As a byproduct of Theorem 3.1 we can give an estimate of the truncation error which arises if one ignores all the samples outside a finite interval. More precisely, we have the following corollary. Theorem 4.1: Let us define the truncation error E N (t) as follows: E N (t) = F(t) 0 jnjN F (t n)S n (t): Then jE N (t)j 2 2p0q bA p C ^ (1 0 p D)(p 0 q 0 1)N p0q01 ; t in the compact set K (14) wher...

The " truncation procedure " initiated by Weiss et al. is best understood as a Darboux transformation. If it leads to the Lax pair of the PDE under study, the Bäcklund transformation follows by an elimination, thus proving the integrability. We present the state of the art of this powerful technique. The easy situations were all handled by the WTC one–family truncation and its homographically i...

We develop a new method to obtain symmetrization inequalities of Sobolev type. Our approach leads to new inequalities and considerable simplification in the theory of embeddings of Sobolev spaces based on rearrangement invariant spaces.

The computation of acoltstic pressure fluctuations in a variable area tube is often done using the K elly-Lochbaum reflection model. The numerical scheme derived from this model can be put into the context of finite-difference approximations to a differential equation describing acoustic wave propagation (a hyperbolic differential equation). Quantitative criteria for goodness of finite-differen...

The a posteriori error evaluation based on differential approximation of a finitedifference scheme and adjoint equations is addressed. The differential approximation is composed of primal equations and a local truncation error determined by a Taylor series in Lagrange form. This approach provides the feasibility of both refining the solution and using the Holder inequality for asymptotic boundi...

We introduce an accurate and efficient alternating-direction method for solving a viscous wave equation which is based on a three-level, second-order correct implicit algorithm and which has a splitting error not significantly larger than the truncation error of the base method.

We study the orientifold truncation that arises when compactifying type II string theory on Calabi-Yau orientifolds with O3/O7-planes, in the context of supergravity. We look at the N=2 to N=1 reduction of the hypermultiplet sector of N=2 supergravity under the truncation, for the case of very special quaternionic-Kähler target space geometry. We explicitly verify the Kähler structure of the tr...