A New Family of Cyclic Difference Sets with Singer Parameters in Characteristic Three

We construct a new family of cyclic difference sets with parameters ((3 ^d – 1)/2, (3 ^{d – 1} – 1)/2, (3 ^{d – 2} – 1)/2) for each odd d. The difference sets are constructed with certain maps that form Jacobi sums. These new difference sets are similar to Maschietti's hyperoval difference sets, of the Segre type, in characteristic two. We conclude by calculating the 3-ranks of the new difference sets.     

An improved algorithm for computing topological entropy

A new algorithm is presented for computing the topological entropy of a unimodal map of the interval. The accuracy of the algorithm is discussed and some graphs of the topological entropy which are obtained using the algorithm are displayed.     

Reactions of Weinreb amides: formation of aldehydes by Wittig reactions

Aldehydes are prepared in excellent yield by Wittig reactions of phosphoranes on the Weinreb amide of formic acid followed by in situ hydrolysis.     

Time-Resolved Photoacoustic Calorimetry: From Carbenes to Proteins

Why have molecules only been seen but not heard? For over a century chemists have probed reactions with various spectroscopic methods to learn about structures, dynamics, and reactivities of their molecules. What they have not done is to listen to their molecules react. Although the photoacoustic phenomenon has been known since 1880, it is only in the last twenty years that technology has developed to the point where sound waves produced by reacting molecules can be time resolved and the information contained within the waves deciphered. The information content within the photoacoustic wave is indeed rich, for one can learn about the dynamics and the magnitude of enthalpy changes associated with the reaction as well as the changes in molecular volume. This review article chronicles the development of time-resolved photoacoustic calorimetry and its application to a variety of reactions encountered in organic and organometallic chemistry and biochemistry.