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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).

PI for ǫ ǫP ǫσ.Theorem 1 can be generalized to any arbitrary protocol with a proper modular structure.

A key advance by Bayly & Childress (1989) was to realise that the adjoint op-erator Tε (working in the space of L.