A numerical method for solving singular boundary value problems

Summary A numerical method is treated for solving singular boundary value problems with solutions that can be represented as series expansions on a subinterval near the singularity. A regular boundary value problem is derived on the remaining interval, for which a difference method is used. Convergence theorems are given for general schemes and for schemes of positive type for second order equations.     

High-speed synthesis of potent C2-symmetric HIV-1 protease inhibitors by in-situ aminocarbonylations

Two novel series of C2-symmetric HIV-1 protease inhibitors were synthesized by microwave-promoted, palladium-catalyzed aminocarbonylations of the o-iodo- and m-bromobenzyloxy P1/P1' substituted core structures. Molybdenum hexacarbonyl was used as a convenient solid source of carbon monoxide in these transformations. After the initial high-speed library generation, biological testing identified highly active HIV-1 protease inhibitors. Selected ortho- and meta-decorated inhibitors were subsequently resynthesized on a larger scale and retested for their affinity toward HIV-1 protease, showing micromolar to low nanomolar inhibition. The discovery of highly active inhibitors containing large phenyl amide ortho substituents in the P1/P1' positions indicates that larger groups than previously believed are tolerated in this part of the S1/S1' pocket.     

Semi-continuous emulsion polymerization of styrene in the presence of poly(methyl methacrylate) seed particles. Polymerization conditions giving core-shell particles

This work reports the morphology of two-phase latex particles prepared by semi-continuous seed emulsion polymerization of styrene in the presence of polar poly(methyl methacrylate), PMMA, seed particles, using different conditions of non-polar styrene feed rate, rate of initiation, seed particle concentration and temperature of polymerization.The expected latex particle morphology at thermodynamic equilibrium is an inverted core-shell structure where the non-polar polystyrene would form the core. However, depending on the set of process conditions used the morphology of the resulting two-phase particles varied from that of a pure core-shell structure, over intermediate structures in which a shell of PS surrounded a PMMA core containing an increasing number of PS phase domains, to a structure in which the entire PS phase was present as discrete PS phase domain, more or less evenly distributed in a matrix of PMMA.By the use of a caloirimetric reactor system the monomer concentration in the particles during the different polymerization experiments could be calculated by comparing the integral of the polymerization rate curve with the integral of the monomer feed rate. A comparison between particle morphology and the calculated concentration of plasticizing monomer in the polymerizing particles strongly suggested that the diffusivity of the entering oligo radicals determined by the difference between polymerization temperature and the glass transition temperature of the monomer-swollen core polymer is a key factor determining the morphology of two-phase particles prepared by semi-continuous seed emulsion polymerization.Two-phase particles with a true core-shell structure were obtained in experiments where the estimated glass transition temperature of the PMMA phase was only a few degrees below the polymerization temperature. The results show that such particles can be obtained under conditions of high as well as low styrene feed rates, provided that the rate of initiation is properly adjusted.     

Hydrogen exchange rates in proteins from water (1)H transverse magnetic relaxation

Access to the fast exchange kinetics of labile protein hydrogens in solution is provided by exchange broadening of the water 1H NMR line. We analyzed the chemical shift modulation contribution of labile hydrogens in bovine pancreatic trypsin inhibitor (BPTI) to the transverse 1H spin relaxation rate, R2, of the bulk solvent. Both the experimental pH dependence and the CPMG dispersion of R2 could be quantitatively accounted for on the basis of known chemical shifts, exchange rates, and ionization constants for BPTI. This analysis provided, for the first time, the hydrogen exchange rate constants for Lys and Arg side chains in a protein and pointed to an internal catalysis of the N-terminal amino protons in BPTI by a salt bridge. The method can be used for mapping the hydrogen exchange rates in protein solutions and biomaterials, which may be important for the control of relaxation-weighted contrast in biological MRI.     

The influence of different parameters on the mercerisation of cellulose for viscose production

A quantitative analysis of degree of transformation from a softwood sulphite dissolving pulp to alkalised material and the yield of this transformation as a function of the simultaneous variation of the NaOH concentration, denoted [NaOH], reaction time and temperature was performed. Samples were analysed with Raman spectroscopy in combination with multivariate data analysis and these results were confirmed by X-ray diffraction. Gravimetry was used to measure the yield. The resulting data were related to the processing conditions in a Partial Least Square regression model, which made it possible to explore the relevance of the three studied variables on the responses. The detailed predictions for the interactive effects of the measured parameters made it possible to determine optimal conditions for both yield and degree of transformation in viscose manufacturing. The yield was positively correlated to the temperature from room temperature up to 45 °C, after which the relation was negative. Temperature was found to be important for the degree of transformation and yield. The time to reach a certain degree of transformation (i.e. mercerisation) depended on both temperature and [NaOH]. At low temperatures and high [NaOH], mercerisation was instantaneous. It was concluded that the size of fibre particles (mesh range 0.25–1 mm) had no influence on degree of transformation in viscose processing conditions, apparently due to the quick reaction with the excess of NaOH.     

