Measurable events indexed by products of trees

A tree T is said to be homogeneous if it is uniquely rooted and there exists an integer b ≥ 2, called the branching number of T, such that every t ∈ T has exactly b immediate successors. A vector homogeneous tree T is a finite sequence (T ₁,...,T _d ) of homogeneous trees and its level product ?T is the subset of the Cartesian product T ₁×...×T _d consisting of all finite sequences (t ₁,...,t _d ) of nodes having common length. We study the behavior of measurable events in probability spaces indexed by the level product ?T of a vector homogeneous tree T. We show that, by refining the index set to the level product ?S of a vector strong subtree S of T, such families of events become highly correlated. An analogue of Lebesgue’s density Theorem is also established which can be considered as the “probabilistic” version of the density Halpern-Läuchli Theorem.     

Development of an egg-white bioassay for monitoring biotin levels in urine and serum.

This article reports on the development of a simple and cost-effective bioassay for the detection of biotin in urine and serum, based on the very selective binding of avidin and biotin. Avidin was allowed to react without isolating it from egg white. Egg white was treated with the dye HABA, which binds to avidin. Upon subsequent treatment with biotin, HABA is released due to the high affinity of biotin to avidin. The amount of HABA released is proportional to the amount of biotin used.     

A finite difference scheme for computing inertial manifolds

A fully discrete method is presented for computing inertial manifolds of dissipative partial differential equations. In particular, only an approximate spectral decomposition of the dominant differential operator needs to be known. The first few of the smallest eigenvalues and eigenvectors of the discretized operator are approximated using the Lanczos algorithm. Numerical experiments are performed for an equation in one space dimension by discretizing the space variable on a sufficiently fine grid. The basic ideas and techniques are exemplified for selected bifurcation diagrams of an integrated form of the Kuramoto-Sivashinsky equation.This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) grant OGP0036901, NSERC and Schweizerischer Nationalfonds zur Förderung der Wissenschaften BEF 0150297, and Forschungsinstitut für Mathematik, ETH Zürich.     

New Calix[4]arene‐Cored Peripherally Functionalized Dendrimers: Synthesis and Conformational Characteristics

New calixarene‐based dendrimers, containing calix[4]arene as the core and different generations of Fréchet‐type poly(benzyl ether) dendrons as building blocks, which possess either Br‐atoms or COO^tBu groups at their surface were synthesized and presented herein for the first time. The new calix[4]arene‐cored dendritic macromolecules were fully characterized and found to prefer strictly the cone conformation.     

Investigation of confined ionic liquid in nanostructured materials by a combination of SANS, contrast-matching SANS, and nitrogen adsorption

Small-angle neutron scattering (SANS), contrast-matching SANS, and nitrogen adsorption have been utilized to investigate the confined ionic liquid (IL) [bmim][PF(6)] phase in ordered mesoporous silica MCM-41 and SBA-15. The results suggest that the pores of SBA-15 are completely filled with IL whereas a small fraction of the pore volume, the pore "core", of MCM-41 is empty. The contrast-matching SANS measurements confirm the enhanced solubility of water in IL. In addition, they provide strong evidence that water does not enter the empty pore core of MCM-41, possibly because of the preferred orientation of the IL molecules in the adsorbed layer.     

Disposable pipette extraction for gas chromatographic determination of codeine, morphine, and 6-monoacetylmorphine in vitreous humor

The availability of a sensitive and rapid analytical method for the determination of opiates, and other substances of forensic interest, in a variety of biological specimens is of utmost importance to forensic laboratories. Solid-phase extraction is very popular in the pre-treatment of forensic samples. Nevertheless, a new approach, disposable pipette extraction (DPX), is gaining increasing interest in sample preparation. DPX has already been applied to the analysis of drugs of abuse in common biological matrices, such as urine and blood, but has not yet been evaluated on alternative biological samples, such as vitreous humor. The objective of this study was to evaluate the applicability of DPX on the analysis of opiates in vitreous humor. The currently developed method is fast, reliable, and easy to perform. The sensitivity, precision, and accuracy are satisfactory. Recoveries obtained are within the range of 72-91%, whereas the sample volume of vitreous humor required is only 100 μL.