Short-Chain Branching in Polyethylene and Poly(vinyl Chloride) Using Pyrolysis Hydrogenation Gas Chromatography and 13C Nuclear Magnetic Resonance Analysis

This study compares the use of pyrolysis hydrogenation gas chromatography (PHGC) and ¹³C Fourier transform nuclear magnetic resonance (FTNMR) methods for the analysis of reference polyethylene (PE) samples, ethylene-α-olefin copolymers, and specially prepared poly(vinyl chloride) (PVC) samples which were reduced to their PE skeletal structures. The nature and relative quantities of the short branches along the polymer chains were determined using both techniques. Improved high-resolution PHGC data, obtained with a fused silica capillary separation column, gave results which were in satisfactory agreement with the ¹³C FTNMR data. This approach confirms that detailed microstructural information can be obtained with these methods by using carefully controlled experimental conditions and appropriate reference systems.     

Tentative Identification of the Reactive Species in the Reaction of Cp2 TiCl2 with Salts of Diacids

The tentative identification of the reactive species in the condensation of Cp₂ TiCl₂ with salts of diacids to form titanium polysters is made. The reactive species are believed to be the same for both aqueous solution and interfacial systems, i.e., R -CO₂ ^? and Cp₂ Ti²⁺ with reaction occurring in the aqueous phase. The condensation of Cp₂ TiCl₂ with disodium terephthalate in interfacial systems occurs via a pseudo-first-order reaction:

Rate = K[Cp₂ TiCl₂] The rate-determining step (s) is believed to be diffusion of CP₂ TiCl₂ into the aqueous layer and/or hydrolysis of Cp₂ TiCl₂     

Analytical representations of the Mössbauer recoilless fraction,Debye-Waller factors,lattice energies,and heat capacities

Simple analytical expansions are given for the recoilless fraction in Mössbauer spectroscopy, the Debye-Waller factor in X-ray scattering, and the lattice energy and heat capacity of solids. While this problem has been discussed in an earlier paper [1], computer technology has now advanced to the point that direct evaluations of the simple expansions of these quantities are useful for quick curve fitting to experimental data at any desired temperature, and these expansions are easier to evaluate than using graphs to estimate recoilless fractions and Debye temperatures. We compare this approach with a polynomial expansion in terms of Bernoulli numbers, which has only a limited domain of convergence. We explicitly evaluate the convergence of these Debye integral expansions as a function of the number of terms used and the time required.This work was prepared with the support of the U.S. Department of Energy, Grant No. DE-FG02-85 ER 45199.     

Applicability of generic linear scoring mosels in the U.S. credit-union environment

Although credit-scoring models represent a widely used managerialaid for large financial intermediaries, the vast majority ofU.S. credit unions—relatively small cooperatively ownedretail intermediaries, constrained by sample and funding limitations—haveyet to adopt such techniques. Lovie & Lovie (1986) havetheorized that the flat-maximum effect or curve of insensitivityassociated with linear scoring models could be advantageousin areas of applied prediction such as credit scoring. In thiscontext, we reported the relative predictive power of genericcredit-scoring models versus customized models in an earlierpaper (Overstreet et al. 1992). Unfortunately, these findingswere not readily adaptable to the credit-union industry dueto a dated sample with incomplete credit-bureau information.Consequently, from 1988 to 1991, we gathered a refined databasefrom which to further develop and field-test generic scoringmodels in the credit-union environment. The results reportedherein not only confirm, but amplify, the relative predictivepower of such models found earlier. Relative costs and benefitsof generic versus customized models are modelled for a representativecredit union. Future research directions are set forth in theconclusions.     

The effect of brittle interfacial compounds on deformation and fracture of molybdenum-aluminum fiber composites

The effect of brittle intermetallic compounds at the fiber-matrix interface on the deformation characteristics of molybdenum-aluminum fiber composites was investigated. If the filament is ductile and notch-insensitive, then composite strength degradation is relatively minor and composite strength can be predicted by a modified mixture-rule which neglects the strength contribution of the brittle compound. For the case of notch-sensitive filaments, severe filament degradation occurs upon compound formation. The degradation was shown to result from cracks formed during deformation at the roots of compound nodules. The presence of 10 per cent compound by volume results in a 50 per cent decrease in tensile strength, but larger amounts of compound cause little additional strength reduction. At filament volume fractions of 25 and 34 per cent and compound volume fractions less than 10 per cent, composite fracture occurs by the statistical accumulation of fiber necks or fractures depending on the notch sensitivity of the fiber. At high fiber or compound volume fractions, composite failure occurs upon the first or the second filament fracture.     

Optimally-weighted dispersion relations II

We construct the optimally-weighted dispersion relation and extrapolation error for an amplitude with unequal, possibly correlated, errors in the experimental boundary values of its real and imaginary parts. The uniqueness of the optimally-weighted dispersion relation is demonstrated.     

Representations of Shavitt Graphs Within the Graphical Unitary Group Approach

The Shavitt graph is a visual representation of a distinct row table (DRT) within the graphical unitary group approach. The DRT is a compact representation of the entire configuration state function expansion space within a molecular electronic structure calculation. Each node of the graph is associated with an integer triple (a _k,b _k,c _k). These integers may be mapped to other quantum numbers, including the number of orbitals, number of electrons, and spin quantum number, and used to display Shavitt graphs in various ways that emphasize different aspects of the expansion space or that reveal different aspects of computed wave functions. The features of several graph density plots are discussed, including electron–hole symmetries and the bonding–antibonding wave function character. © 2019 Wiley Periodicals, Inc.