By J.P. Jesudason, C.H. Lai, Louis H. Y. Chen, J. Packer Jesudason, C. H. Lai, C. H. Oh, K. K. Phua, Eng-Chye Tan

The overseas convention on primary Sciences: arithmetic and Theoretical Physics supplied a discussion board for reviewing a few of the major advancements in arithmetic and theoretical physics within the twentieth century; for the prime theorists in those fields to expound and speak about their perspectives on new principles and traits within the easy sciences because the new millennium approached; for expanding public understanding of the significance of simple study in arithmetic and theoretical physics; and for selling a excessive point of curiosity in arithmetic and theoretical physics between university scholars and academics. This was once a tremendous convention, with invited lectures through a number of the top specialists in numerous fields of arithmetic and theoretical physics.

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Extra resources for Challenges for the 21st century: International Conference on Fundamental Sciences, Mathematics and Theoretical Physics, Singapore, 13-17 March 2000

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Sin X=Sin X COSt 27 THE DECOMPOSrriON MEFHODINSEVERALDIMENS/ONS We are dealing with a methodology for solution of physical systems which have a solution, and we seek to find this solution without changing the problem to make it tractable. The conditions must be known; otherwise, the model is not complete. If the solution is known, but the initial conditions are not, they can be found by mathematical exploration and consequent verification. :o An where the An are generated for the specific f(u).

Thus we will drop terms involving and x3 and higher terms. Then e -t e e =1-t+2 sinx= x x2 cosx=l-2 so that g==2(1-t+ ~}x)-2(1-2t+2e)x(l- ~) Then L-1 g == 0 to the assumed approximation. Hence u0 = x-tx U1 = L~'(ajat)A 0 + L~'(a 2 /ax 2 )u0 = xe/2 Thus the two-term approximation is C/J2 = u0 +u 1 = x- tx +xe/2 = (1- e + e/2 )x == e -t sin X Although we can calculate more terms using Um+t for m ~ 0, substitution verifies that u = e-1sin x is already the correct solution. If we need to recognize the exact solution, we can carry the series for g to a higher approximation to see the clear convergence to e- 1 sinx.

Sin X=Sin X COSt 27 THE DECOMPOSrriON MEFHODINSEVERALDIMENS/ONS We are dealing with a methodology for solution of physical systems which have a solution, and we seek to find this solution without changing the problem to make it tractable. The conditions must be known; otherwise, the model is not complete. If the solution is known, but the initial conditions are not, they can be found by mathematical exploration and consequent verification. :o An where the An are generated for the specific f(u).

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