Effect of crack tip sharpness on the strength of vulcanized rubbers

The effect of crack tip sharpness on crack propagation in vulcanized rubbers has been studied. For very sharp cracks, tearing is found to occur on a small scale at very low energies not far above the threshold required for the onset of mechanical crack growth. The “small-scale” tearing energies show relatively little variation for rubbers that differ widely in tear strength as normally measured. Thus the latter property appears to be strongly influenced by variations in the ability of rubbers to promote tip blunting. The small-scale tear behavior is of relevance to other fracture phenomena, including cutting by sharp objects and tensile failure. Natural variations in tip sharpness occur during cyclic or time-dependent mechanical crack growth and influence the form of the crack growth characteristics.     

Geometric theory of invariants of groups generated by reflections

A survey of results on a number of problems of the geometric theory of invariants of groups generated by orthogonal and skew reflections is given. The paper is a continuation of the author's surveys published in 1980 and 1984.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 21, pp. 155–208, 1989.     

Reaction of 2-formyl-1,3-cyclohexanediones with cyanoacetamide

Chemistry of Heterocyclic Compounds -     

OnQ-order andR-order of convergence

We give sufficient conditions for a sequence to have theQ-order and/or theR-order of convergence greater than one. If an additional condition is satisfied, then the sequence has an exactQ-order of convergence. We show that our results are sharp and we compare them with older results.This work was supported in part by the National Science Foundation under Grant No. DMS-85-03365. The author wishes to thank J. E. Dennis and R. A. Tapia for helpful comments, and the referee for pointing out a number of typographical and mathematical errors in the original version of this paper.     

On the Numerical Range of Operator Polynomials

An upper bound for the number of components of the numerical range of matrix polynomials is established. We also establish a necessary condition and a sufficient condition for the connectedness of the numerical range of a quadratic selfadjoint matrix polynomial. The boundary of the numerical range of linear matrix polynomials is also considered.     

Observation of hydrogen induced intermediate borides in PrFeB based alloys by Mössbauer effect spectroscopy

In the present work, a quantitative analysis of the phase compositions by Mössbauer effect spectroscopy of solid and conventional hydrogen disproportionated Pr_13.7Fe_80.3B_6.0 and Pr_13.7Fe_63.5Co_16.7Zr_0.1B_6.0 alloys was carried out. Significant amounts of intermediate borides t-Fe₃B and Pr(Fe, Co)₁₂B₆ were detected after solid hydrogen disproportionation treatment in Pr_13.7Fe_80.3B_6.0 and Pr_13.7Fe_63.5Co_16.7Zr_0.1B_6.0 alloys, respectively. After conventional hydrogenation–disproportionation–desorption–recombination treatment these phases were not detected and in no case residual Pr₂Fe₁₄B-phase was found. It was observed that the amount of intermediate borides after disproportionation can be correlated with the degree of texture after recombination at various temperatures.     

Detailed Description of Mixed Symmetry States in 94Mo Using Interacting Boson Model

We have investigated the low-lying collective states and electromagnetic transitions in 94Mo within the framework of the interacting boson model. The influence of model parameters on the energy levels and electromagnetic properties has been investigated. The analysis of the obtained results and the parameter values predict that the 23+state is the lowest mixed symmetry state with pure F = Fmax - 1 in this nucleus. The calculated results predicate that the 25+ (two-Q-phonon) mixed symmetry state is closed to the J = 2+ at 2.870 MeV in the experimental data, and the 2.965 MeV state is the lowest mixed symmetry with J = 3+.     

The analysis of thermal stresses in thermopiezoelastic semi-infinite body with an edge crack

Summary  Thermopiezoelastic materials have recently attracted considerable attention because of their potential use in intelligent or smart structural systems. The governing equations of a thermopiezoelastic medium are more complex due to the intrinsic coupling effects that take place among mechanical, electrical and thermal fields. In this analysis, we deal with the problem of a crack in a semi-infinite, transversely isotropic, thermopiezoelastic material by means of potential functions and Fourier transforms under steady heat-flux loading conditions. The problem is reduced to a singular integral equation that is solved. The thermal stress intensity factor for a crack situated in a cadmium selenide material is calculated. Received 20 March 2001; accepted for publication 18 October 2001     

Formal degree and existence of stable arithmetic lattices of cuspidal representations ofp-adic reductive groups

Research at MSRI supported in part by NSF Grant DMS-812079-05