Two distinctively different decomposition algorithms have been developed. Both are analagous to decentralized decision making in the firm. One essentially deals with the allocation of corporate resources by fhe use of transfer prices charged to the divisions, while the other deals with the direct allocation of fvted quantities of the corporate resources to each division. The analogy of a price coordinated, or transfer pricing, technique to decentralization was developed by Baumol and Fabian [ 1 ] and later by Kim [4]. The second approach to decomposition was developed by Kornai and Liptak [5] 161 in an attempt to formulate the planning problem in a Socialist economy. It is the purpose of this paper to develop the analogy of the resource allocation decomposition to decentralized decision making.

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Facsimiles of musical autographs are typically thought to require photography, and to have a primary purpose of clarifying composers’ intentions. But there was a robust culture of music facsimile prior to photography. Made by transfer lithography, these facsimiles served different purposes and reading habits. The activity of collecting handwriting samples was paramount, as was the idea that handwriting was a mirror of character. This article surveys ways of using and finding meaning in composer autographs in the 1820s to the 1840s, focusing especially on music facsimiles in Paris. Here, composers used facsimiles to help shape their public image, and publishers used them to entice consumers. When facsimiles reproduced documents of friendship, they crossed private and public expression in ways that could be advantageous or problematic, as seen through a look at the publication in facsimile of a Rossini waltz by the Revue et gazette musicale and the ensuing legal battles.

Employing the term ‘point of audition’ to describe the spatial position musical works imply for their listeners, this article examines the use of technologies for extending the senses to define new points of audition in the late eighteenth and early nineteenth centuries. Popular literature on natural philosophy promoted magnifying instruments as windows onto distant or hidden realms and as tools for acquiring knowledge. On the operatic stage and in writers' metaphorical musings, kindred sensory extensions were imagined for hearing. These contexts connected (magic) mirrors and magnifying instruments to their musical analogues: muted tone and keyboard fantasizing. The development of these associations in opera and literature made it possible for instrumental music to position listeners as eavesdroppers upon unknown realms. Such a point of audition is shown to be implied by the Adagio un poco mosso of Beethoven's Fifth Piano Concerto. By examining material practices and discourses surrounding sensory extension, this article demonstrates the relevance of technologically mediated observation to musical culture at the turn of the nineteenth century, and its contribution to the otherworldly orientation characteristic of romantic listening.

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