Abstract:
The main result is a linear system of partial differential equations (referred to as the structure equations) that describe the result of signal processing in the cochlea. It is formulated for phase and for the logarithm of the amplitude. The changes of these quantities are the essential physiological observables in the description of signal processing in the auditory pathway.The structure equations display in a quantitative way the subtle balance for processing information on the basis of phase versus amplitude. From a mathematical point of view, the linear system of equations is classified as an inhomogeneous ？ ˉ -equation. In suitable variables the solutions can be represented as the superposition of a particular solution (determined by the system) and a holomorphic function (determined by the incoming signal). In this way, a global picture of signal processing in the cochlea emerges.At the outset of this work is the quest to understand signal processing in the cochlea.It has been known since 1992 that cochlear signal processing can be described by a wavelet transform (Daubechies 1992 [1], Yang, Wang and Shamma, 1992 [2]). There are two basic principles that lie at the core of this description: Linearity and scaling.In the cochlea, an incoming acoustical signal f ( t ) in the form of a pressure fluctuation (t is the time variable) induces a movement u ( x , t ) of the basilar membrane at position x along the cochlea. At a fixed level of sound intensity, the relation between incoming signal and movement of the basilar membrane is surprisingly linear. However as a whole this process is highly compressive with respect to levels of sound - and thus cannot be linear.In the present setting this is taken care of by a ‘quasilinear model’. This is a model that depends on parameters, for example, in the present situation the level of sound intensity. For fixed parameters the model is linear. It is interpreted as a linear approximation to the process at these fixed para

Abstract:
The paper introduces the medical library of the RWTH Aachen University. It starts with a short historical review and describes the status of the medical library inside the library system of the university. Duties and responsibilities and the electronic offers are highlighted. It gives some information about the ranking, which is used for identifying the most important journals. The paper ends with some key data about the medical library and a list of references.

Abstract:
Jazz has firmly established its position in the academic establishment and has its own educational paradigms and pedagogical methodologies. The question arising in this context is the relationship of the central educational and pedagogical paradigms of the educational situation in the imaginary periphery. Is the (so called) central model the only possible way to think about jazz education nowadays? To what the extent does this model of jazz education meet the needs of jazz practices in the periphery? This study tries to give some possible answers to those questions by the example of jazz education and scene in Estonia.

Abstract:
The most important characteristic of {\em multiplicative noise} is that its effects of system's dynamics depends on the recent system's state. Consideration of multiplicative noise on self-referential systems including biological and economical systems therefore is of importance. In this note we study an elementary example. While in a deterministic super critical pitchfork bifurcation with positive bifurcation parameter $\lambda$ the positive branch $\sqrt{\lambda}$ is stable, multiplicative white noise $\lambda_t ={\lambda} + \sigma \zeta_t$ on the unique parameter reduces stability in that the system's state tends to 0 almost surely, even for ${\lambda}>0$, while for 'small' noise $\sigma < \sqrt{2 \lambda}$ the point $\sqrt{\lambda-\sigma^2/2}$ is a meta-stable state. In this case, correspondingly, the system will 'die out', i.e. $X_t \to 0$ within finite time.

Abstract:
Slice-stretching effects are discussed as they arise at the event horizon when geodesically slicing the extended Schwarzschild black-hole spacetime while using singularity excision. In particular, for Novikov and isotropic spatial coordinates the outward movement of the event horizon (``slice sucking'') and the unbounded growth there of the radial metric component (``slice wrapping'') are analyzed. For the overall slice stretching, very similar late time behavior is found when comparing with maximal slicing. Thus, the intuitive argument that attributes slice stretching to singularity avoidance is incorrect.

Abstract:
For a macroscopic, isolated quantum system in an unknown pure state, the expectation value of any given observable is shown to hardly deviate from the ensemble average with extremely high probability under generic equilibrium and nonequilibrium conditions. Special care is devoted to the uncontrollable microscopic details of the system state. For a subsystem weakly coupled to a large heat bath, the canonical ensemble is recovered under much more general and realistic assumptions than those implicit in the usual microcanonical description of the composite system at equilibrium.

Abstract:
For quantum systems that are weakly coupled to a much 'bigger' environment, thermalization of possibly far from equilibrium initial ensembles is demonstrated: for sufficiently large times, the ensemble is for all practical purposes indistinguishable from a canonical density operator under conditions that are satisfied under many, if not all, experimentally realistic conditions.

Abstract:
We demonstrate the equilibration of isolated macroscopic quantum systems, prepared in non-equilibrium mixed states with significant population of many energy levels, and observed by instruments with a reasonably bound working range compared to the resolution limit. Both properties are fulfilled under many, if not all, experimentally realistic conditions. At equilibrium, the predictions and limitations of Statistical Mechanics are recovered.

Abstract:
Stylized facts of empirical assets log-returns $Z$ include the existence of (semi) heavy tailed distributions $f_Z(z)$ and a non-linear spectrum of Hurst exponents $\tau(\beta)$. Empirical data considered are daily prices of 10 large indices from 01/01/1990 to 12/31/2004. We propose a stylized model of price dynamics which is driven by expectations. The model is a multiplicative random process with a stochastic, state-dependent growth rate which establishes a negative feedback component in the price dynamics. This 0-order model implies that the distribution of log-returns is Laplacian $f_Z(z) \sim \exp(-\frac{|z|}{\alpha})$, whose single parameter $\alpha$ can be regarded as a measure for the long-time averaged liquidity in the respective market. A comparison with the (more general) Weibull distribution shows that empirical daily log returns are close to being Laplacian distributed. The spectra of Hurst exponents of both, empirical data $\tau_{emp}$ and simulated data due to our model $\tau_{theor}$, are compared. Due to the finding of non-linear Hurst spectra, the Renyi entropy (RE) $R_\beta(f_Z)$is considered. An explicit functional form of the RE for an exponential distribution is derived. Theoretical REs of simulated asset return trails are in good agreement with the RE estimated from empirical returns.

Abstract:
Slice stretching effects such as slice sucking and slice wrapping arise when foliating the extended Schwarzschild spacetime with maximal slices. For arbitrary spatial coordinates these effects can be quantified in the context of boundary conditions where the lapse arises as a linear combination of odd and even lapse. Favorable boundary conditions are then derived which make the overall slice stretching occur late in numerical simulations. Allowing the lapse to become negative, this requirement leads to lapse functions which approach at late times the odd lapse corresponding to the static Schwarzschild metric. Demanding in addition that a numerically favorable lapse remains non-negative, as result the average of odd and even lapse is obtained. At late times the lapse with zero gradient at the puncture arising for the puncture evolution is precisely of this form. Finally, analytic arguments are given on how slice stretching effects can be avoided. Here the excision technique and the working mechanism of the shift function are studied in detail.