N -Fold ?ech Derived Functors and Generalised Hopf Type Formulas

The notion of n-fold Čech derived functors is introduced and studied. This is illustrated using the n-fold Čech derived functors of the nilization functors Z_k. This gives a new purely algebraic method for the investigation of the Brown–Ellis generalised Hopf formula for the higher integral group homology and for its further generalisation. The paper ends with an application to algebraic K-theory. (Received: December 2004)     

Analysis of volumetric changes through melting using a dilatometer

Summary A conventional push-rod dilatometer is modified in order to accurately correlate the measured density to the predicted sample temperature of alloys in the phase-change regime. This new configuration makes use of a standard furnace assembly; however, the specimen is now symmetrically encased in a well-instrumented, graphite cylindrical shell. The combination of system geometry and high-conductivity sample holder material promotes the development of a simplified heat transfer model. The solution of this model properly correlates the measured density to that of the actual sample temperature based on using remote, sample-holder temperature measurements. Preliminary results using aluminum A356 provide insight into the proposed configuration.     

Thin films of nylon 13,13 casted on water: Morphology and properties

Substrate-free thin film of Nylon 13,13 has been prepared continuously by casting the polymer on a water surface from m-cresol solution. The uniform thickness of film is ca. 500 A, as measured with a Profilometer. Film morphology and properties have been characterized by transmission electronic microscopy (TEM), x-ray photoelectron spectroscopy, wide-angle x-ray scattering, differential scanning calorimetry and by contact angle measurements. Results show that there is no preferential accumulation of the amide group toward the water surface. A spherulite structure exists in this film with a crystallinity of 26% by DSC. Fibers were drawn from the films which had a tensile modulus of 5 GPa, stiffer than reported for this nylon as prepared by other means. Other members of the nylon series, such as Nylon 6, Nylon 12, have also been prepared in films by the same casting method under modified conditions. © 1995 John Wiley & Sons, Inc.     

Mechanical properties of ultra-oriented polyethylene

Semicrystalline polymers generally exhibit moduli well below their theoretical limit due to chain folding and to lack of crystal alignment. Modulus increases attainable through standard drawing procedures are limited by sample fracture before large draw ratios are reached. Using an Instron capillary rheometer which allowed a draw ratio of > 300, transparent polyethylene strands of unusually high c-axis orientation have been produced by a combination of pressure and shear. The virtually perfect crystalline orientation and evidence for extended chains confirm that a significant improvement in modulus can be realized by this technique. The dynamic tensile storage modulus was measured by Vibron over the temperature range ?160°C to +120°C. Room-temperature moduli were 7 × 10¹¹ dyne/cm², higher than any reported values for drawn polyethylene. Values also remained above 10¹¹ dyne/cm² even at 120°C. The moduli and morphological data have been related by a model consisting of an extended-chain component in paralled with a conventional drawn morphology. Experimental and calculated moduli are compared and related to available theory.     

Systems of bilinear and quadratic equations in a finite field

Summary An explicit formula is found for the number of solutions in a finite field of the system of polynomial equations(11), when the coefficients satisfy certain conditions.     

Peroxymercuration-demercuration of lipid hydroperoxides

The course of mercuric-ion catalyzed cyclization of lipid hydroperoxides and the demercuration of the resulting cyclic peroxides is reported. The cyclization products depend on the mercuric ion utilized and the course of demercuration can be altered by conditions of reduction and oxygenation.     

Transverse momentum distribution of lepton-pairs in Drell-Yan process in an asymptotically free scalar field theory

The transverse momentum dependence of the parton distribution function and the Drell-Yan cross section is studied in detail in the asymptotically free scalar field theory in six dimensions. In the context of the renormalization group approach of Collins, particular attention is devoted to the transition between the small q_T formula (due to multe-quanta effects) and the large q_T formula (due to single hard-quantum emission). The calculation represents a case study of the application of the renormalization group method and provides a guide to the corresponding study in QCD.