We introduce crossed interval groups and construct a crossed interval analog IS of the Fiedorowicz-Loday symmetric category ∆S. We prove that the functor FS(−) of the free IS-extension of an I-object does not change homotopy type. We then observe that the operad B of natural operations on the Hochschild cohomology equals FS(T ), where T is an operad whose homotopy type is known. We conclude fro...

We consider a market where a single seller must employ informative advertising to launch a new product of observable quality. The monopolist may use mass, targeted or customer directed advertising. We show that the choice of advertising strategy depends on the economic properties of the advertising technology. If this exhibits strong economies of targeting, customer directed advertising arises ...

Inference rule substitution of equals for equals has been formalized in terms of simple substitution which performs a replacement even though a free occurrence of a variable is captured contextual substitution which prevents such capture and func tion application We show that in connection with pure rst order predicate calculus the function application and no capture versions of the inference r...

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