Evaluating Nearly Singular Multinormal Expectations with Application to Wave Distributions

The numerical computation of expectations for (nearly) singular multivariate normal distribution is a difficult problem, which frequently occurs in widely varying statistical contexts. In this article we discuss several strategies to improve the algorithm proposed by Genz and Kwong (2000) when either a moderate accuracy is requested, the correlation structure is strong, and, most importantly, the dimension of the integral is large. Test results for typical problems show an average speedup of 10 using the modified algorithm, but even more is gained as the dimension of the problem increases. We apply the modified algorithm to compute long-run distributions of Gaussian wave characteristics, a difficult problem where previous algorithms fail to compute accurate values in reasonable time. AMS 2000 Subject Classification 65C60, 65D15, 68W25     

Analytical quality specification for measurements reported on an ordinal scale

A model for evaluation of analytical quality specifications for measurements performed on an ordinal scale is described. It is based on the assumption that the quantity, in principle, can be measured on a ratio (or difference) scale by other methods, but is performed by a cheap, simple and rapid method as 0 or 1 (minus or plus). It is not possible to estimate mean and standard deviations from an ordinal scale, so the measurements of 0 or 1 are characterized by the fraction of measured values of 1 for a certain concentration. For a series of increasing (known) concentrations of the quantity, the fractions of measured values of 1 are plotted on a probit scale. For a pregnancy test with measurements on an ordinal scale – measuring urine-human chorionic gonadotropin as minus or plus – allowable fractions of measured values of 1 are defined for the 'true' concentrations of 3 and 25 U/l based on clinical goals for early detection of pregnancy.     

Conservative solution of the Fokker–Planck equation for stochastic chemical reactions

In this paper we discuss multigrid methods for ill-conditioned symmetric positive definite block Toeplitz matrices. Our block Toeplitz systems are general in the sense that the individual blocks are not necessarily Toeplitz, but we restrict our attention to blocks of small size. We investigate how transfer operators for prolongation and restriction have to be chosen such that our multigrid algorithms converge quickly. We point out why these transfer operators can be understood as block matrices as well and how they relate to the zeroes of the generating matrix function. We explain how our new algorithms can also be combined efficiently with the use of a natural coarse grid operator. We clearly identify a class of ill-conditioned block Toeplitz matrices for which our algorithmic ideas are suitable. In the final section we present an outlook to well-conditioned block Toeplitz systems and to problems of vector Laplace type. In the latter case the small size blocks can be interpreted as degrees of freedom associated with a node. A large number of numerical experiments throughout the article confirms convincingly that our multigrid solvers lead to optimal order convergence. AMS subject classification (2000) 65N55, 65F10     

Localization of Na and K in rat cerebellum with imaging TOF-SIMS

High pressure-frozen (HPF), freeze-fractured and freeze-dried rat cerebellum was analyzed with imaging TOF-SIMS equipped with a Bi-cluster ion source. Data were collected separately as spectra of high mass resolution m/Δm > 8000 and images of high lateral resolution <700 nm. Images were made showing the localization of the peaks m/z = 22.99, and m/z = 39.1.Topographical effects were noted due to the freeze fracture method. This effect was compensated by normalizing images of specific secondary ions to the intensity of total secondary ions and by making PCA analysis of the image. The results showed that potassium ions were localized in blood vessels and cortex cells and sodium ions were localized in blood vessels and cerebellar interstitial tissue and in the nuclei of some cells. The sodium ion concentration was found to be higher in blood vessels than in the interstitium.     

On the Cegrell classes

The Cegrell classes with zero boundary data are defined by certain decreasing approximating sequences of functions with different properties depending on the class in question. It is different for Cegrell classes which are given by a continuous function f, these classes are defined by an inequality. It is proved in this article that it is possible to define the Cegrell classes which are given by f in a similar manner as those classes with zero boundary data. An existence result for the Dirichlet problem for certain singular measures is proved. The article ends with three applications. Results connected to convergence in capacity, subextension of plurisubharmonic functions and integrability are proved.     

Adsorption and film growth of N-methylamino substituted triazoles on copper surfaces in hydrocarbon media

The adsorption of benzotriazole (BTA), tolyltriazole (TTA) and two different N-methylaminosubstituted triazoles on copper surfaces in hydrocarbon media has been examined by in situ ellipsometry and time-of-flight secondary ion mass spectroscopy (ToF-SIMS). All four triazoles were found to form films and from the ellipsometric study were the film thicknesses estimated to be in the range of 0.5-2 nm after 1000 min exposure time. The layers formed from BTA and TTA were thicker (up to 2 nm) than the layers from N-aminomethyl substituted triazoles (roughly 0.5 nm). Desorption was studied qualitatively and 20% or less of the adsorbed material were found to desorb. The ToF-SIMS study showed that while BTA and TTA adsorbed intact did the N-aminomethyl substituted triazoles appear to loose their aminomethyl tails on binding since only signals corresponding to triazole moieties of the compounds were detected.     

Progress of laser spectroscopy at the IGISOL

Magnetic interactions and microstructure in the amorphous and nanocrystalline Fe₉₀Zr₇Cu₁B₂ alloy were investigated. These studies were carried out in the temperature range from 140 up to 380 K, using a Mössbauer spectrometer and completely automated set-up for measurements of magnetic properties. It has been found that the Curie temperature and quadrupole splitting decrease after annealing the sample at 573 K for 1 h (invar effect). However, this behaviour is not observed in nanocrystalline samples. In the early stages of crystallization (the volume fraction of the crystalline phase equal to about 0.06) α-Fe grains above the Curie temperature of amorphous matrix may be treated as non-interacting particles. The particle size estimated by Mössbauer spectra and magnetization curve analysis is equal to about 4 nm.     

Consistency requirements for 1N expandable field theories

It is demonstrated that $\text{1}\text{N}$ expansion in a class of field theories with an internal O(N) symmetry leads to pathologies. Therefore, these models are either not internally consistent, or their perturbation expansions (ordinary as well as $\text{1}\text{N}$ are unreliable.