Tracking poles and representing Hankel operators directly from data

Summary We propose and analyse a method of estimating the poles near the unit circleT of a functionG whose values are given at a grid of points onT: we give an algorithm for performing this estimation and prove a convergence theorem. The method is to identify the phase for an estimate by considering the peaks of the absolute value ofG onT, and then to estimate the modulus by seeking a bestL ² fit toG over a small arc by a first order rational function. These pole estimates lead to the construction of a basis ofL ² which is well suited to the numerical representation of the Hankel operator with symbolG and thereby to the numerical solution of the Nehari problem (computing the bestH , analytic, approximation toG relative to theL norm), as analysed in [HY]. We present the results of numerical tests of these algorithms.Partially supported by grants from the AFOSR and NSF     

The synthesis of 1,4-diazacycl[3,2,2]azine

The diazaanalog of “cycl[3,2,2]azine”, “1,4-diazacycl[3,2,2]azine” (1,4,7b-triazacyclopent-[cd]indene) and its 2-methyl derivative were prepared. These compounds are subject to facile acid-catalyzed hydrolysis affording substituted imidazo[1,2-a]pyridines.     

THE ACTION SPECTRUM FOR INDUCTION OF CHRONIC ACTINIC DERMATITIS IS SIMILAR TO THAT FOR SUNBURN INFLAMMATION

The action spectrum for induction of the abnormal cutaneous response at 24 h in the photosensitivity disorder chronic actinic dermatitis (CAD) was determined in 15 patients and found to be the same in shape as that for normal sunburn in fair-skinned individuals at 24 h, as determined for 47 control volunteers, although displaced in magnitude. This suggests that an endogenous chromophore(s), the same as or similar to that/those responsible for human sunburn, may be responsible for initiation of the abnormal reaction to irradiation in CAD, and that the putative antigen associated with the CAD reaction may be derived from that/those or associated molecules.