A procedure to approximate non-causal adaptive IIR filtering is described. Such structures could be useful, for instance, in the equalization of non-minimum phase communication channels. The procedure is based on backward calculations within blocks of samples and we show that for adaptive filtering the overlap-save method is more suitable than the overlap-add method. Moreover, a temporary freez...

We present a formally verified quantifier elimination procedure for the first order theory over linear mixed real-integer arithmetics in higher-order logic based on a work by Weispfenning. To this end we provide two verified quantifier elimination procedures: for Presburger arithmitics and for linear real arithmetics.

TiCl4-promoted aldol reaction of ketones as aldol acceptors followed by elimination of the titanoxy group from the Ti-aldolates affords β,β-disubstituted α,β-unsaturated carbonyl compounds in a one-pot procedure. The use of additives, such as DMF, N,N,N',N'-tetramethylethylenediamine, and pyridine, in the elimination step was found to be important.

We apply adjoint algorithmic differentiation (AAD) to the risk management of securities when their price dynamics are given by partial differential equations (PDE). We show how AAD can be applied to forward and backward PDEs in a straightforward manner. In the context of one-factor models for interest rates or default intensities, we show how price sensitivities are computed reliably and orders...

‎in this paper a nonlinear backward parabolic problem in one‎ ‎dimensional space is considered‎. ‎using a suitable iterative‎ ‎algorithm‎, ‎the problem is converted to a linear backward parabolic‎ ‎problem‎. ‎for the corresponding problem‎, ‎the backward finite‎ ‎differences method with suitable grid size is applied‎. ‎it is shown‎ ‎that if the coefficients satisfy some special conditions‎, ‎th...

This paper shows how a symmetric and non-deterministic cut elimination procedure for a classical sequent calculus can be faithfully simulated using a non-deterministic choice operator to combine diierent`double-negation' translations of each cut. The resulting interpretation of classical proofs in a-calculus with non-deterministic choice leads to a simple proof of termination for cut elimination.

A new method namely, algebraic elimination method is proposed for finding a complementarity feasible solution to the linear complementarity problem which have applications in non-linear programming, economics, game theory and engineering. Then, the algebraic elimination method is extended to quadratic programming problems. The solution procedure is illustrated by means of numerical examples.