Multidimensional integrable Schrodinger operators with matrix potential

The Schrodinger operators with matrix rational potential, which are D-integrable, i.e., can be intertwined with the pure Laplacian, are investigated. Corresponding potentials are uniquely determined by their singular data which are a configuration of the hyperplanes in C-n with prescribed matrices. We describe some algebraic conditions (matrix locus equations) on these data, which are sufficient for D-integrability. As the examples some matrix generalizations of the Calogero-Moser operators are considered

Collider aspects of flavour physics at high Q

This review presents flavour related issues in the production and decays of heavy states at LHC, both from the experimental side and from the theoretical side. We review top quark physics and discuss flavour aspects of several extensions of the Standard Model, such as supersymmetry, little Higgs model or models with extra dimensions. This includes discovery aspects as well as measurement of several properties of these heavy states. We also present public available computational tools related to this topic.Comment: Report of Working Group 1 of the CERN Workshop ``Flavour in the era of the LHC'', Geneva, Switzerland, November 2005 -- March 200

On a remarkable functional equation in the theory of generalised Dunkl operators and transformations of elliptic genera

The functional equation f(x)(g(x+y)+g(x-y))+f(y)(g(x+y)-g(x-y))=0, arising from the theory of the generalised Dunkl operators is considered. It turns out that f and g in general are the certain elliptic functions related by the composition of the Landen's and imaginary Jacobi's transformations (LJ-transformation). This leads to some new relations in the theory of elliptic genera in topology, which imply certain divisibility relations of a new type for the signatures of the stably almost complex manifold and its canonical virtual submanifolds. (orig.)SIGLEAvailable from TIB Hannover: RR 1596(124) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDeutsche Forschungsgemeinschaft (DFG), Bonn (Germany)DEGerman

On a remarkable functional equation in the theory of generalised Dunkl operators and transformations of elliptic genera

The functional equation f(x)(g(x+y)+g(x-y))+f(y)(g(x+y)-g(x-y))=0, arising from the theory of the generalised Dunkl operators is considered. It turns out that f and g in general are the certain elliptic functions related by the composition of the Landen's and imaginary Jacobi's transformations (LJ-transformation). This leads to some new relations in the theory of elliptic genera in topology, which imply certain divisibility relations of a new type for the signatures of the stably almost complex manifold and its canonical virtual submanifolds. (orig.)SIGLEAvailable from TIB Hannover: RR 1596(124) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDeutsche Forschungsgemeinschaft (DFG), Bonn (Germany)DEGerman