y\ 1.1 -101 1+5 



extremely small. Thus for all practical purposes, equation 

 (27)5 near the boundaries can be written 



^^^Ibxxx -^ ^Ibxyy ' '^ibxxy " ^Ibyyy ^ " ^Ib = Vqxt 



J _i/3 (x-r)e"^^_, 

 = a cos T sm nsy ^ e -^e + 



^ v( -2/3 ^ -1/3 N ,x v/3e X 

 + [(re - 2e -^)cos(- — ) + 



-2/3 ,/- -1/3 . XE-^^3 

 + »™_- sin(-~-2 ™)]e ^ f. (31) 



Near x - 0, the inliomogeneous contribution which contains the 



(x-r)e""'"'^-^ 

 term e can be neglected since its effect is felt only 



near the eastern boundary, i.e., near x = r. Similarly, near 



, X£-^/3 ' 



X = r, the terms multiplied by e~ 2 "^SLn be neglected. Thus 



for the region near x = 0, 



£ [V,, + V,^ - U-,v - U-,, ] - V 

 Ibxxx Ibxyy Ibxxy Ibyyy ib 



r, -2/3 ^ -1/3, ,x l/3£"^'^3 

 - a cos T sm nsyLCre -2s -^)cos(~— i-d — ) + 



-2/3 ,/r -1/3 xel^ .,2) 



re . .X \/3e ,. " T^ • ^3^; 

 ^ sin( — ,- )]e 



\/3 2 



Wow suppose the x coordinate is stretched by substitut- 

 ing X -B^^ (k > 0). Then (32) becomes 



ib^^ ibCyy ib^^y Ibyyy lb 



.k-1/3 



= a cos T sm nsy 



^ ,/- k-1/3 

 [(re-2/3.2s-l/3)cos(illl -) 



-2/3 r\R k-1/3 _ li!!::]:^^ 



rs.ii 3in(i^^l^_) ] e 2 



/3 



