By H. Jacquet, R. P. Langlands

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Extra resources for Automorphic Forms on GL(2) (part 2)

Example text

22 (7) we have 40"Q 8=8-8+'11--_ e 0 oz oz 402 Q (/Je= (/J- (/Jo+ 'II~. Clearly, sinee all the terms of the right-hand sides axeept 8 and (/J ean be regarded as known the problems of finding 8, (/J and 8 e, (/Je are equivalent. This notation often enables a eonsiderable simplifieation to be made in the algebra. 76. 72 (3) we have ·x . 4 OzS = (/J = 2 f-t (en - e",,,,+ 2 z e",,,) = 2 f-t U; - :: + and therefore 4 f-t 0 (u so that 4 f-t (u i (:; 4 f-t o (u-iv) OZ + i v) OZ + iv) = where J(z) is to be determined.

10 (i)], the positive sense of description is counterc1ockwise for Co and c10ckwise for Cl and C2• Fig. 10 (i) We shall designate by L the left-hand region occupied by the material and by R the right-hand region free of the material. Note that in the above example the region L is connected but that the region R is disconnected. Should the contour Co lie entirely at infinity the positive sense of description of the accessible boundaries Cl and C2 is c1ockwise. More generally we shall designate by L the region on the left of an observer who describes C in a prescribed sense.

And so dz .. - = -~e-'rx. /dZ. OZ2 ds ds (7) 32 11. The eomplex stresses and their properties in the isotropie ease If we denote by u n , U s the normal and tangential components of the displacement at P, (4) and (5) give (u n + i u s ) Now ds = = (u + iv) i ~: Idil = Idzl. l (u n + ius) = i I~;I . l (

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