Let A be a local commutative principal ideal ring. We study the double coset space of GLn(A) with respect to the subgroup of upper triangular matrices. Geometrically, these cosets describe the relative position of two full flags of free primitive submodules of A. We introduce some invariants of the double cosets. If k is the length of the ring, we determine for which of the pairs (n, k) the dou...

We consider scheduling of colored packets with transition costs which form a general metric space. We design 1 − O (√ MST (G) L ) competitive algorithm. Our main result is an hardness result of 1 − Ω (√ MST (G) L ) which matches the competitive ratio of the algorithm for each metric space separately. In particular we improve the hardness result of Azar at el. for uniform metric space. We also e...

We present the real-space block renormalization group equations for fermion systems described by a Hubbard Hamiltonian on a triangular lattice with hexagonal blocks. The conditions that keep the equations from proliferation of the couplings are derived. Computational results are presented including the occurrence of a first-order metal-insulator transition at the critical value of U/t ≈ 12.5.

We study the quantal energy spectrum of triangular billiards on a spherical surface. Group theory yields analytical results for tiling billiards while the generic case is treated numerically. We find that the statistical properties of the spectra do not follow the standard random matrix results and their peculiar behaviour can be related to the corresponding classical phase space structure.

In this note, we would like to explore some of the issues suggested by the discussion paper of Pizlo et. al. The context is the study of image of planar objects taken with calibrated cameras. However, in this note, we shall consider the question using notation that has become somewhat standard in the literature of computer vision, particularly in the study of uncalibrated cameras. The projectio...

Let £ be a closed, bounded, convex subset of a Banach space X, /: E —»E. Consider the iteration scheme defined by x"« = xQ e E, x , = ñx ), x = 2" na ,x., nal, where A is a regular weighted mean n + l ' n n * = 0 nk k o er matrix. For particular spaces X and functions /we show that this iterative scheme converges to a fixed point of /. Let X be a normed linear space, E a nonempty closed bounded...

In this article, we formulate and analyze a two-level preconditioner for Optimized Schwarz and 2-Lagrange Multiplier methods for PDEs with highly heterogeneous (multiscale) diffusion coefficients. The preconditioner is equipped with an automatic coarse space consisting of low-frequency modes of the subdomain Dirichlet-to-Neumann maps. Under a suitable change of basis, the preconditioner is a 2 ...