, a numerical yield condition has been computed for two different interatomic energy functions. Therewith, the range of the Cauchy-Born rule validity has been defined, since the strain energy density remains quasiconvex only within the computed yield surface. To provide a possibility to continue the simulation of material response after the loss of quasiconvexity, a relaxation procedure proposed by Tadmor et al. leading necessarily to the development of microstructures has been used. Thereby, various notions of convexity have been overviewed in details. Alternatively to the above mentioned criterion, a stability criterion has been applied to detect the critical deformation. For the study in the postcritical region, the path-change procedure proposed by Wagner and Wriggers has been adapted for the continuum-atomistic and modified. To capture the deformation inhomogeneity arising due to the relaxation, the Cauchy-Born hypothesis has been extended by assumption that it represents only the 1st term in the Taylor's series expansion of the deformation map. The introduction of the 2nd, quadratic term results in the higher-order materials theory. Based on a simple computational example, the relevance of this theory in the postcritical region has been shown. For all simulations including the finite element examples, the development tool MATLAB 6.5 has been used.

Characterization of neuronal activity in the auditory brainstem of rats: An optical imaging approach
(2004)

In this doctoral thesis, several aspects of neuronal activity in the rat superior olivary complex (SOC), an auditory brainstem structure, were analyzed using optical imaging with voltage-sensitive dyes (VSD). The thesis is divided into 5 Chapters. Chapter 1 is a general introduction, which gives an overview of the auditory brainstem and VSD imaging. In Chapter 2, an optical imaging method for the SOC was standardized, using the VSD RH795. To do so, the following factors were optimized: (1) An extracellular potassium concentration of 5 mM is necessary during the incubation and recording to observe synaptically evoked responses in the SOC. (2) Employing different power supplies reduced the noise. (3) Averaging of 10 subsequent trials yielded a better signal-to-noise ratio. (4) RH795 of 100 µM with 50 min prewash was optimal to image SOC slices for more than one hour. (5) Stimulus-evoked optical signals were TTX sensitive, revealing action potential-driven input. (6) Synaptically evoked optical signals were characterized to be composed of pre- and postsynaptic components. (7) Optical signals were well correlated with anatomical structures. Overall, this method allows the comparative measurement of electrical activity of cell ensembles with high spatio-temporal resolution. In Chapter 3, the nature of functional inputs to the lateral superior olive (LSO), the medial superior olive (MSO), and the superior paraolivary nucleus (SPN) were analyzed using the glycine receptor blocker strychnine and the AMPA/kainate receptor blocker CNQX. In the LSO, the known glutamatergic inputs from the ipsilateral, and the glycinergic inputs from the ipsilateral and contralateral sides, were confirmed. Furthermore, a CNQX-sensitive input from the contralateral was identified. In the MSO, the glutamatergic and glycinergic inputs from the ipsilateral and contralateral sides were corroborated. In the SPN, besides the known glycinergic input from the contralateral, I found a glycinergic input from the ipsilateral and I also identified CNQX-sensitive inputs from the contralateral and ipsilateral sides. Together, my results thus corroborate findings obtained with different preparations and methods, and provide additional information on the pharmacological nature of the inputs. In Chapter 4, the development of glycinergic inhibition for the LSO, the MSO, the SPN, and the medial nucleus of the trapezoid body (MNTB) was studied by characterizing the polarity of strychnine-sensitive responses. In the LSO, the high frequency region displayed a shift in the polarity at P4, whereas the low frequency region displayed at P6. In the MSO, both the regions displayed the shift at P5. The SPN displayed a shift in the polarity at E18-20 without any regional differences. The MNTB lacked a shift between P3-10. Together, these results demonstrate a differential timing in the development of glycinergic inhibition in these nuclei. In Chapter 5, the role of the MSO in processing bilateral time differences (t) was investigated. This was done by stimulating ipsilateral and contralateral inputs to the MSO with different t values. In preliminary experiments, the postsynaptic responses showed a differential pattern in the spread of activity upon different t values. This data demonstrates a possible presence of delay lines as proposed by Jeffress in the interaural time difference model of sound localization. In conclusion, this study demonstrates the usage of VSD imaging to analyze the neuronal activity in auditory brainstem slices. Moreover, this study expands the knowledge of the inputs to the SOC, and has identified one glycinergic and three AMPA/kainate glutamatergic novel inputs to the SOC nuclei.

