Estimates of the indeterminacy set for elliptic boundary value problems with uncertain data

Estimates are derived for the so-called indeterminacy set formed by solutions to an elliptic type boundary value problem with not fully determined coefficients. A two-sided estimate for the diameter of the indeterminacy set is obtained in the energy norm. It is shown that this estimate depends on parameters defining the variability range of the coefficients. The analysis is based on functional a posteriori estimates that provide guaranteed bounds of the difference between an approximate solution and any admissible function in the energy space. The estimates are obtained for the diffusion equation. However, the proposed tools can be used for other classes of partial differential equations if functional a posteriori estimates are established. Bibliography: 2 titles. __________ Translated from Problemy Matematicheskogo Analiza, No. 36, 2007, pp. 77–80.     

Die Nusseltsche Zahl für laminare Strömung im zylindrischen Rohr mit konstanter Wandtemperatur

Summary The Nusselt modulus for laminar flow through a pipe with constant temperature of the walls has been determined as a function of the Peclet modulus. This function is represented by a diagram.     

X-ray mapping of freeze-dried cryosections from biological cells

Elemental mapping of freeze-dried cryosections from biological cells was done using the energy window mode and the quantitative mode. Quantitative mapping requires long measuring times and high electron exposure resulting in inhomogeneous shrinkage and distortion of the cryosection. Collection of X-ray spectra for quantitative analysis of intracellular structures and compartments combined with energy window mapping was found to be sufficiently fast and reliable to reveal inhomogeneities of the element distribution in cells. However, this method is suitable only for mapping elements without overlapping peaks in the X-ray spectrum.     

Spatially resolved ultra-trace analysis of elements combining resonance ionization with a MALDI-TOF spectrometer

A combined setup for spatially resolved mass analysis of trace amounts of elements and macromolecules is presented. Using a MALDI-TOF mass spectrometer, a laser spectroscopic setup for resonant ionization of neutral atoms has been implemented. This allows for an efficient and selective detection of trace elements by means of resonance ionization mass spectrometry (RIMS). The instrumental scheme is described, and methodological developments are presented. In a first application pure, laser desorption/ionization with TOF-MS was used to measure mass distributions of cosmic nanodiamonds. For further applications regarding the spatially resolved ultra-trace analysis of elements in solid samples, an implanted target was used to characterize both laser desorption/ionization and laser desorption/resonance ionization for the detection of trace elements within. A perspective of the setup is given and future investigations are outlined.     

Femtodynamics reflected in nanoseconds: bimolecular free electron transfer in nonpolar media

The (free) electron transfer (FET) from electron donor molecules to parent solvent radical cations of alkanes and alkyl chlorides exhibits mechanistic peculiarities that are conditioned by the low polarity of these solvents. Because of the negligible solvation of ions in such systems and the almost complete lack of an activation barrier, the electron jump takes place at the very first encounter of the reactants and, as such, in extremely short times of 相似文献