Quadratic decomposition of symmetric semi-classical polynomial sequences of even class: an example from the case s = 2

In the present work, we deal with the quadratic decomposition of symmetric semi-classical polynomial sequences of even class. An example from class 2 is settled. We give an integral representation of the considered symmetric form.     

Importance Sampling for p-value Computations in Multivariate Tests

Abstract

An importance sampling procedure is developed to approximate the distribution of an arbitrary function of the eigenvalues for a matrix beta random matrix or a Wishart random matrix. The procedure is easily implemented and provides confidence intervals for the p-values of many of the commonly used test statistics in multivariate analysis. An adaptive procedure allows for the control of either absolute error or relative error in this p-value estimation through the choice of importance sample size.     

Torsion balances with fibres of zero length

Torsion balances have good immunity to tilt and low rotational stiffness. However precise control of the position of the suspended torsion ‘bob’ is difficult in the presence of ground vibrations and tilt and this is a limiting factor in applications where Casimir forces or putative non-Newtonian short-range forces are being measured. We describe how the desirable characteristics of torsion balances can be reproduced in a rigid body that is suspended using applied forces rather than a torsion fibre. The suspension system can then provide a more precise control of the degrees of freedom of the suspended body. We apply these ideas to a superconducting levitated torsion balance, developed by the authors, and a generic electrostatic suspension. We present results of preliminary experiments that provide support for our analyses.     

关于全国大学生数学竞赛决赛试题的解析与思考

本文对二道全国大学生数学竞赛决赛试题(数学类)给予了诠释与解析.     

Computer Assisted Spectrophotometric Analysis of Three Component Mixtures (Caffeine Mixtures and Codeine Mixtures)

Abstract

Two mixtures (caffeine mixture (I) and codeine mixture (II)) of 3-components, containing acetaminophen and salicylamide as majors, have been assayed using different computer-assisted spectrophotometric methods. These methods are the Unique Absorbance Method (UAM), the Unique Orthogonal Function Method (UOFM), and Unique Fourier Function Method (UFFM), and also their correspondences under the least squares approach. The parameters have been optimized for the accurate determination of the minor component caffeine in mixture (I). In mixture (II), however. codeine has been extracted - in two steps-prior to the correction of interferences from the major components acetaminophen and salicylamide.     

A new class of multi-wavelet bases: V-system

The V-system is a complete orthogonal system of functions defined on the interval [0, 1], generated by finite Legendre polynomials and the dilation and translation of a function generator, which consists of a finite number of continuous and discontinuous functions. The V-system has interesting properties, such as orthogonality, symmetry, completeness and short compact support. It is shown in this paper that the V-system is essentially a special multi-wavelet basis. As a result, some basic properties of the V-system are established through the well-developed theory of multi-wavelets. From this point of view, more other V-systems are constructed.     

Properties of two amide‐based hydrophilic interaction liquid chromatography columns

Hydrophilic interaction liquid chromatography is a separation technique suitable for the separation of moderately and highly polar compounds. Various stationary phases (SPs) for hydrophilic interaction liquid chromatography are commercially available. While the SPs based on the same type of ligand are available from different providers, they can display a distinct retention characteristics and separation selectivity. The current work is focused on characterization and comparison of the separation systems of two amide‐based HPLC columns from two producers, i.e. XBridge Amide column and TSK gel Amide‐80 column. Several characterization procedures (tests) were used to investigate the differences between these columns. The chromatographic behavior of selected analytes indicates that multimodal interactions are responsible for retention and separation on these columns. Multiple testing approaches were used in order to reveal subtle differences between the SPs. Both amide‐based columns showed certain differences in retention, selectivity, and plate counts. Based on the tests used in this study, we conclude that the investigated columns provide a different degree of H‐bonding interactions.     

Monitoring abiotic degradation of branched polyethylenes formulated with pro-oxidants through different mechanical tests

The mechanical properties of two linear low density and low density polyethylenes containing a pro-oxidant additive were monitored during accelerated aging (60 °C in a convection oven) and weather exposure. Tearing tests (trouser) were performed for the first time in polyethylenes subjected to oxo-degradation revealing a transition from an extensible to a non-extensible material, at exposure times when standard tensile tests were not able to detect any changes in the materials. The essential work of fracture (EWF) technique was also applied and the results were in agreement with those of trouser tests. The specific essential work of fracture first increased with exposure time until the sample experienced a transition to a less ductile state where EWF was no longer applicable. EWF and trouser tear tests were more sensitive detecting the onset of degradation probably because they employ notched specimens that impose more critical stress concentration conditions than conventional tensile tests.     

Effect of Process Variable on the Gelation Time of Sulfonated Polyacrylamide Nanocomposite Hydrogel

Among the methods available to reduce water production during oil recovery, injecting a gelling system composed of a polymer and a crosslinker has been widely used. In this study, a Plackett-Burman design was used for screening a large number of factors such as concentrations of polymer, crosslinker, pH, temperature, and presence or absence of NaCl, CaCl₂, MgCl₂, KCl, thiourea, sodium lactate, and nanoclay on the gelation time of sulfonated polyacrylamide nanocomposite hydrogels by rheological tests. Among these factors, temperature, pH, and CaCl₂ concentration were found to have the greatest effect on the gelation time. The effects of these three factors and their interactions on the gelation time were then determined by using central composite design of response surface method. As a result, the interactions of CaCl₂ concentration with temperature and pH were considerably more than the interactions of pH and temperature on the gelation time. At low pH (3 < pH < 7), the gelation time decreased by decrease of pH while at CaCl₂ concentration of 3750–11250 ppm and at 7 < pH < 11, the gelation time increased with the increase of pH. It was found that temperature was the most effective parameter to control the gelation time.