By expressing the conditional causal risk di¤erence as a sum of products of stratum speci…c risk di¤erences and conditional probabilities, it is possible to give a classi…cation of the types of causal relationships that can give rise to e¤ect modi…cation on the risk di¤erence scale. Directed acyclic graphs make clear the necessary causal relationships for a particular variable to serve as an e¤...

In this paper, two possible switched capacitor implementations of companding lters are discussed. The governing di erence equations, an estimate of the increase in the dynamic range for a given power consumption and possible topologies are given.

"In this article, we give su cient conditions for the existence, uniqueness and Ulam{Hyers stability of solutions a coupled system two-point nabla fractional di erence boundary value problems subject to anti-periodic conditions, using vector approach Precup [4, 14, 19, 21]. Some examples are included illustrate theory."

For two slanted matrices there is shown the close connection between their spectral properties and the zeros of their corresponding symbols The results are applied to two scale di erence equations Subject Classi cation A B

We consider cell centered nite di erence discretizations with lo cal re nement for nonsymmetric boundary value problems Preconditioners with mesh independent convergence properties for corresponding matrices are constructed The method is illustrated with numerical experiments

We investigate numerical valuation of cross-currency interest rate-based derivatives under Babbs' extended Vasicek-style model by numerical solution of the associated partial di erential equation (PDE) | in particular, we consider the terminable di erential (di ) swap. Firstly we precisely formulate, in terms of their cash ows, various types of single and cross-currency swaps and swaptions. We ...

A modi ed triangle based adaptive di erence stencil for the numerical approximation of scalar hyperbolic conservation laws in two space dimensions is constructed. The scheme satis es the maximum principle and approximates the ux with second order accuracy. 3

We compare two load balancing techniques for Cayley graphs based on information and load exchange between neighboring vertices. In the rst scheme, called natural di usion, each vertex gives (or receives) a xed part of the load di erence to (from) its direct neighbors. In the second scheme, called Cayley di usion, each vertex successively gives (or receives) a part of the load di erence to (or f...

In the last decades, fractional diierential equations have become more and more popular among scientists and daring engineers in order to model various stable physical phenomena with anomalous decay, say that are not of exponential type. Moreover in discrete-time series analysis, so-called fractional ARMA models have been proposed in the literature in order to model stochastic processes, the au...

We present benchmark simulations for the 8:1 di erentially heated cavity problem, the focus of a special session at the rst MIT conference on Computational Fluid and Solid Mechanics in June 2001. The numerical scheme is a fourth-order nite di erence method based on the vorticity-stream function formulation of the Boussinesq equations. The momentum equation is discretized by a compact scheme wit...