The present thesis deals with a novel air interface concept for beyond 3G mobile radio systems. Signals received at a certain reference cell in a cellular system which originate in neighboring cells of the same cellular system are undesired and constitute the intercell interference. Due to intercell interference, the spectrum capacity of cellular systems is limited and therefore the reduction of intercell interference is an important goal in the design of future mobile radio systems. In the present thesis, a novel service area based air interface concept is investigated in which interference is combated by joint detection and joint transmission, providing an increased spectrum capacity as compared to state-of-the-art cellular systems. Various algorithms are studied, with the aid of which intra service area interference can be combated. In the uplink transmission, by optimum joint detection the probability of erroneous decision is minimized. Alternatively, suboptimum joint detection algorithms can be applied offering reduced complexity. By linear receive zero-forcing joint detection interference in a service area is eliminated, while by linear minimum mean square error joint detection a trade-off is performed between interference elimination and noise enhancement. Moreover, iterative joint detection is investigated and it is shown that convergence of the data estimates of iterative joint detection without data estimate refinement towards the data estimates of linear joint detection can be achieved. Iterative joint detection can be further enhanced by the refinement of the data estimates in each iteration. For the downlink transmission, the reciprocity of uplink and downlink channels is used by joint transmission eliminating the need for channel estimation and therefore allowing for simple mobile terminals. A novel algorithm for optimum joint transmission is presented and it is shown how transmit signals can be designed which result in the minimum possible average bit error probability at the mobile terminals. By linear transmit zero-forcing joint transmission interference in the downlink transmission is eliminated, whereas by iterative joint transmission transmit signals are constructed in an iterative manner. In a next step, the performance of joint detection and joint transmission in service area based systems is investigated. It is shown that the price to be paid for the interference suppression in service area based systems is the suboptimum use of the receive energy in the uplink transmission and of the transmit energy in the downlink transmission, with respect to the single user reference system. In the case of receive zero-forcing joint detection in the uplink and transmit zero-forcing joint transmission in the downlink, i.e., in the case of linear unbiased data transmission, it is shown that the same price, quantified by the energy efficiency, has to be paid for interference elimination in both uplink and downlink. Finally it is shown that if the system load is fixed, the number of active mobile terminals in a SA and hence the spectrum capacity can be increased without any significant reduction in the average energy efficiency of the data transmission.

The hypoxia inducible factor-1 (HIF-1), a heterodimer composed of HIF-1alpha and HIF-1beta, is activated in response to low oxygen tension and serves as the master regulator for cells to adapt to hypoxia. HIF-1 is usually considered to be regulated via degradation of its a-subunit. Recent findings, however, point to the existence of alternative mechanisms of HIF-1 regulation which appear to be important for down-regulating HIF-1 under prolonged and severe oxygen depletion. The aims of my Ph.D. thesis, therefore, were to further elucidate mechanisms involved in such down-regulation of HIF-1. The first part of the thesis addresses the impact of the severity and duration of oxygen depletion on HIF-1alpha protein accumulation and HIF-1 transcriptional activity. A special focus was put on the influence of the transcription factor p53 on HIF-1. I found that p53 only accumulates under prolonged anoxia (but not hypoxia), thus limiting its influence on HIF-1 to severe hypoxic conditions. At low expression levels, p53 inhibits HIF-1 transactivity. I attributed this effect to a competition between p53 and HIF-1alpha for binding to the transcriptional co-factor p300, since p300 overexpression reverses this inhibition. This assumption is corroborated by competitive binding of IVTT-generated p53 and HIF-1alpha to the CH1-domain of p300 in vitro. High p53 expression, on the other hand, affects HIF-1alpha protein negatively, i.e., p53 provokes pVHL-independent degradation of HIF-1alpha. Therefore, I conclude that low p53 expression attenuates HIF-1 transactivation by competing for p300, while high p53 expression negatively affects HIF-1alpha protein, thereby eliminating HIF-1 transactivity. Thus, once p53 becomes activated under prolonged anoxia, it contributes to terminating HIF-1 responses. In the second part of my study, I intended to further characterize the effects induced by prolonged periods of low oxygen, i.e., hypoxia, as compared to anoxia, with respect to alterations in HIF-1alpha mRNA. Prolonged anoxia, but not hypoxia, showed pronounced effects on HIF-1alpha mRNA. Long-term anoxia induced destabilization of HIF-1alpha mRNA, which manifests itself in a dramatic reduction of the half-life. The mechanistic background points to natural anti-sense HIF-1alpha mRNA, which is induced in a HIF-1-dependent manner, and additional factors, which most likely influence HIF-1alpha mRNA indirectly via anti-sense HIF-1alpha mRNA mediated trans-effects. In summary, the data provide new information concerning the impact of p53 on HIF-1, which might be of importance for the decision between pro- and anti-apoptotic mechanisms depending upon the severity and duration of hypoxia. Furthermore, the results of this project give further insights into a novel mechanism of HIF-1 regulation, namely mRNA down-regulation under prolonged anoxic incubations. These mechanisms appear to be activated only in response to prolonged anoxia, but not to hypoxia. These considerations regarding HIF-1 regulation should be taken into account when prolonged incubations to hypoxic or anoxic conditions are analyzed at the level of HIF-1 stability regulation.

