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On the basis of bivariate data, assumed to be observations of independent copies of a random vector (S,N), we consider testing the hypothesis that the distribution of (S,N) belongs to the parametric class of distributions that arise with the compound Poisson exponential model. Typically, this model is used in stochastic hydrology, with N as the number of raindays, and S as total rainfall amount during a certain time period, or in actuarial science, with N as the number of losses, and S as total loss expenditure during a certain time period. The compound Poisson exponential model is characterized in the way that a specific transform associated with the distribution of (S,N) satisfies a certain differential equation. Mimicking the function part of this equation by substituting the empirical counterparts of the transform we obtain an expression the weighted integral of the square of which is used as test statistic. We deal with two variants of the latter, one of which being invariant under scale transformations of the S-part by fixed positive constants. Critical values are obtained by using a parametric bootstrap procedure. The asymptotic behavior of the tests is discussed. A simulation study demonstrates the performance of the tests in the finite sample case. The procedure is applied to rainfall data and to an actuarial dataset. A multivariate extension is also discussed.
A generalized shear-lag theory for fibres with variable radius is developed to analyse elastic fibre/matrix stress transfer. The theory accounts for the reinforcement of biological composites, such as soft tissue and bone tissue, as well as for the reinforcement of technical composite materials, such as fibre-reinforced polymers (FRP). The original shear-lag theory proposed by Cox in 1952 is generalized for fibres with variable radius and with symmetric and asymmetric ends. Analytical solutions are derived for the distribution of axial and interfacial shear stress in cylindrical and elliptical fibres, as well as conical and paraboloidal fibres with asymmetric ends. Additionally, the distribution of axial and interfacial shear stress for conical and paraboloidal fibres with symmetric ends are numerically predicted. The results are compared with solutions from axisymmetric finite element models. A parameter study is performed, to investigate the suitability of alternative fibre geometries for use in FRP.
A Formulation of Quantum Stochastic Processes and Some of its Properties. Hellwig, K.-E.; Stulpe, W.
(1983)
A nonparametric goodness-of-fit test for random variables with values in a separable Hilbert space is investigated. To verify the null hypothesis that the data come from a specific distribution, an integral type test based on a Cramér-von-Mises statistic is suggested. The convergence in distribution of the test statistic under the null hypothesis is proved and the test's consistency is concluded. Moreover, properties under local alternatives are discussed. Applications are given for data of huge but finite dimension and for functional data in infinite dimensional spaces. A general approach enables the treatment of incomplete data. In simulation studies the test competes with alternative proposals.
The readout of gamma detectors is considerably simplified when the event intensity is encoded as a pulse width (Pulse Width Modulation, PWM). Time-to-Digital-Converters (TDC) replace the conventional ADCs and multiple TDCs can be realized easily in one PLD chip (Programmable Logic Device). The output of a PWM stage is only one digital signal per channel which is well suited for transport so that further processing can be performed apart from the detector. This is particularly interesting for large systems with high channel density (e.g. high resolution scanners). In this work we present a circuit with a linear transfer function that requires a minimum of components by performing the PWM already in the preamp stage. This allows a very compact and also cost-efficient implementation of the front-end electronics.
A Classical Reformulation of Finite-Dimensional Quantum Mechanics. Hellwig, K.-E.; Stulpe, W.
(1993)
Macroporous silicon has been etched from n-type Si, using a vertical etching cell where no rear side contact on the silicon wafer is necessary. The resulting macropores have been characterised by means of Scanning Electron Microscopy (SEM). After etching, SiO₂ was thermally grown on the top of the porous silicon as an insulating layer and Si₃N₄ was deposited by means of Low Pressure Chemical Vapour Deposition (LPCVD) as transducer material to fabricate a capacitive pH sensor. In order to prepare porous biosensors, the enzyme penicillinase has been additionally immobilised inside the porous structure. Electrochemical measurements of the pH sensor and the biosensor with an Electrolyte/Insulator/Semiconductor (EIS) structure have been performed in the Capacitance/Voltage (C/V) and Constant capacitance (ConCap) mode.