Constituents of Tabebuia guayacan: The structure of guayacanin

The heartwood of T. guayacan has yielded tectol and a new, novel dibenz-xanthene derivative (guayacanin). The structure of guayacanin suggests its biogenetic derivation through the condensation of prenylnaphthalene quinols. The tetrahydro derivative of the xanthene was synthesized by an analogous acid catalyzed reaction of prenylnaphthalene quinol derivatives of lapachol and 1,4 naphthalene diol.     

Redfield's lost paper in a modern context

An alternative proof of the main results of the preceding paper by J. Howard Redfield is provided in modern terminology. The relationship of Redfield's results with a number of more recent articles is discussed. This is necessitated by the delay of over forty years between the submission and publication of his lost paper.     

Two linear systems criteria for exponential dichotomy

Summary Two criteria, one postulating the existence of a not necessarily positive definite Lyapunov function and the other postulating conditional input-output stability, are given, ensuring that a system of linear differential equations has an exponential dichotomy.Thanks are due to Mr. W. A. Coppel for suggesting the problems and helpful advice.     

The Placing of Service Points to Minimize Travel

We wish to site a given number of offices or other service points in a district, so that the mean travelling distance between clients and their nearest office is as low as possible. It is shown that the density of the offices should be proportional to the two-thirds power of the population density. This theoretical result does not take account of local conditions, but it may be made the basis for a study on the ground.     

Automated measurement of ultrasound velocity and attenuation

A fully-automated system has been developed to measure changes in ultrasonic velocity and the attenuation coefficient resulting from changes in temperature and magnetic field. Accuracy and sensitivity comparable to the pulse-echo overlap technique have been achieved together with an increase in temperature resolution and sample throughput as a result of the automation. All components of the instrumentation are commercially available.     

Constituents of tabebuia guayacan—II : The structure of guayin

A unique oxalactone dibenzxanthone, guayin, has been isolated from the heartwood of T. guayacan and structurally identified. A biomimetic synthesis of the dihydro derivative of guayin, based upon the probable biosynthetic origin of guayin from the dibenzxanthene guayacanin, has been successfully achieved.