A Structural Investigation of Some Terminally Cyano-Substituted Side Chain Liquid-Crystalline Polysiloxanes

Abstract

A series of terminally cyano substituted side chain polysiloxanes have been characterized using optical microscopy, D.S.C., and X-ray diffraction. Values for the lamellar spacings, d, of the interdigitated smectic A phases were obtained, and the variations in d with temperature and length of the flexible aliphatic spacer are discussed. The spacing for m = 4, 5, and 6 increased regularly with m whereas the short m = 3 spacer gave an anomalously high value.     

Preparation of a reference mussel tissue material for polycyclic aromatic hydrocarbons and trace metals determination

Due to high cost of certified reference materials (CRMs), reference materials (RMs) are preferred to check the method performance in environmental analysis. In this work, a laboratory reference material (LRM) was prepared and characterised to carry out the quality control in monitoring analysis of eight polycyclic aromatic hydrocarbons (PAHs) and nine trace metals in mussel tissue. Mussels were collected in a naturally polluted area. Before the reference material was bottled, the mussel tissue was stabilised by freeze-drying, ground and sieved. For the material characterisation, several statistical tests were applied to check the homogeneity of the analytes in the tissue, and a stability test was performed to study the effect of the storage temperature in the analyte concentration. Other characteristics such as specific density, moisture and lipid contents as well as particle size distribution of the material were determined. Although the LRM had a homogeneous distribution for all PAHs and almost all metals, the stability study showed different results at both storage temperatures studied. For both PAHs and trace metals, the material was suitable to assure the quality control of the analysis.     

On the equivalence of quadratic optimization problems commonly used in portfolio theory

In the paper, we consider three quadratic optimization problems which are frequently applied in portfolio theory, i.e., the Markowitz mean–variance problem as well as the problems based on the mean–variance utility function and the quadratic utility. Conditions are derived under which the solutions of these three optimization procedures coincide and are lying on the efficient frontier, the set of mean–variance optimal portfolios. It is shown that the solutions of the Markowitz optimization problem and the quadratic utility problem are not always mean–variance efficient.     

Setting targets for surrogate-based optimization

In the context of surrogate-based optimization (SBO), most designers have still very little guidance on when to stop and how to use infill measures with target requirements (e.g., one-stage approach for goal seeking and optimization); the reason: optimum estimates independent of the surrogate and optimization strategy are seldom available. Hence, optimization cycles are typically stopped when resources run out (e.g., number of objective function evaluations/time) or convergence is perceived, and targets are empirically set which may affect the effectiveness and efficiency of the SBO approach. This work presents an approach for estimating the minimum (target) of the objective function using concepts from extreme order statistics which relies only on the training data (sample) outputs. It is assumed that the sample inputs are randomly distributed so the outputs can be considered a random variable, whose density function is bounded (a, b), with the minimum (a) as its lower bound. Specifically, an estimate of the minimum (a) is obtained by: (i) computing the bounds (using training data and the moment matching method) of a selected set of analytical density functions (catalog), and (ii) identifying the density function in the catalog with the best match to the sample outputs distribution and corresponding minimum estimate (a). The proposed approach makes no assumption about the nature of the objective functions, and can be used with any surrogate, and optimization strategy even with high dimensional problems. The effectiveness of the proposed approach was evaluated using a compact catalog of Generalized Beta density functions and well-known analytical optimization test functions, i.e., F2, Hartmann 6D, and Griewangk 10D and in the optimization of a field scale alkali-surfactant-polymer enhanced oil recovery process. The results revealed that: (a) the density function (from a catalog) with the best match to a function outputs distribution, was the same for both large and reduced samples, (b) the true optimum value was always within a 95% confidence interval of the estimated minimum distribution, and (c) the estimated minimum represents a significant improvement over the present best solution and an excellent approximation of the true optimum value.     

Ion-beam irradiation of lanthanum compounds in the systems La2O3-Al2O3 and La2O3-TiO2

Thin crystals of La₂O₃, LaAlO₃, La_2/3TiO₃, La₂TiO₅, and La₂Ti₂O₇ have been irradiated in situ using 1 MeV Kr²⁺ ions at the Intermediate Voltage Electron Microscope-Tandem User Facility (IVEM-Tandem), Argonne National Laboratory (ANL). We observed that La₂O₃ remained crystalline to a fluence greater than 3.1×10¹⁶ ions cm⁻² at a temperature of 50 K. The four binary oxide compounds in the two systems were observed through the crystalline-amorphous transition as a function of ion fluence and temperature. Results from the ion irradiations give critical temperatures for amorphisation (T_c) of 647 K for LaAlO₃, 840 K for La₂Ti₂O₇, 865 K for La_2/3TiO₃, and 1027 K for La₂TiO₅. The T_c values observed in this study, together with previous data for Al₂O₃ and TiO₂, are discussed with reference to the melting points for the La₂O₃-Al₂O₃ and La₂O₃-TiO₂ systems and the different local environments within the four crystal structures. Results suggest that there is an observable inverse correlation between T_c and melting temperature (T_m) in the two systems. More complex relationships exist between T_c and crystal structure, with the stoichiometric perovskite LaAlO₃ being the most resistant to amorphisation.     

On-Line Multicomponent Determination of the Flux of Mixtures of Phenols Through a Liquid Membrane in Real Time

 The analysis of mixtures of four phenolic compounds in an on-line system using UV-visible measurements with a fibre optic probe is discussed in this work. The aim of this system is to provide accurate real time concentration profiles in order to monitor the transport of phenols across a solid supported liquid membrane in both the feed and stripping phases. Different calibration models are taking into account the pH of the solution, using experimental designs and the first derivative in combination with different multivariate approaches like multiple linear regression (MLR), inverted least squares (ILS) and partial least squares regression (PLS). The comparison of all these combinations is carried out by means of the predictive residual error sum of squares (PRESS) evaluated from an independent set of spectra. From this comparison it is concluded that a PLS model using first derivative spectra offers the most accurate and robust prediction in the permeation experiments. Additionally, the stability of the model and the figures of merit obtained are also discussed. Received July 22, 1999. Revision October 23, 2000.     

Sampling in a weighted Sobolev space

We show that functions f in some weighted Sobolev space are completely determined by time-frequency samples ${\{f(t_n)\}}_{n\in \mathbb{Z}}\cup {\{\stackrel{?}{f}({\lambda }_k)\}}_{k\in \mathbb{Z}}$ along appropriate slowly increasing sequences ${\{t_n\}}_{n\in \mathbb{Z}}$ and ${\{{\lambda }_n\}}_{n\in \mathbb{Z}}$ tending to ±∞ as $n\to \pm \infty$.     

Pointwise Estimates and Regularity in Geometric Optics and Other Generated Jacobian Equations

The study of reflector surfaces in geometric optics necessitates the analysis of certain nonlinear equations of Monge‐Ampère type known as generated Jacobian equations. This class of equations, whose general existence theory has been recently developed by Trudinger, goes beyond the framework of optimal transport. We obtain pointwise estimates for weak solutions of such equations under minimal structural and regularity assumptions, covering situations analogous to those of costs satisfying the A3‐weak condition introduced by Ma, Trudinger, and Wang in optimal transport. These estimates are used to develop a C^1,α regularity theory for weak solutions of Aleksandrov type. The results are new even for all known near‐field reflector/refractor models, including the point source and parallel beam reflectors, and are applicable to problems in other areas of geometry, such as the generalized Minkowski problem.© 2017 Wiley Periodicals, Inc.