't Hooft Expansion of 1/2 BPS Wilson Loop

We revisit the 't Hooft expansion of 1/2 BPS circular Wilson loop in N=4 SYM studied by Drukker and Gross in hep-th/0010274. We find an interesting recursion relation which relates different number of holes on the worldsheet. We also argue that we can turn on the string coupling by applying a certain integral transformation to the planar result.Comment: 21 pages; v2: minor correction

An algorithm for generating all possible 2(p-q) fractional factorial designs and its use in scientific experimentation

An algorithm and computer program are presented for generating all the distinct 2(p-q) fractional factorial designs. Some applications of this algorithm to the construction of tables of designs and of designs for nonstandard situations and its use in Bayesian design are discussed. An appendix includes a discussion of an actual experiment whose design was facilitated by the algorithm

Parametrizations of density matrices

This article gives a brief overview of some recent progress in the characterization and parametrization of density matrices of finite dimensional systems. We discuss in some detail the Bloch-vector and Jarlskog parametrizations and mention briefly the coset parametrization. As applications of the Bloch parametrization we discuss the trace invariants for the case of time dependent Hamiltonians and in some detail the dynamics of three-level systems. Furthermore, the Bloch vector of two-qubit systems as well as the use of the polarization operator basis is indicated. As the main application of the Jarlskog parametrization we construct density matrices for composite systems. In addition, some recent related articles are mentioned without further discussion.Comment: 31 pages. v2: 32 pages, Abstract and Introduction rewritten and Conclusion section added, references adde

New Identities from a Combinatorial Approach to Generalized Fibonacci and Generalized Lucas Numbers

We present here some new identities for generalizations of Fibonacci and Lucas numbers by combinatorially interpreting these numbers in terms of numbers of certain tilings of a 1 x m board. As a consequence, some new interesting identities involving the ordinaries Fibonacci and Lucas numbers are derived.CNPqFed Univ Sao Paulo UNIFESP, Dept Sci & Technol, BR-12247014 Sao Jose Dos Campos, SP, BrazilFed Univ Sao Paulo UNIFESP, Dept Sci & Technol, BR-12247014 Sao Jose Dos Campos, SP, BrazilWeb of Scienc