Download Berliner Balanced Scorecard: Customer Perspective by Schmeisser W., Clausen L., Lukowsky M. PDF

Download Berliner Balanced Scorecard: Customer Perspective by Schmeisser W., Clausen L., Lukowsky M. PDF

By Schmeisser W., Clausen L., Lukowsky M.

This loose textbook is a precis of "Berliner Balanced Scorecard: the client Perspective". The 'Berliner Balanced Scorecard' technique demonstrates that the views of the Balanced Scorecard are linkable and that every of them may be calculated. even as, the process faces the problem to quantify human source capital.

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T→0 t→0 t→0 t→0 For |t| sufficiently small and t < 0, the set F(t) \ A has five connected components and each of them corresponds to a line component in f −1 (t). Namely, we have: F(t) \ A = ([a1 (t), −5[×{t}) ∪ (] − 5, a2 (t)] × {t}) ∪ ∪ ([a3 (t), 0[×{t}) ∪ (]0, a4 (t)] × {t}) ∪ ([a5 (t), ∞[×{t}) . We also have: F(0) \ A = ([−1, 0[×{0}) ∪ (]0, 5[×{0}) ∪ (]5, ∞[×{0}) . Therefore, when t < 0 tends to zero, the line components in f −1 (t) corresponding to the segments ([a1 (t), −5[×{t}) ∪ (] − 5, a2 (t)] × {t}) will vanish at infinity since limt→0 a1 (t) = limt→0 a2 (t) = −5 ∈ A.

HàL], yields the following criterion: a reduced fibre Xt0 is typical if and only if its Euler characteristic χ (Xt0 ) is equal to the Euler characteristic 28 2 Detecting atypical values via singularities at infinity of a general fibre of f . We also have the following equivalent form of the Hà–Lê criterion, cf. 3: A regular fibre Xt of a complex polynomial function is typical if and only if there are no vanishing cycles at infinity corresponding to this fibre. We observe that in both the real and the complex setting, a criterion containing the idea of ‘nonvanishing’ occurs.

The space FD is obtained from Ft by attaching to it FDext and FDint . We have proved above that the attaching of FDint amounts to attaching n-cells. Next, we have proved that the pair (FDext , Ft ∩ FDext ) is (n − 1)-connected. Then, by Switzer’s result [Sw, Prop. 13], the attaching of FDext to Ft means attaching of cells of dimension ≥ n. It then follows that FD is (up to homotopy) the result of attaching a finite number of cells of dimension ≥ n to Ft . 1, the whole space Cn = FC is obtained by attaching a finite number of cells of dimensions ≥ n to a general fibre Ft .

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