By Abraham Warshawsky, Abraham Deshe, Guy Rossey, Abraham Patchornik
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Extra info for Functionalization of polystyrene. II: Synthesis of chelating polymers by alkylation of 4-aminomethylpolystyrene
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Cina, Phys. Rev. Lett. 66, 1146 (1991). 42 C I N A , SMITH, AND ROMERO-ROCH~N 44. R. L. Whetten, K. S. Haber, and E. R. Grant, J . Chem. Phys. 84, 1270 (1986). 45. L. D. Landau and E. M. Lifshitz, Mechanics, 3rd edition (Pergamon Press, Oxford, 1976), p. 80. 46. M. Messina and R. D. Coalson, J . Chem. Phys. 90, 4015 (1989). 47. G. Delacretaz, E. R. Grant. R. L. Whetten, L. Woste, and J. W. Zwanziger, Phys. Rev. Left. 56, 2598 (1986). 48. R. L. Whetten and E. R. Grant, J . Chem. Phys. 84, 654 (1986).
By writing Eq. 3) explicitly as q,,) = - r,,IMw,( 1 - sin’@ cos’@), we is less see that the range of orientations within which the magnitude of than a certain value, say d m , decreases with increasing pulse energy. In practice, the nonresonant pulse pair will be replaced with a sequence of such pairs, spaced at the ground state pseudorotational period, in order to drive the pseudorotation to large amplitude and discriminate against other low frequency modes [30,49-521. 37 ELECTRONIC GEOMETRIC PHASES APPENDIX B.
8) is usually neglected through the slowly varying amplitude approximation (SVAA) [3,8]. = Ej(r)exp[i+,(r)], Eq. 10) Both Ej(r)and 4j(r) are real, and the real and imaginary parts of Eq. 10) have to be separately satisfied. Thus, both the field amplitude, gj(r) o r Ej(r),and the absolute phase, 4j(r), must not vary with r. On the other hand, E(r, t ) will decrease exponentially with r when kj is complex due to the presence of material resonance. Next consider the case where the nonlinear induced polarization at sth order (s > 1) at the frequency w,, (given by Eq.