Quadratic Algebra associated with Rational Calogero-Moser Models

Classical Calogero-Moser models with rational potential are known to be superintegrable. That is, on top of the r involutive conserved quantities necessary for the integrability of a system with r degrees of freedom, they possess an additional set of r-1 algebraically and functionally independent globally defined conserved quantities. At the quantum level, Kuznetsov uncovered the existence of a quadratic algebra structure as an underlying key for superintegrability for the models based on A type root systems. Here we demonstrate in a universal way the quadratic algebra structure for quantum rational Calogero-Moser models based on any root systems.Comment: 19 pages, LaTeX2e, no figure

On the Rotating Charged Black String Solution

A rotating charged black string solution in the low energy effective field theory describing five dimensional heterotic string theory is constructed. The solution is labelled by mass, electric charge, axion charge and angular momentum per unit length. The extremal limit of this solution is also studied.Comment: 12 pages, IMSC-93/6,(Phyzzx macro), January 199

Endoscopic Management of Upper Tract Urothelial Carcinoma

Nephroureterectomy is currently the gold standard for management of upper urinary tract urothelial carcinoma despite it results. This review article in the loss of a renal unit. The ultimate aim of endoscopic management of this condition is cancer control whilst preserving renal function and the integrity of the urinary tract. Endoscopic treatments of upper tract TCC include the antegrade percutaneous and retrograde ureteroscopic approaches. This review article summarizes the endoscopic management of upper tract urothelial carcinoma, surveillance of the disease after endoscopic management and adjuvant therapy. The main message regarding endoscopic management of upper tract urothelial cancer is that patients must be carefully selected. Patient selection is based on tumour size, grade, and multifocality. Single low-grade tumours, less than 1.5 cm in size, generally have a good outcome with endoscopic treatment provided that they have regular ureteroscopic surveillance. Ureteroscopic treatment of high-grade tumours is essentially palliative. It is essential that patients are motivated and compliant as lifetime follow-up is necessary. However, until large randomized trials with long-term follow-up are performed, endoscopic management cannot be considered a standard treatment and should be limited to poor performance status patients

Algebraic Linearization of Dynamics of Calogero Type for any Coxeter Group

Calogero-Moser systems can be generalized for any root system (including the non-crystallographic cases). The algebraic linearization of the generalized Calogero-Moser systems and of their quadratic (resp. quartic) perturbations are discussed.Comment: LaTeX2e, 13 pages, no figure

Magnetic Wormholes and Vertex Operators

We consider wormhole solutions in $2+1$ Euclidean dimensions. A duality transformation is introduced to derive a new action from magnetic wormhole action of Gupta, Hughes, Preskill and Wise. The classical solution is presented. The vertex operators corresponding to the wormhole are derived. Conformally coupled scalars and spinors are considered in the wormhole background and the vertex operators are computed. ( To be published in Phys. Rev. D15)Comment: 18 pages of RevTex, preprint IP/BBSR/94-2

Exactly solvable potentials of Calogero type for q-deformed Coxeter groups

We establish that by parameterizing the configuration space of a one-dimensional quantum system by polynomial invariants of q-deformed Coxeter groups it is possible to construct exactly solvable models of Calogero type. We adopt the previously introduced notion of solvability which consists of relating the Hamiltonian to finite dimensional representation spaces of a Lie algebra. We present explicitly the $G_2^q$-case for which we construct the potentials by means of suitable gauge transformations.Comment: 22 pages Late

Quantum Calogero-Moser Models: Integrability for all Root Systems

The issues related to the integrability of quantum Calogero-Moser models based on any root systems are addressed. For the models with degenerate potentials, i.e. the rational with/without the harmonic confining force, the hyperbolic and the trigonometric, we demonstrate the following for all the root systems: (i) Construction of a complete set of quantum conserved quantities in terms of a total sum of the Lax matrix (L), i.e. (\sum_{\mu,\nu\in{\cal R}}(L^n)_{\mu\nu}), in which ({\cal R}) is a representation space of the Coxeter group. (ii) Proof of Liouville integrability. (iii) Triangularity of the quantum Hamiltonian and the entire discrete spectrum. Generalised Jack polynomials are defined for all root systems as unique eigenfunctions of the Hamiltonian. (iv) Equivalence of the Lax operator and the Dunkl operator. (v) Algebraic construction of all excited states in terms of creation operators. These are mainly generalisations of the results known for the models based on the (A) series, i.e. (su(N)) type, root systems.Comment: 45 pages, LaTeX2e, no figure

OmniCAV : a simulation and modelling system that enables “CAVs for All”

OmniCAV is laying the foundations for the development of a comprehensive, robust and secure simulator, aimed at providing a certification tool for Connected Autonomous Vehicles (CAVs) that can be used by regulatory and accreditation bodies, insurers and manufacturers to accelerate the safe development of CAVs. To achieve this, OmniCAV is using highly detailed road maps, together with a powerful combination of traffic management, accident and CCTV data, to create a high-fidelity traffic and driving simulation environment to interact with the AV under test. Scenarios for testing are developed and randomised in a holistic way to avoid CAVs training to specific conditions. Critically, the simulator offers coverage of a representative element of the U.K. road network, through encompassing rural roads, peri-urban and urban roads to enable autonomy for all. The validity of the synthetic test environment compared to the real-world is of particular importance, and OmniCAV will be tested and refined through an iterative approach involving real-world comparisons and working in conjunction with a CAV testbed