We surview variants and extensions of the LLL-algorithm of Lenstra, Lenstra Lovász, extensions to quadratic indefinite forms and to faster and stronger reduction algorithms. The LLL-algorithm with Householder orthogonalisation in floating-point arithmetic is very efficient and highly accurate. We surview approximations of the shortest lattice vector by feasible lattice reduction, in particular ...

In this paper, we introduce admissible vectors of covariant representations of a dynamical system which are extensions of the usual ones, and compare them with each other. Also, we give some sufficient conditions for a vector to be admissible vector of a covariant pair of a dynamical system.  In addition, we show the existence of Parseval frames for some special subspaces of $L^2(G)$ related to...

The magnetic properties of strained thin films of gadolinium are characterized by a wave vector and thickness dependence of the exchange splitting. The spin-resolved band structure has been mapped by spin polarized photoemission, and provides considerable insight into the relationship between magnetism of local moment systems, and band structure. For more than 30 years theorists [l] have predic...

We compute non–perturbatively the renormalization coefficients of scalar and pseudoscalar operators, local vector and axial currents, conserved vector and axial currents, and O LL over a wide range of energy scales using a scaling technique that connects the results of simulations at different values of coupling β. We use the domain wall fermion formulation in the quenched approximation at a se...

We compute non–perturbatively the renormalization coefficients of scalar and pseudoscalar operators, local vector and axial currents, conserved vector and axial currents, and O∆S=2 LL over a wide range of energy scales using a scaling technique that connects the results of simulations at different values of coupling β. We use the domain wall fermion formulation in the quenched approximation at ...