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1 Oct 2012: Define a continuous process X by. Xt =. {Yt if 0 t 1,[Y1 cos(Blog t) Z sin(Blog t)]. ... X〉t = 1 t1. [Y1 sin(Blog s) Z cos(Blog s)]2 ds. =

15 Aug 2012: of change of n(a;b) in the direction(cos ; sin ), where 0 < 2 , isrn (cos ; sin ) = @n@a cos @n@b sin (4.8) @n@a (cos sin ) 0so long ... Let (a0;b0) = (a;b) (cos ; sin )where is small and positive.

15 Aug 2012: of change of n(a;b) in the direction(cos ; sin ), where 0 < 2 , isrn (cos ; sin ) = @n@a cos @n@b sin (4.8) @n@a (cos sin ) 0so long ... Let (a0;b0) = (a;b) (cos ; sin )where is small and positive.

15 Aug 2012: θna. (cos α γ sin α) 0. so long as tan α γ1.Suppose θ(a,b) = 0, and tan α = γ1. ... Let. (a′,b′) = (a,b) ǫ(cos α, sin α). where ǫ is small and positive.