By Kim H.

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**Example text**

4 Global Approximation Within global approximation two directions can be distinguished. In the ﬁrst case from the given data an expression in a closed form is to be derived being valid for the whole interesting domain and containing parameters, the number of which being as small as possible, but nevertheless representing the unknown function suﬃciently precisely. e. of a mathematical structure for the approximating function. g. g. g. recorded by an electronic medium. e. functions, which are diﬀerent from zero only over a small subdomain), in order that the specialist will be able to consider or investigate the local behaviour of the function at every place of the interesting domain.

It seems reasonable to introduce the resulting intervals as sets of all possible results for single values: A ∗ B := {a ∗ b | a ∈ A, b ∈ B} with ∗ ∈ {+, −, ·, :} . 9) already strange eﬀects occur. , this results in: A − A = [−4, 4]; B − B = [−2, 2]; B : B = 1 ,2 . e. one can change the sequence of summands or factors and put in brackets arbitrarily. But for a simultaneous use of addition and multiplication there are no longer a distributive law, by which sums could be multiplied out. , for A = [−2, 1] to the astonishing result A2 + A = [−4, 5] and A(A + 1) = [−4, 2].

G. Hughes (1987). The problem is interesting for data analysis by the inﬂuence of model impreciseness. The mixed boundary value problem is an idealization of the practical problem; hence the coeﬃcients of the diﬀerential equation may be characterizing values of the material used, which are known, in the case given, only imprecisely. g. when they are obtained by measurement or observation. Both inﬂuences are investigated today by sensitivity analysis, by which the eﬀect of small changes is considered theoretically.

### 4-dimensional anti-Kahler manifolds by Kim H.

by Steven

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