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δP = dim(ÕP /OP ). • Milnor number µ = O/ < J(P ) >. • Tjurina number τ = O/ < P, J(P ) >. Note: The first table is motivated by exercise 3.8 of Hartshorne [8] page

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op, yop), thenthe following inequality holds:. DJ(uop, yop)(u uop, y yop) 0 (u, y) Uad Yad.

1. Introduction. Quasi-interpolation operators, that is, operators achieving op-timal rates of convergence also for classes of functions of low regularity have a long his-tory, for example in splines

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The Dirac operators of prime interest to low-energy QCD have zero (or small) mass.To express the massless nature ofDA one introduces an object called thechirality op-eratorΓ in mathematics

exp. (1. tlog. (1. S(t). A(t). ))= exp. (S(t). tA(t)(1 op(1)). )= ... 1. S(t). tA(t)(1 op(1)). Substituting this into (9.3) yields. tA(t).