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This means that it is necessary to use the variational Pad6-Ritz principle with the upper bound on 63 . As a consequence it is important to know how to get not too bad upper bounds for 63 = <~ [(T-}) + o (V-If) This problem will be considered in future work. VI - THE CASE OF AN INFINITE NUMBER OF BODIES Let us consider the case where the number Z of bodies tends to infinity. Let us suppose that the ground state energy per body, E(Z)/z" has a finite limit when Z o tends to infinity and that this limit E ° is such that E o E (Z) o Z < for Z > Z (VI-I) o" This case seems to be not unlikely for nuclear physics.

That the covariance condition equation the line S 4 is a diagonal between it states Qm to f(Zl,O ) and to zero the (h,2m+l-~) and is "shared" a geometrical they would usually I had to select m. to pairs O~Xr~2m+l; in the points the reason why only half the equations square I showed however; (O,2m) suggested line $4, with corresponding , and 2m + 1 , out of which is that we need to choose the lattice square, points, = (vi) such as SI+$2+$3 since the next hl + X2 contained up to (2m,O) of the Pad~ approximants these points, property two requirements region O~Xr~m , in Qm had to be the projection This left me short of m equations, and f(O,z2); of points the points that Qm might be a triangular-shaped Figure chose was the square must of with the to a R may be lie on a single 38 line making an angle are adopted, Figure i.

Ed. 4, 2 (1974). 31 (1970), Common & P. R. Graves-Morris, (1974), 841. 147. J. Inst. Math. Applic. 13 229. 6. L. Gammel (Private Communication). 7. R. 8. R. J. Makinson, 299. 9. R. Graves-Morris, R. J. Applic. 13 (1974), 311. Inst. iO. R. Graves-Morris, 18 (1975), 81. J Ii. R. Hughes Jones, Theory. 12. R. Chisholm 421. 13. R. Graves-Morris AMD 674 (1974). 14. R. Chisholm A344, 365. 15. R. E. Roberts, Kent preprint (1975). 16. R. J. Samwell, Kent preprint (1975). 17. W. P. 18. P. W. A 19. R. Graves-Morris 46-50.

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A Relativist's Toolkit - The Math of Black Hole Mechanics by E. Poisson


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