In the filling process of a car tank, the formation of foam plays an unwanted role, as it may prevent the tank from being completely filled or at least delay the filling. Therefore it is of interest to optimize the geometry of the tank using numerical simulation in such a way that the influence of the foam is minimized. In this dissertation, we analyze the behaviour of the foam mathematically on the mezoscopic scale, that is for single lamellae. The most important goals are on the one hand to gain a deeper understanding of the interaction of the relevant physical effects, on the other hand to obtain a model for the simulation of the decay of a lamella which can be integrated in a global foam model. In the first part of this work, we give a short introduction into the physical properties of foam and find that the Marangoni effect is the main cause for its stability. We then develop a mathematical model for the simulation of the dynamical behaviour of a lamella based on an asymptotic analysis using the special geometry of the lamella. The result is a system of nonlinear partial differential equations (PDE) of third order in two spatial and one time dimension. In the second part, we analyze this system mathematically and prove an existence and uniqueness result for a simplified case. For some special parameter domains the system can be further simplified, and in some cases explicit solutions can be derived. In the last part of the dissertation, we solve the system using a finite element approach and discuss the results in detail.

Inappropriate speed is the most common reason for road traffic accidents world wide. Thus, a necessity for speed management exists. The so-called SUNflower states Sweden, the United Kingdom and the Netherlands - each spending strong effort in traffic safety policies - have great success in reducing mean road speeds and speed variances through speed management. However, the effect is still insufficient for gaining real traffic safety. Thus, there is a discussion to make use of technical in-vehicle devices. One of these technologies called Intelligent Speed Adaptation (ISA) reduces vehicle speeds. This is done either by warning the driver that he is speeding, or activating the accelerator pedal with a counterforce, or reducing the gasoline supply to the motor. The three ways of reducing the speed are called version 1-3. The EC-project for research on speed adaptation policies on European roads (PROSPER) deals with strategic proposals for the implementation of the different ISA-versions. This thesis includes selected results of PROSPER. In this thesis two empiric surveys were done in order to give an overview about the basic conditions (e.g. social, economic, technical aspects) for an ISA implementation in Germany. On one hand, a stakeholder analysis and questionnaire using the Delphi-method has been accomplished in two rounds. On the other hand, a questionnaire with speed offenders has been accomplished, too, in two rounds. In addition, the author created an expert pool consisting of 23 experts representing the most important fields of science and practice in which ISA is involved. The author made phone or personal interviews with most of the experts. 12 experts also produced a detailed publication on their professional point of view towards ISA. The two surveys and the professional comments on ISA led to four possible implementation scenarios for ISA in Germany. However, due to a strong political opposition against ISA it is also thinkable that ISA is not implemented or the implementation process starts after 2015 (i.e. outside the aimed period of time). The scenarios are as follows: A) Implementation of version 1 by market forces with governmental subventions. B) Implementation of version 2 by market forces supported by traffic safety institutions and image-making processes. C) Implementation of a modified version 3 by law for speed offenders instead of cancellation of the driving licence. D) Implementation of various versions in Germany because of a broad implementation of ISA in the SUNflower states. X) Non-implementation of ISA leads to the necessity of alternative speed management measures. The author prefers scenario B because - ceteris paribus - it seems to be the most likely way to implement the technology. As soon as ISA reaches technical maturity, the implementation process has to be accomplished in three steps. 1) Marketing and image making 2) Margin introduction 3) Market penetration This implementation process for ISA by market forces could effect a percentage of at least 15% of all vehicles equipped with ISA before the year 2015.

In traditional portfolio optimization under the threat of a crash the investment horizon or time to maturity is neglected. Developing the so-called crash hedging strategies (which are portfolio strategies which make an investor indifferent to the occurrence of an uncertain (down) jumps of the price of the risky asset) the time to maturity turns out to be essential. The crash hedging strategies are derived as solutions of non-linear differential equations which itself are consequences of an equilibrium strategy. Hereby the situation of changing market coefficients after a possible crash is considered for the case of logarithmic utility as well as for the case of general utility functions. A benefit-cost analysis of the crash hedging strategy is done as well as a comparison of the crash hedging strategy with the optimal portfolio strategies given in traditional crash models. Moreover, it will be shown that the crash hedging strategies optimize the worst-case bound for the expected utility from final wealth subject to some restrictions. Another application is to model crash hedging strategies in situations where both the number and the height of the crash are uncertain but bounded. Taking the additional information of the probability of a possible crash happening into account leads to the development of the q-quantile crash hedging strategy.