Iterated Differential Forms II: Riemannian Geometry Revisited

A natural extension of Riemannian geometry to a much wider context is presented on the basis of the iterated differential form formalism developed in math.DG/0605113 and an application to general relativity is given.Comment: 12 pages, extended version of the published note Dokl. Math. 73, n. 2 (2006) 18

Special functions from quantum canonical transformations

Quantum canonical transformations are used to derive the integral representations and Kummer solutions of the confluent hypergeometric and hypergeometric equations. Integral representations of the solutions of the non-periodic three body Toda equation are also found. The derivation of these representations motivate the form of a two-dimensional generalized hypergeometric equation which contains the non-periodic Toda equation as a special case and whose solutions may be obtained by quantum canonical transformation.Comment: LaTeX, 24 pp., Imperial-TP-93-94-5 (revision: two sections added on the three-body Toda problem and a two-dimensional generalization of the hypergeometric equation

Algebraic theories of brackets and related (co)homologies

A general theory of the Frolicher-Nijenhuis and Schouten-Nijenhuis brackets in the category of modules over a commutative algebra is described. Some related structures and (co)homology invariants are discussed, as well as applications to geometry.Comment: 14 pages; v2: minor correction

Distributed modular RT-systems for detector DAQ, trigger and control applications

A modular approach to development of distributed modular system architecture for detector control, data acquisition and trigger data processing is proposed. A multilevel parallel-pipeline model of data acquisition, processing and control is proposed and discussed. Multiprocessor architecture with SCI-based interconnections is proposed as good high-performance system for parallel-pipeline data processing. A network (Ethernet -100) can be used for loading, monitoring and diagnostic purposes independent of basic interconnections. The modular cPCI-based structures with high speed modular interconnections are proposed for DAQ and control applications. For distributed control RT-systems, to construct the effective (cost-performance) systems the same platform of an Intel compatible processor board should be used. The basic computer multiprocessor nodes consist of high-power PC MB (Industrial Computer Systems), which are interconnected by SCI modules and link to embedded microprocessor-based sub-systems for control applications. The required number of multiprocessor nodes should be interconnected by SCI for parallel-pipeline data processing in real time (according to the multilevel model) and link to RT-systems for embedded control. (19 refs)

Separating Solution of a Quadratic Recurrent Equation

In this paper we consider the recurrent equation $$\Lambda_{p+1}=\frac1p\sum_{q=1}^pf\bigg(\frac{q}{p+1}\bigg)\Lambda_{q}\Lambda_{p+1-q}$$ for $p\ge 1$ with $f\in C[0,1]$ and $\Lambda_1=y>0$ given. We give conditions on $f$ that guarantee the existence of $y^{(0)}$ such that the sequence $\Lambda_p$ with $\Lambda_1=y^{(0)}$ tends to a finite positive limit as $p\to \infty$.Comment: 13 pages, 6 figures, submitted to J. Stat. Phy

Discretized rotation has infinitely many periodic orbits

For a fixed k in (-2,2), the discretized rotation on Z^2 is defined by (x,y)->(y,-[x+ky]). We prove that this dynamics has infinitely many periodic orbits.Comment: Revised after referee reports, and added a quantitative statemen

On the continuous spectral component of the Floquet operator for a periodically kicked quantum system

By a straightforward generalisation, we extend the work of Combescure from rank-1 to rank-N perturbations. The requirement for the Floquet operator to be pure point is established and compared to that in Combescure. The result matches that in McCaw. The method here is an alternative to that work. We show that if the condition for the Floquet operator to be pure point is relaxed, then in the case of the delta-kicked Harmonic oscillator, a singularly continuous component of the Floquet operator spectrum exists. We also provide an in depth discussion of the conjecture presented in Combescure of the case where the unperturbed Hamiltonian is more general. We link the physics conjecture directly to a number-theoretic conjecture of Vinogradov and show that a solution of Vinogradov's conjecture solves the physics conjecture. The result is extended to the rank-N case. The relationship between our work and the work of Bourget on the physics conjecture is discussed.Comment: 25 pages, published in Journal of Mathematical Physic