Hétérocycles contenant du phosphore. XXXII. Etude de l'action des phosphorhydrazides sur les orthoesters,l'anhydride acétique et l'acide formique

The reaction of phosphodi- or trihydrazides with orthoesters affords mainly 2,3,4,5-tetrahydro-1,2,4,5,3-tetrazaphosphorines and sometimes 4-amino-1,2,4,3-triazaphospholidines. These 1,2,4,5,3-tetrazaphosphorines present a prototropy which explains different pathways of the reaction of these derivatives with formaldehyde or acetone, The structure of all heterocycles which were obtained was established by nmr spectra.     

Pitfalls and problems in flexible fiberoptic videolaryngoscopy

The flexible fiberoptic laryngoscope is a valuable tool in the examination of laryngeal and supraglottic structure and function. Nevertheless, persistent questions remain about the validity of the perceived image, and a variety of concerns arise relative to the equipment used, the difficult to examine patient, and the difficulty in obtaining measurable objective data. All of these areas are discussed. Distortions of the video image that result from the wideangle lens effect are described. Given an awareness of the distortions that may be present in the fiberoptic video image, it is clear that it is necessary to exercise caution in making judgments of anatomic or physiologic integrity based on fiberoptic information alone.     

On the prime zeta function

The basic properties of the prime zeta function are discussed in some detail. A certain Dirichlet series closely connected with the function is introduced and investigated. Its dependence on the structure of the natural numbers with respect to their factorization is particularly stressed.     

On a class of locally convex closed curves

Summary For a certain type of locally convex plane curves some relations are shown between the numbers of double points and double tangents and the order and class of the curve. It is proved that the curve has an equal number of double points and double tangents and at least v-1 where 2v denotes the order (and class) of the curve. At last it is shown how a curve with more that v-1 double points (tangents) may be deformed into a curve with the minimum number. To Enrico Bompiani on his scientific Jubilee