Treatment of uncorrected measurement bias in uncertainty estimation for chemical measurements

Consistent treatment of measurement bias, including the question of whether or not to correct for bias, is essential for the comparability of measurement results. The case for correcting for bias is discussed, and it is shown that instances in which bias is known or suspected, but in which a specific correction cannot be justified, are comparatively common. The ISO Guide to the Expression of Uncertainty in Measurement does not provide well for this situation. It is concluded that there is a need for guidance on handling cases of uncorrected bias. Several different published approaches to the treatment of uncorrected bias and its uncertainty are critically reviewed with regard to coverage probability and simplicity of execution. On the basis of current studies, and taking into account testing laboratory needs for a simple and consistent approach with a symmetric uncertainty interval, we conclude that for most cases with large degrees of freedom, linear addition of a bias term adjusted for exact coverage ("U(e)") as described by Synek is to be preferred. This approach does, however, become more complex if degrees of freedom are low. For modest bias and low degrees of freedom, summation of bias, bias uncertainty and observed value uncertainty in quadrature ("RSSu") provides a similar interval and is simpler to adapt to reduced degrees of freedom, at the cost of a more restricted range of application if accurate coverage is desired.     

A new series of siloxane liquid crystalline dimers exhibiting the antiferroelectric phase

In this paper, we report the study of a new series of symmetric chiral liquid crystalline siloxane dimers, their related monomers, and two of those monomers with heptamethyltrisiloxane attached. All the dimers coupled with a trisiloxane show the SmC_A phase, which in several cases has a large tilt angle greater than 40° over a wide temperature range, as well as high spontaneous polarisation in the field‐induced ferroelectric state. Spacer lengths of 3–6 and 11 carbons between the siloxane central unit and the mesogenic cores were used. Monomers with 3–6 carbons in the spacer showed only orthogonal phases while the monomer with an 11‐carbon spacer, as well as the monomers with siloxane attached, have a high tilt angle ferroelectric phase. The materials were characterized by means of DSC, NMR, X‐ray diffraction, electro‐optical methods (tilt angle and texture characterization) and polarization measurements.     

Spin relaxation in cubic liquid crystals. The role of symmetry

Abstract

Cubic liquid-crystalline phases are usually regarded as isotropic systems. This view is justified for physical properties that transform as second rank tensors. However, the time correlation functions describing spin relaxation in cubic phases include components that transform as fourth rank tensors, which distinguish between cubic and spherical symmetry. In this work we explore the consequences of this fact for spin relaxation behaviour in cubic phases using group theoretical methods. We identify the two irreducible crystal frame time correlation functions of a cubic phase, derive the orientation dependence of the laboratory frame time correlation functions for single crystal samples, and discuss the relation of the cubic (fourth rank) order parameter to the microstructure of the phase. Finally, as an illustration of the general results, we derive the time correlation functions for a specific model of a micellar cubic phase.     

Use of characteristic functions derived from proficiency testing data to evaluate measurement uncertainties

Interlaboratory comparisons show that reproducibility standard deviations are dependent on the concentration of the analyte. Many attempts have been made to model this. In this paper, ??characteristic?? functions are used for modelling the concentration dependence of the reproducibility standard deviations based on data from proficiency tests for water analysis. The characteristics of the resulting functions can be used for the estimation of measurement uncertainties at different concentration levels. These functions are especially useful to determine the concentration levels below which absolute uncertainties tend to be constant and above which the relative uncertainties are more constant. By comparing the characteristic functions of different analytical procedures for the determination of the same analyte, the performance of these procedures under routine application can be compared. Finally, these functions may be used to get an indication on the average quality of analytical result in a specific field to be used by regulators in order to formulate requirements in the legislation that are in accordance with current measurement quality.     

Stable reduction of curves and tame ramification

We study stable reduction of curves in the case where a tamely ramified base extension is sufficient. If X is a smooth curve defined over the fraction field of a strictly henselian discrete valuation ring, there is a criterion, due to Saito, that describes precisely, in terms of the geometry of the minimal model with strict normal crossings of X, when a tamely ramified extension suffices in order for X to obtain stable reduction. For such curves we construct an explicit extension that realizes the stable reduction, and we furthermore show that this extension is minimal. We also obtain a new proof of Saito’s criterion, avoiding the use of ℓ-adic cohomology and vanishing cycles.