Ultimate tensile behavior of linear polyethylene solids

The influence of the elongation rate and temperature on the ultimate tensile properties of melt‐crystallized linear polyethylene solids was investigated, with a double‐edge‐notched specimen to avoid necking, in which uniform deformation could be assumed throughout the experiment. The data on ultimate properties such as the tensile strength and elongation at break for different temperatures could be superimposed, by shifts along the elongation rate axis, to give a master curve as a function of the time to rupture. The shift factors obtained from the superpositioning of both the tensile strength and ultimate strain took the form of the Williams–Landel–Ferry equation. As a result, the ultimate data provided a failure envelope curve that made it possible to predict rupture times when the tensile tests were conducted under any experimental conditions. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 2018–2026, 2002     

CFD modelling of the flow and reactions in the Olympic Dam flash furnace smelter reaction shaft

The performance of flash furnace burners can be evaluated quickly and efficiently using CFD modelling. Gas flows are modelled using the conventional Eulerian approach, while Lagrangian particle tracking is used to model the flow of solid feed through the burner and into the reaction shaft. A composite particle model has been developed that considers the solid feed to be made up of single particles containing appropriate quantities of concentrate, flux and dust. Solid fuels (such as coal) can also be included in the composite particle. Reactions between the solids and gas are then modelled using standard heat and mass transfer relationships. Results from the modelling process are shown for BHP-Billiton’s Olympic Dam copper flash smelter with the burner that was used from 1998–2003. Flow patterns, temperature and gas composition distributions, particle dispersion and residence time, and overall extent of sulphur removal are predicted and used to evaluate furnace performance. However, results are sensitive to the assumed size of the composite particles, and plant measurements are required to determine the appropriate composite particle size to predict quantitative data.     

Viscoelastic properties of bis(phenyl)fluorene‐based cardo polymers with different chemical structure

Viscoelastic properties of urethane and ester conjugation cardo polymers that contain fluorene group, 9,9‐bis(4‐(2‐hydroxyethoxy)phenyl)fluorene (BPEF), were investigated. As for the urethane‐type cardo polymers containing BPEF in the main chain, it had a high glass‐transition temperature (T_g), which was observed as the α dispersion on viscoelastic measurement, and its temperature depended on the chemical structure of the spacing unit, such as toluene diisocyanate (TDI), 4,4′‐methylene diphenyl diisocyanate (MDI), methylene dicycloexyl diisocyanate (CMDI), and hexamethylene diisocyanate (HDI). Moreover, the T_g of urethane‐type cardo copolymers with various cardo contents increased with an increase of cardo content. Owing to the increase of T_g of cardo polymers, another molecular motion can be measured at the temperature between the α and β dispersion that was assigned to the molecular motion of urethane conjugation unit around 200 K, and it was referred to as the α_sub dispersion. The peak temperature of the α_sub dispersion was influenced by the chemical structure of the spacing unit, but it did not change for the cardo polymer containing the same spacing unit. Consequently, it was deduced that the α_sub dispersion was originated in the subsegmental molecular motions of the cardo polymers. Ester‐type cardo polymer had higher T_g in comparison with noncardo polymer that consisted of dimethyl groups (BPEP) instead of BPEF as well. The α_sub dispersion was also measured at the temperature between the α and β dispersion, which was assigned to the molecular motion of ester conjugation unit, around 220 K. For ester cardo polymer, the γ dispersion was measured in a low‐temperature region around 140 K, and it was due to a small unit motion in the ester‐type cardo polymers, such as ethoxyl unit, ? C₂H₄O? . Moreover, the intensity of the γ dispersion of noncardo polymer was higher than that of cardo polymer, which means the molecular motion was much restricted by the cardo structure of BPEF. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2259–2268, 2005     

Templated synthesis of silver nanoparticles in amphiphilic poly(vinylidene fluoride‐co‐chlorotrifluoroethylene) comb copolymer

