We move the classical, divided-di erence construction for B-splines into a connectionmatrix setting by establishing a one-sided basis for connection-matrix splines together with a di erencing process that transforms the one-sided basis into a compact-support basis that partitions unity.

Some oscillation criteria for the oscillatory behavior of fourth order superlinear dynamic equations on time scales are established. Criteria are proved that ensure that all solutions of superlinear and linear equations are oscillatory. Many of our results are new for corresponding fourth order superlinear di¤erential equations and fourth order superlinear di¤erence equations.

The Finite-Diierence Time Domain (FDTD) method has received considerable attention recently. The popularity of the FDTD method stems from the fact that it is not limited to a speciic geometry and it does not restrict the constitutive parameters of a scatterer. Furthermore, it provides a direct solution to problems with transient illumination, but can also be used for harmonic analysis. However,...

Several recent papers have shown how to approximate the diierence P i jai ? bi j or P jai ? bi j 2 between two functions, when the function values ai and bi are given in a data stream, and their order is chosen by an adversary. These algorithms use little space (much less than would be needed to store the entire stream) and little time to process each item in the stream and approximate with sma...

We present results for three new algorithms for setting the step-size parameters, and , of temporal-diierence learning methods such as TD(). The overall task is that of learning to predict the outcome of an unknown Markov chain based on repeated observations of its state trajectories. The new algorithms select step-size parameters online in such a way as to eliminate the bias normally inherent ...

We consider Lebesgue{integrable, compactly supported solutions of two{ scale diierence equations and investigate the relations between translates of these solutions. A detailed study of corresponding invariant subspaces leads to new observations concerning the factorization of the reenement mask and certain spectral properties of corresponding coeecient matrices. In particular, new necessary co...

Classical nite-diierence methods apply only over regions that are rectangular or decomposed in several rectangular subdomains. We call a nite-diierence scheme direct if it can be applied over any region decomposed by means of a logically-rectangular grid. We introduce a second-order and easy-to-use direct scheme to solve boundary-value problems. Deduction of the method is elementary and its res...

Non-deleting Word-into-Trees Transducers with bounded difference are investigated in this paper. Informally, these transducers which produce trees from words have the property that the diierence of height of any couple of trees (the input tree being a word) is bounded. We establish the fact that the tree transformations induced by such transducers have some good closure properties.

Clock Di erence Diagrams (CDDs), a BDD-like data structure for model checking of timed automata, were presented in 1999. After the original article the work on them seems to have stopped, although there are still important open questions. The proposed algorithm relied on the traditionally used data structure (DBMs) for most operations. CDDs de nition required that repeated subtrees were aliased...

The point source traveltime eld has an upwind singularity at the source point. Consequently, all formally high-order nite-diierence eikonal solvers exhibit rst-order convergence and relatively large errors. Adaptive upwind nite-diierence methods based on high-order Weighted Essentially NonOscillatory (WENO) Runge-Kutta diierence schemes for the paraxial eikonal equation overcome this diiculty. ...