Pseudo-Strong Regularity Around a Set

A generalization of strong regularity around a vertex subset C of a graph Γ, which makes sense even if Γis non-regular, is studied. Such a structure appears, together with a kind of distance-regularity around C , when an spectral bound concerning the so-called predistance polynomial of C is attained. As a main consequence of these results, it is shown that a regular (connected) graph Γwith d + 1 distinct eigenvalues is distance-regular, and its distance- d graph Γ d is strongly regular with parameters a = c , if and only if the number of vertices at distance d from each vertex satisfies an expression which depends only on the order of Γand the different eigenvalues of Γ.     

Development of new dyes for use in integrated optical sensors

New chromoionophores have been developed, focused on NIR applications so that optode membranes may be used in monolithically integrated optical sensors. The wavelength of maximum absorbance has been estimated for a new model compound by the Pariser-Parr-Pople (PPP) method. Several cyanine type dyes have been tested as membrane chromoionophores. Membrane composition has been altered to overcome solubility problems. In this way, simple pH-sensitive optode membranes have been produced.     

Toughening of epoxies via craze-like damage

The fracture behavior of a core-shell rubber (CSR) modified epoxy is investigated using both fracture mechanics and microscopy tools. The CSR-modified epoxy is found to be toughened via numerous line-array cavitations of the CSR particles, followed by plastic flow of the epoxy matrix. The toughening effect via the above craze-like damage process is found to be as effective as that of the well-known widespread rubber cavitation/matrix shear yielding mechanisms. The conditions for triggering the craze-like damage appear to be both stress state and rubber concentration dependent. The type of rubber tougheners utilized also plays a critical role in triggering this rather unusual craze-like damage in epoxy systems. © 1993 John Wiley & Sons, Inc.     

Orbifolds, Sheaves and Groupoids

We characterize orbifolds in terms of their sheaves, and show that orbifolds correspond exactly to a specific class of smooth groupoids. As an application, we construct fibered products of orbifolds and prove a change-of-base formula for sheaf cohomology.     

Chemical composition and reaction analysis of single aerosol particles

In situ measurements of gas-liquid surface reactions of single aerosol microdroplets are presented. By means of optical levitation in combination with elastic (Mie) and inelastic (Raman) light scattering it is possible to get information on the chemistry of e.g. acid/base reactions as well as the physical behavior of single microparticles.     

Solution of the 2D ising model on a triangular lattice by the method of auxiliaryq-deformed Grassmann fields

A representation in the form of a functional integral is obtained for the partition function of the inhomogeneous 2D Ising model on a triangular lattice where the coupling parameters are arbitrary functions of coordinates. The method for transforming the partition function into an integral uses an auxiliary six-component Grassmann field in which the Grassmann fields corresponding to one of the components commute with the others. Thus, one pair of components realizes a representation of the q-deformed group SL_q(2, R) with q=–1 and the other two pairs correspond to the usual Grassmann spinors (q=1). An explicit expression in terms of the modified Pfaffian is found for the Gaussian integral over these fields and its relation to the ordinary Grassmann functional integral is established.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 109, No. 3, pp. 441–463, December, 1996.     

THE USE OF THERMOELASTICITY TO EVALUATE STRESS REDISTRIBUTION AND NOTCH SENSITIVITY IN CERAMIC MATRIX COMPOSITES

Thermoelastic stress analysis was used to document the effect of composite damage on the stress distribution in three ceramic matrix composites. Composite damage was found to significantly alter the thermoelastic response of each material, with the greatest effect noted in SiC/CAS. Thermoelastic imaging of these materials affords a more complete picture of how the various damage mechanisms affect the stress distribution. In particular, a stress concentration factor computed from thermoelastic images, serves as an indicator of stress redistribution. The stress concentration factors were computed by comparing notch root to far field temperatures, and monitored after the introduction of various amounts of damage. In each material, the stress concentration factor diminished as the damaging load approached the ultimate stress. Reduction in the stress concentration is associated with local changes in modulus, mechanistically arising from combinations of fiber, matrix and interface fracture. Stress redistribution occurs as a consequence of modulus changes, leading to lower notch sensitivity in each of the tested composites.     

Letters to the Editor

The Mathematical Intelligencer encourages comments about the material in this issue. Letters to the editor should be sent to either of the editors-in-chief, Chandler Davis or Marjorie Senechal.