On the optimal strategy of stochastic-based reliability assessment of railway bridges for high-speed trains

Meccanica - The scope of this paper is to evaluate the performance and computational efficiency of various stochastic simulation methods for a stochastic based reliability assessment of railway...     

Positivity and positive definiteness in generalized function algebras

The definitions of positivity and positive definiteness are extended to generalized function algebras in coherence with the corresponding notions for distributions. Versions of Bochner's theorem for a positive definite Colombeau generalized function are given.     

Symmetrisers and generalised solutions for strictly hyperbolic systems with singular coefficients

This paper is devoted to strictly hyperbolic systems and equations with non‐smooth coefficients. Below a certain level of smoothness, distributional solutions may fail to exist. We construct generalised solutions in the Colombeau algebra of generalised functions. Extending earlier results on symmetric hyperbolic systems, we introduce generalised strict hyperbolicity, construct symmetrisers, prove an appropriate Gårding inequality and establish existence, uniqueness and regularity of generalised solutions. Under additional regularity assumptions on the coefficients, when a classical solution of the Cauchy problem (or of a transmission problem in the piecewise regular case) exists, the generalised solution is shown to be associated with the classical solution (or the piecewise classical solution satisfying the appropriate transmission conditions).     

Global Representatives of Colombeau Holomorphic Generalized Functions

It is proved that a holomorphic generalized function in the sense of Colombeau has a representative consisting of a net of holomorphic functions. More generally, the existence of global representatives of Colombeau solutions to elliptic partial differential equations is proved. Further, it is shown that a generalized holomorphic function on Ω, which is equal to zero in an open set L ì WL\subset{\rm{\Omega}} , is equal to zero.     

Generalized Flows and Singular ODEs on Differentiable Manifolds

Based on the concept of manifold-valued generalized functions, we initiate a study of nonlinear ordinary differential equations with singular (in particular: distributional) right-hand sides in a global setting. After establishing several existence and uniqueness results for solutions of such equations and flows of singular vector fields, we compare the solution concept employed here with the purely distributional setting. Finally, we derive criteria securing that a sequence of smooth flows corresponding to the regularization of a given singular vector field converges to a measurable limiting flow.     

Development and validation of a liquid chromatography–tandem mass spectrometry method for the simultaneous quantification of tamoxifen, anastrozole, and letrozole in human plasma and its application to a clinical study

There is substantial evidence that circulating estrogens promote the proliferation of breast cancer. Consequently, adjuvant hormonal treatment strategies targeting estrogen action have been established. Such hormonal therapies include selective estrogen receptor modulators, such as tamoxifen, which interfere at the estrogen receptors directly, or non-steroidal aromatase inhibitors, such as anastrozole and letrozole, which inhibit estrogen synthesis through blocking the aromatase, a key enzyme of estrogen production. Despite considerable therapeutic success, in several cases, the use of these drugs is limited by side effects that have been described to significantly impair the adherence of patients to endocrine treatment. However, objective data concerning patient adherence and its clinical relevance are limited. One promising approach to check patient-reported adherence is drug monitoring in human plasma. Therefore, a liquid chromatography–tandem mass spectrometry method to determine the plasma concentrations of tamoxifen, anastrozole, and letrozole has been developed and fully validated according to guidelines for clinical and forensic toxicology. The validation criteria evaluated were selectivity, linearity, accuracy and precision, limit of quantification, recovery and matrix effects, sample stability, and carryover. The six-point calibration curves showed linearity over the range of concentrations from 25 to 500 ng/ml for tamoxifen, 5 to 200 ng/ml for anastrozole, and 10 to 300 ng/ml for letrozole. The intra- and inter-day precision and accuracies were always better than 15%. The validated procedure was successfully applied to a clinical study (Patient-Reported Outcomes in Breast Cancer Patients undergoing Endocrine Therapy, PRO-BETh). A major aim of PRO-BETh study is the comprehensive evaluation of adherence to treatment in pre- and post-menopausal women with breast cancer. Plasma samples of 310 breast cancer patients undergoing anti-estrogen therapy were analyzed. Eight samples did not contain a quantifiable amount of drug, strongly indicating non-adherence of the corresponding patients to adjuvant breast cancer treatment. Furthermore, plasma concentrations at the lower end of the observed plasma level distribution might represent a hint but not a confirmation for non-adherence in terms of non-daily and irregular intake of the prescribed drug.     

Set-valued processes induced by parameterised stochastic differential equations with an application to Tuned Mass Dampers

In this paper ordinary stochastic differential equations whose coefficients depend on uncertain parameters are considered. An approach is presented how to combine both types of uncertainty (stochastic excitation and parameter uncertainty) leading to set-valued stochastic processes. The latter serve as a robust representation of solutions of the underlying stochastic differential equations. The mathematical concept is applied to a problem from earthquake engineering, where it is shown how the efficiency of Tuned Mass Dampers can be realistically assessed in the presence of uncertainty. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Microlocal hypoellipticity of linear partial differential operators with generalized functions as coefficients

We investigate microlocal properties of partial differential operators with generalized functions as coefficients. The main result is an extension of a corresponding (microlocalized) distribution theoretic result on operators with smooth hypoelliptic symbols. Methodological novelties and technical refinements appear embedded into classical strategies of proof in order to cope with most delicate interferences by non-smooth lower order terms. We include simplified conditions which are applicable in special cases of interest.