In this study, poly(vinylidene fluoride‐co‐chlorotrifluoroethylene)‐graft‐poly(oxyethylene methacrylate), P(VDF‐co‐CTFE)‐g‐POEM, an amphiphilic comb copolymer with hydrophobic P(VDF‐co‐CTFE) backbone and hydrophilic POEM side chains at 73:27 wt % was synthesized. The POEM side chains were grafted from the P(VDF‐co‐CTFE) mainchain backbone via atom transfer radical polymerization (ATRP) using direct initiation of the chlorine atoms in CTFE units. Synthesis of microphase‐separated P(VDF‐co‐CTFE)‐g‐POEM comb copolymer was successful, as confirmed by nuclear magnetic resonance (¹H NMR), FTIR spectroscopy, and transmission electron microscopy (TEM). Nanocomposite films were prepared using the comb copolymer as a template film and the in situ reduction of AgCF₃SO₃ precursor to silver nanoparticles under UV irradiation. Silver nanoparticles with 4–8 nm in average size were in situ created in the solid state template film, as revealed by TEM, UV–visible spectroscopy, and wide angle X‐ray scattering (WAXS). Differential scanning calorimetry (DSC) and thermogravimetric analysis (TGA) presented the selective incorporation and the in situ growth of silver nanoparticles within the hydrophilic POEM domains of microphase‐separated comb copolymer film. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 702–709, 2008     

Analytical application of porphyrins-I Spectrophotometric determination of ultramicro amounts of copper with alpha,beta,gamma,delta-tetra-(3-N-methylpyridyl)porphine

A new water-soluble porphyrin, alpha,beta,gamma,delta-tetra(3-N-methylpyridyl)porphine [T(3-MPy)P], has been synthesized, and its reaction with copper(II) studied spectrophotometrically. Sensitive methods for the determination of copper at ppM level have been established. The spectrophotometric sensitivity and relative standard deviation of the recommended procedure for copper are 0.18 ng/cm(2) (for A = 0.001) and 1.0%, respectively. The interference of 19 ions and 20 salts has been examined, and found to be minimal. The methods established could be applied to the determination of copper in water samples with satisfactory results.     

On the matrix ring over a finite field

Let F_n be the ring of n × n matrices over the finite field F; let o(F_n) be the number of elements in F_n, and s(F_n) be the number of singular matrices in F_n. We prove that $\text{o(F}{}_{\mathrm{n}}\text{)<s(F}{}_{\mathrm{n}}\text{)}{}^{\mathrm{<mtext>1+1</mtext><mtext>n(n-1)</mtext>}}$ if n ? 2, and if n = 2 and o(F) ? 3, then .     

On Poljak's improved subgradient method

Poljak has suggested an improved subgradient method and provided a lower bound on the improvement of the Euclidean distance to an optimal solution. In this paper, we provide a stronger lower bound and show that the direction of movement in this method forms a more acute angle with the direction toward the set of optimal solutions than that in the subgradient method.Most of this research has been performed while the first author was visiting the Decision and Information Systems Department, College of Business, Arizona State University, Tempe, Arizona.     

Products of graceful trees

We give some conditions on H and $\text{G}$ for the rooted product H($\text{G}$) to be graceful. These conditions extend and unify previous results.     

A smoothing spline based test of model adequacy in polynomial regression

For the regression model % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-qqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xHapdbiqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEamaaBa% aajeaWbaGaamyAaaWcbeaakiabeccaGiabg2da9iabeccaGiaabAga% caGGOaGaamiDamaaBaaajeaWbaGaamyAaaWcbeaakiaacMcacaqGGa% Gaey4kaSIaaeiiamaavababeqcbaCaaiaadMgaaSqab0qaaiabew7a% LbaakiaabccacaGGOaGaeqyTduMaai4jaiaadohacaqGGaGaamyAai% aadMgacaWGKbGaaeiiaiaad6eacaGGOaGaam4taiaacYcacaqGGaGa% eq4Wdm3aaWbaaSqabKqaGgaacaaIYaaaaOGaaiykaiaacMcaaaa!57B9!\[y_i = {\rm{f}}(t_i ){\rm{ }} + {\rm{ }}\mathop \varepsilon \nolimits_i {\rm{ }}(\varepsilon 's{\rm{ }}iid{\rm{ }}N(O,{\rm{ }}\sigma ^2 ))\], it is proposed to test the null hypothesis that f is a polynomial of degree less than some given value m. The alternative is that f is such a polynomial plus a scale factor b ^1/2 times an (m–1)-fold integrated Wiener process. For this problem, it is shown that no uniformly (in b) most powerful test exists, but a locally (at b=0) most powerful test does exist. Derivation and calculation of the test statistic is based on smoothing spline theory. Some approximations of the null distribution of the test statistic for the locally most powerful test are described. An example using real data is shown along with a computing algorithm.This author's research was supported by the National Science Foundation under grants numbered DMS-8202560 and DMS-8603083.