For the nite volume method applied to scalar hyperbolic conservation law in two space dimensions, the uniform BV estimate for an approximate solution is not available on unstructured grids. Therefore the convergence proofs are based on methods which needs less regularity, e.g. on the Young measure theory. In this contribution we discuss the so-called ((t)-condition which serves as a suitable re...

For an infinite-dimensional linear quadratic control problem in Hilbert space, approximation of the solution of the algebraic Riccati operator equation in the strong operator topology is considered under conditions weaker than uniform exponential stability of the approximating systems. As an application, strong convergence of the approximating Riccati operators in case of a previously developed...

In magnetic resonance imaging (MRI), methods that use a non-Cartesian, e.g. spiral, grid in k-space are becoming increasingly important. This talk focuses on a recently proposed implicit discretisation scheme which generalises the standard approach based on gridding. While the latter succeeds for sufficiently uniform sampling sets and accurate estimated density compensation weights, the implici...

Abstract. We deal with random processes obtained from a homogeneous random process with independent increments by replacement of the time scale and by multiplication by a norming constant. We prove the convergence in distribution of these processes to Wiener process in the Skorohod space endowed by the topology of uniform convergence. An integral type almost sure version of this limit theorem i...

Constraint propagation is a general algorithmic approach for pruning the search space of a CSP. In a uniform way, K. R. Apt [1] has defined a computation as an iteration of reduction functions over a domain. In [2] he has also demonstrated the need for integrating static properties of reduction functions (commutativity and semi-commutativity) to design specialized algorithms such as AC3 and DAC...

For supervised classification problems, it is well known that learnability is equivalent to uniform convergence of the empirical risks and thus to learnability by empirical minimization. Inspired by recent regret bounds for online convex optimization, we study stochastic convex optimization, and uncover a surprisingly different situation in the more general setting: although the stochastic conv...

Necessary and sufficient conditions are given so that the space C(X, E) of all continuous functions from a zero-dimensional topological space X to a nonArchimedean locally convex space E, equipped with the topology of uniform convergence on the compact subsets of X, to be polarly absolutely quasi-barrelled, polarly אo-barrelled, polarly `∞-barrelled or polarly co-barrelled. Also, tensor product...

We consider a dynamic programming problem with arbitrary state space and bounded rewards. Is it possible to define in an unique way a limit value for the problem, where the “patience” of the decision-maker tends to infinity ? We consider, for each evaluation θ (a probability distribution over positive integers) the value function vθ of the problem where the weight of any stage t is given by θt,...

The Joyal bijection between doubly-rooted trees and mappings can be lifted to a transformation on function space which takes tree-walks to mapping-walks. Applying known results on weak convergence of random tree walks to Brownian excursion, we give a conceptually simpler rederivation of the 1994 Aldous-Pitman result on convergence of uniform random mapping walks to reeecting Brownian bridge, an...