Vertical integration or specialisation: producing and commercialising cotton goods (1815-1913)

This article describes the ways in which cotton goods were commercialised during the nineteenth century and the first third of the twentieth. Several national cases are analysed: Britain, as the Workshop of the World; France, Germany, Switzerland and the US, as core economies; and Italy and Spain as countries on the European periphery. The main question that we address is why some cotton industries vertically integrated their production and commercialisation processes, but others did not. We present a model that combines industrial district size and product differentiation to explain why vertical integration was present in most cases and why there was vertical specialisation in Lancashire and Lowell.

Vertical integration or specialisation: producing and commercialising cotton goods (1815-1913)

This article describes the ways in which cotton goods were commercialised during the nineteenth century and the first third of the twentieth. Several national cases are analysed: Britain, as the Workshop of the World; France, Germany, Switzerland and the US, as core economies; and Italy and Spain as countries on the European periphery. The main question that we address is why some cotton industries vertically integrated their production and commercialisation processes, but others did not. We present a model that combines industrial district size and product differentiation to explain why vertical integration was present in most cases and why there was vertical specialisation in Lancashire and Lowell.

Free and fragmenting filling length

The filling length of an edge-circuit η in the Cayley 2-complex of a finite presentation of a group is the minimal integer length L such that there is a combinatorial null-homotopy of η down to a base point through loops of length at most L. We introduce similar notions in which the full-homotopy is not required to fix a base point, and in which the contracting loop is allowed to bifurcate. We exhibit a group in which the resulting filling invariants exhibit dramatically different behaviour to the standard notion of filling length. We also define the corresponding filling invariants for Riemannian manifolds and translate our results to this setting.

An ordinal shapley value for economic environments (Revised version)

We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The problem is formulated in the preferences-endowments space. The solution is defined recursively, incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for Transferable Utility (TU) games. We show a solution exists, and call it the Ordinal Shapley value (OSV). We characterize the OSV using the notion of coalitional dividends, and furthermore show it is monotone and anonymous. Finally, similarly to the weighted Shapely value for TU games, we construct a weighted OSV as well.

Encryption methods using formal power series rings

Recently there has been a great deal of work on noncommutative algebraic cryptography. This involves the use of noncommutative algebraic objects as the platforms for encryption systems. Most of this work, such as the Anshel-Anshel-Goldfeld scheme, the Ko-Lee scheme and the Baumslag-Fine-Xu Modular group scheme use nonabelian groups as the basic algebraic object. Some of these encryption methods have been successful and some have been broken. It has been suggested that at this point further pure group theoretic research, with an eye towards cryptographic applications, is necessary.In the present study we attempt to extend the class of noncommutative algebraic objects to be used in cryptography. In particular we explore several different methods to use a formal power series ring R && x1; :::; xn && in noncommuting variables x1; :::; xn as a base to develop cryptosystems. Although R can be any ring we have in mind formal power series rings over the rationals Q. We use in particular a result of Magnus that a finitely generated free group F has a faithful representation in a quotient of the formal power series ring in noncommuting variables.