A novel sequential aminodiene Diels-Alder strategy for the rapid construction of substituted analogues of Kornfeld's ketone

Through a novel sequence of aminodiene Diels-Alder reactions, amidofurans 18a-c were converted to tricyclic ketones 21a-c in moderate to good yields. Ketone 21a could be converted to Uhlé's ketone (6) by cleaving the tert-butyl carbamate and oxidatively removing the methyl ester. Tricycle 21a readily underwent bromination to give 22. Formation of the corresponding enol triflate 25 followed by carbonylation gave ester 27, which was then coupled with N-methyl propriolamide to furnish 26. [reaction: see text]     

A Banach space where minimal weak cuscos are generically compact-valued

The space of continuous functions on the double arrow space has long been of interest in differentiability theory since many convex functions on this space are densely but not generically Gâteaux differentiable. We show that this space has the property that minimal weak* cuscos into its dual take compact values at the points of a denseG set.     

Characterizing the dynamics of auditory perception

After listening to a sound that is presented repeatedly, subjects report hearing different transforms of the original sound. The frequency of reported transforms is a sensitive index of some speech disorders as well as cognitive flexibility in aging. In this paper, we propose and investigate quantitative measures that characterize the dynamics of this phenomenon, known as the verbal transformation effect. In particular, we show that the distribution of the dwell time, the time spent perceiving a string of a given phonemic form before switching to another form, obeys a power law for normal subjects with an exponent valued between 1 and 2. This result suggests that within this paradigm there is no characteristic time scale for the perceptual process. Additionally, we analyze the correlation properties of the transforms. We suggest that the complexity measures and techniques introduced here might be useful diagnostic tools for a number of speech and cognitive disorders. (c) 1995 American Institute of Physics.     

Spin correlations in amorphous Bi2Sr2CaCu2Ox

Zero and longitudinal field SR has been used to probe the magnetic state of amorphous Bi₂Sr₂CaCu₂O_x prepared by rapid quenching from the melt. The results suggest quasi-static spin correlations between extremely dilute Cu²⁺ ions.Work performed while at the J J Thomson Physical Laboratory, University of Reading.     

A tandem of discrete-time queues with arrivals and departures at each stage

A discrete-time system of a tandem of queues with exogenous arrivals and departures at each stage is considered. A customer leaving queuek–1 departs the system with probability 1– ^[k] and continues to queuek with probability ^[k] . Exogenous arrivals to each stage are i.i.d. at each time slot. An approximate analysis of the occupancy and busy-period distributions of each stage based on a General Busy-period with batches and Memoryless (geometric) Idle period renewal Process (GBMIP) provides improved performance over two-state Markov approximations and gives exact results when there are no interstage departures.This research was supported in part by NSF grant NCR-8708282.     

Codes Based on Complete Graphs

We consider the problem of embedding the even graphical code based on the complete graph onn vertices into a shortening of a Hamming code of length 2^m-1, wherem = h(n) should be as small as possible. As it turns out, this problem is equivalent to the existence problem for optimal codes with minimum distance 5, and optimal embeddings can always be realized as graphical codes based onK _n. As a consequence, we are able to determineh(n) exactly for alln of the form 2 ^k + 1 and to narrow down the possibilities in general to two or three conceivable values.Dedicated to Hanfried Lenz on the occasion of his 80th birthdayThe research for this note was done while the first author was visiting the University of Waterloo and the University of Rome, respectively. He thanks his colleagues there for their hospitality and also acknowledges the financial support of the Consiglio Nazionale delle Ricerche (Italy). The third author acknowledges the support of the National Science and Engineering Research Council of Canada given under grant #0GP0009258.     

Boundary value estimates for harmonic forms

We prove a bound for the -norm of harmonic forms in terms of certain -norms of their normal and tangential components. In turn, this is used to show the -norm equivalence of the normal and tangential components of harmonic forms on manifolds.