The determination of tervalent chromium and iron in chromic acid

Chromic acid is analysed for tervalent chromium by separation of Cr(III) from Cr(VI) by precipitation as the hydrous oxide, with Zn(OH)(2) as a carrier. The hydrous oxide is collected by centrifugation and dissolved in perchloric acid, then Cr(III) is complexed with 1,2-diaminocyclohexanetetra-acetic acid and measured spectrophotometrically at 540 mmicro. Repetitive analysis of a sample of chromic acid showed 93 ppm of Cr(III) (s = 13, n = 9). Iron in chromic acid is also separated as the hydrous oxide, then dissolved in HCl, reduced to Fe(II) with hydroxylamine hydrochloride, complexed with bathophenanthroline disulphonic acid and measured spectrophotometrically at 533 mmicro. Repetitive analyses of a sample of chromic acid showed 2-6 ppm of iron (s = 0.35, n = 8).     

Numerical solutions of fully non‐linear and highly dispersive Boussinesq equations in two horizontal dimensions

This paper investigates preconditioned iterative techniques for finite difference solutions of a high‐order Boussinesq method for modelling water waves in two horizontal dimensions. The Boussinesq method solves simultaneously for all three components of velocity at an arbitrary z‐level, removing any practical limitations based on the relative water depth. High‐order finite difference approximations are shown to be more efficient than low‐order approximations (for a given accuracy), despite the additional overhead. The resultant system of equations requires that a sparse, unsymmetric, and often ill‐conditioned matrix be solved at each stage evaluation within a simulation. Various preconditioning strategies are investigated, including full factorizations of the linearized matrix, ILU factorizations, a matrix‐free (Fourier space) method, and an approximate Schur complement approach. A detailed comparison of the methods is given for both rotational and irrotational formulations, and the strengths and limitations of each are discussed. Mesh‐independent convergence is demonstrated with many of the preconditioners for solutions of the irrotational formulation, and solutions using the Fourier space and approximate Schur complement preconditioners are shown to require an overall computational effort that scales linearly with problem size (for large problems). Calculations on a variable depth problem are also compared to experimental data, highlighting the accuracy of the model. Through combined physical and mathematical insight effective preconditioned iterative solutions are achieved for the full physical application range of the model. Copyright © 2004 John Wiley & Sons, Ltd.     

Infinite horizon BSDEs in infinite dimensions with continuous driver and applications

This paper is devoted to forward-backward systems of stochastic differential equations in which the forward equation is not coupled to the backward one, both equations are infinite dimensional and on the time interval [0, + ∞). The forward equation defines an Ornstein-Uhlenbeck process, the driver of the backward equation has a linear part which is the generator of a strongly continuous, dissipative, compact semigroup, and a nonlinear part which is assumed to be continuous with linear growth. Under the assumption of equivalence of the laws of the solution to the forward equation, we prove the existence of a solution to the backward equation. We apply our results to a stochastic game problem with infinitely many players.     

Generalized Mehler Semigroups: The Non-Gaussian Case

We study generalized Mehler semigroups, introduced in [7], with special emphasis on the non-Gaussian case. We review and simplify the method of construction. In the general (non-Gaussian) case we construct an associated cadlag Markov process in an appropriate state space obtained as a solution of a stochastic equation which can be solved by . We also show tightness of the associated (r, p)-capacities. Invariant measures, time regularity and a definition of the generator are also studied.     

Backward Stochastic Differential Equations in Infinite Dimensions with Continuous Driver and Applications

In this paper we prove the existence of a solution to backward stochastic differential equations in infinite dimensions with continuous driver under various assumptions. We apply our results to a stochastic game problem with infinitely many players.