Super self-duality for Yang-Mills fields in dimensions greater than four

Self-duality equations for Yang-Mills fields in d-dimensional Euclidean spaces consist of linear algebraic relations amongst the components of the curvature tensor which imply the Yang-Mills equations. For the extension to superspace gauge fields, the super self-duality equations are investigated, namely, systems of linear algebraic relations on the components of the supercurvature, which imply the self-duality equations on the even part of superspace. A group theory based algorithm for finding such systems is developed. Representative examples in various dimensions are provided, including the Spin(7) and G(2) invariant systems in d=8 and 7, respectively.Comment: 51 pages, late

The hidden symmetry algebras of a class of quasi-exactly solvable multi dimensional operators

Let $P(N,V)$ denote the vector space of polynomials of maximal degree less than or equal to $N$ in $V$ independent variables. This space is preserved by the enveloping algebra generated by a set of linear, differential operators representing the Lie algebra $gl(V+1)$. We establish the counterpart of this property for the vector space $P(M,V) \oplus P(N,V)$ for any values of the integers $M,N,V$. We show that the operators preserving $P(M,V) \oplus P(N,V)$ generate an abstract superalgebra (non linear if $\Delta=\mid M-N\mid\geq 2$). A family of algebras is also constructed, extending this particular algebra by $\Delta -1$ arbitrary complex parameters.Comment: 19 pages, late

Term Structure of Interest Rates. Emergence of Power Laws and Scaling Laws

The technique of Pad\'e Approximants, introduced in a previous work, is applied to extended recent data on the distribution of variations of interest rates compiled by the Federal Reserve System in the US. It is shown that new power laws and new scaling laws emerge for any maturity not only as a function of the Lag but also as a function of the average inital rate. This is especially true for the one year maturity where critical forms and critical exponents are obtained. This suggests future work in the direction of constructing a theory of variations of interest rates at a more ``microscopic'' level.}Comment: 22 pages, 9 figures and 2 table

Term Structure of Interest Rates.Emergence of Power Laws and Scaling Laws

The technique of Pad\'e Approximants, introduced in a previous work, is applied to extended recent data on the distribution of variations of interest rates compiled by the Federal Reserve System in the US. It is shown that new power laws and new scaling laws emerge for any maturity not only as a function of the Lag but also as a function of the average inital rate. This is especially true for the one year maturity where critical forms and critical exponents are obtained. This suggests future work in the direction of constructing a theory of variations of interest rates at a more ``microscopic'' level.interest rates, scaling laws

Term Structure of Interest Rates. Emergence of Power Laws and Scaling Laws

The technique of Pad\'e Approximants, introduced in a previous work, is applied to extended recent data on the distribution of variations of interest rates compiled by the Federal Reserve System in the US. It is shown that new power laws and new scaling laws emerge for any maturity not only as a function of the Lag but also as a function of the average inital rate. This is especially true for the one year maturity where critical forms and critical exponents are obtained. This suggests future work in the direction of constructing a theory of variations of interest rates at a more ''microscopic'' level.Interest rates scaling laws