Trapezoidal Configuration Research Articles

The length of parallel fibers in the cat cerebellar cortex. An experimental light and electron microscopic study.

Experimental light and electron microscopic studies were carried out to determine the length of parallel fibers in the cat cerebellar cortex. Using a fine surgical knife, vermal and hemispheral folia were cut perpendicular to their long axis. The animals were sacrificed 1-10 days after the operation. Sections of the transected folia were then stained with a Fink-Heimer procedure. The resulting degeneration appeared as fine dots that extended lateral to the lesion, as predictable from the course of the parallel fibers. Densitometer readings indicate that the density of degeneration declines gradually lateral to the lesion. The specificity of the silver impregnation was checked by processing silver stained sections for electron microscopy. This confirmed the location of the silver precipitate on degenerating parallel fibers. The pattern of parallel fiber degeneration in the molecular layer has a trapezoidal configuration centered on the lesion. The shorter parallel fibers are located at the base of the molecular layer and extend for 5 mm. The parallel fibers become progressively longer as they approach the pial surface where they attain a maximum length of 7 mm. Our studies suggest that in folia longer than 7 mm parallel fibers are 6 mm long on the average. In addition, it was determined on Golgi sections that the average center-to-center distance between en passant boutons of individual parallel fibers is 5.2 mum. The data indicate that an average parallel fiber, 6 mm long, forming approximately 1100 boutons, may synapse with each Purkinje dendritic tree it traverses.

Organometallic compounds of group III : XXXIV. Steric factors in the carbalumination of olefins. The question of the anomalous, reduced reactivity of olefins versus acetylenes.

In order to understand the reasons for the anomalous, reduced reactivity of olefins toward electrophilic carbalumination, compared with that of acetylenes, the reactivity, stereochemistry and regiochemistry of a series of acyclic and cyclic olefins in carbalumination with triphenylaluminum were investigated. The following substrates underwent reaction between 80 and 225°C with decreasing ease in the order: norbornadiene > cis-β-methylstyrene > trans-β-methylstyrene ∼ 1,2-dihydronaphthalene ∼ 1,1-dimethylindene > cis-1,2-diphenylethylene > 3,3,3-triphenylpropene > trans-1,2-diaryethylenes ∼ phenylcyclopropanes. The stereochemistry of the mono- and bis-carbaluminations of norbornadiene was shown to be syn, exo. The regiochemistry observed with unsymmetrical olefins could readily be rationalized by a steric effect operative in the preferential collapse of an olefin—(C 6H 5) 3Al π-complex. Besides carbalumination, several other reactions were observed with these olefins: (1) cis, trans-isomerization of acyclic olefins; (2) metallation of vinylic carbon atoms by (C 6H 5) 3Al; (3) elimination of (C 6H 5) 2AlH from carbalumination adducts; (4) by inference from the foregoing reaction with certain systems, epimerization at sp 3-hybridized carbon-aluminum bonds; and (5) decarbalumination with carbon-carbon bond scission. These side reactions were considered together with relative reactivities, stereochemistry and regiochemistry in developing energy profiles for the carbalumination of olefins and acetylenes. The reduced reactivity of olefins is thought to arise from steric factors that destabilize a π-complex-with (C 6H 5) 3Al and that cause a trapezoidal-like transition state to be of higher energy and rate-determining. The higher reactivity of acetylenes is ascribed to less steric hindrance both to π-complexation with (C 6H 5) 3Al, and to the collapse of the complex via a trapezoidal configuration. For acetylenes, it is judged that the formation of an intimate π-complex is rate-determining.

A study of the field around magnetic heds of trapezoidal shape

A trapezoidal configuration of the magnetic head which is a better approximation to the actual head shape as compared to the shapes treated so far is assumed. The Schwartz-Christoffel transformation is used to determine the magnetic field distribution around this head shape, and a field mapping equation is obtained. Examples of the field distribution around the trapezoidal as well as the finite head configurations are computed with the aid of an electronic digital computer using the mapping equation obtained. The results are compared and discussed. The digital computer program used is written in FORTRAN II, and is listed and described.