A (2, 11) combinatorial groupoid

The variety of groupoids defined by the identitites (yx)x = xy and ((xy)(yx))(xy) = y has the properties that every groupoid generated by two elements is of order 11. The two generating identities imply others with a wide variety of combinatorial implications.     

A method for improving measurement reliability in laryngeal videostroboscopy

We describe a simple clinical tracing technique for making reliable test-retest comparisons of laryngeal stroboscopic images. Six young adults with normal larynges served as subjects. Results show the technique to be useful in estimating repeated examination changes. The technique is safe, quick, simple to perform, and inexpensive.     

Changing Children's Conceptions of Burning

Relatively few studies have examined the effects of instruction on children's understanding of burning. This study focused on three questions: (a) What are children's views of burning prior to and after instruction? (b) Do children's views become more scientific, that is, more in accord with scientists' views, with instruction, and if so, how? (c) Are the changes in children's understanding of burning correlated to their ages? Data were collected before and after five hours of instruction in a Saturday Science Program, using both a short multiple choice test based on common misconceptions from the literature and "interviews about events." Children were divided into two classes according to their grade in school. A significant difference was found in children's understanding before and after instruction on the multiple‐choice test that was corroborated with interview data. Younger children (ages 8 to 11) made more significant gains than did the older children (ages 11 to 13), with both groups reaching similar levels of understanding after instruction. Although notable gains were made in recognizing the need for oxygen in burning and in distinguishing between decomposition and burning, interviews revealed that few children at any age could explain specifically what was happening on the phenomena level.     

Antichains of monomial ideals are finite

The main result of this paper is that all antichains are finite in the poset of monomial ideals in a polynomial ring, ordered by inclusion. We present several corollaries of this result, both simpler proofs of results already in the literature and new results. One natural generalization to more abstract posets is shown to be false.

     

Antibody-catalyzed aminolysis of a chloropyrimidine derivative

We have generated antibody FTB8E9 by immunization with the designed hapten to catalyze the aminolysis reaction of a chloropyrimidine derivative.     

The set-indexed Ito integral

We construct an Ito-type stochastic integral where the integrator is a process indexed by a semilattice of compact subsets of a fixed topological spaceT and the integrands, which are indexed by the points inT, possess a natural form of predictability. The definition of the integral involves, among other things, an Ito-type isometry defined in terms of the set-indexed quadratic variation of the integrator. The martingale property and quadratic variation for the resulting integral process are derived. In addition, employing the notion of stopping set from Ivanoff and Merzbach (1995), we construct and study a set-indexed local integral. A novel and flexible notion of predictability for set-indexed processes is defined and characterized, permitting the integration of a set-indexed integrand against a set-indexed process. Research supported in part by the Israel Science Foundation (grant no.: 0321423). Research supported in part by a grant from the Natural, Sciences and Engineering Research Council of Canada.