A new interpretation of Problem 10 of the Moscow Mathematical Papyrus

Although much discussed, the original intent of Problem 10 of the Moscow Mathematical Papyrus continues to be an unresolved question. This essay proposes a possible solution to the issue by joining together aspects of two theories on the subject advanced in the 1930s by W. W. Struve and T. E. Peet. From this point of beginning it is shown that the problem’s “basket” may originally have been intended to be understood as being of a specific actual size, thus revealing a set of correlations and insights regarding early Middle Kingdom mathematical capabilities and grain measurement concerns.     

Synthesis and solution properties of comblike poly(mono-n-alkyl itaconates). I. Poly(monodecyl itaconate)

The monoester of itaconic acid with n-decyl alcohol was prepared and polymerized. The polymer was fractionated and characterized by viscometry, size-exclusion chromatography (SEC) and light scattering. Some of the common semiempirical relations for flexible and rigid polymers were used in order to obtain the unperturbed dimensions and the conformational parameters. Thermodynamic and dimensional parameters were determined and calculated. The results are compared with those reported previously for similar compounds.     

Middle ear prosthesis: significance in magnetic resonance imaging

The Armstrong model of the Schuknecht gel foam and wire prosthesis was tested in the magnetic field of a 1.5 Tesla magnet. The wire component of the prosthesis was found to be non-magnetic. Patients with this prosthesis can therefore undergo MRI examination safely. Two previous articles from the non radiologic literature concerning the magnetic properties of metallic middle ear prostheses are reviewed.     

Joint Wigner distribution for spin-1/2 particles

The Wigner distribution has proven to be a useful tool in many quantum problems requiring a joint distribution of position and momentum. In the present paper we develop a joint distribution for spin components within the spirit of the Wigner distribution. This distribution provides an insight into the quantum theory of measurement. We also discuss how one may write joint distributions for two arbitrary noncommuting operators.It is a pleasure to dedicate this paper to Professor John A. Wheeler—physicist, philosopher, poet—an inspiration to us all.Work supported by the Office of Naval Research.     

Prediction of yield and long‐term failure of oriented polypropylene: Kinetics and anisotropy

The time‐dependent yield and failure behavior of off‐axis loaded uniaxially oriented polypropylene tape is investigated. The yield and failure behavior is described with an anisotropic viscoplastic model. A viscoplastic flow rule is used with an equivalent stress, based on Hill's anisotropic yield criterion, and the Eyring flow theory combined with a critical equivalent strain definition. This model is based on factorization of the rate and draw ratio dependence and is capable of quantitatively predicting the rate, angle and draw ratio dependence of the yield stress as well as time‐to‐failure in various off‐axis tensile loading conditions characterized solely from the transverse direction. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2026–2035, 2009     

A new wavelet multigrid method

The standard multigrid procedure performs poorly or may break down when used to solve certain problems, such as elliptic problems with discontinuous or highly oscillatory coefficients. The method discussed in this paper solves this problem by using a wavelet transform and Schur complements to obtain the necessary coarse grid, interpolation, and restriction operators. A factorized sparse approximate inverse is used to improve the efficiency of the resulting method. Numerical examples are presented to demonstrate the versatility of the method.