The Topology of Foliations Formed by the Generic K-Orbits of a Subclass of the Indecomposable MD5-Groups

The present paper is a continuation of [13], [14] of the authors. Specifically, the paper considers the MD5-foliations associated to connected and simply connected MD5-groups such that their Lie algebras have 4-dimensional commutative derived ideal. In the paper, we give the topological classification of all considered MD5-foliations. A description of these foliations by certain fibrations or suitable actions of $\mathbb{R}^{2}$ and the Connes' C*-algebras of the foliations which come from fibrations are also given in the paper.Comment: 20 pages, no figur

Asymptotic Lattices, Good Labellings, and the Rotation Number for Quantum Integrable Systems

This article introduces the notion of good labellings for asymptotic lattices in order to study joint spectra of quantum integrable systems from the point of view of inverse spectral theory. As an application, we consider a new spectral quantity for a quantum integrable system, the quantum rotation number. In the case of two degrees of freedom, we obtain a constructive algorithm for the detection of appropriate labellings for joint eigenvalues, which we use to prove that, in the semiclassical limit, the quantum rotation number can be calculated on a joint spectrum in a robust way, and converges to the well-known classical rotation number. The general results are applied to the semitoric case where formulas become particularly natural

Cyclic tridiagonal pairs, higher order Onsager algebras and orthogonal polynomials

The concept of cyclic tridiagonal pairs is introduced, and explicit examples are given. For a fairly general class of cyclic tridiagonal pairs with cyclicity N, we associate a pair of `divided polynomials'. The properties of this pair generalize the ones of tridiagonal pairs of Racah type. The algebra generated by the pair of divided polynomials is identified as a higher-order generalization of the Onsager algebra. It can be viewed as a subalgebra of the q-Onsager algebra for a proper specialization at q the primitive 2Nth root of unity. Orthogonal polynomials beyond the Leonard duality are revisited in light of this framework. In particular, certain second-order Dunkl shift operators provide a realization of the divided polynomials at N=2 or q=i.Comment: 32 pages; v2: Appendices improved and extended, e.g. a proof of irreducibility is added; v3: version for Linear Algebra and its Applications, one assumption added in Appendix about eq. (A.2

Detailed comparison of injection-seeded and self-seeded performance of a 1060nm gain-switched Fabry-Perot laser diode

We investigate and compare the performance of a gain-switched picosecond Fabry-Perot laser diode operated at 1.06 µm under both injection- and self-seeded conditions. Our experiments show that comparable performance can be obtained for both modes of operation, with the self-seeding arrangement offering overall benefits in terms of reduced system complexity and cost, providing the associated quantization of available pulse repetition rate can be tolerated

Europe, Middle East, and North Africa region population projections : 1988-89 edition

Population projections are provided in this paper for the individual countries comprising EMENA region. The projections cover the period 1985-2150. The length of the projection period was chosen to allow countries to approach stability, which for several is projected to take as long as two centuries. The paper begins with an introduction which explains what projection results are provided in the detailed tables, describes the projection methodology, and summarizes and interprets the main results.Demographics,Health Indicators,,Health Information&Communications Technologies,Health Monitoring&Evaluation