Proceedings of the California Academy of Sciences, 4th series.

4th ser. v. 10 (1920)

Proceedings of the California Academy of Sciences, 4th series.

4th ser. v. 13 (1923)

Proceedings of the California Academy of Sciences, 4th series.

4th ser. v. 15 (1926-1927)

Proceedings of the California Academy of Sciences, 4th series.

4th ser. v. 5 (1915)

Proceedings of the California Academy of Sciences, 4th series.

4th ser. v. 19 (1930-1931)

Proceedings of the California Academy of Sciences, 4th series.

4th ser. v. 14 (1924)

Proceedings of the California Academy of Sciences, 4th series.

4th ser. v. 16 (1927-1928)

Proceedings of the California Academy of Sciences, 4th series.

4th ser. v. 22 (1936-1941)

Proceedings of the California Academy of Sciences, 4th series.

4th. ser. v. 25 (1943-1949)

Proceedings of the California Academy of Sciences, 4th series.

4th ser. v. 24 (1942-1950)

Proceedings of the California Academy of Sciences, 4th series.

4th ser. v. 20 (1931-1933)

Proceedings of the California Academy of Sciences, 4th series.

4th ser. v. 23 (1935-1947)

Transactions of the Linnean Society of London, 2nd series: Botany

v.9 (1916-1922)

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.

Co-movements between US and UK stock prices: the roles of macroeconomic information and time-series varying conditional correlations

This paper provides evidence on the sources of co-movement in monthly US and UK stock price movements by investigating the role of macroeconomic and financial variables in a bivariate system with time-varying conditional correlations. Crosscountry communality in response is uncovered, with changes in the US Federal Funds rate, UK bond yields and oil prices having similar negative effects in both markets. Other variables also play a role, especially for the UK market. These effects do not, however, explain the marked increase in cross-market correlations observed from around 2000, which we attribute to time variation in the correlations of shocks to these markets. A regime-switching smooth transition model captures this time variation well and shows the correlations increase dramatically around 1999-2000. JEL classifications: C32, C51, G15 Keywords: international stock returns, DCC-GARCH model, smooth transition conditional correlation GARCH model, model evaluation.